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Applications of broadband Chirped-Pulse Fourier Transform Microwave spectroscopy

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Graduate School ETD Form 9
(Revised 12/07)
PURDUE UNIVERSITY
GRADUATE SCHOOL
Thesis/Dissertation Acceptance
This is to certify that the thesis/dissertation prepared
By Kelly Michelle Hotopp
Entitled APPLICATIONS OF BROADBAND CHIRPED-PULSE FOURIER TRANSFORM
MICROWAVE SPECTROSCOPY
For the degree of Doctor of Philosophy
Is approved by the final examining committee:
Brian Dian
Chair
Garth Simpson
M. Daniel Raftery
Timothy Zwier
To the best of my knowledge and as understood by the student in the Research Integrity and
Copyright Disclaimer (Graduate School Form 20), this thesis/dissertation adheres to the provisions of
Purdue University’s “Policy on Integrity in Research” and the use of copyrighted material.
Brain Dian
Approved by Major Professor(s): ____________________________________
____________________________________
Approved by: R. E. Wild
4-16-2012
Head of the Graduate Program
Date
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PURDUE UNIVERSITY
GRADUATE SCHOOL
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Title of Thesis/Dissertation:
APPLICATIONS OF BROADBAND CHIRPED-PULSE FOURIER TRANSFORM
MICROWAVE SPECTROSCOPY
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Choose of
your
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Kelly M. Hotopp
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4/12/2012
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APPLICATIONS OF BROADBAND CHIRPED-PULSE FOURIER TRANSFORM
MICROWAVE SPECTROSCOPY
A Dissertation
Submitted to the Faculty
of
Purdue University
by
Kelly Michelle Hotopp
In Partial Fulfillment of the
Requirements for the Degree
of
Doctor of Philosophy
May 2012
Purdue University
West Lafayette, Indiana
UMI Number: 3545250
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ii
For my parents.
iii
ACKNOWLEDGMENTS
I would like to thank my research advisor, Dr. Brian Dian for his support and
guidance through my years at Purdue University. I would also like to thank the past and
present group members for their scientific assistance and camaraderie. Two members of
the Jonathan Amy Center for Chemical Instrumentation deserve special thanks, namely
Dr. Mike Everly for his patient help with the development of the LabVIEW code for the
2D CP-FTMW experiments and Dr. Hartmut Hedderich for leak testing and guidance in
designing the waveguide system. I would like to especially thank my family for their
unwavering love and support. Finally, I want to say a special thank you to Dr. Mark
Thoreson for the priceless encouragement.
iv
TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES ......................................................................................................... viii
ABSTRACT ...................................................................................................................... xv
CHAPTER 1. INTRODUCTION TO CHIRPED-PULSE FOURIER TRANSFORM
MICROWAVE SPECTROSCOPY ............................................................................. 1
1.1. Introduction .............................................................................................................. 1
1.2. Stark-Effect Microwave Spectrograph ..................................................................... 2
1.3. Fabry-Perot Cavity ................................................................................................... 4
1.4. Chirped-Pulse Fourier Transform Microwave Spectroscopy ................................... 6
1.5. References .............................................................................................................. 10
CHAPTER 2. INSTRUMENTATION AND EXPERIMENTAL PROCEDURES ......... 12
2.1. Broadband Chirped-Pulse Fourier Transform Microwave Spectroscopy .............. 12
2.2. Microwave Pulse Generation Mixing with 13.0 GHz ............................................ 15
2.3. Microwave Pulse Generation x4 Frequency Stretcher ........................................... 21
2.4. One-Dimensional Data Processing ......................................................................... 23
2.5. Balle-Flygare Type Fabry-Perot Cavity ................................................................. 25
2.6. Two-Dimensional Program .................................................................................... 29
2.7. Two-Dimensional Data Processing ........................................................................ 34
2.8. References .............................................................................................................. 36
CHAPTER 3. CONFORMATIONAL ANALYSIS OF N-BUTANAL BY CHIRPEDPULSE FOURIER TRANSFORM MICROWAVE SPECTROSCOPY .................. 37
3.1. Introduction ............................................................................................................ 37
3.2. Experimental Details .............................................................................................. 41
3.3. Calculations ............................................................................................................ 43
3.4. Results and Discussion ........................................................................................... 48
3.5. Kraitchman Analysis .............................................................................................. 53
v
Page
3.6. Conclusion .............................................................................................................. 57
3.7. References .............................................................................................................. 72
CHAPTER 4. TWO-DIMENSIONAL CHIRPED-PULSE FOURIER TRANSFORM
MICROWAVE SPECTROSCOPY ........................................................................... 74
4.1. Introduction ............................................................................................................ 74
4.2. Experimental Methods............................................................................................ 78
4.3. Results and Discussion ........................................................................................... 81
4.3.1. General Description and Modeling .................................................................. 81
4.3.2. Regressive Narrowband 2D Autocorrelation ................................................... 87
4.3.3. Progressive Three-Level Autocorrelation ........................................................ 91
4.3.4. Broadband Pulse Sequences ............................................................................. 96
4.3.5. Phase Cycling ................................................................................................. 101
4.3.6. Quadrature Detection in ω1 ............................................................................ 102
4.4. Conclusion ............................................................................................................ 108
4.5. Appendix: Phase Angle Correction ...................................................................... 109
4.6. Pulse Details ......................................................................................................... 111
4.7. References ............................................................................................................ 117
CHAPTER 5. FURTHER APPLICATIONS OF ROTATIONAL SPECTROSCOPY . 119
5.1. Toward Microwave Chemical Sensing at Room Temperature ............................ 119
5.2. Overmoded Waveguide Design ............................................................................ 120
5.3. Overmoded Waveguide Fabrication ..................................................................... 124
5.4. Overmoded Waveguide Experimental.................................................................. 124
5.5. Overmoded Waveguide Results ........................................................................... 128
5.6. RT-CP-FTMW Spectroscopy: Overmoded Coaxial Line .................................... 131
5.7. Quadrature Coupler Microwave Circuit ............................................................... 140
5.8. Future Applications of 2D CP-FTMW Spectroscopy .......................................... 142
5.9. References ............................................................................................................ 145
APPENDIX. LABVIEW PROGRAM FOR TWO-DEMENSIONAL CHIRPEDPULSE FOURIER TRANSFORM MICROWAVE SPECTROSCOPY ..................146
VITA ............................................................................................................................... 189
PUBLICATION .............................................................................................................. 191
vi
LIST OF TABLES
Table
Page
Table 3.1 Calculated relative energies of n-butanal geometries. (kcal/mol) .................... 45
Table 3.2 Results from DFT calculations at the B3LYP level of theory with a
6-311++G(d,p) basis set. ............................................................................................ 46
Table 3.3 List of parameters used to fit the n-butanal conformers. (JB95) ...................... 50
Table 3.4 Isotopic assignments for the cis/trans conformer of n-butanal. ........................ 54
Table 3.5 Isotopic assignments for the cis/gauche conformer of n-butanal. .................... 55
Table 3.6 Comparison of the molecular structure according to ab initio predictions
and Kraitchman analysis. ............................................................................................55
Table 3.7 Rotational transitions of cis/trans n-butanal ..................................................... 59
Table 3.8 Rotational transitions of cis/trans (HO13C-CH2-CH2-CH3) n-butanal .............. 60
Table 3.9 Rotational transitions of cis/trans (HOC-13CH2-CH2-CH3) n-butanal .............. 61
Table 3.10 Rotational transitions of cis/trans (HOC-CH2-13CH2-CH3) n-butanal ............ 62
Table 3.11 Rotational transitions of cis/trans (HOC-CH2-CH2-13CH3) n-butanal ............ 63
Table 3.12 Rotational transitions of cis/gauche n-butanal ................................................ 63
Table 3.13 Rotational transitions of cis/gauche (HO13C-CH2-CH2-CH3) n-butanal ........ 65
Table 3.14 Rotational transitions of cis/gauche (HOC-13CH2-CH2-CH3) n-butanal ........ 66
Table 3.15 Rotational transitions of cis/gauche (HOC-CH2-13CH2-CH3) n-butanal ........ 67
Table 3.16 Rotational transitions of cis/gauche (HOC-CH2-CH2-13CH3) n-butanal ........ 68
Table 3.17 A-state rotational transitions of gauche/trans n-butanal .................................. 69
Table 3.18 E-state rotational transitions of gauche/trans n-butanal .................................. 70
Table 3.19 Rotational transitions of gauche/gauche n-butanal ......................................... 71
Table
vii
Page
Table 4.1 2D Autocorrelation of CFE............................................................................. 111
Table 4.2 (a) Single-Quantum Correlation of TFP (ΔJ=2←1) (b) Single-Quantum
Correlation of TFP (ΔJ=3←2) ................................................................................. 112
Table 4.3 Broadband Autocorrelation of TFP ................................................................ 112
Table 4.4 Coherence Propagation of DFA ...................................................................... 113
Table 4.5 Extended Broadband Autocorrelation of DFA ............................................... 113
Table 4.6 Single-Quantum Correlation of TFP with Phase Cycling .............................. 114
Table 4.7 Broadband Autocorrelation of TFP with Phase Cycling ................................ 114
Table 4.8 Double-Quantum Filtered Sequence of TFP with Phase Cycling .................. 115
Table 4.9 Hypercomplex Autocorrelation of CFE .......................................................... 116
Table 5.1 Rotational Transitions of Methanol Observed Using the Overmoded
RT-CP-FTMW Spectrometer .................................................................................. 133
viii
LIST OF FIGURES
Figure
Page
Figure 2.1 (a) The vacuum chamber shown in a top-down cutaway view. The pulsed
valve and horn antenna (right) are used for Chirped-Pulse Fourier Transform
Microwave spectroscopy. The Fabry-Perot cavity mirrors and translation stage
(center) are based upon the Balle-Flygare design. (b) Side view of the vacuum
chamber and two 10 inch (25.4 cm) diameter diffusion pumps. Total length of the
chamber is about 1.5 m. ..............................................................................................13
Figure 2.2 Block diagram of the 13 GHz mixing microwave circuit of the CP-FTMW
spectrometer. The chirped microwave polarizing pulses are produced by the
arbitrary waveform generator in the 0.1-5 GHz range. The pulses were filtered,
pre-amplified, mixed with a phase stabilized 13 GHz frequency source, power
amplified by 200 W and then broadcast into the vacuum chamber. A manual step
attenuator and circulator were used to control the amplitude of the signal entering
the 200 W amplifier. ...................................................................................................18
Figure 2.3 Block diagram of the detection electronics of the CP-FTMW spectrometer.
The molecular signal collected by the microwave horn antenna was mixed down
with a phase stabilized 18.9 GHz frequency source. ..................................................20
Figure 2.4 Block diagram of the microwave circuit including the x4 frequency
stretcher (quadrupler). The 13 GHz PLDRO and associated components are
replaced by a x4 frequency stretcher to achieve an 11 GHz bandwidth (7.5-18.5
GHz). ...........................................................................................................................22
Figure 2.5 The time-domain, frequency-domain, and frequency-resolved optical gate
(FROG) signals of a 1 μs polarizing pulse using the 13 GHz mixing (a-c) or
quadrupler (c-f) microwave circuit. ............................................................................24
Figure 2.6 Block diagram of the Fabry-Perot cavity FTMW spectrometer based on the
Balle-Flygare design. The 30 MHz signal from the arbitrary waveform generator
was mixed with the frequency (ν) from microwave synthesizer (30 MHz + ν).
After interaction with the molecules in the cavity, the shifted molecular signal (30
MHz + ν) ±Δ was mixed down with ν and recorded by a digital oscilloscope. ..........27
Figure 2.7 Flow chart of the 2D data collection program written in LabVIEW version
8.5. ...............................................................................................................................30
ix
Figure
Page
Figure 3.1 Optimized molecular geometries of n-butanal. The two torsional angles,
τ1 = O–C1–C2–C3 and τ2 = C1–C2–C3–C4, are used to name the structures as
cis/trans (τ1 = 0°/τ2 = 180°), cis/gauche (τ1 ≈ 5°/τ2 ≈ 70°), gauche/trans
(τ1 ≈ 130°/τ2 ≈ 180°), and gauche/gauche (τ1 ≈ -130°/τ2 ≈ 70°). The naming
convention was chosen to be consistent with previously reported work. ...................38
Figure 3.2 Rotational spectrum of n-butanal. The 12989.34 MHz and 12997.13 MHz
peaks shown in the inset figure correspond to 13C isotopologues from C3 and C1,
respectively, of the cis/trans geometry of n-butanal. ..................................................44
Figure 3.3 Relaxed potential energy scan about the methyl torsional coordinate of the
cis/gauche geometry of n-butanal calculated with Gaussian03. The vibrational
geometry optimization was performed using DFT calculations at the B3LYP
level of theory with a 6-311++G(d,p) basis set. The methyl rotational barrier (V3)
of the cis/gauche structure has a value of 967 cm-1. ...................................................47
Figure 3.4 Relaxed potential scan of the τ2 = C1–C2–C3–C4 dihedral angle of
n-butanal. Calculated with Gaussian03, the τ2 angle of the energetically optimized
gauche/trans structure was rotated in 4° steps to identify two additional local
minima.........................................................................................................................49
Figure 4.1 Schematic of the single-quantum correlation pulses sequence of a threelevel progressive system. The initial π/2 pulse prepares the σab coherence out of
thermal equilibrium. Following a variable time delay, t1, a second non-selective
pulse irradiates both the Ea←Eb and Eb←Ec transitions, mixing the σab and σbc
coherences. A free induction decay is then measured with respect to t2 and
Fourier transformed into the ω2 spectrum. Stepping the t1 time delay changes the
magnitude of the freely precessing σab coherence, thereby modulating the
intensities of the σab and σbc coherences in the ω2 spectrum. Fourier transform
with respect to t1 reveals coherences peaks sharing a common energy level that
are coupled by the mixing pulse..................................................................................82
Figure 4.2 Real portion of the coherence oscillation in the interaction picture subject
to an arbitrary linear frequency sweep covering 10 MHz. The resonant frequency
was set to zero. As the field passes through the center frequency, the coherence
terms oscillate slowly, corresponding to an adiabatic following of the Bloch
vector with the field. ...................................................................................................86
x
Figure
Page
Figure 4.3 Autocorrelation 2D spectrum of the ΔJKaKc=111←000 transition of 1-chloro1-fluoroethylene (CFE). (a) Autocorrelation non-selectively excites all transitions
under the bandwidth of two identical pulses separated by a stepped delay (t1). (b)
The hyperfine structure of CFE splits the JKaKc=111 levels that form regressive
connections with the JKaKc=000. Selection rules (ΔF = 0, ±1) permit the transitions
ΔF = 0.5←1.5 (14120.2(1) MHz), ΔF = 2.5←1.5 (14127.9(1) MHz), and ΔF =
1.5←1.5 (14137.7(1) MHz). (c) 2D autocorrelation plot constructed by Fourier
transforming the t2 time data to the ω2 frequency domain and Fourier
transforming intensity modulations with respect to t1 to the ω1 frequency domain.
Cross peaks indicate that transitions share a common energy level. The coupling
between non-adjacent regressive energy levels is weak, resulting in the apparent
absence of off-diagonal “corner” peaks in the 2D plot. ..............................................89
Figure 4.4 Single-quantum correlation of 3,3,3-trifluoropropyne (TFP) in two
separate experiments: (a) ω1 spectrum of the ΔJ=2←1 (11511.8(1) MHz)
transition containing the coherence peak of the ΔJ=3←2 (17267.7(1) MHz in ω2,
aliased frequency at 267.6(4) MHz in ω1) transition. The ΔJ=3←2 was initially
prepared and transferred to the ΔJ=2←1 transition following t1 evolution with a
non-selective mixing pulse. (b) ω1 spectrum of the ΔJ=3←2 (17267.7(1) MHz)
transition containing the coherence peak of the ΔJ=2←1 (11511.8(1) MHz in ω2,
aliased frequency at 511.7(4) MHz in ω1) transition. The preparation pulse
excites the ΔJ=2←1 in this similar experiment and the mixing pulse transfers the
prepared coherence to the ΔJ=3←2 transition. (c) Ground state ω2 spectrum of
TFP. Intensity oscillations of peaks are Fourier transformed with respect to t1 to
yield their respective ω1 spectrum, or 1D slice of a 2D plot. With single-quantum
correlation, two separate experiments are required to transfer coherences to
produce the 1D slices of (a) and (b). ...........................................................................93
xi
Figure
Page
Figure 4.5 Experimental ω1 broadband autocorrelation spectrum of the ΔJ=2←1
transition of 3,3,3-trifluoropropyne (black trace). Simultaneous irradiation of the
ΔJ=2←1 (11511.8(1) MHz) and ΔJ=3←2 (17267.7(1) MHz) before and after t1
transfers coherences to all ω1 channels. Peaks labeled A correspond to direct
coherence information: ΔJ=2←1 parent and ΔJ=3←2 coherence transfer peaks
with aliased frequencies 488.3(4) MHz and 267.6(4) MHz, respectively. Label B
refers to mixing peaks that result from the simultaneous irradiation of multiple
transitions. Mixing peaks are identified by the sums and differences of coherence
fundamental and harmonic frequencies. All peaks, particularly those with direct
coherence information, are resolved with the broad bandwidth in ω1. Simulated
data (red trace) reproduce the frequency response of the pulse sequence. Peak
widths were chosen to match the experimental conditions. Intensities are only
approximate and were derived from Boltzmann population differences at thermal
equilibrium. .................................................................................................................95
Figure 4.6 Coherence propagation of 1,3-difluoroacetone (DFA). (a) Map of the
coherence propagation path shown in the ω2 representation. The ΔJKaKc=212←101
(marked with an asterisk*) was initially prepared with the pulse sequence of (b).
Following t1 the coherence was transferred to ΔJKaKc=202←101 and then
propagated up the ΔJKaKc =404←303←202 K-stack with selective π/2 pulses. (c)
The respective 1D slices of all signal frequencies collected in ω2 contain the
initial coherence information of the ΔJKaKc=212←101 transition with a coherence
transfer peak at 376.6(4) MHz (aliased frequency). Global connectivity is
revealed with broadband detection in ω2.....................................................................97
Figure 4.7 Extended broadband autocorrelation. a) The energy level structure of 1,3difluoroacetone (DFA) investigated with the extended broadband autocorrelation
pulse sequence (panel b). Both progressive and regressive connected transitions
were directly irradiated (red arrows). c) The 1D slice of the ΔJKaKc=212←101
transition (labeled “A”, 12380.4(1) MHz). Coherences from adjacent transitions
or nearest neighbors (“B”, 11658.5(1) MHz and “F”, 8390.8(1) MHz) transferred
by the first pulse after t1 and next-nearest adjacent transitions (labeled “C”
15459.3(1) MHz and “E”, 11376.5(1) MHz) transferred by the second pulse after
t1 are present in the ω1 spectrum. d) The ΔJKaKc=404←303 was not directly
pumped (black arrow of panel a), however coherences were transferred through
indirect population cycling through the JKaKc=303 energy level. Both coherence
(labeled G, E, and F) and a mixing peak (*) were identified in the 1D slice of
ΔJKaKc=404←303. ..........................................................................................................99
xii
Figure
Page
Figure 4.8 Phase cycling with chirped pulses. a) The ΔJ=3←2 channel resulting from
broadband autocorrelation with the ΔJ=2←1 transition. The black trace is the raw
1D slice in the absence of phase-cycling. With two-step phase cycling (red trace),
the mixing peak labeled with an asterisk (*) was eliminated, leaving only direct
coherence information at 267.6(4) and 488.3(4) MHz. b) Similarly, in the
ΔJ=3←2 channel of the single-quantum correlation pulse sequence, the second
harmonic mixing peak (*) was eliminated in the two-step phase-cycled red trace...103
Figure 4.9 a) Double-quantum filtered pulse sequence. A π/2 pulse prepares ΔJ=3←2
(17267.7(1) MHz) transition of TFP. Following t1, π pulses subsequently irradiate
the ΔJ=3←2 and ΔJ=2←1 transitions, first converting the prepared coherence
into a double-quantum coherence and then back into observable signal. By
converting to double-quantum coherence rather than occupation differences, the
branching out of coherence pathways is reduced. Therefore, P- and N-type
signals corresponding to the sign of the relative pathway are revealed after
Fourier transformation of the complex t1 signal. b) The dominant P-type
coherence (+267.6(4) MHz aliased) and a less intense quadrature image
(-267.6(4) MHz) were observed in the 1D slice of the ΔJ=2←1 transition. Aside
from Rabi angle imperfections that contribute to the quadrature image, the
magnitude is also highly dependent on the center frequency of the ΔJ=2←1
transition in ω2...........................................................................................................105
Figure 4.10 Hypercomplex autocorrelation of the ΔJKaKc=111←000 of CFE showing
the 1D slice of the transition ΔF=2.5←1.5 hyperfine transition. The preparation
pulse was shifted by 90o in two consecutive experiments to yield cosine and sine
modulated t1 channels. The complex signal was constructed by subtracting the
imaginary oscillations from the real prior to Fourier transformation, producing an
N-type coherence peak in ω1. The dominant peaks in the negative quadrant
(-120.4(4), -128.2(4), and -137.7(4) MHz) carry the coherence information of the
system. Mixing peaks that are even harmonics of the coherence fundamental do
not carry the sign information and are present in both quadrants. The sign of the
third harmonic mixing peak is preserved, though opposite to the fundamental.
The real and imaginary channels were recorded separately in consecutive
experiments, introducing phase noise from small drifts in the spectrometer over
several hours. Therefore, quadrature images of the parent and coherence transfer
peaks are present, though the magnitude is small (roughly 10%).............................107
Figure 5.1 WR90 to overmoded waveguide adaptor. The solid line is the 6-section
Chebyshev multistep transform used to match the WR90 waveguide to the
overmoded waveguide, and the dashed line is the piecewise, smooth model used
for fabrication. ...........................................................................................................122
xiii
Figure
Page
Figure 5.2 Overmoded waveguide. (a) Interior channel of the overmoded waveguide
showing the two 3 cm bifurcations near the tapered sections. These bifurcations
are used to improve the electric field uniformity. (b) Exterior of the overmoded
waveguide. Mica sheets form a vacuum seal closure on the ends of the
overmoded cell. (c) Photograph of the RT-FTMW overmoded waveguide sample
cell. ............................................................................................................................123
Figure 5.3 Block diagram of the RT-CP-FTMW spectrometer. (a) Microwave pulse
generation circuit, (b) overmoded waveguide probe channel, and (c) FID
detection circuit. ........................................................................................................126
Figure 5.4 Microwave polarizing pulse. (a) Time domain signal with 1μs duration. (b)
Frequency domain signal showing the 100 MHz bandwidth centered about 9.957
GHz. ..........................................................................................................................127
Figure 5.5 Molecule free induction decay (FID) of methanol recorded using the
overmoded waveguide RT-CP-FTMW spectrometer. ..............................................129
Figure 5.6 Rotational spectrum of methanol acquired using the RT-CP-FTMW
overmoded waveguide spectrometer. The polarizing microwave pulse swept from
9.9 to 12.2 GHz and was power amplified by 30 W. Five methanol rotational
transitions were observed in this spectrum. ..............................................................130
Figure 5.7 Measured methanol spectra using a 3 W solid-state amplifier with a
chirped pulse at a center frequency of 9.957 GHz and 100 MHz bandwidth. ..........132
Figure 5.8 Measured methanol spectra using a 3 W solid-state amplifier with a
chirped pulse at a center frequency of 12.344 GHz and 400 MHz bandwidth. ........133
Figure 5.9 Overmoded coaxial line RT-CP-FTMW spectrometer sample analysis
chamber. The 32 cm coaxial cable was housed in the stainless steel tube
connected to the 4-way cross that allowed for quick and easy connection to the
electrical feeds, the vacuum pumping system, and the sample inlet port. ................134
Figure 5.10 Outer conductor and center pin of the overmoded coaxial cable. The
Hamming tapered transmission line (curved regions) method was used to match
the impedance of the 16 mm cable to the 2.4 mm connectors. .................................136
Figure 5.11 Microwave excitation and detection circuit of the overmoded coaxial
cable RT-CP-FTMW spectrometer. ..........................................................................137
Figure 5.12 The 9-1 9  8-2 7 rotation transition of methanol measured with an
overmoded coaxial cable RT-CP-FTMW spectrometer. The polarizing pulse
swept from 9907 to 10007 MHz. ..............................................................................138
xiv
Figure
Page
Figure 5.13 Rotational transitions 20 2  3-1 3 (12178.4 MHz) and 165 12  174 13
(12229.1 MHz) of methanol measured with an overmoded coaxial cable RT-CPFTMW spectrometer. The polarizing pulse swept from 12144 to 12544 MHz. The
peak at 12169.0 MHz is expected to be noise from the electric field. ......................139
Figure 5.14 Block diagram showing the detection electronics of the 2D CP-FTMW
quadrature circuit. A 90° phase shift was induced on channel 3 by the quadrature
coupler and phase shifter. Two channels (ch1 and ch3) were simultaneously
recorded by the digital oscilloscope. .........................................................................141
Figure 5.15 Dissociation products of 2,3-dihydrofuran measured by Chirped-Pulse
Fourier Transform Microwave spectroscopy (top). Predicted molecular spectra of
discharge products (bottom).. ....................................................................................144
Appendix Figure
Figure A 1 Screen shot of the 2D program’s Hardware Configuration user interface
tab. GPIB addresses are selected from the drop down menus (left) and
communication is opened with the instruments by pressing Connect (right). The
200 W amplifier and electronic switch must be connected to the proper channels
of the DG535, as indicated. .......................................................................................147
Figure A 2 Screen shot of the 2D program’s Pulse Parameters user interface tab. The
user types in values for the Index Number, Step Size, and Initial Loop Count for
each dynamic delay of the pulse sequence. These values must match the pulse
sequence programmed into the arbitrary waveform generator. ................................148
Figure A 3 Screen shot of the 2D program’s Scan Parameters user interface tab. The
user sets the timing of the DG535 channels which trigger the 200 W amplifier
and the electronic switch. The user also specifies the Source (oscilloscope
channel), Number of Steps (or iterations), File Name, and File Path for the data.
Pressing Start (right) begins the data collection process. The current step and
approximate time remaining are displayed while the program is acquiring data. ....149
xv
ABSTRACT
Hotopp, Kelly Michelle Ph.D. Purdue University, May 2012. Applications of
Broadband Chirped-Pulse Fourier Transform Microwave Spectroscopy. Major Professor:
Brian C. Dian.
Rotational spectroscopy is a powerful and sensitive technique that can be used to
study the structure of gas phase molecules exhibiting a permanent dipole moment. The
principal moments of inertia of a molecule determine the frequencies of the rotational
transitions for the molecule. This dependence can be exploited in modern rotational
spectroscopy to provide a direct method for the structural characterization of gas phase
molecules. Experimentally, the rotational transitions of a molecule are observed in the
microwave spectral range, and these transition frequencies often can be accurately
predicted using theoretical calculations.
In this work we used the broadband technique of Chirped-Pulse Fourier
Transform Microwave (CP-FTMW) spectroscopy to experimentally study the structure
and rotational spectra of chemically interesting molecules in the gas phase. We also
performed a number of calculations to compare and understand our experimental
observations. We start with a review of the extensive literature on rotational
spectroscopy, including Stark-field spectroscopy, microwave spectroscopy with FabryPerot cavities, and the relatively new technique of broadband CP-FTMW spectroscopy.
We also describe some advanced modifications to the CP-FTMW technique that we have
xvi
pursued in the course of our studies, including an extension into Two-Dimensional CPFTMW spectroscopy. We finish with a review of our recent cross-departmental
collaboration results and an outlook for developing the CP-FTMW technique even
further.
1
CHAPTER 1. INTRODUCTION TO CHIRPED-PULSE FOURIER TRANSFORM
MICROWAVE SPECTROSCOPY
1.1 Introduction
The power of rotational spectroscopy is the shape sensitive nature of the
technique. The principal moments of inertia of a molecule determine the frequencies of
rotational transitions observed in the microwave spectral range.1 This dependency is
exploited by modern rotational spectroscopy to provide a direct method for structural
characterization of gas phase molecules.2,3
The rotational spectrum of a molecule is inherently related to the molecular
moments of inertia. The moment of inertia, I, is defined by Equation 1 where m is the
mass of each atom and r is the perpendicular distance from the atom to the rotational axis
of interest.1
I   mi ri 2
(1)
We can define three mutually perpendicular rotational axes (axis a, axis b, and axis c)
that intersect at the center of mass of the molecule and calculate the moment of inertia
about each axis separately. These moments of inertia are then named Ia, Ib, and Ic with the
established labeling convention that Ia ≤ Ib ≤ Ic. Rigid rotor molecular structures can be
classified into four categories according to their moments of inertia.1 The first type,
spherical rotors such as CH4 and SF6, have three equal moments of inertia (Ia = Ib = Ic).
2
Linear rotors like OCS and HCl, on the other hand, have two equal moments of inertia (Ib
= Ic) and one moment of inertia equal to zero (Ia=0). Symmetric rotors also have two
equal moments of inertia, but their third moment of inertia is non-zero and different from
the first two. The axis of the molecule that is unique is called the principal axis. Prolate
symmetric tops, such as CH3Cl, are shaped like a cigar with Ia ˂ Ib = Ic, while oblate
symmetric tops are pancake shaped with Ia = Ib ˂ Ic. Examples of oblate symmetric tops
include C6H6 and CH3CF3. Lastly, asymmetric tops like H2O and CH3OH have three
unique moments (Ia ≠ Ib ≠ Ic) of inertia.1 Nearly all of the molecules studied in this
document fall into the asymmetric top category, however sometimes a description of
“near-prolate” or “near-oblate” and be used to predict and explain the observed rotational
spectra.
The rotational constants (A, B, and C) of a molecule are defined according to the
moments of inertia as follows:
A
h
h
h


,
B
,
C
8 2cIa
8 2cIb
8 2cIc
(2)
where c is the speed of light and h is Planck’s constant.1 With accurate rotational
constants, the full rotational spectrum of a molecule can be obtained numerically. This
becomes a powerful tool to facilitate the fitting and assignment of experimental spectra.
1.2 Stark-Effect Microwave Spectrograph
Rotational spectroscopy was first established with indirect detection based on
Stark effect modulation in a waveguide absorption cell.4,5 The Stark effect, or the shifting
of spectral lines in the presence of an external electric field, is named after the 1919
3
Nobel laureate Johannes Stark. Early founders in the field of rotational spectroscopy
applied the Stark effect principle to study the absorption of gas phase molecules. By the
late 1940s, experimental sensitivity advancements of the waveguide design were made by
Hughes and Wilson,6 and McAfee et al.7 This experimental apparatus was constructed of
a section of waveguide fit with a flat, brass electrode strip mounted parallel to the broad
side of the waveguide. The electrode was used to introduce the Stark field inside the
waveguide in order to produce the splitting of the spectral absorption lines of the
molecules. Teflon pieces held the electrode in place and insulated the electrode from the
interior walls of the waveguide. The spectral absorption of a gas sample was modulated
by the application of the electric field and measured using frequency domain detection.
The frequency source was held constant at the molecular rotational frequency of interest
and the electric field was used to shift the molecular system in and out of resonance. The
net absorption of the microwave radiation was observed to identify rotational transitions.
This design was later commercialized by Hewlett-Packard, thus making it very popular.8
The mathematical description of the Stark-field absorption spectroscopy is based
upon quantum mechanics. For a symmetric rotor, the total rotational angular moment
quantum number J has a component along the external, laboratory-fixed axis.1 This
orientation of the molecule’s rotation in space with respect to an external axis is
described with the quantum number MJ which may have the values MJ = 0, ±1, … , ±J to
give a total of 2J+1 values. By applying an electric field, splitting of the energy levels
occur which partially removes the MJ degeneracy. Each energy level is doubly degenerate
except when MJ = 0. Note that the positive- and negative-valued levels of the same
magnitude remain degenerate even under Stark splitting, so the MJ = +1 level is
4
indistinguishable from MJ = 1, for example. The observed Stark splitting of each state’s
energy depends upon the square of the permanent electric dipole moment, μ, of the
molecule.1
Substantial contributions to the field of rotational spectroscopy were made using
this early type of Stark field, waveguide spectrometer. Jones and Owen 9 and Scroggins et
al. 10 were able to identify structural conformers separated by low energy low barriers. In
his work on gaseous methyl vinyl ether, Owen was also able to observe the internal
rotation effects caused by the torsion of the methyl group.11 However, there are several
limitations to the waveguide methodology. Because the signal power is proportional to
the square of the number of molecules,12 long waveguide lengths (up to 10 meters) are
needed to obtain a high enough sample molecule number density to produce a measurable
signal. Also, the physical size (height and width) of the waveguide limits the allowed
frequency range due to the waveguide cutoff, therefore making it difficult to study a
broad spectral range.
1.3 Fabry-Perot Cavity
New instrumental designs were developed to improve the sensitivity and utility of
the rotational spectrometer.13 Combining several of these advancements, including pulsed
Fourier transform microwave spectroscopy, a Fabry-Perot cavity, and a pulsed sample
inlet nozzle, an innovative instrument design was introduced by Balle and Flygare in
1979.14,15 A Fabry-Perot microwave cavity is made of two reflective mirrors which form
a resonator with a high quality factor, Q.
5
Q
2π (total energy stored)
(energy dissipated per cycle)
(3)
The coherent polarization of the molecules, induced by the electric field, must be
maintained for a period of time that is long compared to the duration of the probing
microwave pulse. Working in the time domain, the coherent molecular free induction
decay (FID) signal is recorded directly and the Fourier transform is taken to obtain the
frequency domain rotational spectrum. Compared to Stark-field absorption spectroscopy,
the Fabry-Perot cavity reduces the power broadening effects that contribute to spectral
line distortion. In this scenario, good signal-to-noise ratios are maintained at lower
powers because of the high Q of the cavity. The additional of a pulsed nozzle produces a
supersonic expansion of sample molecules in order to provide vibrational and rotational
cooling of the molecules. This also makes it possible to probe species such as weak van
der Waals molecular complexes that would otherwise be difficult to observe. A few
examples of such complexes that have been studied using a Balle and Flygare style cavity
are KrHCl,14 ArHBr,16 and KrHBr16.
Although very high resolutions (approximately 10 kHz) can be obtained with
Fabry-Perot cavity spectroscopy, the data acquisition process using a Balle-Flygare style
cavity is extremely time consuming.17 In order to obtain a broadband spectrum with a
bandwidth of 11 GHz, a long, tedious series of narrowband experiments must be
completed.18 Each measurement step has a bandwidth of approximately 500 kHz, and
signal averaging is also necessary to increase the signal-to-noise ratio of the collected
data. Then the cavity length must be adjusted for a new narrowband frequency range by
repositioning a mobile mirror. These processes are repeated at each measurement step,
6
leading to very long data acquisition times. For instance, it takes about 14 hours to obtain
a spectral bandwidth of 11 GHz using automatic computer control for the mirror
adjustments.18 Manual mirror adjustment between steps produce prohibitively long
acquisition times. Over such long timeframes, maintaining instrumental stability can be a
significant issue. In addition, these long data collection times make it very difficult to
observe excited electronic or vibrational states prepared via laser excitation since laser
frequency drift may occur.19 A very recent development overcomes many of these
drawbacks and is a truly broadband method that drastically reduces the data acquisition
times for rotational spectroscopy. This new method, called broadband Chirped-Pulse
Fourier Transform Microwave spectroscopy,19 was developed in 2008 and is discussed in
detail in the next section.
1.4 Chirped-Pulse Fourier Transform Microwave Spectroscopy
The research presented in this document capitalizes on the broadband nature of
Chirped-Pulse Fourier Transform Microwave (CP-FTMW) spectroscopy. Compared to
the Balle-Flygare style Fabry-Perot microwave cavity design, CP-FTMW spectroscopy
offers significantly shorted data acquisition times because the entire 11 GHz bandwidth is
probed with each measurement event.19 Instead of building up a broadband spectrum by
recording many averages at each of a large number of discrete wavelengths, the chirpedpulse method relies on a sweep in frequency generated by advanced electronics in order
to probe a large spectral bandwidth in a relatively short period of time.
The technique of CP-FTMW spectroscopy utilizes high-speed digital electronics
to produce a broadband, chirped microwave pulse that linearly sweeps from 7.5 to 18.5
7
GHz in 1 μs. Thus in this short timeframe, we can probe the entire 11 GHz bandwidth. In
contrast, using a Balle-Flygare setup the per-step bandwidth is a narrow 500 kHz, and at
each frequency step a mechanical adjustment is necessary to change the distance between
two reflective mirrors within the cavity to tune the cavity resonance frequency. In order
to record the full 11 GHz bandwidth, a Balle-Flygare system would require roughly
22,000 adjustments; even with automated control of these movements, a relatively
advanced Balle-Flygare system would take about 14 hours to collect such a bandwidth,
and more than half of that time is spent just in mechanical mirror adjustments.18 Clearly,
therefore, the CP-FTMW technique is a significant leap forward in terms of acquisition
time and research efficiency for molecular spectroscopists.
The CP-FTMW technique does not employ a resonant cavity to probe the
rotational transitions of a gas-phase ensemble of molecules. Instead of using reflective
mirrors and a resonant cavity to produce a polarizing field, the CP-FTMW technique uses
a set of broadband antenna horns to project the short, 1-s chirped microwave pulse
inside the vacuum chamber. This pulse induces a macroscopic polarization of the gasphase sample molecules, and the resulting free induction decay (FID) is recorded and
analyzed to produce the rotational spectrum. Using CP-FTMW spectroscopy, in a matter
of seconds a single FID can be acquired and processed to obtain a broadband spectrum of
a molecule. Even with signal averaging to increase the signal-to-noise level in the final
result, the CP-FTMW technique significantly increases the speed with which broadband
molecular rotational spectra can be collected.
Let us take the time to go through a detailed explanation of the CP-FTMW
technique since it is a major component of the work described in this document. Like
8
traditional FTMW, CP-FTMW spectroscopy requires sample molecules that have a
permanent dipole moment and are in the gas phase. The sample molecules are pulsed into
a vacuum chamber just like in the Balle-Flygare cavity case above; this is done in order
to produce a low-temperature, supersonic expansion of vibrationally and rotationally
cooled molecules. Perpendicular to the pulsed sample-molecule beam, a pair of
transmit/receive microwave horn antennas are positioned facing each other inside the
vacuum chamber. These horn antennas broadcast the polarizing microwave field
experienced by the sample molecules and detect the subsequent signal. Although
identical, one horn is used for introducing the chirped microwave pulse and the other is
used for detecting the FID emitted by the sample molecules. The FID signals are then
processed electronically to produce the rotational energy spectrum of the molecules under
study.
The CP-FTMW technique provides a wealth of structural information about a
sample in a relatively short amount of time. Some proponents of the technique are now
focusing on collecting and disseminating the vast amount of rotational spectral data
arising from the technique, meaning that data analysis and storage are becoming
increasingly important for rotational spectroscopists.3 With all its benefits, CP-FTMW
spectroscopy is not without limitations as well. One of the most significant limitations is
that the technique is only useful for samples in the gas phase, since solid and liquid
samples would not experience free molecular rotation. In addition, as with the case of
other FTMW techniques, we are limited to molecules that exhibit a permanent dipole
moment. Molecules without a permanent dipole moment would not be susceptible to the
initial polarizing field and hence would not be aligned to supply a measurement FID.
9
Finally, the CP-FTMW technique is restricted by the very electronics that have permitted
its existence – the resolution of CP-FTMW is lower than that of the Balle-Flygare setup,
for instance, due to the fact that the digitization rates of the electronics are not capable of
supporting higher spectral resolutions.
The next chapters of the thesis begin with an application of the CP-FTMW
technique to the study of the conformational preferences of n-butanal. Next we consider
an advancement to CP-FTMW called two-dimensional CP-FTMW spectroscopy,20 which
is conceptually similar to 2D NMR but is in a different frequency range. Finally we
summarize a few additional experiments which focused on the development of a
miniaturized molecular interaction chamber to perform room temperature CP-FTMW
spectroscopy, and we also provide an outlook for future work in the field.
10
1.5 References
(1)
Levine, I. N. Physical Chemistry; 6th ed.; McGraw-Hill: New York, 2009.
(2)
Evangelisti, L.; Grabowiecki, A.; van Wijngaarden, J. Journal of Physical
Chemistry A 2011, 115, 8488.
(3)
Pate, B. H. Science 2011, 333, 947.
(4)
Hershberger, W. D. J. Appl. Phys. 1946, 17, 495.
(5)
Walter, J. E.; Hershberger, W. D. J. Appl. Phys. 1946, 17, 814.
(6)
Hughes, R. H.; Wilson, E. B. Physical Review 1947, 71, 562.
(7)
McAfee, K. B.; Hughes, R. H.; Wilson, E. B. Review of Scientific Instruments
1949, 20, 821.
(8)
Reinhold, B.; Finneran, I. A.; Shipman, S. T. Journal of Molecular Spectroscopy
2011, 270, 89.
(9)
Jones, G. I. L.; Owen, N. L. Journal of Molecular Structure 1973, 18, 1.
(10)
(11)
Scroggin, D. G.; Riveros, J. M.; Wilson, E. B. Journal of Chemical Physics 1974,
60, 1376.
Owen, N. L.; Seip, H. M. Chemical Physics Letters 1970, 5, 162.
(12)
Dicke, R. H.; Romer, R. H. Review of Scientific Instruments 1955, 26, 915.
(13)
Somers, R. M.; Poehler, T. O.; Wagner, P. E. Review of Scientific Instruments
1975, 46, 719.
(14)
Balle, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. Journal of Chemical
Physics 1979, 71, 2723.
(15)
Balle, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. Journal of Chemical
Physics 1980, 72, 922.
(16)
Keenan, M. R.; Campbell, E. J.; Balle, T. J.; Buxton, L. W.; Minton, T. K.; Soper,
P. D.; Flygare, W. H. Journal of Chemical Physics 1980, 72, 3070.
(17)
Campbell, E. J.; Lovas, F. J. Review of Scientific Instruments 1993, 64, 2173.
(18)
Suenram, R. D.; Grabow, J. U.; Zuban, A.; Leonov, I. Review of Scientific
Instruments 1999, 70, 2127.
11
(19)
Brown, G. G.; Dian, B. C.; Douglass, K. O.; Geyer, S. M.; Shipman, S. T.; Pate,
B. H. Review of Scientific Instruments 2008, 79.
(20)
Wilcox, D. S.; Hotopp, K. M.; Dian, B. C. Journal of Physical Chemistry A 2011,
115, 8895.
12
CHAPTER 2. INSTRUMENTATION AND EXPERIMENTAL PROCEDURES
2.1 Broadband Chirped-Pulse Fourier Transform Microwave Spectroscopy
The broadband Chirped-Pulse Fourier Transform Microwave (CP-FTMW)
spectrometer was used to acquire the majority of the data discussed within this
document.1 The vacuum chamber, shown in a top-down cutaway view in Figure 2.1 a),
had two independent sections: one for CP-FTMW spectroscopy and the second for
traditional Balle-Flygare-type cavity measurements.2 The stainless steel chamber was
purchased from Applied Vacuum Technology as a custom design and is approximately
1.5 m by 0.9 m by 0.6 m. Both sections of the chamber were simultaneously evacuated to
approximately 1.0  10-6 Torr (1.33 10-6 mbar) by a pumping system composed of two
10-inch (25.4 cm), stainless steel diffusion pumps (Varian VHS 10) which were backed
by a roots blower (BOC Edwards: EH 500) and a two-stage roughing pump (Alcatel
2063). The diffusion pump under the center section of the chamber was topped with a
water-cooled baffle (Varian F8600310) to block the rise of the pump oil from the hot jet
assembly. Figure 2.1 b) shows a side view of the vacuum chamber and pumps. Both the
roots blower and diffusion pumps were cooled by the in-house chilled water system with
a water flow rate of about 1.5 liters per minute and a temperature of approximately 53ºC.
The maximum throughput of the diffusion pumps was 8.0 Torr-L/s (10.64 mbar-L/s) at
0.01 Torr (0.0133 mbar).
13
Figure 2.1: (a) The vacuum chamber shown in a top-down cutaway view. The pulsed
valve and horn antenna (right) are used for Chirped-Pulse Fourier Transform Microwave
spectroscopy. The Fabry-Perot cavity mirrors and translation stage (center) are based
upon the Balle-Flygare design. (b) Side view of the vacuum chamber and two 10 inch
(25.4 cm) diameter diffusion pumps. Total length of the chamber is about 1.5 m.
14
This translates to a maximum pumping speed of 8000 L/s (air). The interior walls of the
vacuum chamber were covered with metal-lined microwave-absorbing foam (Emerson
and Cuming: Eccosorb HR-25/ML: 5-70 GHz) to reduce reflections of the scattered
microwave field. Using this pumping arrangement, pressures suitable to for a CP-FTMW
spectroscopic experiment can be obtained in approximately one hour when beginning at
atmospheric pressure.
CP-FTMW spectroscopy is a gas phase technique which is limited to molecules
that have a permanent electric dipole moment. Based on the physical properties of the
sample, one of three sample preparation methods was employed. Gas samples such as 1chloro-1-fluoroethylene (CFE) or 3,3,3-trifluoro-1-propyne (TFP) were purchased and
used without further purification. By means of a stainless steel gas manifold, a gas
cylinder (approximately 17.78 cm outside diameter by 68.58 cm outside height including
valve) was evacuated, filled with approximately 0.084 bar (1.2 psi) of sample gas, and
then balanced to approximately 6.89 bar (100.0 psi) with an inert carrier gas (a He/Ne
mixture at 30/70%). Liquid samples such as crotonaldehyde (CA) were also purchased
and used with no further purification. A freeze-pump-thaw technique was performed for
liquid samples using the same gas manifold. The sample was first frozen with liquid
nitrogen, then the air above the sample was pumped away before the sample was allowed
to return to room temperature. This method transfers the sample molecules to an
evacuated gas cylinder, which was then balanced with He/Ne to 6.89 bar. The last
method of sample preparation was for high vapor pressure liquids. Approximately 0.5 mL
of sample was placed in a cylindrical (3.5 cm by 1.5 cm) stainless steel sample container
which was packed lightly with clean cotton. This sample container was placed inside the
15
vacuum chamber and He/Ne buffer gas flowed over the sample to entrain the molecules
in the carrier gas. Typical backing pressures were near 1 bar, and if necessary a heating
rope could be wrapped around the sample container to warm the sample thereby
increasing its vapor pressure.
Regardless of the preparation method, a supersonic expansion of sample
molecules was introduced into the vacuum chamber through either a 1.8-mm or 0.8-mm
orifice. With a Teflon poppet, a pulsed solenoid (Series 9, Parker General Valve) and
spring assembly were used to repeatedly open and close the orifice at a rate of 10 Hz.3
The pulsed-valve driver for the sample inlet valve was built by Purdue University’s
Jonathan Amy Facility for Chemical Instrumentation. The resulting supersonic expansion
cooled the molecules to an estimated rotational temperature of 2.5 K. While the sample
molecules were flowing into the vacuum chamber, the chamber pressure rose to
approximately 2.0  10-4 Torr (2.66  10-4 bar) using the 1.8-mm nozzle or 2.0  10-5
Torr (2.66  10-5 bar) using the 0.8 mm nozzle. In order to reduce the possibility of crosscontamination, prior to each sample change the valve assembly was disassembled and
cleaned with methanol and benzene. This cleaning procedure was performed before
beginning each new experiment.
2.2 Microwave Pulse Generation Mixing with 13.0 GHz
The polarizing microwave pulses were produced by an arbitrary waveform
generator (Tektronix AWG 7101) with a sampling rate of 10 GS/s. Each chirped
polarizing pulse was linearly swept from 0.1 to 5 GHz in 1.0 μs. Once emitted by the
arbitrary waveform generator, the microwave pulse was filtered with a 5 GHz low-pass
16
filter (Lorch 10LP-5000-S) and power amplified (Mini-circuits ZX60-6013ES+6000MHz) to level the output power of the arbitrary waveform generator. The
microwave pulse (RF input) was then mixed (Miteq TB0218LW2) with a singlefrequency source of 13.0 GHz generated by a phase-locked dielectric resonator oscillator
(PLDRO) (Microwave Dynamics PLO-2000-13.00). To match the power specifications
of the local oscillator (LO) input of the mixer, excess power from the PLDRO was
suppressed using a total of -7 dB attenuation from two in-line microwave attenuators. The
attenuated signal from the PLDRO (15.99 dBm) was filtered with a 13.0 GHz cavity
notch filter (Lorch 6BR6-13000/100-S) to remove any overtone signals outside of the
12.537-13.467 MHz range. After mixing, the intermediate frequency (IF) signal was
filtered with a cavity filter (Lorch 6CF7-13000/100-S) that removed the impulse function
generated at 13.0 GHz. A manual step attenuator with an attenuation range from 0 to -69
dB and a step size of 1 dB (Weinschel AF117A-69-11) controlled the power of the
microwave field entering the 200-watt traveling wave-tube (TWT) amplifier (Amplifier
Research 200T8G18A). The saturation point of the power amplifier was 355.84 W at 0
dBm input and a frequency of 13 GHz using a gain setting of 71%. To avoid back
reflections, the signal entering and exiting the TWT amplifier was passed through
matching isolators (Ditom DMI6018). The arbitrary waveform generator and all PLDROs
were phase-stabilized by a 100 MHz phase-locked quartz oscillator plate assembly
(Wenzel Associates 501-10137B) which was synchronized with a 10 MHz rubidium
frequency standard (Stanford Research Systems FS725) providing an overall phase noise
of less than -100 dBc/Hz for the phase-locked loop. Compared to the internal clock of the
arbitrary waveform generator, this was a stability improvement of -10 dBc/Hz. The
17
microwave pulse entered the evacuated chamber through a mica window which forms a
vacuum seal with the double-ridge waveguide (Advanced Technical Materials 750130/PU). A block diagram of the microwave circuit’s components is shown in Figure 2.2.
Inside the chamber, the electric field was broadcast across the molecular interaction
region by a gain-enhanced microwave horn antenna (Amplifier Research AT4004). The
matching horn antennas used in the CP-FTMW system are highly directional, unpolarized
antennas with an optimal operational frequency range from 8 GHz to 18 GHz. At a
frequency of 12.0 GHz, which is near the center of our frequency range of interest, the
maximum gain of the horn antenna is -10 dBi at a zero azimuth angle. With the gain
enhancer, the beamwidths of the antennas at 12.0 GHz are 18 and 20 degrees in the Eplane and H-plane, respectively. In the E-plane, side lobes appear at azimuth angles of +/30 degrees with an intensity of -21 dBi. There are no appreciable side lobes in the Hplane radiation pattern. The microwave field was projected from the horn antenna into
free space in a direction perpendicular to the axis of the molecular flow. A macroscopic
polarization of the molecules was induced by the microwave pulse, and the resulting freeinduction decay (FID) was collected with a second microwave horn antenna. The
receiving horn was mounted to a custom-designed XYZ-translation stage so that its
collection efficiency could be optimized. The Y position was optimized by rotating the
manual control wheel to maximize the intensity of the detected molecular signal.
Although translating the receiving horn in the X and Z directions made minimal
differences in the magnitude of the detected signal, these axes were also optimized. After
optimization, the position of the receiving horn was held constant for all the described
experiments.
18
Figure 2.2: Block diagram of the 13 GHz mixing microwave circuit of the CP-FTMW
spectrometer. The chirped microwave polarizing pulses are produced by the arbitrary
waveform generator in the 0.1-5 GHz range. The pulses were filtered, pre-amplified,
mixed with a phase stabilized 13 GHz frequency source, power amplified by 200 W and
then broadcast into the vacuum chamber. A manual step attenuator and circulator were
used to control the amplitude of the signal entering the 200 W amplifier.
19
The polarizing microwave pulse and the resulting molecular signal were
transmitted through a PIN diode limiter (Advanced Control Components ACLS 4619FC36-1K).To protect the detection electronics from the strong polarizing electric field, a
single-pole single-throw (SPST) switch was placed in the circuit. The SPST switch was
opened while the intense polarizing microwave pulse was broadcast and then closed to
allow the collection of the molecular FID. A digital pulse generator (Stanford Research
Systems Model DG535) toggled a reflective SPST (Advanced Technical Materials
S1517D, isolation 80 dB, 2-18 GHz) on one channel and turned on and off the 200-watt
TWT amplifier via a separate channel. This arrangement was made so that we could
remotely control the timing of the amplifier and the switch for 2D CP-FTMW
experiments by communicating with the DG535. The isolated coherent molecular FID
was amplified by a low-noise amplifier (Miteq AMF-6F-06001800-15-10P) with a gain
of +45.0 dB. This signal (RF) was then down-converted using a triple-balanced mixer
(Miteq TB0440LW1) and a PLDRO operating at 18.9 GHz (Microwave Dynamics PLO2000-18.90). To ensure phase stability, the PLDRO was also driven by the phase-locked
loop through the 100 MHz quartz oscillator plate. The output from the PLDRO was
filtered with an 18.9 GHz cavity bandpass filter (Lorch 7CF7-18900/100S) before being
introduced to the RF signal through the local oscillator (LO) port of the mixer. After
mixing, the lower sideband (0.4-11.4 GHz) of the intermediate frequency (IF), was
transmitted through a DC block (MCL 15542 BLK-18) and low-pass 12 GHz filter
(Lorch 7LA-2000-S). The resulting time-domain signal was recorded on a 12 GHz
oscilloscope (Tektronix TDS6124C) at a rate of 40 GS/s. A block diagram of the
detection circuit is shown in Figure 2.3.
20
Molecular Signal
(Free Induction Decay)
DC Block
10 MHz
Rb Clock
100 MHz Quartz
Oscillator
12 GHz
Digital
Oscilloscope
PLDRO
(18.9 GHz)
Figure 2.3: Block diagram of the detection electronics of the CP-FTMW spectrometer.
The molecular signal collected by the microwave horn antenna was mixed down with a
phase stabilized 18.9 GHz frequency source.
21
A 20-output timing control Masterclock (Thales Laser) was used to manage the
synchronized delays of the valve, digital pulse generator, and arbitrary waveform
generator. The Masterclock had a jitter of less than 50 ps root-mean-squared (RMS) and
was driven by the phase-locked loop. The excellent phase stability of our system allowed
for signal averaging of 100,000 spectra which required approximately 7.5 hours to
collect.
2.3 Microwave Pulse Generation x4 Frequency Stretcher
An alternative microwave circuit configuration was used for some experiments to
obtain a slightly larger excitation bandwidth. The 13.0 GHz PLDRO, -7 dB attenuators,
13.0 GHz cavity notch filter, and mixer were all removed from the circuit. They were
replaced with a frequency quadrupler (Phase One Microwave PS06-0161). With this
design, the arbitrary waveform generator emitted a chirped pulse from 1.875-4.625 GHz.
The pulse frequency was then quadrupled and the power increased with the 200 W
amplifier (Amplifier Research) to produce a bandwidth of 11 GHz (7.5-18.5 GHz). This
bandwidth was 1 GHz larger than that achieved with the signal mixing circuit
configuration (8.0-18.0 GHz). A block diagram of the circuit is shown in Figure 2.4. The
detection electrical components remained the same as described in Section 2.2 of this
chapter. Although a slightly larger bandwidth was achieved in this scenario, it was at the
cost of homogeneity in the electric field. This was the case because the x4 frequency
stretcher (quadrupler) is an indiscriminate device that does not distinguish useful signals
from noise.
22
Figure 2.4: Block diagram of the microwave circuit including the x4 frequency stretcher
(quadrupler). The 13 GHz PLDRO and associated components are replaced by a x4
frequency stretcher to achieve an 11 GHz bandwidth (7.5-18.5 GHz).
23
Therefore, any spurious noise tones were also multiplied by the quadrupler along with the
desired signal. This caused the noise tones to be repeated in regular internals throughout
the linear polarizing sweep. Figure 2.5 (a-c) and (d-f) show the time-domain, frequencydomain, and frequency-resolved optical gate (FROG) signals of a 1 μs polarizing pulse
using the 13 GHz mixing circuit and quadrupler microwave circuit, respectively. In
Figure 2.5 c) and f), the spurious noise signals have been suppressed.
2.4 One-Dimensional Data Processing
For a standard one-dimensional CP-FTMW spectroscopic experiment, 20 μs of
the molecular FID was digitized by the 12 GHz oscilloscope and saved in a .txt file
format. The typical ring down time for the molecules was approximately 15 μs, so
digitizing beyond 20 μs would introduce superfluous noise. This data was then processed
on a PC using a program written with the Mathcad 14.0 software package. A KaiserBessel digital filter was applied to the data to suppress the amplitude of any frequencydomain side lobes. With this type of filtering window, there is a tradeoff between the
main peak width and the suppression of the side lobes which is set by the term α. For 70
dB down suppression of the side lobes, α was set to 3 to provide a balanced filtering
window. The data set was then zero-padded to a power of 2 so a Fast Fourier transform
(FFT) could be calculated efficiently using the Cooley-Turkey algorithm.4,5 This
algorithm increases the FT computational speed by breaking the calculation into a series
of smaller, discrete Fourier transforms which can be performed more quickly because the
real and imaginary portions of the FT are equal.6
24
a)
Arbitrary Intensity
Arbitrary Intensity
d)
0.2
0.4
0.6
0.8
Time (s)
1.0
1.2
1.4
b)
0.0
0.6
0.8
Time (s)
1.0
1.2
1.4
Arbitrary Intensity
Arbitrary Intensity
10000 12000 14000 16000 18000
Frequency (MHz)
f)
18000
16000
14000
12000
10000
10000
12000
14000
16000
Frequency (MHz)
18000
18000
16000
14000
12000
10000
8000
8000
0.0
8000
Frequency (MHz)
Frequency (MHz)
0.4
e)
8000
c)
0.2
0.2
0.4
0.6
Time (s)
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Time (s)
Figure 2.5: The time-domain, frequency-domain, and frequency-resolved optical gate
(FROG) signals of a 1 μs polarizing pulse using the 13 GHz mixing (a-c) or quadrupler
(c-f) microwave circuit.
25
A noise threshold was set using background data (valve off) and then was masked from
the molecular signal. The final file was written out in .txt or .prn format. The frequencydomain rotational spectrum had approximately 20 kHz resolution which could be
interpolated to 5 kHz in the spectral fitting program JB95.7
2.5 Balle-Flygare Type Fabry-Perot Cavity
Prior to the development of CP-FTMW spectroscopy in 2008,8 the dominant
method of measuring microwave rotational spectra was based on a tunable Fabry-Perot
cavity with a Balle-Flygare-type design.9-11 The vacuum chamber shown in Figure 2.1
includes this style of measurement setup. The microwave cavity was located directly
above the water-cooled baffle of the central diffusion pump (see Figure 2.1), and as in the
case of the broadband CP-FTMW spectrometer, the same pulsed-nozzle assembly was
used to generate the supersonic expansion of sample molecules. However, to perform
measurements using the cavity assembly, the valve flange was relocated so that the
molecular pulse was directed downward (parallel to the z-axis of Figure 2.1) toward the
diffusion pump and perpendicular to the cavity axis (the y-axis of Figure 2.1). The
microwave cavity was formed by two 7.5-inch (20.32 cm), polished 5086 aluminum alloy
mirrors of a custom design by Applied Vacuum Technology. The mirrors have a radius of
curvature of 12 inches (30.48 cm) and are nominally separated by a distance of 23 inches
(58.42 cm).
Balle-Flygare cavities support resonant transverse electromagnetic (TEMm,n,q)
modes that in general can be described with Hermite-Gaussian field distributions,
although the fundamental, lowest-order TEM0,0,q mode has a Gaussian cross-section.12
26
The cavity in our spectrometer is designed to operate with a dominant, fundamental
TEM0,0,q mode; which does not have any nodes in the beam profile which are prevalent in
the higher order TEM modes.12,13 This is accomplished through coupling antennas as
described later.11 A single beam waist occurs at the center of the cavity between the two
spherical concave mirrors.14
One mirror in our cavity was stationary, and the second mirror was mounted on a
manually controlled single-axis translation stage (Velmex A4009W2-S4) in order to
adjust the length of the cavity along the y-axis and thereby tune the resonant cavity
frequency. In practice, the cavity tuning is accomplished in a more elegant and efficient
manner, than the brute-force method of tuning the mobile mirror trough all available
cavity lengths until a resonant mode is found. To do this we set the frequency source to
generate a stair-step frequency sweep that includes the frequency of interest. We then
find a resonance in the swept range by adjusting the mirror position and monitoring the
detected signal for a transmission peak. This tells us that we have a resonance somewhere
in the range of the sweep, but it does not guarantee that the resonance is at the frequency
of interest. To hone in on the frequency of interest, we repeat the adjustment process with
consecutively narrower and narrower frequency ranges until we have finally tuned the
cavity precisely to the frequency of interest.
A block diagram of the cavity circuit is shown in Figure 2.6. A 1-μs duration, 30
MHz sine wave was generated from the two-channel arbitrary waveform generator
(Tektronix AFG3102) at a digitization rate of 1 GS/s. This signal is herein called the local
oscillator (LO) source.
27
Arbitrary
Waveform
Generator
30 MHz
30 MHz
+
Cavity
30 MHz
+±
50/50

Microwave
Synthesizer
30 MHz

±
12 GHz
Oscilloscope
Figure 2.6: Block diagram of the Fabry-Perot cavity FTMW spectrometer based on the
Balle-Flygare design. The 30 MHz signal from the arbitrary waveform generator was
mixed with the frequency (ν) from microwave synthesizer (30 MHz + ν). After
interaction with the molecules in the cavity, the shifted molecular signal (30 MHz + ν)
±Δ was mixed down with ν and recorded by a digital oscilloscope.
28
Simultaneously, a microwave synthesizer (Agilent E8257D) generated a continuouswave sinusoidal signal at a frequency 30 MHz below the frequency of the rotational
transition of interest. This signal, called the radio frequency (ν), was then split with a
50/50 power splitter (Narda 4456-2). Half of the radio frequency signal was mixed with
the LO source using a single side band mixer (Miteq SMO218LC1MDA). The upper side
band was controlled by a manual step attenuator (Weinschel AF117A-69-11) and power
amplified with a 1 W solid state amplifier (Microwave Power Inc. L0818-30-T358). The
amplified signal then passed through an isolator (Ditom DMI6018) to eliminate back
reflections. After transmission through the circulator (Ditom DMC6018), the microwave
signal was broadcast into the Fabry-Perot cavity through a copper, L-shaped microwave
antenna mounted in the center of the stationary mirror. This antenna was oriented parallel
to the molecular flow (the z-axis) and perpendicular to cavity axis (the y-axis), such that
the microwave signal was linearly polarized along the z-axis. There are a total of two
antennas in the cavity; the stationary mirror has one antenna mounted in the vertical
position (z-axis) and one in the horizontal position (x-axis). The horizontal antenna on the
stationary mirror is grounded to remove light polarized in this plane and to remove nodes
in the electric field. The shifted, reflected signal was emitted through a single-pole singlethrow switch (Advanced Technical Materials S1517D, isolation 80 dB, 2-18 GHz),
amplified by a low-noise amplifier (+45 dB, Miteq AMF-6F-06001800-15-10P LNA),
and mixed down (Miteq IRM0218LC1A) with the signal from the radio frequency
microwave synthesizer (ν). The detected signal was therefore 30 MHz plus the emitted
molecular signal from the sample molecules. This resulting signal was recorded on the 12
GHz oscilloscope. Note that even with automated control of the cavity tuning, FTMW
29
measurements with this type of cavity instrument are tedious and inefficient both in terms
of time and sample amounts. The CP-FTMW instrument is a much more efficient design
since the measurements can be acquired rapidly and with smaller amounts of sample
molecules.
2.6 Two-Dimensional Program
Applications of Two-Dimensional Chirped-Pulse Fourier Transform Microwave
spectroscopy are discussed in Chapter 4. In order to develop the applications of the 2D
CP-FTMW technique, however, it was necessary to demonstrate the feasibility of the
method by manually measuring preliminary proof-of-principle data. For a typical 2D
experiment, two microwave polarizing pulses, separated by a time delay (t1), were
broadcast from the arbitrary waveform generator. This time delay was stepped out in
increments of either 500 ps or 1 ns, and the signal-averaged FID was recorded at each
measurement step. As the time delay between the pulses was stepped out, the “on”
duration of the 200 W amplifier and the “open” duration for the microwave switch also
followed the same stepping pattern. With these groundwork experiments, the time delays
between the microwave pulses, amplification duration, switch timing, and the file saving
process were all performed manually.
In order to efficiently implement the 2D CP-FTMW technique, computerized
control of the data collection process was clearly necessary, and represented a significant
step forward in the further application of the 2D technique. The data acquisition process
of the 2D experiments was automated using National Instruments LabVIEW version 8.5.
30
START
SW Init
Exit
User Input
Start
Connect
HW Init Control
Pre‐Scan Control
HW Init DG535
Pre‐Scan DG535
HW Init TDS6124
Pre‐Scan TDS6124
HW Init AWG7000
Pre‐Scan AWG7000
HW Init SW
Pre‐Scan SW
Scan Control
Take Data
Done
Post‐Scan Control
Set DG535 Chan Delay
Post‐Scan DG535
Set AWG7000 Count
Post‐Scan TDS6124
Init TDS 6124 Scan
Post‐Scan AWG7000
Wait TDS6124 Complete
Post‐Scan SW
Yes
No
Read TDS6124 Data
HW Close Control
Process Data
HW Close DG535 Com
Display Data
HW Close TDS6124 Com
Wait 100 ms
HW Close AWG7000 Com
Write Data File
HW Close SW
Shutdown
Exit
END
Figure 2.7: Flow chart of the 2D data collection program written in LabVIEW version
8.5.
31
Images of the computer code are provided in the Appendix of this document, and a flow
chart of the program’s function is shown in Figure 2.7. Note that the graphical LabVIEW
computer code was prepared so that it generally can be read from left to right and top to
bottom.
Broadly speaking, the computer program automates the data collection process for
the 2D CP-FTMW technique. The program prepares the 2D system for operation, sets all
necessary equipment parameters, controls the equipment throughout the experiment and
provides convenient and real-time user feedback. The program also performs input errorchecking, file-saving, and equipment shutdown functions. The program’s architecture, or
organizational structure, was designed to build a queue of cases which can be thought of
as a stack of cards with a set of commands written on each card. The commands on a card
are executed each time that card is on the top of the stack. When the user begins the
program, the first case is placed in the queue. Screen shots of the user interface are found
in Figures A 1 through A 3 of the Appendix. The first case executed by the program is
the “Software Initialization” case which grays out and disables the function of the front
panel Start button. This is a safety feature designed to protect the instruments so that the
user does not begin a data collection process before providing proper experimental
parameters. The program then waits in the “User Input” case for the user to press the
Connect button or the Exit button. These buttons are displayed on the first font panel tab
called hardware configuration, as shown in Figure A 1 of the Appendix. The user should
verify that the 200 W amplifier and the microwave switch are connected to the correct
channels on the DG535, select the GPIB addresses for each instrument (Arbitrary
Waveform Generator, GPIB0::9::INSTR) (DG535, GPIB::15::INSTR) (Oscilloscope 12
32
GHz, GPIB0::8::INSTR), and then press Connect. The “Hardware Initialization Control”
case will call the subsequent hardware initialization cases, “Hardware Initialization
DG535”, “Hardware Initialization TDS6124”, “Hardware Initialization AWG7000” and
“Hardware Initialization Software” in that order. These cases open communication with
their designated instruments and the “Hardware Initialization Software” case grays out
and disables the hardware configuration tab on the front panel. It also makes available to
the user the pulse parameters and scan parameters tabs.
The user then fills in the pulse and scan parameter values for the 2D experiment.
The pulse parameters depend on the pulse sequence which was uploaded to the arbitrary
waveform generator. The index number of the delay (t1), duration of the delay, which
also sets the step size for the experiment, and the repeat number of the index are entered
on this tab. For example, if a 1 ns step size with an initial delay of 100 ns were the
desired parameters for an experiment, a 1 ns pulse train of zeros would be loaded into
index 2 of the arbitrary waveform generator, and 10 would be entered as the initial loop
count of index 2. Next, the user enters values for the initial settings of the DG535. The
DG535 provides timing control of the 200 W amplifier and the SPST electronic switch.
The amplifier start time A(To) and switch start time C(To) are the time delays relative to
the DG535’s start time (To). For a standard 2D experiment, the switch would open at 620
ns to block the intense polarizing pulses, and the amplifier would be turned on at 690 ns.
These values remain constant for the entire experiment. Starting values for the amplifier
duration B(A) (how long amplifier is on) and switch duration D(C) (how long the switch
is open and blocks the polarizing pulses) are also set on the scan parameters tab. Standard
durations are 400 ns and 900 ns, respectively. These two values are systematically
33
increased by the program in an increment equal to the step size set on the pulse
parameters tab. The user also specifies the desired source from the 12 GHz scope
(channel 2), file path, and file name for the data saved by the program. The number of
steps or iterations is also entered here. This value is usually a power of 2, such as 1024 or
2048, so that the fast Fourier transform may be taken efficiently in the second dimension.
This streamlines the data processing procedure. When the user presses Start, the “Prescan DG535” case removes the DG535 from a free-running mode and places it into a
trigger mode. This case also sets the amplifier start time A(To) and switch start time
C(To). The “Pre-scan Software” case retrieves the time stamp from the computer running
LabVIEW to record the time when the scan was started. This time stamp is later used to
calculate the time required to complete the experiment. “Pre-scan Software” disables and
grays out the input values so that the user may not change them while the scan is running.
The “Scan Control” case of the program is a decision-making case that performs a
comparison of the current step count to the number of steps set by the user. If the current
step is less than the total number of steps set by the user, the program will proceed down
the take data path. If the current step equals the number set by the user, the program will
follow the “Post Scan Control” case. To take data, the program sets the amplifier and
switch delays with the “Set DG535 Channel Delay” case, and then it updates the repeat
count of the specified index on the arbitrary waveform generator. The “Initialize
TDS6124” case then initiates the waveform acquisition, and the 12 GHz scope waits for
an external trigger to begin collecting the FID. The LabVIEW program then waits for the
scope to finish its signal averaging. When the busy query finds the scope is finished with
a set of averages, the waveform is read, and the display on the front panel of the
34
LabVIEW code is updated. The time remaining to finish the experiment is calculated by
the following process: [(time started – time current time) / number of steps completed] x
number of steps remaining. This is then made into an easy-to-read hour : minute format
shown on the front panel. A “Wait” case of 100 ms then allows the instruments time to
catch up. The program selects the specified source (channel 2) from the 12 GHz scope
and writes the data file to the designated file path on the 12 GHz scope. The file names
are sequentially numbered with leading digits followed by a root name specified by the
user. The program then returns to “Scan Control” where the internal step count is
incremented, the timing of the amplifier and the switch are increased by the step size, and
the repeat count of the index is also incremented.
When the program has reached the designated number of steps, the “Post-scan
TDS 6124” case puts the scope back into a free-running mode so that LabVIEW no
longer has control over the instrument. The “Post-scan Software” case notifies the user
that the scan is complete with a pop-up message. This case also enables the input
parameter boxes on the front panel. The “Hardware Control” case oversees the systematic
communication closure with the DG535, TDS6124, and AWG7000. Finally, the
“Shutdown” case stops the fundamental while loop of the program, thereby ending the
program.
2.7 Two-Dimensional Data Processing
The 2D data processing procedure is similar to the 1D method described in
section 2.4 of this chapter. For the 2D CP-FTMW experiments, the t1 delay between the
microwave pulses was incremented for 2048 or 4096 steps with a dwell time
35
augmentation of 1 ns or 500 ps respectively. For each measurement step the 4 μs signal
averaged FID was digitized and automatically saved with a .dat file extension. These files
were processed offline with a digital Kaiser-Bessel filter and Fourier transform, to yield
2048 or 4096 spectra with 125 kHz resolution in the 2 domain. This first stage of the 2D
data processing procedure is the same as the data processing method used for a typical
1D experiment. Then modulations in the intensity magnitude, with respect to t1, of the
irradiated rotational transitions were then filtered with a Kaiser-Bessel function and
Fourier transformed once more, revealing coherence peaks in the 1 magnitude spectrum
with approximately 400 kHz resolution. The resolution of the 1 and 2 transition
frequencies reflect the sampling time in each dimension and not the highest resolution
achievable with the CP-FTMW spectrometer.15
36
2.8 References
(1)
Shirar, A. J.; Wilcox, D. S.; Hotopp, K. M.; Storck, G. L.; Kleiner, I.; Dian, B. C.
Journal of Physical Chemistry A 2010, 114, 12187.
(2)
Balle, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. Journal of Chemical
Physics 1979, 71, 2723.
(3)
Campbell, E. J.; Lovas, F. J. Review of Scientific Instruments 1993, 64, 2173.
(4)
Mou, Z. J.; Duhamel, P. Ieee Transactions on Acoustics Speech and Signal
Processing 1988, 36, 1642.
(5)
Proakis, J. G.; Manolakis, D. G. Digital Signal Processing: Principles,
Algorithms and Applications; 3 ed.; Prentice Hall, 1995.
(6)
Fertner, A. Ieee Transactions on Signal Processing 1999, 47, 1061.
(7)
Plusquellic, D. F.; Suenram, R. D.; Mate, B.; Jensen, J. O.; Samuels, A. C.
Journal of Chemical Physics 2001, 115, 3057.
(8)
Brown, G. G.; Dian, B. C.; Douglass, K. O.; Geyer, S. M.; Shipman, S. T.; Pate,
B. H. Review of Scientific Instruments 2008, 79.
(9)
Balle, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. Journal of Chemical
Physics 1980, 72, 922.
(10)
Balle, T. J.; Flygare, W. H. Review of Scientific Instruments 1981, 52, 33.
(11)
Suenram, R. D.; Grabow, J. U.; Zuban, A.; Leonov, I. Review of Scientific
Instruments 1999, 70, 2127.
(12)
Kogelnik, H.; Rigrod, W. W. Proceedings of the Institute of Radio Engineers
1962, 50, 220.
(13)
Kogelnik, H.; Li, T. Applied Optics 1966, 5, 1550.
(14)
Campbell, E. J.; Buxton, L. W.; Balle, T. J.; Flygare, W. H. Journal of Chemical
Physics 1981, 74, 813.
(15)
Wilcox, D. S.; Hotopp, K. M.; Dian, B. C. Journal of Physical Chemistry A 2011,
115, 8895.
37
CHAPTER 3. CONFORMATIONAL ANALYSIS OF N-BUTANAL BY CHIRPEDPULSE FOURIER TRANSFORM MICROWAVE SPECTROSCOPY
3.1 Introduction
The molecule n-butanal (butyraldehyde C4H8O) is an important intermediate in
the reaction mechanism for the pyrolysis and combustion of the alcohol biofuel, nbutanol.1 As an alternative fuel, n-butanol is an appealing option because it has higher
energy content than ethanol, is less corrosive than ethanol, and could be used in a
standard combustion engine without mechanical modification.2 However, when released
into the atmosphere, the photochemical oxidation of n-butanol leads to the formation of
n-butanal.3 Listed as an air toxin in the US Clean Air Act Amendments of 1990,4 nbutanal is an odorous atmospheric pollutant that is toxic to human health.5 A fuller
understanding of the molecular geometry of n-butanal will aid in the determination of its
role as an environmental pollutant.
Stable molecular geometries of n-butanal are formed by the rotation of two
torsional angles, τ1 = O–C1–C2–C3 and τ2 = C1–C2–C3–C4, shown in Figure 3.1. Early
NMR spectroscopy work by Lehn et al. supports the existence of two liquid phase
isomers of n-butanal.6 In 1970, the IR and Raman spectra of liquid and crystalline nbutanal were published by Sbrana and Schettino.7
38
Figure 3.1: Optimized molecular geometries of n-butanal. The two torsional angles,
τ1 = O–C1–C2–C3 and τ2 = C1–C2–C3–C4, are used to name the structures as cis/trans
(τ1 = 0°/τ2 = 180°), cis/gauche (τ1 ≈ 5°/τ2 ≈ 70°), gauche/trans (τ1 ≈ 130°/τ2 ≈ 180°), and
gauche/gauche (τ1 ≈ -130°/τ2 ≈ 70°). The naming convention was chosen to be consistent
with previously reported work.8
39
The vibrational assignments of the crystalline structure were identified as arising from the
cis/trans (τ1 = 0°/τ2 = 180°) planar conformation of n-butanal. In the liquid phase, the
relative intensities of the infrared bands were recorded as a function of temperature to
measure the enthalpy difference between rotational isomers cis/trans (τ1 = 0°/τ2 = 180°)
and a second stable geometry. The results of that study were slightly ambiguous because
ΔH values of 1030, 915, or 815 cal/mol ± 130 were obtained when different IR bands
were selected for the calculation. This discrepancy could be the result of the presence of
more than two isomers in the liquid phase. However, no conclusive evidence of the
second isomer’s geometry or the existence of a third isomer was provided by their study.
In addition to a limited number of experimental studies, previous work has also
been performed computationally to explore the structure of n-butanal. An ab initio study
of geometry optimization was completed by Klimkowski et al. in 1983, resulting in a
large amount of information about the molecular conformations.9 Using the Pulay
gradient method at the 4-21 level, the lowest energy structure was calculated to be the
cis/trans (τ1 = 0°/τ2 = 180°) geometry. Energy minima for the τ1 dihedral angle were
found at 0° and slightly above 120°, with maxima near 70° and 180°. For the optimized
molecular geometries of n-butanal, bond distances, bond angles, torsions, and total
energies were also published by Klimkowski et al.9 They found that rotation about τ2, the
hydrocarbon chain, produced little change in the energy pattern observed from the τ1 0°
to 180° torsion. From their theoretical study, the τ1 rotation of the O–C1–C2–C3 dihedral
was found to have a potential energy barrier of 0.570 kcal/mol (199 cm-1). For the
cis/trans (τ1 = 0°/τ2 = 180°) structure of n-butanal, theoretically calculated bond lengths(–
CHO,–CH3, and C=O), O atom charge, and
HCOangle
values were published by
40
Dwivedi et al. in 2009.10 Three different methods were used for these calculations:
restricted Hartree-Fock, density functional theory (B3LYP), and MP2 with a 6-311G*
basis set.
The relative conformational energies of n-butanal were calculated by Langley et
al. using molecular mechanics (MM3 and MM4) and density functional theory (DFT)
calculations.8 The DFT calculations, performed at the B3LYP level of theory with a
6-31G* basis set, were found to be in good agreement with the MM4 force field results.
With the τ1 dihedral angle constrained to zero, the cis/trans (τ1 = 0°/τ2 = 180°) geometry
of n-butanal was calculated to be the global minimum, and a secondary minimum was
formed by the cis/gauche (τ1 ≈ 5°/τ2 ≈ 70°) structure. The cis/trans to cis/gauche, τ2,
barrier to rotation was found to be 2.68 kcal/mol (MM4) and 2.76 kcal/mol (DFT). The
cis/skew (τ1 = 0°/τ2 ≈ 120°) and cis/cis (τ1 = 0°/τ2 = 0°) transition states are energetic
maxima, which are difficult to observe experimentally. With the τ1 dihedral constraint
relaxed, two more structures can be formed, gauche/trans (τ1 ≈ 130°/τ2 ≈ 180°) and
gauche/gauche (τ1 ≈ 120°/τ2 ≈ 70°). Experimental and calculated dipole moments (both
induced and not induced) are also reported by Langley et al. In their computational study,
the gauche/gauche structure of n-butanal was not addressed.
Rotational spectroscopy provides significant structural information about gas
phase molecules and is therefore an extremely useful tool in determining the molecular
geometry of conformational isomers. In this work, we have used the broadband capability
of Chirped-Pulsed Fourier Transform Microwave (CP-FTMW) spectroscopy to study the
conformational properties of n-butanal. The rotational spectrum of n-butanal was first
presented in a thesis by P. L-S. Lee in 1971.11 Nine rotational transitions of the cis/trans
41
(τ1 = 0°/τ2 = 180°) structure were assigned for the ground state and the first two
vibrationally excited states. The cis/gauche (τ1 ≈ 5°/τ2 ≈ 70°) geometry was also
observed, and 19 rotational assignments were made for the ground state and the first
excited state of this structure. Rotational constants, moments of inertia, Paa, Pbb, Pcc, κ,
Stark coefficients, and dipole moments were found for both the cis/trans (τ1 = 0°/τ2 =
180°) and cis/gauche (τ1 ≈ 5°/τ2 ≈ 70°) geometries. No other isomers of n-butanal could
be identified by Lee 11, and no further rotational spectroscopy studies with this molecule
have been published in the intervening years.
3.2 Experimental Details
The broadband Chirped-Pulsed Fourier Transform Microwave (CP-FTMW)
spectrometer used in this study was based upon the design by Brown et al.12 The full
details of the operation of this spectrometer can be found in Chapter 2; a brief summary is
given here.13 Compared to the Fabry-Perot style microwave spectrometer, developed by
Balle and Flygare, the major advancement of the CP-FTMW spectrometer is that with
each acquisition event the entire broadband (7.5-18.5 GHz) rotational spectrum is
obtained.14-16 To acquire the rotational spectrum of n-butanal, a 1 μs polarizing
microwave pulse was emitted by an arbitrary waveform generator (Tektronix AWG
7101) with a digitization rate of 10 GS/s. This pulse was linearly swept from 1.875 GHz
to 4.625 GHz. The pulse was then filtered with a 5 GHz low-pass filter (Lorch 10LP5000-S) and pre-amplified (Mini-circuits ZX60-6013E-S+6000MHz) to produce a more
uniform power intensity within the pulse. The bandwidth of the electric field was
expanded to 11 GHz (7.5-18.5 GHz) using a microwave frequency quadrupler (Phase
42
One PS06-0161) and was then amplified by a 200-watt traveling wave tube (TWT)
amplifier (Amplifier Research 200T8G18A). The power of the electric field entering the
TWT amplifier was controlled with a manual step attenuator with a working range of 0 to
-69 dB. The electric field was broadcast into an evacuated chamber using a gainenhanced microwave horn antenna (Amplifier Research AT4004).
The vacuum chamber of the spectrometer was evacuated to approximately 1.0 
106 Torr (1.33 109 bar) by a pumping system composed of two ten-inch, stainless steel
diffusion pumps (Varian VHS 10) which were backed by a roots blower (BOC Edwards:
EH 500) and a two-stage roughing pump (Alcatel 2063). Purchased from Sigma-Aldrich,
n-butanal (purity greater than or equal to 99.5%) was used with no additional
purification. A sample of 0.5 mL of n-butanal was transferred to a gas cylinder using a
freeze-pump-thaw method performed with an in-house built gas manifold. The sample
cylinder was balanced with 100 psi (6.89 bar) of He/Ne (30/70%) buffer gas. Sample
molecules, entrained with the buffer gas, were introduced into the chamber through a
pulsed 1.8 mm orifice Series 9 General Valve with a backing pressure of 2 psi (0.14 bar).
The supersonic expansion of the gas into the chamber cooled the n-butanal molecules to
approximately 4 K. Upon interaction with the microwave field, a macroscopic
polarization was induced in the sample molecules, and the resulting molecular reemission signal (free induction decay) was detected with a second gain-enhanced
microwave horn antenna (Amplifier Research AT4004).
The molecular signal then was passed through a p-i-n diode limiter (Advanced
Control Components ACLM-4619FC361K) and a solid-state switch (Advanced
Technical Materials PNR S1517D). After power amplification with a gain of 45 dB
43
(Miteq AMF-6F-06001800-15-10P), the molecular signal was downconverted by mixing
with an 18.9 GHz phase-locked dielectric resonator oscillator (PLDRO) and recorded by
a digital sampling oscilloscope (Tektronix TDS6124C) with an operating range from DC
to 12 GHz and a digitization rate of 40 GS/s. Signal averaged in the time domain,
100,000 measurement spectra and 100,000 background spectra were obtained. The
averaged molecular free induction decay (20 μs) was processed with a Kaiser-Bessel
digital filter, background substituted, and Fourier transformed to produce the frequency
domain spectrum of n-butanal (Figure 3.2). This rotational spectrum has a bandwidth of
11 GHz.
3.3 Calculations
As shown in Figure 3.1, n-butanal has two torsional angles, (τ1 and τ2), and a
terminal methyl group that experiences internal rotation. Using the GAUSSIAN03
computational suite17, ab initio calculations were completed to identify the energetically
favored structures of n-butanal as well as the barrier heights to internal rotation of the
methyl rotor. Vibrational geometry optimizations were performed using density
functional theory (DFT) calculations at the B3LYP level of theory with a 6-311++G(d,p)
basis set.
The cis/trans, cis/gauche, gauche/trans, and gauche/gauche geometries were
identified as the four most stable conformations of n-butanal and were verified to be local
minima by the vibrational calculations. The relative zero point corrected energies of these
geometries are 0.00, 1.88, 2.87 and 3.57 kJ/mol, respectively.
44
Figure 3.2: Rotational spectrum of n-butanal. The 12989.34 MHz and 12997.13 MHz
peaks shown in the inset figure correspond to 13C isotopologues from C3 and C1,
respectively, of the cis/trans geometry of n-butanal.
45
These values are approximately within kT at room temperature, which is generally a good
indicator of the structures that will be present in the detected rotational spectrum. A
comparison to the previously published values8-9 is provided in Table 3.1. With one
exception, the results from our calculations are consistently lower than those published in
the past, however the relative energy ordering of the n-butanal structures matches the
work by both Langley et al.8 and Klimkowski et al.9
Table 3.1: Calculated relative energies of n-butanal geometries. (kJ/mol)
cis/trans
cis/gauche
gauche/trans
gauche/gauche
a
B3LYPa
6-311++G(d,p)
0.00
1.88
2.87
3.57
B3LYP 6-31G*b
MM3b
MM4b
Pulay 4-21Gc
0.00
1.23
4.48
-
0.00
1.67
4.23
-
0.00
0.63
5.19
-
0.00
0.08
6.07
9.96
this study
Published by Langley et al. Ref. 8
c
Published by Klimkowski et al. Ref. 9
b
The lowest energy conformer (cis/trans) has a planar heavy- atom structure, while
the remaining three (cis/gauche, gauche/trans, gauche/gauche) have either the aldehyde or
ethyl moieties tilted out of the plane. The calculated rotational constants and projection of
the dipole moment onto the principal axes are listed in Table 3.2. From these results the
cis/trans structure is expected to result in an a-,b-type spectrum while the other three will
result in some combination of an a-,b-, and c-type rotational spectrum.
The presence of the methyl moiety introduces an additional source of angular
momentum because the methyl rotation that can couple to the overall rotation of the
molecule. An asymmetric rotor on a symmetric frame results in a threefold symmetric
46
potential. The symmetry of the potential results in a splitting of the vibrational energy
levels associated with the methyl torsion into a singly degenerate A-level and a doubly
degenerate E-level. The magnitude of this splitting is directly related to the height of the
barrier to internal rotation for the methyl group (V3).18
Table 3.2: Results from DFT calculations at the B3LYP level of theory with a
6-311++G(d,p) basis set.
cis/trans
A (MHz)
B (MHz)
C (MHz)
μa (D)
μb (D)
μc (D)
V3(cm-1)
15271.63
2513.75
2247.41
-1.98
1.94
0.00
700
cis/gauche
8599.88
3489.23
2866.31
0.85
2.47
-0.81
967
gauche/trans
20430.13
2129.83
2089.43
2.85
0.47
1.23
1041
gauche/gauche
10173.27
2912.70
2528.88
2.51
1.68
0.76
986
Relaxed potential energy scans (RPES) were performed at the B3LYP/6311++G(d,p) level of theory in 4° steps to calculate the height of the V3 barrier to internal
rotation. Using this method, methyl rotor torsional barriers of 700 cm-1 (cis/trans), 967
cm-1 (cis/gauche), 1041 cm-1 (gauche/trans), and 986 cm-1 (gauche/gauche) were found. A
plot of the cis/gauche structure’s relaxed potential energy surface of the methyl rotor
torsion is shown in Figure 3.3. Overall, these results suggest that the relatively large
barrier heights will result in energy level splitting that is smaller than the experimental
resolution of 20 kHz. The exception to this is the gauche/trans structure which will be
discussed in detail below.
47
-1
Relative Energy (cm )
1000
800
600
400
200
0
0
50
100
150
200
250
300
350
Methyl Rotor Torsional Angle (degrees)
Figure 3.3: Relaxed potential energy scan about the methyl torsional coordinate of the
cis/gauche geometry of n-butanal calculated with Gaussian03.17 The vibrational geometry
optimization was performed using DFT calculations at the B3LYP level of theory with a
6-311++G(d,p) basis set. The methyl rotational barrier (V3) of the cis/gauche structure
has a value of 967 cm-1.
48
Relaxed potential energy scans were also completed for rotations about the τ1 =
O–C1–C2–C3 and τ2 = C1–C2–C3–C4 dihedral angles. Beginning with an energetically
optimized structure, τ1 and τ2 were rotated independently in 10° steps. An example of this
type of computational result is shown in Figure 3.4. Starting with the gauche/trans
geometry, the τ2 dihedral angle was tuned with the Gaussian03 software suite17 to
identify two local minima, which can be recognized in Figure 3.4 at approximately 120°
and 250°. The molecular structures of these local minima were not observed
experimentally.
These torsional calculations predicted three additional, unique conformers that
were not seen experimentally. The lowest energy conformer of these three was 8.2 kJ/mol
higher in energy than the global minimum structure cis/trans. In addition, no minima
were identified when 2 was restricted to the cis configuration. Instead, 2 relaxed to a
gauche position after the first dihedral step. Vibrational analysis on the cis/cis structure
identified that the two lowest vibrational frequencies were negative in value, confirming
that the cis/cis structure was not a minimum.
3.4 Results and Discussion
The microwave spectrum of n-butanal in the spectral region of 7.5-18.5 GHz is
presented in Figure 3.2.The experimental resolution (20 kHz) of the rotational spectrum
was interpolated to a resolution of 5 kHz using the spectral fitting program JB95.19
Beginning with the calculated rigid rotor rotational constants from the vibrational
geometry optimizations, the assignment of three unique conformers were identified in the
spectrum. The cis/trans and cis/gauche were the first two geometries to be assigned.
49
1800
1600
-1
Relative Energy (cm )
1400
1200
1000
800
600
400
200
0
gauche/trans
gauche/trans
-200
-50
0
50
100
150
200
250
2 Angle (degrees)
300
350
400
Figure 3.4: Relaxed potential scan of the τ2 = C1–C2–C3–C4 dihedral angle of n-butanal.
Calculated with Gaussian0317, the τ2 angle of the energetically optimized gauche/trans
structure was rotated in 4° steps to identify two additional local minima.
50
Both of these molecular conformations have been previously observed in the microwave
work by Lee.11 However, we were able to increase the number of assigned lines from 9 to
16 for the cis/trans geometry and from 19 to 58 for the cis/gauche geometry. Using the
fitting parameters listed in Table 3.3, our rotational constants are in good agreement with
the values published by Lee. Quartic distortion terms were required in the effective
Hamiltonian of the cis/gauche assignments to reduce the root-mean-square error.
Table 3.3: List of parameters used to fit the n-butanal conformers. (JB95a)
a
A (MHz)
B (MHz)
C (MHz)
ΔJ (MHz)
ΔJK (MHz)
ΔK (MHz)
δJ (MHz)
δK (MHz)
ΔI (μÅ2)b
κ
Nc
σ (kHz)d
cis/trans
cis/gauche
gauche/trans
gauche/gauche
15069.347(5)
2555.983(2)
2278.608(1)
5.0(5)x10-4
-4.3(3)x10-3
8508.527(3)
3588.809(1)
2928.5749(9)
3.63(1)x10-3
-1.204(8)x10-2
2.33(1)x10-2
1.101(4)x10-3
5.3(1)x10-3
-27.65
-0.76
58
14.65
20489.74(2)
2145.671(7)
2101.12(6)
7(2)x10-4
-3.58(6)x10-2
9960.365(5)
3021.861(1)
2591.258(1)
6.35(2)x10-3
-5.68(1)x10-2
1.8459(4)x10-1
1.892(4)x10-3
9.9(2)x10-3
-22.95
-0.88
38
12.32
-9.47
-0.96
16
7.91
-9(2)x10-5
-19.67
-0.995
21
32.18
Ref 19
Inertial defect, ΔI = Ic – Ib – Ia
c
Number of transitions in the fit
d
Observed minus calculated root-mean-square deviation of the fit.
b
Using the calculated rotational constants as a starting point, a new, third
conformer of n-butanal was also identified in the spectrum. The results of these fits are
presented in Table 3.3. A total of 38 a-, b-, and c-type lines were fit for this structure.
Quartic distortion terms were used to bring the observed-minus-calculated (omc) error
51
down to 12.32 kHz. The low A constant (9960.365(5) MHz) compared to the minimum
energy cis/trans structure (15069.347(5) MHz) as well as the large inertial defect (I =
-22.95) suggest a twisted conformation with heavy atom out-of-plane structure. Based on
the value of the rotational constants and this secondary information, we have assigned
this structure to the gauche/gauche conformer. Ab initio calculations at the B3LYP/6311++G(d,p) level place this conformer 3.57 kJ/mol above the global minimum cis/trans
conformer. Rotational parameters are given in Table 3.3.
The values of the observed-minus-calculated (omc) root-mean-square deviation of
the
fit,
particularly
for
the
cis/gauche
and
gauche/gauche
structures,
are
uncharacteristically large for our experimental resolution when fitting a structure to a
rigid rotor Hamiltonian. However, n-butanal is not a purely rigid rotor due to the presence
of the methyl group, providing an additional source of angular momentum through the
methyl rotation that couples to the overall rotation of the molecule. The degree of
coupling is inversely proportional to the height of the barrier to internal rotation. Indeed,
several transitions, particularly for the cis/gauche and gauche/gauche conformers at
higher ΔJKaKc, have oddly shaped shoulders that deviate from the expected gaussian peak
shape. It is possible to infer from this that the larger omc values of the rigid rotor
Hamiltonian are indications of the height of the barrier to internal rotation. The
predictions provided by the ab initio calculations of the V3 barriers do not follow this
trend, however. There is no correlation between the predicted barrier heights and the omc
values, especially given the fact that the conformer with the lowest barrier (cis/trans; V3 =
700 cm-1) has the lowest omc (7.91 kHz). Although we have tried to improve the
52
resolution of the experiment by extending the sampling time of the FID to 100 μs, the
signal-to-noise degrades too much to provide a reliable analysis at this time.
Finally, a fourth structure was fit in the rotational spectrum with a signal-to-noise
similar to that of the gauche/gauche structure. Twenty-one a- and c-type lines were fit to
an omc of 32.18 kHz using the ΔJ, ΔJK, or δJ quartic distortion terms. Curiously, most of
these lines appear as doublets, with a-type lines split by approximately 700 kHz. The
assigned, weak c-type lines appear as a Q-branch (ΔKa = 1 ← 0) and have a smaller
(although resolved) splitting, particularly at higher J (up to J = 9).
A torsional analysis was performed using XIAM20 to determine the V3 barrier for
this structure. There were large errors associated with this analysis, likely due to the
relatively small number of lines and the weak c-type Q-branch. However, a best fit
produced a barrier height for V3 = 523 ± 15 cm-1. This value is significantly smaller than
the lowest V3 barrier of 700 cm-1 predicted by ab initio calculations for the cis/trans
geometry.
Our initial analysis suggested that this assignment may be a second new
conformer: gauche/trans. First, the assigned A, B, and C rotational constants are within
1% or less of those predicted by ab inito calculations (see Tables 3.2 and 3.3), which is
generally a good indication of a structural match. Second, ab initio calculations predict a
fourth structure close to kT behind the nozzle, at 2.87 kJ/mol above the global minimum
structure. Third, the absence of b-type lines in the spectrum corresponds to the predicted
ab initio values that μa/μc >> μb. The caveat to this final assertion is that the large value of
the A rotational constant (A = 20489.81(3) MHz) moves any b-type lines with significant
population at the final supersonic expansion temperature (~2.5 K) outside of our spectral
53
range. However, it is difficult to reconcile this circumstantial evidence with the
comparably low barrier of this conformer. There is no clear chemical argument for why
the barrier to internal rotation would be so much lower than the other conformers,
particularly given that the ab initio calculations predict that this conformer has the
highest barrier to internal rotation (V3 = 1041 cm-1). Given these unresolved
complications, we therefore tentatively assign this to the gauche/trans structure.
Although the relative energy of the gauche/trans structure is 0.16 kcal/mol lower
than that of the gauche/gauche geometry, fewer gauche/trans lines were observed in our
data because many of the strong c-type rotational transitions expected of this conformer
lie at frequencies outside of our spectral range. Therefore, only 21 lines were fit for this
geometry. As expected according to Boltzmann statistics, the relative line intensities of
these two higher energy structures, gauche/trans and gauche/gauche, are lower compared
the line strengths of the cis/trans and cis/gauche geometries.
3.5 Kraitchman Analysis
To further facilitate the fitting of the rotational spectrum of n-butanal, the rigid
rotor rotational constants of the isotopologues were also calculated using DFT at the
B3LYP level of theory (6-311++G(d,p)).17 The
13
C isotopologues were observed in
natural abundance for both the cis/trans and cis/gauche conformers of n-butanal. The
fitting parameters used to make these assignments in JB95 are listed in Tables 3.4 and
3.5. We were able to include distortion terms for the fits of both the cis/trans and
cis/gauche 13C isotopologues because a sufficient number of spectral lines were observed.
54
The
18
O isotopologues were also investigated, for but definitive spectral assignments
could not be made.
Bond lengths and angles of the cis/trans and cis/gauche conformers were obtained
by applying Kraitchman equations21 for the observed isotopomers. This method yields the
square of the coordinates of the substituted atom in a specific isotopomer in the inertial
principal axis frame. The sign for each coordinate then was deduced from the predicted
structure while the error was calculated with the Costain formula22, dzi = 0.0012/|zi| Å.
Assuming that the structure does not change with the change of isotope, those coordinates
were then used to derive the bond distances and angles presented in Table 3.6.
Table 3.4 Isotopic assignments for the cis/trans conformer of n-butanal.
HO13C-CH2-CH2-CH3
HOC-13CH2-CH2-CH3
HOC-CH2-13CH2-CH3
HOC-CH2-CH2-13CH3
A (MHz)
14975.253(5)
14810.525(6)
14975.472(6)
15066.836(6)
B (MHz)
2529.391(1)
2556.134(2)
2545.370(2)
2484.466(2)
C (MHz)
2255.2253(9)
2272.677(1)
2268.051(1)
2221.453(1)
ΔJ (MHz)
6.0(3)x10
-4
-4
-4
5.8(4)x10-4
ΔJK (MHz)
-4.0(2)x10-3
-4.3(3)x10-3
-4.3(3)x10-3
-4.2(3)x10-3
J(MHz)
1.13(4)x10-4
1.08(6)x10-4
9.8(6)x10-5
1.06(6)x10-4
ΔI (μÅ2)a
-9.46
-9.46
-9.47
-9.46
κ
-0.96
-0.95
-0.96
-0.96
21
21
18
21
7.72
9.42
8.98
9.41
N
b
σ (kHz)
a
c
6.1(3)x10
Inertial defect, ΔI = Ic – Ib – Ia.
b
Number of transitions in the fit.
c
Observed minus calculated root-mean-square deviation of the fit.
6.1(4)x10
55
Table 3.5 Isotopic assignments for the cis/gauche conformer of n-butanal.
HO13C-CH2-CH2-CH3
HOC-13CH2-CH2-CH3
HOC-CH2-13CH2-CH3
HOC-CH2-CH2-13CH3
A (MHz)
8490.822(6)
8346.259(8)
8450.952(9)
8421.309(6)
B (MHz)
3544.073(4)
3588.440(3)
3551.222(6)
3512.264(2)
C (MHz)
2898.942(4)
2909.439(3)
2906.066(6)
2870.880(2)
ΔJ (MHz)
3.46(9)x10
-3
-3
-3
3.50(9)x10-3
ΔJK (MHz)
-1.13(7)x10-2
-1.07(6)x10-2
-1.18(9)x10-2
-1.22(3)x10-2
ΔK (MHz)
2.3(2)x10-2
2.0(2)x10-2
2.3(2)x10-2
2.3(1)x10-2
δJ (MHz)
1.02(2)x10-3
1.12(2)x10-3
1.08(2)x10-3
1.08(2)x10-3
δK (MHz)
5(2)x10-3
3(1)x10-3
7(2)x10-3
6.7(6)x10-3
ΔI (μÅ2)a
-27.79
-27.68
-28.21
-27.87
κ
-0.77
-0.75
-0.77
-0.77
21
19
19
21
9.31
9.89
11.13
8.67
N
b
σ (kHz)
c
3.4(1)x10
3.4(3)x10
a
Inertial defect, ΔI = Ic – Ib – Ia.
b
Number of transitions in the fit.
c
Observed minus calculated root-mean-square deviation of the fit.
Table 3.6 Comparison of the molecular structure according to ab initio predictions and
Kraitchmana analysis.
cis/trans
Ab initiob
cis/gauche
Ab initiob
Kraitchman
Kraitchman
B3LYPc
MP2c
M05-2Xc
Costaind
B3LYPc
MP2c
M05-2Xc
Costainf
r(C1C2) Å
1.509
1.509
1.503
1.58(1)
1.510
1.511
1.504
1.52(2)
r(C2C3) Å
1.528
1.524
1.521
1.48(1)
1.530
1.527
1.524
1.51(3)
r(C3C4) Å
1.531
1.529
1.526
1.531(5)
1.533
1.530
1.527
1.524(8)
C1C2C3°
115.33
114.26
114.04
112.4(6)
115.69
114.30
114.08
114.4(7)
110(1)
113.52
112.46
112.20
113.2(7)
C2C3C4°
112.66
112.00
111.64
Ref 20.
b
Ref 18.
c
6-311++G(d,p) basis set. d
Errors corrected with Costain’s method (Ref 22).
a
A comparison of the ab initio results between the two conformers yields little
difference between the carbon bond lengths and angles. In fact the B3LYP functional
56
does surprisingly well with the cis/gauche conformer as all of the calculated bond lengths
and errors fall within the experimental Costain error, with the exception of the C1C2C3
bond angle from the DFT (B3LYP:6-311++G(d,p)) calculation which is 0.6° greater than
experimental uncertainty. The C2C3C4 bond angle also deviates slightly from the
Kraitchman result for the MP2 and M05-2X calculations. This general agreement
suggests that dispersion effects do not play a significant role in the cis/gauche conformer.
It is therefore surprising that there is a large discrepancy between the calculated
and experimentally measured distances and angles for the cis/trans geometry. With the
B3LYP functional the C1C2 bond angle is calculated to be 0.07 Å shorter than measured
value, the C2C3 bond angle is calculated to be 0.05 Å longer than measured and the
C1C2C3 bond angle is expanded almost 3° over the measured result, all well outside the
Costain error of the measurement. The best agreement is found for the C3C4 bond length
which is located at the end of the carbon chain away from the oxygen.
These large discrepancies between experiment and theory suggest that dispersion
effects may play an important role in the conformation of the cis/trans conformer.
However, with the absence of any conjugation in the molecule it is difficult to say how
important these effects would be. The methylene hydrogens of C3 are oriented toward
both lone pairs of the aldehyde oxygen. An interaction between these two groups could
explain these differences. Also, the oxygen may be removing electron density from C1
inducing a slight positive charge on C1 and thereby lengthening the C1C2 bond. To
balance the charge distribution, C2 would also have a slight positive charge which would
in turn shorten the C2C3 bond. This type of effect would be less pronounced far from the
57
oxygen, so the C3C4 bond would be less affected. This explains the strong agreement
between the calculated and experimental results for the C3C4 bond.
3.6 Conclusion
The microwave spectrum of n-butanal was measured using a CP-FTMW
spectrometer in the 7.5-18.5 GHz spectral range. In addition to the previously observed
cis/trans and cis/gauche conformers, a new conformer gauche/gauche was assigned.
Tentative assignments were also made on a second new conformer, gauche/trans. Density
functional theory (DFT) calculations using GAUSSIAN03 allowed us to predict the four
most stable geometries (cis/trans, cis/gauche, gauche/trans, and gauche/gauche), which
were verified as local minima in vibrational calculations. The lowest energy conformer,
cis/trans, is planar, with the other three conformers being non-planar in geometry.
The spectral fitting program JB95 reduced the 20 kHz experimental spectral
resolution down to 5 kHz through interpolation. Using our experimental results, we
increased the number of assigned lines in the cis/trans geometry from 9 to 16 and in the
cis/gauche geometry from 19 to 58. In the new, third conformer identified in our spectral
results we fit 38 lines and assigned this to the gauche/gauche geometry, with an omc
similar to that of cis/gauche. A new, fourth structure was also fit in the rotational
spectrum with a relatively high omc value; with 21 lines, we tentatively assigned this
structure as gauche/trans. The GAUSSIAN03 program was used to perform relaxed
potential energy scans to find internal methyl rotor torsional barriers of V3 = 700 cm-1
(cis/trans), 967 cm-1 (cis/gauche), 1041 cm-1 (gauche/trans), and 987 cm-1 (tran/gauche).
We also calculated the relaxed potential energy scans for the dihedral angles τ1 = O–C1–
58
C2–C3 and τ2 = C1–C2–C3–C4, although many of the conformers predicted by these
calculations were not observed experimentally. The internal rotor analysis program
XIAM was used to determine a V3 barrier of V3 = 523 ± 15 cm-1 for the gauche/gauche
structure, which is significantly smaller than the lowest V3 barrier predicted by ab initio
calculations of 700 cm-1. Because of the high signal-to-noise of the CP-FTMW
spectrometer, we resolved the
13
C n-butanal isotopologues in natural abundance.
Kraitchman analysis was performed to determine the molecular angles and bond
distances. Tables 3.7 to 3.19 list the frequency, omc, and rotational quantum numbers of
each assigned line in the n-butanal spectrum.
59
Table 3.7: Rotational transitions of cis/trans n-butanal
J'
Ka'
Kc'
J"
Ka"
Kc"
Observed (MHz)
JB95 omca
4
2
2
2
5
1
2
3
3
4
3
3
3
5
3
1
0
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
4
2
2
1
5
0
1
2
3
3
3
2
1
4
2
1
3
1
1
1
4
1
2
3
2
4
2
2
2
5
2
0
1
1
0
1
1
0
0
0
1
0
0
2
2
0
1
0
3
1
1
0
4
1
2
3
2
4
2
1
0
5
1
0
7452.764
9391.792
9664.596
9946.560
12760.088
12790.736
13072.696
13504.156
14084.857
14095.201
14485.489
14503.825
14522.053
14859.049
14916.945
17347.969
0.003
-0.017
-0.010
0.002
-0.003
-0.011
-0.003
0.011
0.001
0.006
0.002
0.003
-0.002
-0.010
0.012
0.007
a
Observed minus calculated root-mean-square deviation of the fit. (MHz)
60
Table 3.8: Rotational transitions of cis/trans (HO13C-CH2-CH2-CH3) n-butanal
J'
Ka'
Kc'
J"
Ka"
Kc"
Observed (MHz)
JB95 omca
4
2
2
2
5
1
2
3
3
4
3
3
3
5
3
6
7
1
6
8
4
0
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
4
2
2
1
5
0
1
2
3
3
3
2
1
4
2
5
6
1
6
7
4
3
1
1
1
4
1
2
3
2
4
2
2
2
5
2
6
7
0
5
8
3
1
1
0
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
1
3
1
1
0
4
1
2
3
2
4
2
1
0
5
1
6
7
0
5
8
3
7314.760
9295.120
9564.724
9843.320
12567.008
12718.532
12997.128
13423.380
13939.893
14007.217
14335.885
14353.885
14371.777
14761.573
14762.137
15702.141
16846.613
17229.073
17900.273
18213.909
18581.345
-0.002
-0.009
-0.011
-0.008
0.004
-0.011
-0.008
-0.006
0.003
0.006
0.005
0.002
-0.001
-0.003
0.007
0.007
-0.004
0.019
-0.002
0.000
-0.004
a
Observed minus calculated root-mean-square deviation of the fit. (MHz)
61
Table 3.9: Rotational transitions of cis/trans (HOC-13CH2-CH2-CH3) n-butanal
J'
4
2
2
2
1
2
5
3
4
3
3
3
3
5
3
6
7
1
8
6
4
a
Ka'
0
1
0
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
0
1
Kc'
4
2
2
1
0
1
5
2
3
3
3
2
1
4
2
5
6
1
7
6
4
J"
3
1
1
1
1
2
4
3
4
2
2
2
2
5
2
6
7
0
8
5
3
Ka" Kc"
1
3
1
1
0
1
1
0
0
1
0
2
1
4
0
3
0
4
1
2
0
2
2
1
2
0
0
5
1
1
0
6
0
7
0
0
0
8
1
5
1
3
Observed (MHz)
7699.464
9374.156
9652.732
9941.064
12537.844
12826.184
13007.792
13267.752
13873.329
14058.217
14466.949
14486.477
14505.913
14656.889
14908.505
15635.409
16827.861
17083.221
18254.381
18397.097
18738.657
Observed minus calculated root-mean-square deviation of the fit. (MHz)
JB95 omca
-0.009
-0.011
-0.010
-0.009
-0.012
-0.002
0.013
-0.001
0.016
0.007
0.013
0.004
0.008
-0.010
0.002
0.002
-0.008
0.012
0.004
-0.003
-0.016
62
Table 3.10: Rotational transitions of cis/trans (HOC-CH2-13CH2-CH3) n-butanal
J'
Ka'
Kc'
J"
4
2
2
2
1
5
2
3
4
3
3
3
3
5
3
1
6
8
0
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
0
1
4
2
2
1
0
5
1
2
3
3
3
2
1
4
2
1
6
7
3
1
1
1
1
4
2
3
4
2
2
2
2
5
2
0
5
8
a
Ka" Kc"
1
1
0
1
0
1
0
0
0
1
0
2
2
0
1
0
1
0
3
1
1
0
1
4
2
3
4
2
2
1
0
5
1
0
5
8
Observed (MHz)
JB95 omca
7450.756
9349.512
9622.224
9904.148
12707.420
12736.280
12989.340
13420.796
14011.941
14021.417
14421.857
14440.309
14458.641
14776.037
14853.309
17243.549
18103.041
18275.833
-0.007
-0.013
-0.011
-0.009
-0.010
0.015
-0.012
-0.003
0.006
0.005
0.003
0.006
-0.007
0.002
0.008
0.018
-0.007
0.000
Observed minus calculated root-mean-square deviation of the fit. (MHz)
63
Table 3.11: Rotational transitions of cis/trans (HOC-CH2-CH2-13CH3) n-butanal
J'
Ka'
Kc'
J"
2
2
2
5
1
2
3
3
4
3
3
3
3
5
6
7
6
1
8
4
4
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
2
2
1
5
0
1
2
3
3
3
2
1
2
4
5
6
6
1
7
4
4
1
1
1
4
1
2
3
2
4
2
2
2
2
5
6
7
5
0
8
3
3
a
Ka" Kc"
1
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
1
1
0
4
1
2
3
2
4
2
1
0
1
5
6
7
5
0
8
3
3
Observed (MHz)
JB95 omca
9148.880
9407.728
9674.776
11999.716
12843.892
13110.932
13519.107
13720.785
14077.477
14101.397
14117.805
14134.105
14509.577
14797.849
15694.605
16783.997
17238.477
17286.885
18083.629
18289.649
18782.829
-0.012
-0.016
-0.009
0.002
-0.006
-0.008
-0.011
0.002
0.001
0.004
0.005
-0.001
0.006
-0.006
0.016
-0.005
-0.003
0.018
-0.001
-0.013
0.017
Observed minus calculated root-mean-square deviation of the fit. (MHz)
Table 3.12: Rotational transitions of cis/gauche n-butanal
J'
Ka'
Kc'
J"
Ka"
Kc"
Observed (MHz)
JB95 omca
1
2
3
7
5
5
2
4
7
6
5
7
0
0
1
2
2
2
0
1
3
2
1
3
1
2
2
6
3
3
2
3
5
5
4
4
0
1
3
7
4
4
1
4
6
6
5
6
0
1
0
1
3
3
1
0
4
1
1
4
0
0
3
6
1
2
1
4
2
5
5
3
6517.346
7392.623
7496.432
7701.456
7973.284
7998.822
8052.828
9271.115
9357.842
9445.493
9800.089
10089.279
-0.024
-0.013
-0.016
-0.001
-0.002
-0.001
-0.012
-0.008
0.015
-0.003
-0.005
0.007
64
Table 3.12, Continued
J'
5
5
1
5
5
6
6
1
2
9
4
2
3
5
4
6
4
4
6
2
3
6
7
3
2
2
6
3
8
6
6
6
8
7
2
2
8
2
8
9
Ka'
1
2
1
1
1
2
2
1
1
4
2
0
0
2
1
2
1
2
1
1
2
1
2
2
2
2
1
0
2
2
2
1
3
1
2
2
1
1
3
2
Kc'
5
4
1
5
4
5
5
0
2
5
3
2
3
3
3
4
3
2
5
1
2
6
5
1
1
0
5
3
6
4
4
6
6
7
1
0
8
2
5
7
J"
4
5
0
4
5
5
5
0
1
8
4
1
2
5
3
6
3
4
6
1
3
5
7
3
2
2
6
2
8
5
5
5
7
6
2
2
7
1
7
9
Ka" Kc"
2
2
1
4
0
0
2
3
0
5
3
2
3
3
0
0
1
1
5
4
1
3
0
1
1
1
1
4
2
1
1
5
2
2
1
3
1
6
1
0
1
2
2
3
1
6
1
2
1
1
1
1
0
6
1
2
1
7
3
2
3
3
2
4
4
3
2
4
1
2
1
2
2
5
0
1
4
4
1
8
Observed (MHz)
10649.531
11101.445
11437.100
11546.306
11713.630
11959.352
12060.455
12097.307
12374.527
12531.389
12577.388
12972.577
13004.796
13100.590
13136.450
13184.573
13443.201
13474.161
13562.584
13694.885
13809.892
13817.233
13875.423
14116.692
14759.093
14821.169
14839.181
14985.377
15285.432
15698.418
15799.531
15816.375
15911.893
15946.792
16739.670
16801.743
17003.489
17294.289
17462.501
17488.245
JB95 omca
-0.007
-0.011
-0.003
-0.002
-0.002
0.019
0.009
-0.001
0.005
0.000
-0.011
0.004
-0.001
-0.018
0.014
-0.022
-0.034
-0.008
0.044
0.007
-0.003
-0.005
-0.014
-0.001
0.002
-0.001
-0.008
0.020
0.037
-0.014
-0.014
-0.014
0.002
-0.005
0.018
0.013
0.018
0.033
-0.025
0.010
65
Table 3.12, Continued
J'
7
3
4
3
3
7
a
Ka'
2
2
0
2
1
1
Kc'
6
2
4
1
3
6
J"
6
3
3
3
2
7
Ka" Kc"
3
3
1
3
1
2
1
3
1
2
0
7
Observed (MHz)
17554.364
17767.180
17982.021
18073.983
18524.512
18564.887
JB95 omca
0.005
-0.010
0.014
-0.005
0.001
-0.017
Observed minus calculated root-mean-square deviation of the fit. (MHz)
Table 3.13: Rotational transitions of cis/gauche (HO13C-CH2-CH2-CH3)
n-butanal
J'
Ka' Kc' J" Ka" Kc"
Observed (MHz)
JB95 omca
3
2
4
1
5
1
2
3
2
4
5
2
4
3
3
6
3
2
2
2
3
a
1
0
1
1
1
1
1
0
0
1
2
1
2
2
2
1
0
2
2
1
2
2
2
3
1
4
0
2
3
2
3
3
1
2
2
1
5
3
0
1
2
2
3
1
4
0
5
0
1
2
1
3
5
1
4
3
3
6
2
2
2
1
3
0
1
0
0
0
0
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
3
1
4
0
5
0
1
1
1
2
4
0
3
2
2
6
2
1
2
1
3
7457.908
7880.085
9182.020
11389.752
11555.004
12034.862
12240.886
12799.614
12826.860
13020.842
13166.300
13531.060
13559.470
13911.575
14203.617
14597.339
14734.896
14899.235
16775.438
17187.663
17778.530
Observed minus calculated root-mean-square deviation of the fit. (MHz)
-0.011
-0.012
0.002
-0.013
0.003
-0.005
-0.003
-0.014
0.000
-0.001
-0.005
0.017
0.014
0.004
-0.013
-0.001
0.012
0.001
0.009
0.011
-0.012
66
Table 3.14: Rotational transitions of cis/gauche (HOC-13CH2-CH2-CH3)
n-butanal
J'
Ka'
Kc'
J"
3
2
4
1
5
2
5
6
2
4
3
2
4
2
6
3
2
2
3
1
0
1
1
1
1
2
2
0
2
2
1
1
2
1
0
2
1
2
2
2
3
1
4
2
3
4
2
2
1
1
3
0
5
3
1
2
2
3
1
4
0
5
1
5
6
1
4
3
1
3
2
6
2
2
1
3
a
Ka" Kc"
0
1
0
0
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
3
1
4
0
5
1
4
5
1
3
2
0
2
1
6
2
2
1
3
Observed (MHz)
JB95 omca
7423.300
8170.196
9271.491
11255.692
11814.101
12316.735
12691.442
12869.878
12928.045
13010.692
13633.442
13674.649
13900.023
14340.992
15052.893
15080.727
16310.301
17074.584
17369.188
-0.013
-0.021
-0.007
-0.005
0.010
-0.005
-0.005
0.004
-0.003
-0.003
0.002
0.003
-0.006
-0.018
-0.003
0.018
0.006
0.014
0.008
Observed minus calculated root-mean-square deviation of the fit. (MHz)
67
Table 3.15: Rotational transitions of cis/gauche (HOC-CH2-13CH2-CH3)
n-butanal
J'
Ka'
Kc'
J"
3
2
4
1
5
2
2
5
4
2
3
3
6
2
2
3
2
2
3
1
0
1
1
1
1
0
2
2
1
2
2
1
2
2
0
2
1
2
2
2
3
1
4
2
2
3
2
1
2
1
5
1
0
3
1
2
2
3
1
4
0
5
1
1
5
4
1
3
3
6
2
2
2
2
1
3
a
Ka" Kc"
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
3
1
4
0
5
1
1
4
3
0
2
2
6
1
1
2
2
1
3
Observed (MHz)
JB95 omca
7413.134
7955.112
9140.601
11357.016
11518.223
12269.413
12854.872
13042.936
13426.748
13559.612
13770.877
14065.505
14564.560
14699.133
14758.717
14822.165
16634.441
17169.188
17637.897
-0.026
-0.013
-0.013
-0.007
0.018
-0.007
-0.002
-0.001
0.003
0.008
-0.010
-0.003
-0.006
-0.002
-0.008
-0.001
0.003
0.019
0.017
Observed minus calculated root-mean-square deviation of the fit. (MHz)
68
Table 3.16: Rotational transitions of cis/gauche (HOC-CH2-CH2-13CH3)
n-butanal
J'
Ka'
Kc'
J"
3
2
4
1
5
1
2
4
4
5
6
2
4
3
3
2
2
2
2
3
3
1
0
1
1
1
1
1
2
1
2
2
1
2
2
0
2
2
2
1
2
1
2
2
3
1
4
0
2
3
3
3
4
1
2
2
3
1
0
1
2
2
3
3
1
4
0
5
0
1
4
3
5
6
1
4
3
2
2
2
2
1
3
2
a
Ka" Kc"
0
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
3
1
4
0
5
0
1
3
2
4
5
0
3
2
2
1
1
2
1
3
2
Observed (MHz)
JB95 omca
7406.004
7798.280
9120.688
11292.192
11480.692
11933.536
12124.904
12604.328
12881.944
13066.324
13110.424
13407.548
13455.408
13803.961
14590.433
14727.081
14785.901
16651.093
17033.977
17648.433
18152.009
-0.014
-0.016
-0.006
-0.001
0.002
-0.006
0.002
0.008
-0.002
0.002
0.003
0.002
-0.013
-0.018
0.003
-0.006
-0.002
0.013
0.011
0.011
0.004
Observed minus calculated root-mean-square deviation of the fit. (MHz)
69
Table 3.17: A-state rotational transitions of gauche/trans n-butanal
J'
2
2
2
1
3
3
3
4
4
4
4
4
4
9
7
6
5
4
3
2
1
a
Ka'
1
0
1
1
1
0
1
1
0
2
2
3
1
1
1
1
1
1
1
1
1
Kc'
2
2
1
0
3
3
2
4
4
3
2
2
3
9
7
6
5
4
3
2
1
J"
1
1
1
2
2
2
2
3
3
3
3
3
3
9
7
6
5
4
3
2
1
Ka" Kc"
1
1
0
1
1
0
0
2
1
2
0
2
1
1
1
3
0
3
2
2
2
1
3
1
1
2
0
9
0
7
0
6
0
5
0
4
0
3
0
2
0
1
Observed (MHz)
8449.104
8493.472
8538.256
9895.180
12673.628
12740.028
12807.380
16898.009
16986.221
16988.061
16988.881
16989.761
17076.249
17387.145
17752.437
17904.469
18035.541
18145.289
18233.437
18299.813
18344.185
Observed minus calculated root-mean-square deviation of the fit. (MHz)
JB95 omca
-0.065
-0.020
-0.007
-0.018
-0.027
0.036
0.074
-0.014
0.023
-0.031
-0.021
0.011
0.005
-0.018
0.037
0.026
0.010
-0.021
-0.048
-0.010
0.040
70
Table 3.18: E-state rotational transitions of gauche/trans n-butanal
J'
Ka'
Kc'
J"
2
2
3
3
3
4
4
4
4
4
7
6
4
3
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
1
3
3
2
4
4
3
2
3
7
6
4
3
1
1
1
2
2
2
3
3
3
3
3
7
6
4
3
1
a
Ka" Kc"
1
1
1
0
1
1
0
2
2
1
0
0
0
0
0
1
0
2
2
1
3
3
2
1
2
7
6
4
3
1
Observed
JB95 omca
8448.978
8538.399
12673.550
12739.876
12807.221
16897.829
16986.041
16988.149
16988.794
17076.157
17752.553
17904.597
18145.393
18233.558
18344.276
-0.113
0.142
0.024
-0.005
-0.053
0.001
0.025
0.076
-0.091
-0.001
-0.018
0.044
-0.002
-0.025
0.000
Observed minus calculated root-mean-square deviation of the fit.
71
Table 3.19: Rotational transitions of gauche/gauche n-butanal
J'
Ka'
Kc'
J"
1
1
4
2
3
3
6
5
4
5
3
2
5
2
2
1
6
1
4
7
7
6
3
4
6
3
3
3
6
3
8
2
8
7
9
5
5
6
1
1
3
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
2
2
2
1
1
1
2
2
2
0
2
2
1
0
1
1
2
3
5
4
3
4
3
2
4
2
1
1
5
0
4
6
6
5
3
4
5
3
2
1
5
2
7
2
6
5
7
5
4
4
1
1
5
2
3
2
6
4
4
4
2
1
5
1
1
0
6
0
3
7
7
5
2
3
5
2
2
2
6
2
8
1
8
7
9
4
5
6
a
Ka" Kc"
0
0
2
0
0
1
1
2
0
2
1
1
0
0
1
0
0
0
1
0
1
2
1
1
2
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
4
2
3
1
6
2
4
3
2
1
5
1
0
0
6
0
2
7
6
3
2
3
4
2
1
0
5
1
8
1
7
6
8
3
4
5
Observed (MHz)
JB95 omca
6938.443
7368.996
7809.028
7819.147
8530.095
8942.129
8989.571
9411.513
9542.392
9699.965
10233.687
10795.756
10904.148
11206.622
11656.767
12551.562
12662.852
12982.114
13729.076
14854.138
15754.540
15806.914
16181.533
16311.376
16471.665
16761.321
16840.027
16917.399
17117.318
17472.239
17490.360
17734.226
17906.426
18031.107
18120.950
18143.617
18321.704
18420.181
-0.017
-0.012
0.001
-0.007
-0.004
-0.014
0.004
0.000
0.002
0.000
-0.009
-0.005
0.006
0.002
0.001
0.008
-0.006
0.012
-0.006
-0.007
0.005
0.007
0.024
0.008
0.000
0.024
-0.010
-0.015
0.009
-0.003
0.001
0.005
0.025
-0.038
0.007
-0.010
0.013
-0.021
Observed minus calculated root-mean-square deviation of the fit.
72
3.7 References
(1)
Harper, M. R.; Van Geem, K. M.; Pyl, S. P.; Merchant, S. S.; Marin, G. B.;
Green, W. H. Combustion and Flame 2011, 158, 2075.
(2)
Duerre, P. Biotechnology Journal 2007, 2, 1525.
(3)
Hurley, M. D.; Wallington, T. J.; Lauirsen, L.; Javadi, M. S.; Nielsen, O. J.;
Yamanaka, T.; Kawasaki, M. Journal of Physical Chemistry A 2009, 113, 7011.
(4)
Dossi, N.; Susmel, S.; Toniolo, R.; Pizzariello, A.; Bontempelli, G. Journal of
Chromatography A 2008, 1207, 169.
(5)
Pal, R.; Kim, K.-H.; Hong, Y.-J.; Jeon, E.-C. Journal of Hazardous Materials
2008, 153, 1122.
(6)
Lehn, J. M.; Riehl, J. J. Journal De Chimie Physique 1965, 62, 573.
(7)
Sbrana, G.; Schettin.V Journal of Molecular Spectroscopy 1970, 33, 100.
(8)
Langley, C. H.; Lii, J. H.; Allinger, N. L. Journal of Computational Chemistry
2001, 22, 1396.
(9)
Klimkowski, V. J.; Vannuffel, P.; Vandenenden, L.; Vanalsenoy, C.; Geise, H. J.;
Scarsdale, J. N.; Schafer, L. Journal of Computational Chemistry 1984, 5, 122.
(10)
Dwivedi, Y.; Rai, S. B. Vib. Spectrosc. 2009, 49, 278.
(11)
Lee, P. L.-S. 7208731, Michigan State University, 1971.
(12)
Brown, G. G.; Dian, B. C.; Douglass, K. O.; Geyer, S. M.; Shipman, S. T.; Pate,
B. H. Review of Scientific Instruments 2008, 79.
(13)
Shirar, A. J.; Wilcox, D. S.; Hotopp, K. M.; Storck, G. L.; Kleiner, I.; Dian, B. C.
Journal of Physical Chemistry A 2010, 114, 12187.
(14)
Balle, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. Journal of Chemical
Physics 1979, 71, 2723.
(15)
Balle, T. J.; Campbell, E. J.; Keenan, M. R.; Flygare, W. H. Journal of Chemical
Physics 1980, 72, 922.
(16)
Balle, T. J.; Flygare, W. H. Review of Scientific Instruments 1981, 52, 33.
73
(17)
Frisch, M. J. Frisch, M. J.; et al., Gaussian 03, Revision C.02. Gaussian, Inc.,
Wallingford, CT, 2004.
(18)
Gordy, W.; Cook, R. L. Microwave Molecular Spectra; 3rd ed.; John Wiley &
Sons Inc., 1984.
(19)
Plusquellic, D. F.; Suenram, R. D.; Mate, B.; Jensen, J. O.; Samuels, A. C.
Journal of Chemical Physics 2001, 115, 3057.
(20)
Hartwig, H.; Dreizler, H. Zeitschrift Fur Naturforschung Section a-a Journal of
Physical Sciences 1996, 51, 923.
(21)
Kraitchman, J. American Journal of Physics 1953, 21, 17.
(22)
Vaneijck, B. P. Journal of Molecular Spectroscopy 1982, 91, 348.
74
CHAPTER 4. TWO-DIMENSIONAL CHIRPED-PULSE FOURIER TRANSFORM
MICROWAVE SPECTROSCOPY
4.1 Introduction
The traditional utility of microwave spectroscopy has been its ability to precisely
determine the structure and shape of gas phase molecules, as well as associated molecular
parameters including centrifugal distortion, quadrupole coupling, and barriers to
inversion or internal rotation that perturb rotational energy levels.1 High sensitivity and
high resolution are signatures of Fourier transform microwave (FTMW) spectrometers
employing molecular beam techniques. Efficient cooling through the molecular beam
free expansion eliminates the contribution of large amplitude vibrations to the overall
rotation. Although rigidity and symmetry often limit the number of observed rotational
transitions, the “pure” rotational spectra of small to medium sized molecules (3 to 10
heavy atoms) can nevertheless be dense and difficult to interpret. Measuring and
structurally assigning the rotational spectra of larger molecules, such as those of
astronomical or biological relevance, pose significantly greater challenges. Here we
report the development and application of a two-dimensional (2D) broadband microwave
strategy which facilitates the collection and structural assignment of the rotational spectra
of flexible polyatomic molecules.
Some flexible, and relatively small, biomimetic molecules including N-acetylalanine N’-methylamide,2 N-methylacetamide,3 ethylacetamidoacetate,4 and N-acetyl
75
alanine methyl ester5 have recently been investigated with rotational spectroscopy. The
results have been used to understand conformational preferences of protein backbone
folding and experimentally test the accuracy of quantum chemical calculations. Such
studies are complicated by multiple equilibrium conformations, lack of symmetry,
tunneling-splitting of methyl rotations, and 14N quadrupole coupling. While it is possible
to eliminate quadrupole angular momenta by isotopic substitution,2 a high spectral
density originating from multiple stable asymmetric configurations is expected. The
presence of one or more internal rotors further congests the rotational spectrum,
particularly when low-barrier top-top interaction becomes non-negligible (the
implications of which are an active field of research6).
2D double resonance techniques simplify multi-component spectra by associating
transitions sharing a common energy level. Using a chirped-pulse Fourier transform
microwave (CP-FTMW) spectrometer, we devise global coherence transfer strategies by
exploiting the broad bandwidth, fast electronics, and arbitrary waveform generation
(AWG) of the CP-FTMW technology. Pulse sequences are designed to transfer energy
level structure information to multiple coherence channels in a single 2D experiment. The
transitions of different rotational components are efficiently isolated, thereby assisting in
the assignment of complex spectra.
Developed originally for NMR spectroscopy7, 2D spectroscopy has been adapted
for microwave,8-10 infrared,11 and electronic radiation,12,13 finding rich applications in the
study of modern chemical problems in all but rotational spectroscopy. Aside from
revealing the energy level structure of a molecule, 2D techniques decouple the temporal
and frequency resolution into separate dimensions, thus permitting time-resolved tracking
76
of coherent states in an evolving system.14 Protein structure and kinetics have been
studied with 2D NMR15 and 2D IR16 spectroscopy. Energy transport pathways of the
Fenna-Mathews-Olson light harvesting complex have also been illuminated with 2D
electronic spectroscopy.17
In the microwave region the majority of work developing 2D spectroscopy
culminated in the late 1980s due largely to technological limitations. For example,
multiple frequency synthesizers were required to correlate rotational transitions outside
the bandwidth of transform-limited pulses, placing a practical restriction on the number
of energy levels involved in coherence transfer. Transform-limited pulses and the low
resolution in the indirectly measured frequency dimension (ω1) restricted the information
obtained in a 2D plot to a narrow region around a signal frequency. Global rotational
level structural changes caused by a dynamically evolving molecule, for example, would
not be observable in a single narrowband experiment. Despite these limitations, a
significant body of work was accomplished detailing coherence transfer of three- and
four-level systems.
Aue et al.7 first suggested applying 2D NMR techniques at microwave
frequencies. The basic principles of microwave 2D correlation were subsequently
realized8,9 followed by the first demonstration of a 2D microwave spectrum.10 A
considerable connection with 2D NMR methods was established by Bauder and
coworkers who adapted many of the acronymic NMR techniques for microwave radiation:
COSY (autocorrelation),18 hetero-COSY (single-quantum correlation),19 INADEQUATE
(double-quantum correlation),19 n-quantum filtering (n=zero or double),19 and novel pulse
sequences20 were shown to correlate both progressive (ladder-type) and regressive (v- or
77
w-type) connected rotational energy levels of three-18,19 and four-20 level systems and to
access dipole-forbidden multiple quantum coherences. NOESY21 was used to investigate
collision-induced population transfer and relaxation of a four-level system. The phasecycling procedure of Stahl and Dreizler22 was extended to select rotational coherence
transfer pathways and eliminate unwanted signals for diverse pulse sequences. Jäger et
al.23 applied RF radiation in one-dimension, obtaining low energy l-type doublet
information with microwave detection.
Extending the Bloch vector model of two-level spin systems, the earlier
theoretical descriptions of 2D microwave spectroscopy used linear combinations of
density matrix elements to form “pseudo-spin” Bloch vector components.21,23 The
solutions of these equations described coherence pathways as a function of the applied
radiation and were later extended to include relaxation24 and phase cycling.19,22 The
qualitative picture of the Bloch vector model is helpful in understanding the coherence
transfer mechanism in analogy with NMR, but the physical interpretation is not always
clear. Consequently, Vogelsanger and Bauder’s formalism19 explained 2D FTMW
spectroscopy entirely by the evolution of the density matrix, successfully handling
relaxation and phase cycling of progressive and regressive three-level systems.
The 2D CP-FTMW spectroscopy is first illustrated using spectra arising from
approximately isolated three- and four-level systems with a density matrix formalism.
Broadband detection affords 10 GHz of signal frequency bandwidth in a single
acquisition. The distinction between “pump” and “signal” coherences, strictly speaking,
is no longer required, although the terminology will be used for clarity in description.
AWG eliminates the need for multiple frequency synthesizers without sacrificing
78
multiple coherence excitations and also increases the bandwidth in the indirectly
measured dimension. Accordingly, the single-quantum and autocorrelation pulse
sequences are then extended to incorporate broadband excitation and detection in both
frequency dimensions. Finally, phase cycling and quadrature detection in ω1 with chirped
excitation pulses is discussed.
4.2 Experimental Methods
A detailed description of the CP-FTMW spectrometer has been previously
described in Chapter 2 therefore only an overview will be given here.25 The microwave
polarizing pulses were produced by an arbitrary waveform generator (Tektronix AWG
7101) in the DC to 5 GHz range at a sampling rate of 10 GS/s. Pulses were filtered with a
5 GHz low pass filter (Lorch 10LP-5000-S) and amplified with a pre-amplifier (Minicircuits ZX60-6013E-S+6000MHz, +10dB gain). The signal was then mixed with a 13.0
GHz phase-locked dielectric resonator oscillator (PLDRO) which was held in a phase
locked loop with a 100 MHz quartz oscillator plate assembly (Wenzel Associates 50110137B) driven by a 10 MHz rubidium frequency standard (Stanford Research Systems
FS725). The upper and lower sidebands were then passed through a 13 GHz cavity notch
filter (Lorch 6BR6-13s000/100-S) and a manual step attenuator (Weinschel AF117A-6911) before amplification via a 200 Watt traveling wave tube amplifier (Amplifier
Research 200T8G18A). The microwave signal was then broadcast into the molecular
interaction chamber by a gain enhanced microwave horn antenna (Amplifier Research
AT4004). The sample molecules were introduced into the chamber, which was evacuated
to 1 x 10-6 Torr, through a 2 mm orifice pulsed valve (General Valve Series 9) with a
79
backing pressure of 2 psi. The sample molecules were mixed with a Helium/Neon
(30/70%) buffer gas and cooled in the supersonic expansion to approximately 5 K. The
molecular free induction decay (FID) was detected with a receiving horn antenna. The
signal was then transmitted through a PIN diode limiter (Advanced Control Components
ACLS 4619F-C36-1K) and a reflective single pole single throw switch (Advanced
Technical Materials S1517D). After mixing down with an 18.9 GHz PLDRO
(Microwave Dynamics PLO-2000-18.90), a 4 μsec free induction decay was digitized at a
rate of 40 GS/s by a 12 GHz oscilloscope (Tektronix TDS6124C).
A typical 2D CP-FTMW spectroscopy experiment utilized two polarizing
microwave pulses separated by a variable time delay designated t1. Pulses would excite
single or multiple rotational transitions; in the latter case, the AWG was used to
simultaneously generate multiple pulses. This was achieved by co-adding two or more
chirp-pulse envelopes with different frequency sweeps over the same duration of time.
The t1 delay between the pulses was automatically incremented in 2048 or 4096 steps
with a dwell time of 1 ns or 500 ps, respectively, using National Instrument’s LabVIEW
software. At each measurement step, the FID was signal averaged and recorded. The time
domain data of all t1 steps were processed offline with a digital Kaiser-Bessel filter and
Fourier transformed, yielding spectra with 125 kHz resolution in the 2 domain.
Modulations in the magnitude intensity of the irradiated rotational transitions with respect
to t1 were then filtered with a Kaiser-Bessel function and Fourier transformed once more,
revealing coherence peaks in the 1 magnitude spectrum with approximately 400 kHz
resolution. All experiments were processed by this method unless stated otherwise. The
80
resolution of the 1 and 2 transition frequencies reflect the sampling time in each
dimension (and not the highest resolution achievable with the CP-FTMW spectrometer).
Coherence transfer pathways in 2D experiments are dependent on the pulse angles
of the excitation radiation. In the Bloch vector model, a π/2 pulse maximizes the coherent
superposition between two dipole-allowed states, whereas a π pulse induces a population
inversion. Experimentally, pulse excitation angles are a function of the integrated electric
field strength and the rotational transition moment. The π/2 pulse for a specific rotational
transition was determined by varying the pulse length and/or the manual step attenuator
to maximize the signal intensity in the ground state rotational spectrum. It was found that
at full power (i.e. zero attenuation), pulses with durations from 100 to 125 ns and
bandwidths from 5 to 25 MHz satisfactorily approximated the π/2 pulse for molecules
with dipole moments on the order of a few Debye. The π/2 pulse was then fine-tuned
with the manual step attenuator. Doubling the π/2 pulse length at a fixed attenuation then
provided an approximate π pulse. Further adjustment of the pulse duration to minimize
the spectral intensity gave the most precise π pulse for a given transition.
In practice, the pulse angle parameters were often not optimal. This particularly
included cases where the transition moments differed between dipole-allowed transitions,
or when chirped-pulses were co-added to excite multiple transitions simultaneously,
therefore diluting the total power over multiple frequency ranges. However, because the
π/2 and π pulses were well-separated within the parameter space, it was not necessary to
correct for these small deviations from optimal conditions. Approximate pulse angles
affect the intensities in the ω1 dimension, but as will be demonstrated, these
measurements are fairly robust and coherence information is resolved under the
81
experimental conditions. Finally, it should be noted that after mixing the excitation pulse
generated by the AWG with the 13.0 GHz PDRO, only one of the sidebands was resonant
with a molecular transition in the systems investigated in this study. For more dense
spectra, it would be advisable to upconvert the signal with a voltage multiplier rather than
mixing with a PDRO if the sidebands unintentionally excite unwanted coherences. The
details of each pulse are given in the text and figures when necessary. A full description
of each pulse sequence is available in appendix (4.5) of this chapter.
4.3 Results and Discussion
4.3.1 General Description and Modeling
We first consider the single-quantum correlation (SQC) of a progressive threelevel system to explain the origin of signals in a 2D experiment (Figure 4.1). Two π/2
pulses separated by a delay (t1) are used to decode the molecular coherences induced by
the light fields along two frequency axes: ω1 and ω2. The first polarizing microwave
pulse prepares the Ea←Eb superposition, σab, out of thermal equilibrium. Population
cycles between the coupled states at the angular Rabi frequency for the duration of the
pulse. Though not directly excited, changes in the number density of level Eb necessarily
create a population difference, Nbc, between the Eb and Ec levels. Indirect population
cycling does not contribute to the final signal in one-photon experiments, but in multiple
dimensions it will be demonstrated that indirect population cycling of Nbc can give rise to
coherence signal in ω2.
82
Figure 4.1: Schematic of the single-quantum correlation pulses sequence of a three-level
progressive system. The initial π/2 pulse prepares the σab coherence out of thermal
equilibrium. Following a variable time delay, t1, a second non-selective pulse irradiates
both the Ea←Eb and Eb←Ec transitions, mixing the σab and σbc coherences. A free
induction decay is then measured with respect to t2 and Fourier transformed into the ω2
spectrum. Stepping the t1 time delay changes the magnitude of the freely precessing σab
coherence, thereby modulating the intensities of the σab and σbc coherences in the ω2
spectrum. Fourier transform with respect to t1 reveals coherences peaks sharing a
common energy level that are coupled by the mixing pulse.
83
When the light field is turned off, the σab superposition evolves coherently with a
frequency of ωab and intensity proportional to the pulse angle and the population
difference at thermal equilibrium ( N 0ab ).
Following the t1 free precession period, a second π/2 pulse simultaneously
irradiates both Ea←Eb and Eb←Ec transitions, and the free induction decay (FID) is
measured in t2. The σab and σbc t2 coherence intensities are not only a function of the
population differences induced by the first pulse, but are also parametrically coupled to
the magnitude of the σab coherence at the end of t1. Stepping the time delay between the
pulses changes the instantaneous magnitude of the σab coherence which oscillates with a
frequency of ωab. Diagonal and off-diagonal peaks in a ω1 by ω2 2D plot originate from
this mechanism. The σab coherence intensity in ω2 parametrically oscillates at a frequency
of ωab with respect to t1, appearing as a diagonal peak in a 2D plot. No energy level
connectivity is obtained as this is a result of irradiating the same transition multiple times.
The σbc coherence intensity in ω2 also oscillates at a frequency ωab with respect to t1 since
the two coherences are coupled (mixed) by the second pulse. This oscillation appears as
an off-diagonal cross peak in the 2D plot and directly reflects the connectivity between
energy levels. The SQC sequence, which has been demonstrated experimentally,19 is
relatively simple in terms of the coherence transfer pathway, but the general concepts are
applicable to more complex pulse sequences.
The quantitative multi-photon response of a statistical ensemble of molecules can
be described by the time evolution of the density matrix
i t   H (t ),  (t ) 
where the Hamiltonian is given by
(1)
84
 
H t   H 0    E t 
(2)
The eigenvalues of the diagonal field-free rotational Hamiltonian, H0, are coupled by the
off-diagonal projection of the electric field onto the transition moment of the molecule.
Constructing the Hamiltonian matrix for a progressive (ladder-type) or regressive (v- or
w-type) energy level structure is a straightforward application of one-photon selection
rules. The most general Hamiltonian describes a combination of progressive and
regressive energy level configurations.
Following the derivation of Vogelsanger and Bauder19, Equation 1 was
transformed into a rotating frame. When irradiated by a classical sinusoidal field, the
density matrix elements in this interaction picture oscillate as a function of the difference
between the resonant and excitation frequencies. In the rotating wave approximation
(RWA), counter-rotating terms are dropped, leaving the near resonant, slowly oscillating
functions that are principally responsible for describing coherence information of the
system. The complex, time-independent amplitudes of the coherence terms include
contributions from the phase of the excitation radiation. As a result, phase cycling
schemes can be designed to effectively select coherence transfer pathways and eliminate
unwanted signals. In our lab, the solutions to these equations were solved numerically
according to
 
X (t )  P diag e t P 1 X t 0  ,
(3)
where P and λ are the eigenvectors and eigenvalues, respectively, of the coefficient
matrix of the coupled linear differential equations, and X is the tetradic column vector
representation of the density matrix.
85
With the CP-FTMW spectrometer, coherences in the rotating frame are more
complex owing to the time-dependent phase,  t  , of the chirp waveform:
Defining  t  
 f1  f 0 
2t total
x t   sin 2  f 0 t   t  .
(4a)
 
f  f   
xt   sin2  f 0  1 0 t t 
2ttotal  
 
(4b)
t2,
where f 0 and f 1 are the initial and final frequencies of the chirp and ttotal is the pulse
length. The dynamics of the Bloch vector subject to the linear frequency sweep of
Equation 4 are best analyzed in the interaction picture. Figure 4.2 shows the real portion
of the coherence response as the field sweeps through resonance. When the light field is
far from resonance, rapid oscillations integrate to zero and can be neglected in
accordance with the RWA. As the incident frequency approaches the transition (center)
frequency, the Bloch vector adiabatically follows the field through resonance as reflected
by the slow variation in coherence amplitude. The interaction between the density matrix
and Hamiltonian is then approximately sinusoidal near resonance leading to a
simplification in modeling coherence transfer: the incident field is treated sinusoidally
and the time-dependence is solved with Equation 3.
Intensity (Arb Units)
86
1
0
-1
-5
-4
-3
-2
-1
0
1
2
Relative Frequency (MHz)
3
4
5
Figure 4.1: Real portion of the coherence oscillation in the interaction picture subject to
an arbitrary linear frequency sweep covering 10 MHz. The resonant frequency was set to
zero. As the field passes through the center frequency, the coherence terms oscillate
slowly, corresponding to an adiabatic following of the Bloch vector with the field.
87
Given that the T(2) dephasing time is much longer than the duration of a typical
pulse, irradiating transitions over different periods of the frequency sweep does not affect
the frequency information of coherence transfer. Intensities of low J transitions, for this
reason, are only approximately modeled with thermally equilibrated population
differences (given optimal experimental conditions). Non-equilibrium conditions induced
at the start of the frequency sweep produce small changes in coherence intensity. At
higher J transitions, intensities deviate more profoundly as we have neglected to include
the M-degeneracy contribution to intensity into the model, although the general trends are
predicted.
In multi-photon sequences, non-zero initial conditions of the density matrix
coherence elements after subsequent pulses give rise to off-diagonal peaks in a 2D plot.
The final density matrix is tailored using multiple pulses associated with different Rabi
angles. The angular Rabi frequency,    g  1 , is a function of the transition moment,
μg, (g = a, b, c in the principal axis frame) and integrated electric field envelope, , and
represents the tipping angle of the Bloch vector off of the ground state axis in the pseudospin analogy. The power under the time integrated chirped field envelope decreases as a
function of one over the square root of the bandwidth, increasing the tipping angle range
and efficiency with respect to transform-limited excitation. These concepts will be
demonstrated experimentally in the following sections with three- and four-level systems.
4.3.2 Regressive Narrowband 2D Autocorrelation
The microwave spectra of molecules containing atoms with non-vanishing
quadrupole moments exhibit hyperfine splitting from coupling of the nuclear field
88
gradient with the rotational angular momentum.26 Selection rules for hyperfine multiplets
permit transitions from a single lower (upper) state to multiple upper (lower) levels.
These regressively connected systems have been previously studied with a 2D
autocorrelation technique that probes connections between close-lying transitions (<50
MHz).18,19 No separate pump pulse was needed since the excitation and detection
channels would coincide. These experiments generated the necessary bandwidth through
fast microwave switches, yielding transform-limited pulses on the order of 50 MHz (10
ns pulse duration). Using chirped π/2 pulses covering the bandwidth of the hyperfine
transitions, a 2D autocorrelation plot of a four-level regressive system was constructed.
The 2D autocorrelation spectrum of the ΔJKaKc=111←000 transition of 1-chloro-1fluoroethylene (CFE) is presented in Figure 4.3. Selection rules for the total angular
momentum quantum number, F, allow ΔF = 0, ±1, corresponding to three transitions
from the JKaKc=000 (F=1.5) to the JKaKc=111 level (F=0.5, 2.5, and 1.5). The main spectral
features of the 2D plot are diagonal and off-diagonal peaks indicating connected
transitions. Off-diagonal intensities are generally enhanced by the adiabatic excitation of
the linear frequency sweep relative to the diagonal such that the two are on the same
order. However, the apparent connections between the ΔF = 0.5←1.5 and 1.5←1.5
transitions are missing in the spectrum despite the transitions originating from the
common JKaKc=000 (F=1.5) level. The cross peak intensity is predicted to be very weak by
empirically derived density matrix selection rules which indicate that the strongest
coherence transfer is between adjacent energy levels in an approximately closed
regressive scheme.
89
a) Time Domain Excitation b) Energy Level Scheme
100 ns
probe
pump
t1
(Scan)
F=1.5
F=2.5
F=0.5
t2
111
100 ns
000
F=1.5
Frequency (MHz) 
c)
14120
14125
14130
Frequency (MHz) 
14135
Figure 4.2: Autocorrelation 2D spectrum of the ΔJKaKc=111←000 transition of 1-chloro-1fluoroethylene (CFE). (a) Autocorrelation non-selectively excites all transitions under the
bandwidth of two identical pulses separated by a stepped delay (t1). (b) The hyperfine
structure of CFE splits the JKaKc=111 levels that form regressive connections with the
JKaKc=000. Selection rules (ΔF = 0, ±1) permit the transitions ΔF = 0.5←1.5 (14120.2(1)
MHz), ΔF = 2.5←1.5 (14127.9(1) MHz), and ΔF = 1.5←1.5 (14137.7(1) MHz). (c) 2D
autocorrelation plot constructed by Fourier transforming the t2 time data to the ω2
frequency domain and Fourier transforming intensity modulations with respect to t1 to the
ω1 frequency domain. Cross peaks indicate that transitions share a common energy level.
The coupling between non-adjacent regressive energy levels is weak, resulting in the
apparent absence of off-diagonal “corner” peaks in the 2D plot.
90
2D autocorrelation is one of the few pulse sequences designed to correlate several
microwave transitions belonging to the same energy level structure by directly
transferring multiple coherences in one experiment (Jäger et al.23 used double-quantum
correlation to transfer l-type coherence doublets, but as in autocorrelation the doublet
transitions were within the bandwidth of transform-limited pulses). Most pulse sequences
transferred single coherences and required phase cycling in consecutive experiments to
isolate the transition of interest. The reason was twofold: First, n-1 excitation sources
were needed to convert population differences of n-level systems into observable
coherences if transitions were separated by more than 50 MHz. Second, a long dwell time
between successive measurements, Δt1, limited the bandwidth in ω1 required to resolve
multiple peaks. The technology of the CP-FTMW spectrometer validates an extension of
the autocorrelation technique approach of transferring multiple coherences in one
experiment. The AWG in our lab resolves Δt1 as low as 100 ps, increasing the maximum
available ω1 bandwidth by a factor of 100. It is therefore possible to spectrally resolve
numerous lines in the ω1 domain, and any frequency within 8-18 GHz is accessible with
the programmable pulse sequences of the AWG. Preceding methods18,19 reserved the term
autocorrelation for probing connections of transitions lying within the bandwidth of the
transform-limited
excitation
pulse.
However,
we
adopt
the
term
broadband
autocorrelation (BAC) for its all-inclusive, non-selective pulse sequence specification
that fosters coherence transfer between every adjacent transition in the irradiated system.
91
4.3.3 Progressive Three-Level Autocorrelation
In order to satisfy the Nyquist theorem in the 8 to 18 GHz region of the
microwave spectrum, a minimum of 36 GS/s must be recorded to fully sample all signals.
For low kilohertz resolution, this corresponds to about 800,000 data points per FID (20 μs
sampling time). Expanding these requirements into a second dimension would result in
nearly a terabyte of data and take approximately two months to complete one ultrabroadband 2D spectrum. Fortunately, this conventional approach to multi-dimensional
spectroscopy can be avoided. 2D NMR researchers have used intentional undersampling
in the analysis of large biomolecules, reducing data acquisition time by up to 50%.27 This
same technique was used in our lab to reduce the t1 data acquisition time by nearly a
factor of 1000 to approximately 3.5 to 7 hours, depending on the sampling rate.
By adopting this practice, the aliased frequencies in the undersampled ω1
dimension were assigned based on the frequency shifts predicted with the known t1
sampling rate. It was observed that when sampling t1 at 1 or 2 GS/s, the molecular
frequencies aliased in units of megahertz. Therefore it was only necessary to properly
sample up to 1 GHz to identify the megahertz portion of the total transition frequency.
Ambiguity was of course introduced if two transition frequencies shared identical
megahertz frequencies, but this aliasing degeneracy could be predicted from the ω2
ground state transition frequencies and excluded, if necessary, in the final analysis. The
sampling of the t2 FID satisfied the Nyquist condition after mix-down, so there was no
ambiguity in the ω2 spectrum. As a consequence of undersampling, the natural frequency
spacing of transitions in ω2 became distorted in ω1, as did the geometric connections in a
2D array. Rather than constructing 2D plots, 1D slices (i.e. the individual peak
92
oscillations in the ω2 spectrum) of the 2D plot were instead analyzed. The diagonal and
off-diagonal peaks in the 2D representation are therefore redefined as parent and
coherence transfer peaks, respectively, in the 1D channels.
Aliasing in the 1D representation is recognized in SQC (Figure 4.4) experiments
performed on the ΔJ=2←1 and ΔJ=3←2 transitions of the prolate top 3,3,3trifluoropropyne (TFP). The K-stack transitions are unresolved at our experimental
resolution, so the progressive connections were treated as an isolated three-level system.
The results of two separate SQC experiments differing in the transferred coherence
comprise Figure 4.4. The molecular resonances exhibit aliasing from undersampling t1:
by preparing the ΔJ=3←2 (17267.7(1) MHz) transition, one coherence transfer peak
appears exclusively at 267.6(4) MHz in the ΔJ=2←1 ω1 spectrum. Similarly, preparing
the ΔJ=2←1 (11511.8(1) MHz) results in a coherence transfer peak at 511.7(4) MHz in
the ΔJ=3←2 ω1 spectrum.
Broadband signal acquisition in ω2 coupled with the increased ω1 bandwidth
allowed for the coherence transfer information of two SQC experiments to be obtained
with one BAC pulse sequence. Non-selective π/2 irradiation before and after t1 evolution
simultaneously mixed coherences between the ΔJ=2←1 and ΔJ=3←2 transitions of TFP.
Both signal frequencies were detected in ω2; the ΔJ=2←1 1D channel is shown in Figure
4.5. Parent and coherence transfer peaks were identified with knowledge of the ω2
frequencies and t1 sampling rate. The benefit of BAC is that in one experiment, every
irradiated 1D channel contains energy level connectivity information of the interrogated
system.
a)
200
3←2
Coherence
267 MHz
300
Arbitrary Intensity
Arbitrary Intensity
93
400
400
2←1
Coherence
511 MHz
500
FT
FT
c)
2←1
11511.815 MHz
10000
600
Aliased Frequency (MHz)
Aliased Frequency (MHz)
Intensity (Arb Units)
b)
nc
re
e
h
Co
12000
e
s
an
r
T
r
fe
14000
3←2
17267.697 MHz
16000
18000
Absolute Frequency (MHz)
Figure 4.3: Single-quantum correlation of 3,3,3-trifluoropropyne (TFP) in two separate
experiments: (a) ω1 spectrum of the ΔJ=2←1 (11511.8(1) MHz) transition containing the
coherence peak of the ΔJ=3←2 (17267.7(1) MHz in ω2, aliased frequency at 267.6(4)
MHz in ω1) transition. The ΔJ=3←2 was initially prepared and transferred to the
ΔJ=2←1 transition following t1 evolution with a non-selective mixing pulse. (b) ω1
spectrum of the ΔJ=3←2 (17267.7(1) MHz) transition containing the coherence peak of
the ΔJ=2←1 (11511.8(1) MHz in ω2, aliased frequency at 511.7(4) MHz in ω1) transition.
The preparation pulse excites the ΔJ=2←1 in this similar experiment and the mixing
pulse transfers the prepared coherence to the ΔJ=3←2 transition. (c) Ground state ω2
spectrum of TFP. Intensity oscillations of peaks are Fourier transformed with respect to t1
to yield their respective ω1 spectrum, or 1D slice of a 2D plot. With single-quantum
correlation, two separate experiments are required to transfer coherences to produce the
1D slices of (a) and (b).
94
However, in addition to coherence signals, extra peaks appear in BAC spectra as a
result of simultaneously preparing all transitions. Coherence amplitudes in the evolution
of Equation 1 vary parametrically as a function of t1, multiplying the t2 FID at each step.
The t2 FID therefore acts similar to a local oscillator, mixing with the t1 oscillations to
create sum and difference sidebands of the ΔJ=2←1 and ΔJ=3←2 coherence frequencies,
or “classical mixing” peaks in ω1. Alternatively, spectroscopically forbidden transitions
accessible in 2D FTMW spectroscopy (double-quantum coherence, zero-quantum beats,
etc) are referred to as “quantum mixing” peaks, since the quantum mechanical
phenomenon is described by the density matrix. Mixing of either classification are linear
combinations of the coherence frequencies in the ω1 spectra, and are not distinguishable
unless quantum mixing peaks are directly accessed by pulse sequences such as doublequantum correlation.19
In general, mixing of the coherence fundamental frequencies accounted for the all
of the mixing peaks. Due to the strong intensity of the ΔJ=2←1 parent peak in Figure 4.5,
higher order mixing off of the ΔJ=2←1 second harmonic (23.4 MHz aliased; the peaks
around the ΔJ=3←2 coherence transfer peak are spaced by approximately 23 MHz) was
also observed. Of course, it was possible to eliminate mixing peaks with phase cycling in
multiple successive experiments to simplify the 1D slices, but all peaks were clearly
resolved in ω1 due to the broad bandwidth. Mixing peaks, which were clearly identified,
did not obscure the coherence information and therefore phase cycling was not a
necessity.
95
A
Intensity (Arb Units)
Experimental
Predicted
B
B
0
B
100
A
BB B
200
300
B
400
Aliased Frequency (MHz)
500
Figure 4.4: Experimental ω1 broadband autocorrelation spectrum of the ΔJ=2←1
transition of 3,3,3-trifluoropropyne (black trace). Simultaneous irradiation of the
ΔJ=2←1 (11511.8(1) MHz) and ΔJ=3←2 (17267.7(1) MHz) before and after t1 transfers
coherences to all ω1 channels. Peaks labeled A correspond to direct coherence
information: ΔJ=2←1 parent and ΔJ=3←2 coherence transfer peaks with aliased
frequencies 488.3(4) MHz and 267.6(4) MHz, respectively. Label B refers to mixing
peaks that result from the simultaneous irradiation of multiple transitions. Mixing peaks
are identified by the sums and differences of coherence fundamental and harmonic
frequencies. All peaks, particularly those with direct coherence information, are resolved
with the broad bandwidth in ω1. Simulated data (red trace) reproduce the frequency
response of the pulse sequence. Peak widths were chosen to match the experimental
conditions. Intensities are only approximate and were derived from Boltzmann
population differences at thermal equilibrium.
96
4.3.4 Broadband Pulse Sequences
Complex energy level structures are ubiquitous characteristics of all but the
simplest molecules. The asymmetric rotor 1,3-difluoroacetone (DFA), for instance,
exhibits both regressive and progressive rotational transitions. With the CP-FTMW
spectrometer, there is no practical restriction on the number of energy levels probed in
coherence transfer. Accordingly, pulse sequences were designed to examine the largescale response of coherence propagation through DFA’s mixed progressive-regressive
system with a series of π/2 chirped pulses (Figure 4.6). The b-type ΔJKaKc=212←101
transition was prepared and mixed with the a-type ΔJKaKc=202←101 transition following t1
in a regressive analogue to SQC. Successive irradiation of the ΔJKaKc=303←202 and
ΔJKaKc=404←303 transitions propagated the prepared ΔJKaKc=212←101 coherence up the
ΔJKaKc=404←303←202 K-stack. All irradiated transitions were recorded in ω2. Global
connectivity was confirmed by the observation of a coherence transfer peak at 376.6(4)
MHz in the 1D channels of each irradiated transition. This peak originated from the
aliased frequency of the prepared ΔJKaKc=212←101 transition (11376.5(1) MHz, Figure
4.6c). The relatively simple interpretation of the 1D slices may be useful in tracking the
response of the rotational energy level structure to external perturbations.
Coherence propagation utilized the bandwidth of only ω2. By exploiting the
bandwidth in both dimensions, an extension of BAC was used to transfer multiple
coherences of DFA to single 1D channels (Figure 4.7). The first π/2 pulse of the extended
BAC sequence following t1 mixed all prepared coherences with adjacent regressive or
progressive energy levels, or nearest neighbors.
97
Intensity (Arb Units)
a)
212←101
8000
b)
π
2
10000
t1
404←303
303←202
202←101
*
12000 14000 16000
Frequency (MHz)
*
212←101
(11,377 MHz)
c)
π
2
π
2
202←101
(8,391 MHz)
π
2
303←202
(12,380 MHz)
404←303
(16,168 MHz)
π
2
time
18000
350
377
400
Aliased Frequency (MHz)
450
Figure 4.5: Coherence propagation of 1,3-difluoroacetone (DFA). (a) Map of the
coherence propagation path shown in the ω2 representation. The ΔJKaKc=212←101 (marked
with an asterisk*) was initially prepared with the pulse sequence of (b). Following t1 the
coherence was transferred to ΔJKaKc=202←101 and then propagated up the ΔJKaKc
=404←303←202 K-stack with selective π/2 pulses. (c) The respective 1D slices of all
signal frequencies collected in ω2 contain the initial coherence information of the
ΔJKaKc=212←101 transition with a coherence transfer peak at 376.6(4) MHz (aliased
frequency). Global connectivity is revealed with broadband detection in ω2.
98
The additional mixing pulse transferred coherences to the next nearest neighbor such that
multiple coherences were transferred to each irradiated transition’s ω1 spectrum. For
example, the 1D slice of the ΔJKaKc=212←101 transition is shown in Figure 4.7c.
Coherence peaks corresponding to the adjacent transitions ΔJKaKc=313←212 and
ΔJKaKc=202←101 were observed as well as the non-adjacent (or next nearest neighbor)
ΔJKaKc=414←313 and ΔJKaKc=303←202 transitions. In the absence of any open system
interference, the pulse sequence on this system resulted in a geometric expansion of
coherence transfer. The extended BAC pulse sequence transfers a large amount of
information in a single experiment. For the purposes of spectral assignment, this pulse
sequence is the most efficient. It should be noted that the transition moments of DFA
differ by nearly a factor of 3 (μa=2.55 D and μb=0.93 D from DFT calculations
(B3LYP/6-311++G(d,p))), though the same time-integrated power was delivered to aand b-type transitions. BAC results have shown that the coherence transfer is a robust
process with chirped excitation which is advantageous when associating unknown lines
with differing transition moments.
With the introduction of more complex energy level configurations and pulses
sequences, open system effects were observed. In the extended BAC of the DFA system,
the ΔJKaKc=404←303 rotational transition was not irradiated, but intensity oscillations
corresponding to the ΔJKaKc=303←202 and ΔJKaKc=202←101 coherences were observed in
the ω2 spectrum (Figure 4.7d). No direct radiation moved population between the
JKaKc=303 and JKaKc=404 levels, but indirect population cycling with the irradiated
ΔJKaKc=303←202 transition was suspected to induce occupation differences between the
JKaKc=303 and JKaKc=404 levels through changes in the number density of JKaKc=303.
99
a)
414
C
D
G
303
313
B
b)
404
E
202
212
A
101
F
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
π
2
t1
A
B
C
D
E
F
c)
Intensity (Arb Units)
Time A
B
Intensity (Arb Units)
300
d)
C
E F
350
400
450
500
Aliased Frequency (MHz)
G
E
*
F
200
300
400
Aliased Frequency (MHz)
500
Figure 4.6: Extended broadband autocorrelation. a) The energy level structure of 1,3difluoroacetone (DFA) investigated with the extended broadband autocorrelation pulse
sequence (panel b). Both progressive and regressive connected transitions were directly
irradiated (red arrows). c) The 1D slice of the ΔJKaKc=212←101 transition (labeled “A”,
12380.4(1) MHz). Coherences from adjacent transitions or nearest neighbors (“B”,
11658.5(1) MHz and “F”, 8390.8(1) MHz) transferred by the first pulse after t1 and nextnearest adjacent transitions (labeled “C” 15459.3(1) MHz and “E”, 11376.5(1) MHz)
transferred by the second pulse after t1 are present in the ω1 spectrum. d) The
ΔJKaKc=404←303 was not directly pumped (black arrow of panel a), however coherences
were transferred through indirect population cycling through the JKaKc=303 energy level.
Both coherence (labeled G, E, and F) and a mixing peak (*) were identified in the 1D
slice of ΔJKaKc=404←303.
100
With the exact solutions of a three-level progressive system derived by Vogelsanger and
Bauder,19 a qualitative description of this process is proposed. For the system of Figure
4.1, consider the extended BAC irradiating only the Ea←Eb transition with each
subsequent pulse. Tracing the relevant coherence pathway with the analytical solutions
after each of the three pulses, P1, P2, and P3 (suppressing coefficients and complex
conjugate terms),
0
Nbc P1  Nab
 Nbc0
 ab P1  iNab0
 t1
Nbc P2;t1   Nbc P1;t1   i ab P1;t1 

bc P3;t1   iNbc P2;t1  .
The σab coherence and non-equilibrium population difference are prepared by P1. After
t1, the relevant terms parametrically vary with t1 and are dependent on the conditions
induced by the previous pulses. By P3, the σbc is turned on by population cycling of Nbc,
the magnitude of which varies as ωab in accordance with the σab coherence frequency in
the t1 evolution. This demonstrates that coherent processes can be observed without direct
interrogation.
Further deviations from closed model predictions were detected in the DFA
system studied with the extended BAC. Coherence transfer was generally prevented
though the ΔJKaKc=414←303 channel. For this reason, the ΔJKaKc=414←303 and
ΔJKaKc=414←313
coherences
were
not
observed
in
the
indirectly
populated
101
ΔJKaKc=404←303 1D channel. According to the predicted Boltzmann distribution and in
concert with the ω2 signal intensity, this was attributed to the relatively small equilibrium
population difference. Indirect coherence transfer to the dipole allowed ΔJKaKc=303←212
or ΔJKaKc=313←202 transitions was also not observed. Unlike coherence transfer to the
ΔJKaKc=404←303 through indirect population cycling, which only interacted with the
irradiated system through JKaKc=303, every energy level of the ΔJKaKc=303←212 or
ΔJKaKc=313←202 transitions was irradiated with the light field. This behavior therefore
cannot be adequately reduced to a three-level, closed system description.
4.3.5 Phase Cycling
Less emphasis has been placed thus far on phase cycling the ω1 spectra. For the
following application, it is advantageous to demonstrate aspects of phase cycling with 2D
CP-FTMW spectroscopy. The phase of the chirped pulse is not constant in time, but
analysis of coherence in the interaction picture (Figure 4.2) reveals that the relative phase
of the chirped frequency sweep is transferred to molecular precession. The slowly
oscillating coherence near resonance is inverted by application of a π-shifted chirped
pulse, and the imaginary part of the coherence oscillation becomes real with a π/2-shifted
chirped pulse. Experimentally these phase shifts were achieved by interchanging the sine
function of the chirped pulse (Equation 4) with cosine, -sine, or -cosine.
As a proof of principle, two-step phase cycling19 was demonstrated with the SQC
and BAC pulses sequences with TFP. The ΔJ=3←2 1D channel is analyzed in Figure 4.8.
Mixing peaks at 465 MHz and 220 MHz resulting from the SQC (Figure 4.8a) and BAC
(Figure 4.8b) pulse sequences, respectively, were both eliminated with two-step phase
102
cycling, leaving only coherence information in the 1D slices. The phase-cycled spectra
were produced by inverting the sign of pump pulse in consecutive experiments and
subtracting the t1 oscillations. Other published phase-cycling schemes were not evaluated
in this lab. Based upon the two-step phase cycling results and negligible differences in
the coherence transfer mechanisms between chirped and sinusoidal excitation, other
proposed phase-cycling schemes are expected to be applicable to 2D CP-FTMW
spectroscopy.
4.3.6 Quadrature Detection in ω1
In the data processing of the ω1 preceding spectra, the real t2 FIDs were Fourier
transformed to yield a complex t1 signal. Phase information was subsequently neglected
by taking the magnitude in ω2. However, t1 quadrature can reveal information on the
relative coherence pathway. For example, the SQC pulse sequence of Figure 4.1 will
once again be considered. The pulse following t1 directly mixes the initially prepared
coherence, σab, and its counterrotating complex conjugate, σab*, with σbc and σbc* yielding
four separate coherence channels contributing to the final signal. Channels maintaining
their relative signs during t1 and t2 (i.e. σab → σbc and σab* → σbc*) are analogous to Ptype signals in NMR28 and are superimposed in the ω1 spectrum.19 Those coherence
pathways changing sign (σab → σbc* and σab* → σbc or N-type signals28) pick up a phase
that is symmetric about ω1=0 through Fourier transformation of a complex t1 signal. For
many pulse sequences, peaks originating from coherence pathways differing in relative
signs must be isolated with phase cycling.19
Intensity (Arb Units)
103
a)
Without Phase Cycling
With Phase Cycling
*
Intensity (Arb Units)
100
200
300
400
500
Aliased Frequency (MHz)
b)
100
*
200
300
400
Aliased Frequency (MHz)
500
Figure 4.7: Phase cycling with chirped pulses. a) The ΔJ=3←2 channel resulting from
broadband autocorrelation with the ΔJ=2←1 transition. The black trace is the raw 1D
slice in the absence of phase-cycling. With two-step phase cycling (red trace), the mixing
peak labeled with an asterisk (*) was eliminated, leaving only direct coherence
information at 267.6(4) and 488.3(4) MHz. b) Similarly, in the ΔJ=3←2 channel of the
single-quantum correlation pulse sequence, the second harmonic mixing peak (*) was
eliminated in the two-step phase-cycled red trace.
104
Higher order quantum filtering sequences such as the double-quantum filtered (DQF)
technique achieve similar results by reducing the number of coherence channel pathways
and avoiding the branching out effect.
Quadrature detection with the DQF pulse sequence was evaluated on the ΔJ=2←1
and ΔJ=3←2 transitions of TFP (Figure 4.9). Although Fourier transform of the real t2
signal produced the real and imaginary channels of the t1 oscillations, the time-dependent
phase of the chirped waveforms and the variable time delay between pulses resulted in
lineshapes that were not purely absorptive or dispersive. Therefore, it was necessary to
correct the phase of the real and imaginary ω2 spectra to produce orthogonal t1 channels
(see Appendix). After phase cycling the complex t1 signal to suppress peaks near ω1=0,
two peaks appeared in the ΔJ=2←1 1D slice (Figure 4.9). The dominant peak in the
positive quadrant at 267.6(4) MHz corresponds to the P-type coherence signal transferred
from the ΔJ=3←2 transition. The less intense peak in the negative quadrant (-267.6(4)
MHz) was assigned as a quadrature image. If this were not the case, P- and N-type peaks
would be mirror images with equal intensities. Quadrature detection of the P-type
coherence signal gives information on the relative coherence pathway: the sign did not
change between t1 and t2 periods as the coherence evolved through double-quantum
coherence rather than through occupation differences.
The magnitude of the quadrature image is highly dependent on the center
frequency of the ω2 peak. The resolution of 125 kHz in ω2 translates to two points
defining the peak width. Recording more t2 data points would increase the resolution, but
also the time requirements of the experiment. Moreover, quadrature detection by this
method is sensitive to the coherence pathways and thus to the specific pulse sequence.
105
a)
π
2
π
t1
∆J=3←2
π
Intensity (Arb Units)
b)
Quad
Image
(-267.6 MHz)
-400
-200
∆J=2←1
P-type
Coherence
(+267.6 MHz)
0
200
Aliased Frequency (MHz)
400
Figure 4.8: a) Double-quantum filtered pulse sequence. A π/2 pulse prepares ΔJ=3←2
(17267.7(1) MHz) transition of TFP. Following t1, π pulses subsequently irradiate the
ΔJ=3←2 and ΔJ=2←1 transitions, first converting the prepared coherence into a doublequantum coherence and then back into observable signal. By converting to doublequantum coherence rather than occupation differences, the branching out of coherence
pathways is reduced. Therefore, P- and N-type signals corresponding to the sign of the
relative pathway are revealed after Fourier transformation of the complex t1 signal. b) The
dominant P-type coherence (+267.6(4) MHz aliased) and a less intense quadrature image
(-267.6(4) MHz) were observed in the 1D slice of the ΔJ=2←1 transition. Aside from
Rabi angle imperfections that contribute to the quadrature image, the magnitude is also
highly dependent on the center frequency of the ΔJ=2←1 transition in ω2.
106
While P- and N-type pathways are distinguishable in one experiment with the DQF pulse
sequence, phase cycling in four consecutive experiments is required to isolate P- or Ntype coherence signals with the SQC and autocorrelation pulse sequences.19 Therefore, an
alternative and completely general procedure for obtaining relative phase information
was implemented based on the States method of hypercomplex quadrature detection.
Two channels are required to construct a complex signal: a real channel
modulated as cos(ωt) and an imaginary channel modulated as sin(ωt). The hypercomplex
method pioneered by States et al. achieves t1 quadrature by shifting the relative phase of
one of the pulses bracketing t1 by 90o in two consecutive experiments.29 For every data
point in t1, two t2 FIDs 90o out of phase were collected. The t1 x t2 data matrices were
Fourier transformed separately with respect to t2. The magnitude of the sine modulated ω2
spectra were then added or subtracted to the magnitude of the cosine modulated ω2
spectra to produce a P- or N-type complex signal, respectively.30 Fourier transformation
with respect to t1 yields peaks in ω1 with minimal quadrature images. Hypercomplex
quadrature requires a maximum of two experiments, independent of pulse sequencedependent coherence pathways.
The 2D autocorrelation spectrum of the ΔJKaKc=111←000 transition of CFE was
repeated with a hypercomplex pulse sequence, and the 1D slice of the ΔF=2.5←1.5
hyperfine transition is reported in Figure 4.10. The orthogonal chirped functions were
generated by interchanging the sine function of Equation 4 with the cosine function while
keeping the arguments constant. The ΔF=2.5←1.5 hyperfine transition displays the Ntype transition of the parent and coherence transfer peaks.
107
Intensity (Arb Units)
Coherences
Even
Harmonics
Even
Harmonics
Quad
Image
-400
-200
0
200
Odd
Harmonics
400
Aliased Frequency (MHz)
Figure 4.9: Hypercomplex autocorrelation of the ΔJKaKc=111←000 of CFE showing the 1D
slice of the transition ΔF=2.5←1.5 hyperfine transition. The preparation pulse was
shifted by 90o in two consecutive experiments to yield cosine and sine modulated t1
channels. The complex signal was constructed by subtracting the imaginary oscillations
from the real prior to Fourier transformation, producing an N-type coherence peak in ω1.
The dominant peaks in the negative quadrant (-120.4(4), -128.2(4), and -137.7(4) MHz)
carry the coherence information of the system. Mixing peaks that are even harmonics of
the coherence fundamental do not carry the sign information and are present in both
quadrants. The sign of the third harmonic mixing peak is preserved, though opposite to
the fundamental. The real and imaginary channels were recorded separately in
consecutive experiments, introducing phase noise from small drifts in the spectrometer
over several hours. Therefore, quadrature images of the parent and coherence transfer
peaks are present, though the magnitude is small (roughly 10%).
108
Mixing peaks of even order appear as quadrature images in the 1D slice, while those of
odd order are opposite in sign to the coherence peaks and much lower in intensity. With
the hypercomplex autocorrelation, the distinction between coherence and mixing peaks is
made possible without phase cycling. The quadrature images, while still present, have
also been significantly reduced to about 10% of N-type coherence signal.
4.4 Conclusion
Technological advances of the CP-FTMW spectrometer have permitted an
extension of 2D correlation techniques of rotational transitions. Pulse sequences were
developed to transfer and measure multiple coherence channels in single experiments.
These results utilized arbitrary waveform generation which significantly increased the
bandwidth in the ω1 and ω2 dimensions. We have narrowed much of our focus onto the
SQC and autocorrelation pulse sequences, initially studying the results on three- and
four-level systems to establish the method. An alternative representation of the data, 1D
slices of a 2D plot, was prompted by practical limitations that prevented ultra-broadband
2D arrays. Aliasing of multiple coherences in BAC are best analyzed in 1D channels
since spectral aliasing and mixing peaks distort the geometric interpretation of a 2D plot.
These small systems were then extended to incorporate broadband excitation and
detection with the coherence propagation and extended BAC pulse sequences. Both
sequences demonstrated global connectivity in single 2D experiments. Unlike coherence
propagation, the extended BAC pulse sequence does not require a priori knowledge of
the rotational energy level structure. Thus, it can be used to aid in the assignment of
complex rotational spectra.
109
The theoretical investigation of 2D CP-FTMW has revealed only subtle
differences in the mechanism of coherence transfer with respect to sinusoidal excitation.
By examining the relative phase of the chirped frequency sweep, phase cycling was
shown to correspond with previous methods utilizing transform-limited radiation. It was
found that quadrature detection with the DQF pulse sequence required phase correction
of the absorptive and dispersive components of the ω2 spectra, but the coherence pathway
of the pulse sequence was unchanged by chirped irradiation. Quadrature detection was
generalized for 2D CP-FTMW spectroscopy by application of the hypercomplex States
method. Along with the relative phase information, a clear distinction between coherence
and mixing peaks is possible with this technique in a maximum of two consecutive
experiments. While efficient assignment of complex rotational spectra has been a main
focus of this paper, we anticipate the relevance of 2D CP-FTMW spectroscopy is farreaching. Novel applications of the spectrometer, for example in studying discharge
chemistry, quantum computing, or the rotational dependence of intramolecular
vibrational redistribution, may benefit from 2D techniques described in this study.
4.5 Appendix: Phase Angle Correction
Phase angle correction for linearly chirped systems has recently been
demonstrated by Xian et al. for Fourier transform ion cyclotron resonance mass
spectrometry.31 Their analysis revealed that the phase angle varies not only as a function
of the frequency sweep but also the time delay from the end of the pulse to the final
detection. In terms of 2D spectroscopy, this implies a different mixed absorptivedispersive phase for each complex t1 data point, the Fourier transform of which is pure
110
noise. Phase correction was necessary for orthogonal real and imaginary channels in t1.
Since only 1D channels were of interested in this study, a 3 MHz window was chosen
around the signal transitions in ω2 such that the misphased spectra acquired with chirped
radiation were approximately linear with respect to frequency-dependent phase
corrections.
A number of phase correction techniques exist in the literature for transformlimited excitation radiation.32 The objective of these procedures is to optimize the
frequency-dependent phase angle,
i
n
i  PH0  PH1 ,
(A1)
at the ith data point of an n-point spectrum. PH0 is a zero-order correction and PH1 is the
first-order correction accounting for frequency-dependent phase shifts. Linear
combinations of the real ( Ri0 ) and imaginary ( I i0 ) parts of the misphased spectra, when
correctly phased, yield purely absorption (Ai) and dispersive (Di) spectra:33
Ai  R i0 cos  i   I i0 sin  i 
(A2)
D i  R i0 sin  i   I i0 cos  i  .
(A3)
Phase corrections PH0 and PH1 were obtained by minimizing the negative intensities in
the ω2 absorptive spectra (Eq A2). The conjugate gradient method was employed to find
the values of PH0 and PH1 that minimized the following “penalty” function:33
PPH 0, PH1   F  Ai Ai2
i
(A4)
111
with
0, Ai  0
F ( Ai )  
1, Ai  0
The optimization time of small frequency windows around a signal transition was
essentially instantaneous. The complex t1 oscillation was subsequently constructed by
addition (P-type) or subtraction (N-type) of the absorptive and dispersive components.
4.6 Pulse Details
The following tables give in detail the pulse specification and irradiated
transitions. The molecules 1-chloro-1-fluoroethylene, 3,3,3-trifluoropropyne, 1,3difluoroacetone are abbreviated CFE, TFP, and DFA, respectively. Spectral resolution
corresponds to the conditions of the 2D experiment (125 kHz in ω2), not the maximum
achievable with the chirped-pulse Fourier transform microwave spectrometer.34
Table 4.1: 2D Autocorrelation of CFE
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Bandwidth (MHz)
25
25
Duration (ns)
100
100
Transitions (MHz)
ΔJKaKc=111←000
ΔJKaKc=111←000
Hyperfine Multiplets
ΔF = 0.5←1.5 (14120.2)
ΔF = 0.5←1.5 (14120.2)
ΔF = 2.5←1.5 (14127.9)
ΔF = 2.5←1.5 (14127.9)
ΔF = 1.5←1.5 (14137.7)
ΔF = 1.5←1.5 (14137.7)
112
Table 4.2 (a): Single-Quantum Correlation of TFP (ΔJ=2←1)
(b): Single-Quantum Correlation of TFP (ΔJ=3←2)
(a)
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Bandwidth (MHz)
10
10
Duration (ns)
125
125
Transitions (MHz)
ΔJ=2←1 (11511.8)
ΔJ=2←1 (11511.8)
ΔJ=3←2 (17267.7)
(b)
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Bandwidth (MHz)
10
10
Duration (ns)
125
125
Irradiated (MHz)
ΔJ=3←2 (17267.7)
ΔJ=2←1 (11511.8)
ΔJ=3←2 (17267.7)
Table 4.3: Broadband Autocorrelation of TFP
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Bandwidth (MHz)
10
10
Duration (ns)
125
125
Transitions (MHz)
ΔJ=2←1 (11511.8)
ΔJ=2←1 (11511.8)
ΔJ=3←2 (17267.7)
ΔJ=3←2 (17267.7)
113
Table 4.4: Coherence Propagation of DFA
Pulse 1 (π/2)
Bandwidth
(MHz)
Duration (ns)
Transitions
(MHz)
t1
Pulse 2 (π/2)
Pulse 3 (π/2)
Pulse 4 (π/2)
5
5
5
5
100
ΔJKaKc=212←101
(11376.5)
100
ΔJKaKc=202←101
(8390.8)
ΔJKaKc=212←101
(11376.5)
100
ΔJKaKc=303←202
(12380.4)
100
ΔJKaKc=404←303
(16167.8)
Table 4.5: Extended Broadband Autocorrelation of DFA
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Pulse 3 (π/2)
Bandwidth
(MHz)
Duration (ns)
5
5
5
100
100
100
Transitions
(MHz)
ΔJKaKc=202←101
(8390.8)
ΔJKaKc=202←101
(8390.8)
ΔJKaKc=202←101
(8390.8)
ΔJKaKc=212←101
(11376.5)
ΔJKaKc=212←101
(11376.5)
ΔJKaKc=212←101
(11376.5)
ΔJKaKc=313←212
(11658.5)
ΔJKaKc=313←212
(11658.5)
ΔJKaKc=313←212
(11658.5)
ΔJKaKc=303←202
(12380.4)
ΔJKaKc=303←202
(12380.4)
ΔJKaKc=303←202
(12380.4)
ΔJKaKc=414←313
(15459.3)
ΔJKaKc=414←313
(15459.3)
ΔJKaKc=414←313
(15459.3)
ΔJKaKc=414←303
(17723.2)
ΔJKaKc=414←303
(17723.2)
ΔJKaKc=414←303
(17723.2)
.
114
Table 4.6: Single-Quantum Correlation of TFP with Phase Cycling
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Bandwidth (MHz)
5
5
Duration (ns)
125
125
Pulse Phase
0o/180o
0o
Transitions (MHz)
ΔJ=3←2 (17267.7)
ΔJ=2←1 (11511.8)
ΔJ=3←2 (17267.7)
Table 4.7: Broadband Autocorrelation of TFP with Phase Cycling
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Bandwidth (MHz)
5
5
Duration (ns)
125
125
Pulse Phase
0o/180o
0o
Transitions (MHz)
ΔJ=2←1 (11511.8)
ΔJ=2←1 (11511.8)
ΔJ=3←2 (17267.7)
ΔJ=3←2 (17267.7)
115
Table 4.8: Double-Quantum Filtered Sequence of TFP with Phase Cycling
Pulse 1 (π/2)
t1
Pulse 2 (π)
Pulse 3 (π)
Bandwidth (MHz)
5
5
5
Duration (ns)
125
220
220
Pulse Phase
0o/180o
0o
0o
Transitions (MHz)
ΔJ=2←1 (11511.8)
ΔJ=3←2 (17267.7)
ΔJ=2←1 (11511.8)
116
Table 4.9: Hypercomplex Autocorrelation of CFE
Pulse 1 (π/2)
t1
Pulse 2 (π/2)
Bandwidth (MHz)
50
50
Duration (ns)
125
125
Pulse Phase
0o/90o
0o
Transitions (MHz)
ΔJKaKc=111←000
ΔJKaKc=111←000
Hyperfine Multiplets
ΔF = 0.5←1.5 (14120.2)
ΔF = 0.5←1.5 (14120.2)
ΔF = 2.5←1.5 (14127.9)
ΔF = 2.5←1.5 (14127.9)
ΔF = 1.5←1.5 (14137.7)
ΔF = 1.5←1.5 (14137.7)
117
4.7 References
(1)
Wollrab, J.E. Rotational Spectra and Molecular Structure; Academic Press, 1967.
(2)
Lavrich, R.J.; Plusquellic, D.F.; Suenram, R.D.; Fraser, G.T.; Hight Walker, A.R.;
Tubergen, M.J. J. Chem. Phys. 2003, 118, 1253.
(3)
Ohashi, N.; Hougen, J.T.; Suenram, R.D.; Lovas, F.J.; Kawashima, Y.; Fujitake,
M; Pyka, J. J. Mol. Spec. 2004, 227, 28.
(4)
Lavrich, R.J.; Hight Walker, A.R.; Plusquellic, D.F.; Kleiner, I.; Suenram, R.D.;
Hougen, J.T.; Fraser, G.T. J. Chem. Phys. 2003, 119, 5497.
(5)
Plusquellic, D.F.; Kleiner, I.; Demaison, J.; Suenram, R.D.; Lavrich, R.J.; Lovas,
F.J.; Fraser, G.T.; Ilyushin, V.V. J. Chem. Phys. 2006, 125, 104312.
(6)
Kleiner, I. J. Mol. Spec. 2010, 260, 1.
(7)
Aue, W.P.; Bartholdi, E.; Ernst, R.R. J. Chem. Phys. 1976, 64, 2229.
(8)
Andrews, D.A.; Baker, J.G.; Blundell, B.G.; Petty, G.C. J. Mol. Struct. 1983, 97,
271.
(9)
Stahl, W.; Fliege, E.; Dreizler, H. Z. Naturforsch. Teil A 1984, 39, 858.
(10)
Andrews, D.A.; Baker, J.G. J. Phys. B. 1987, 20, 5705.
(11)
Noda, I. J. Am. Chem. Soc. 1989, 111, 8116.
(12)
Lepetit, L.; Joffre, M. Opt. Lett. 1996, 21, 564.
(13)
Hybl, J.D.; Albrecht, A.W.; Gallagher Faeder, S.M.; Jonas, D.M. Chem. Phys.
Lett. 1998, 297, 307.
(14)
Hybl, J.D.; Ferro, A.A.; Jonas, D.M. J. Chem. Phys. 2001, 115, 6606.
(15)
Schanda, P.; Brutscher, B. J. Am. Chem. Soc. 2005, 127, 8014.
(16)
Mukherjee, P.; Kass, I.; Arkin, I.T.; Zanni, M.T. PNAS 2006, 103, 3528.
(17)
Brixner, T.; Stenger, J.; Vaswani, H.M.; Cho, M.; Blankenship, R.E.; Fleming,
G.R. Nature 2005, 434, 625.
(18)
Vogelsanger, B.; Andrist, M.; Bauder, A. Chem. Phys. Lett. 1988, 144, 180.
118
(19)
Vogelsanger, B.; Bauder, A. J. Chem. Phys. 1990, 92, 4101.
(20)
Vogelsanger, B.; Bauder, A. Z. Naturforsch. Teil A 1989, 44, 726.
(21)
Vogelsanger, B.; Bauder, A.; Mäder, H. J. Chem. Phys. 1989, 91, 2059.
(22)
Stahl, W.; Dreizler, H. Z. Naturforsch. Teil A 1985, 40, 1096.
(23)
Jäger, W.; Haekel, J.; Andresen, U.; Mäder, H. Mol. Phys. 1989, 68, 1287.
(24)
Feuillade, C.; Baker, J.G.; Bottcher, C. Chem. Phys. Lett. 1976, 40, 121.
(25)
Shirar, A.J.; Wilcox, D.S.; Hotopp, K.M.; Storck, G.L.; Kleiner, I.; Dian, B. J.
Phys. Chem. A 2010, 114, 12187.
(26)
The exact rotational splitting observed in the nuclear hyperfine structure is
directly dependent on the magnitude nuclear quadrupole, therefore the magnitude
of the splitting is dependent on the atomic nuclei of a given molecule. Excitation
bandwidths on the order of 100 MHz are generally sufficient to simultaneously
excite the hyperfine structure in our rotational spectra.
(27)
Pantoja-Uceda, D.; Santoro, J. J. Biomol. NMR 2009, 45, 351.
(28)
Bodenhausen, G.; Kogler, H.; Ernst, R.R. J. Magn. Reson. 1984, 58, 370.
(29)
States, D.J.; Haberkorn, R.A.; Ruben, D.J. J. Magn. Reson. 1982, 48, 286.
(30)
Bain, A.D.; Burton, I.W. Concept Magnetic Res. 1996, 8, 191.
(31)
Xian, F.; Hendrickson, C.L.; Blakney, G.T.; Beu, S.C.; Marshall, A.G. Anal.
Chem. 2010, 82, 8807.
(32)
de Brouwer, H. J. Magn. Reson. 2009, 201, 230.
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Chen, L.; Weng, Z.; Goh, L.; Garland, M. J. Magn. Reson. 2002, 158, 164.
(34)
Reproduced with permission from: Wilcox, D.S.; Hotopp, K.M.; Dian, B.C. J.
Phys. Chem. A, 2011, 115, 8895–8905. Copyright 2011 American Chemical
Society.
119
CHAPTER 5 FURTHER APPLICATIONS OF ROTATIONAL SPECTROSCOPY
5.1 Toward Microwave Chemical Sensing at Room Temperature
Room temperature chirped-pulsed Fourier transform microwave (RT-CP-FTMW)
spectroscopy has been demonstrated using two different designs, one based on an
overmoded waveguide and a second based on an overmoded coaxial cable. These new
sample analysis chambers were developed in a cross-departmental collaboration with Dr.
William J. Chappell’s research group from Purdue University’s School of Electrical and
Computer Engineering. With the development of high frequency chips, micropumps, and
high sampling rate analog-to-digital signal converters, many of the components of the
broadband CP-FTMW spectrometer described in Chapter 2 of this document are ripe for
miniaturization. This trend towards a more integrated system in combination with its
sensitivity to molecular shape makes CP-FTMW spectroscopy an appealing option for
the development of a chemical sensing device.1 A robust microwave chemical sensing
device would ideally have a fast data acquisition rate, facilitated by a large probing
bandwidth, be portable in size, and function at room temperature. In 2011, the RT-CPFTMW spectrum of anisole (C6H5OCH3) was recorded from 8.7 to 18.3 GHz by Shipman
et al.2 using a WRD750 double ridge waveguide spectrometer. With this design the
electric field is mostly concentrated within the small ridge area of the waveguide which
has a cross section of only 4.39 mm x 3.45 mm, so a 10 m length of waveguide is
120
required to compensate for the lack of sample space in the cross section. Even when the
waveguide is in a coiled shape, as used in the Shipman2 static gas cell spectrometer, a 10meter-long waveguide is impractical for a field deployable chemical sensing device. In
this section, we describe a RT-CP-FTMW spectrometer using a compact overmoded
waveguide as the probe channel and we demonstrate, with this design, the successful
measurements of methanol (CH3OH) at room temperature.3
5.2 Overmoded Waveguide Design
This works focuses on the miniaturization of the sample cell used for RT-CPFTMW spectroscopy. The design originates from a standard WR90 waveguide, which
has cross-section dimensions of 22.86 mm 10.16 mm. Methanol, the sample used for
this study, has several rotational transitions which lie within the working range (8.2-12.4
GHz) of the WR90 waveguide. For the overmoded design the width of the waveguide is
kept constant while the height is increased to twice the initial height so that the final
dimensions of the overmoded waveguide are 22.86 mm  20.82 mm. The width is kept
constant so the fundamental mode, TE10, will not couple to higher order TEn0 modes, n
being an odd number, in the desired frequency range. The increased cross-section also
allows the length of the waveguide to be reduced to 22 cm while still maintaining 65% of
the volume contained in the ridge region of a 10 m WRD750 waveguide. A 6-section
Chebyshev multistep transformer is used to match the impedance of the WR90
waveguide to that of the overmoded waveguide.4 A schematic of the transformer is
shown in Figure 5.1; the stepped segments, shown with solid lines, were calculated using
a Chebyshev impedance matching polynomial,4 and the dashed lines show the piecewise,
121
smooth model actually used for fabrication. The final dimensions of the overmoded
waveguide cross section are 22.86 mm  20.82 mm. The tapered coupling sections make
a smooth transition from the standard WR90 waveguide to the overmoded waveguide
from 8 GHz to 16 GHz. However, the final working range is limited by the commercial
coaxial to rectangular waveguide adapter (HP X281A), which narrows the operational
frequencies to a more restricted 8.2-12.4 GHz. In order to eliminate the strong coupling
between the TE10 and TM12 modes and resolve the resonance in the waveguide, we have
included two bifurcations in the two tapered sections to improve the field uniformity in
the overmoded waveguide. With the 500 m thick, 3 cm long bifurcations, the two
coupling sections work as a power divider and combiner.5 The input coupling section
excites the overmoded waveguide with two simultaneous TE10 modes, and the output
coupling section recombines the overmoded TE10 mode from two identical TE10 modes.
The interior channel of the waveguide is shown in Figure 5.2 (a). Compared to the nonovermoded waveguide design, our overmoded waveguide reduces the length of the probe
channel while enclosing approximately the same number of molecules.
122
Figure 5.1: WR90 to overmoded waveguide adaptor. The solid line is the 6-section
Chebyshev multistep transform used to match the WR90 waveguide to the overmoded
waveguide, and the dashed line is the piecewise, smooth model used for fabrication.
123
a) b) c) Figure 5.2: Overmoded waveguide. (a) Interior channel of the overmoded waveguide
showing the two 3 cm bifurcations near the tapered sections. These bifurcations are used
to improve the electric field uniformity. (b) Exterior of the overmoded waveguide. Mica
sheets form a vacuum seal closure on the ends of the overmoded cell. (c) Photograph of
the RT-FTMW overmoded waveguide sample cell.
124
5.3 Overmoded Waveguide Fabrication
The overmoded waveguide spectrometer, shown in Figure 5.2, consists of two
tapered waveguide sections which function as adaptors from the WR90 waveguide to the
overmoded waveguide. The tapered sections are each 10 cm in length and the overmoded
waveguide is 22 cm long for a total length of 42 cm. Because of fabrication limitations,
the overmoded waveguide had to be divided into two halves. In order to limit the effects
of dividing the waveguide, we chose to divide it along the E-plane where the surface
current flows longitudinally along the seam. The current on the other two sidewalls does
not encounter any discontinuity. Therefore, dividing the waveguide along the E-plane has
the least impact on waveguide performance. The long edges of one of these pieces were
grooved and sealed with two pieces of Viton O-ring strips. The input and output flanges
of the overmoded waveguide were also grooved and fit with O-rings to seal the flanges
with 150 m thick mica windows. On the sidewalls of the waveguide, there are three
orifices of 2 mm diameter for pumping, gas inlet, and a vacuum gauge. The openings
were made small to minimize the disturbance to the electric field. The overmoded
waveguide can hold a vacuum of 0.01 mTorr based on a leak test with helium.
5.4 Overmoded Waveguide Experimental
A detailed description of the pulsed valve CP-FTMW spectrometer is provided in
Chapter 2 of this document. The overmoded waveguide RT-CP-FTMW measurements
were achieved with the same microwave pulse generation and detection electronics used
by the pulsed valve CP-FTMW spectrometer; however, modifications were made to the
microwave pulse power, sample interaction chamber, and the sample preparation method.
125
A block diagram of the major components of the RT-CP-FTMW circuit is shown in
Figure 5.3.
A polarizing chirped pulse was produced by the arbitrary waveform generator
(Tektronix AWG 7101) to linearly sweep from 2993 MHz to 3093 MHz. The signal was
then filter by a 5 GHz low pass filter (Lorch Microwave 10LP-5000-S) to remove any
spurious tones from the arbitrary waveform generator, preamplified by a solid-state
amplifier (Minicircuit ZX-60-6013+), and upconverted to the frequency range of interest
by mixing with the signal from 13 GHz phase-locked dielectric resonator oscillator
(PDRO). The final chirped pulse sweep from 9.907 GHz to 10.007 GHz was filtered by a
13 GHz notch filter (Lorch Microwave 6BR6-13000/100- S) to remove the residual
signal of the 13 GHz PDRO. The last stage before emission into the overmoded
waveguide is power amplification. A 3 W solid state power amplifier (Microwave Power
L0818-32-T358) was used for the narrow-band 100 MHz chirped pulses. Alternatively,
this solid state amplifier was replaced by a traveling wave tube (TWT) amplifier (AR
200T8G18A) used in combination with a step attenuator giving an output power of 30 W.
This increased the power spectral density to support the broadband chirp from 9.9 GHz to
12.3 GHz. The time and frequency domain plots of the 1μs, 100 MHz bandwidth,
microwave polarizing pulse centered about 9.957 GHz is shown in Figure 5.4.
The overmoded waveguide was evacuated to the sub-mTorr level by the pumping
system described in Chapter 2. The methanol sample was then introduced into the
waveguide using a freeze, pump, and thaw technique to purge the air from the sample
inlet line. The RT-CP-FTMW measurements were acquired with a steady sample gas
flow to maintain a pressure of 10 mTorr.
126
Figure 5.3: Block diagram of the RT-CP-FTMW spectrometer. (a) Microwave pulse
generation circuit, (b) overmoded waveguide probe channel, and (c) FID detection circuit.
127
Figure 5.4: Microwave polarizing pulse. (a) Time domain signal with 1μs duration.
(b) Frequency domain signal showing the 100 MHz bandwidth centered about 9.957 GHz.
128
After polarization, the molecular re-emission signal, or free induction decay (FID), was
transmitted through a low noise amplifier (LNA) (Miteq AMF-6F-06001800-15-10P)
with a 45 dB gain and a p-i-n diode limiter (Advanced Control Components ACLM4619FC361K). Because the digital sampling oscilloscope used to record the FID
(Tektronix TDS6124C) has an operating range from DC to 12 GHz, the molecular reemission signal was downconverted by mixing with the 18.9 GHz PDRO. To protect the
detection electronics from the intense polarizing pulse, a solid-state switch (ATM PNR
S1517D) was placed in the circuit between the p-i-n diode limiter and the LNA. The
molecular re-emission signal of methanol, detected using the RT-CP-FTMW overmoded
waveguide spectrometer, is shown in Figure 5.5. This signal was digitized for 4 μs and
was the result of the 9.907 GHz to 10.007 GHz chirped pulse.
5.5 Overmoded Waveguide Results
Using the wideband chirped pulse to sweep from 9.9 to 12.3 GHz, five rotational
transitions were identified in the frequency domain spectrum of methanol. The peaks at
9936.1 MHz, 9978.6 MHz, 10058.1 MHz, 12178.5 MHz, and 12229.3 MHz are marked
in Figure 5.6. To acquire this 2.4 GHz wideband spectrum, we used a 30 W output power
from the TWT amplifier and signal averaged 1000 FIDs in the time domain. The data was
Fourier transformed offline using a PC.
Two separate frequency ranges were surveyed using pulses with the narrow
bandwidths of 100 MHz and 400 MHz in order to probe from 9.907 GHz to 10.007 GHz
and 12.144 GHz to 12.544 GHz, respectively.
129
Figure 5.5: Molecule free induction decay (FID) of methanol recorded using the
overmoded waveguide RT-CP-FTMW spectrometer.
130
0.0004
Intensity (arbitrary units)
9936.1
0.0003
0.0002
12229.3
9978.6
12178.5
10058.1
0.0001
0.0000
9500
10000
10500
11000
11500
12000
12500
Frequency (MHz)
Figure 5.6: Rotational spectrum of methanol acquired using the RT-CP-FTMW
overmoded waveguide spectrometer. The polarizing microwave pulse swept from 9.9 to
12.2 GHz and was power amplified by 30 W. Five methanol rotational transitions were
observed in this spectrum.
131
With these narrow-band pulses, a commercial 3 W solid-state amplifier was used in the
place of the 30 W TWT because a sufficient power density can be obtained at a lower
power. The 100 MHz pulse was chirped from 9.907 to 10.007 GHz and probed the
rotational transitions 91 9  82 7 at 9936.1 MHz and 43 2  52 3 at 9978.6 MHz, which
are clearly observed in the spectrum shown in Figure 5.7. The higher-frequency spectrum
of Figure 5.8, which corresponds to the 12.144 GHz to 12.544 GHz chirped pulse,
contains peaks at 12178.5 MHz (20
2
 31 3), 12229.3 MHz (165
12
174
13),
and
12511.2 MHz (51 4 51 5). A complete list of rotational transitions observed using the
RT-CP-FTMW overmoded waveguide spectrometer is shown in Table 5.1.
We have demonstrated that room temperature rotational spectra can be obtained
using a miniaturized probe channel. The design of the overmoded waveguide includes
two adaptors which provide good impendence matching for the transition from a standard
WR90 waveguide to an overmoded waveguide cell while preserving the frequency range.
Furthermore, the 22-cm-long overmoded waveguide contains enough sample molecules
to allow for chemical detection, even though the total volume is only 68% of a 10-meterlong WRD750 waveguide. In all, we have greatly reduced the waveguide length from 10
m to 22 cm and probed 6 rotational transitions of methanol.6
5.6 RT-CP-FTMW Spectroscopy: Overmoded Coaxial Line
The second room temperature CP-FTMW spectrometer was based on an
overmoded coaxial line instead of an overmoded waveguide. The spectrometer’s analysis
cell, shown in Figure 5.9, has an improved design which used commercially available
high vacuum components to house the coaxial line.
132
0.00030
9936.1
Intensity (Arbitrary Units)
0.00025
0.00020
0.00015
9978.6
0.00010
0.00005
0.00000
9910
9920
9930
9940
9950
9960
9970
9980
9990
Frequency (MHz)
Figure 5.7: Measured methanol spectra using a 3 W solid-state amplifier with a chirped
pulse at a center frequency of 9.957 GHz and 100 MHz bandwidth.
133
0.0004
12178.5
Intensity (Arbitrary Units)
0.0003
12229.2
0.0002
12511.2
0.0001
0.0000
12100
12200
12300
12400
12500
Frequency (MHz)
Figure 5.8: Measured methanol spectra using a 3 W solid-state amplifier with a chirped
pulse at a center frequency of 12.344 GHz and 400 MHz bandwidth.
Table 5.1 Rotational transitions of methanol observed using the overmoded RT-CPFTMW spectrometer
Rotational Transition Measured Frequency
(MHz)
J ' Ka' Kc'  J " Ka" Kc"
91 9  82 7
43 2  52 3
43 1  52 4
20 2  31 3
9936.139
9978.635
10058.095
12178.535
165 12 174 13
51 4 51 5
12229.308
12511.177
134
Figure 5.9: Overmoded coaxial line RT-CP-FTMW spectrometer sample analysis
chamber. The 32 cm coaxial cable was housed in the stainless steel tube connected to the
4-way cross that allowed for quick and easy connection to the electrical feeds, the
vacuum pumping system, and the sample inlet port.
135
This small vacuum assembly included Klein Flange (KF) flanges which were superior to
the leak-prone custom machined components of the overmoded waveguide.
A diagram of the overmoded coaxial cable is shown in Figure 5.10. The outer
conductor, machined from aluminum, formed a cylindrical enclosure around the 305 mm
long copper center pin. The outer and center conductors were designed to have diameters
of 16 mm and 1 mm, respectively, so that the coaxial cable would support electrical
modes in the 3 GHz to 18.9 GHz range. To smoothly match the impedance of the 2.4 mm
end connectors with that of the 16 mm diameter overmoded coaxial cable, a tapered
transmission line was designed using the Hamming functions described by Wang.7 This
curved section is evident in Figure 5.10. Six 2 mm diameter holes were drilled into the
outer conductor of the overmoded cable to allow the sample molecules to flow into the
electric field interaction region. Between 3 GHz and 18 GHz, the return loss of the
overmoded cable is below -10 dB.
The overmoded coaxial cable was tested using the same microwave circuit
described in Section 5.4 of this chapter. A block diagram of the spectrometer’s major
components is shown in Figure 5.11. Using the 3 W solid state amplifier, the 9907 MHz
to 10007 MHz and the 12144 MHz to 12544 MHz regions were probed in two separate
experiments. The rotational transitions of methanol were observed at 9936.1 MHz,
12178.4 MHz, and 12229.1 MHz. The spike at 12169.0 MHz could not be identified, but
is expected to be from the electric field because it was present in the background (sample
free) spectra.8
136
Figure 5.10: Outer conductor and center pin of the overmoded coaxial cable. The
Hamming tapered transmission line (curved regions) method was used to match the
impedance of the 16 mm cable to the 2.4 mm connectors.
137
Figure 5.11: Microwave excitation and detection circuit of the overmoded coaxial cable
RT-CP-FTMW spectrometer.
138
10
8
Intensity (V)
9936.14
6
4
2
0
9875
9900
9925
9950
9975
10000
Frequency (MHz)
Figure 5.12: The 9-1 9  8-2 7 rotation transition of methanol measured with an
overmoded coaxial cable RT-CP-FTMW spectrometer. The polarizing pulse swept from
9907 to 10007 MHz.
139
16
Intensity (V)
12
12178.4
12229.1
8
4
0
12180
12250
12320
12390
12460
12530
Frequency (MHz)
Figure 5.13: Rotational transitions 20 2  3-1 3 (12178.4 MHz) and 165 12  174 13
(12229.1 MHz) of methanol measured with an overmoded coaxial cable RT-CP-FTMW
spectrometer. The polarizing pulse swept from 12144 to 12544 MHz. The peak at
12169.0 MHz is expected to be noise from the electric field.
140
5.7 Quadrature Coupler Microwave Circuit
Phase sensitive detection for the 2D CP-FTMW spectroscopic experiments was
explored using a quadrature coupler. In NMR, quadrature detection is achieved by
detecting on both the x and y-axes of the transverse plane simultaneously.9 These two
FIDs are called the real and imaginary signals, with the phase of the imaginary shifted 90
degrees with respect to the real channel.10 These FIDs serve as the inputs for the Fourier
transform.
To apply this type of detection to the 2D CP-FTMW experiments, several
modifications had to be made to our experimental procedure. First, the 2D LabVIEW
program described in Chapter 2 was adapted to record two channels on the detection
oscilloscope instead of only one. In addition, a quadrature coupler (Planar Monolithics
Industries Inc. QA-8018) was placed in the existing CP-FTMW circuit to split the input
signal and provide a 90 degree phase delay. This was implemented in two different ways.
One method used the molecular signal as the quadrature coupler input, and the other
method shifted the 18.9 GHz PLDRO signal which is used as the mix down local
oscillator.
It was found that the quadrature coupler provided unsatisfactory control over the
imaginary signal, so a manual phase shifter (Advanced Technical Materials P1507) was
later added to the circuit to solve this problem. Using the molecular FIDs of TFP, it was
found that 5.5 turns of the manual phase shifter knob shifted the imaginary signal by 360
degrees. Hence we were able to approximate the number of turns necessary to induce a
90 degree phase delay. A block diagram of the most successful quadrature circuit is
shown in Figure 5.14.
141
Molecular Signal
(Free Induction Decay)
DC Block
CH1
J2
12 GHz
Digital
Oscilloscope
PLDRO
(18.9 GHz)
DC Block
CH3
Power
Divider
Phase
Shifter
J1
Quadrature
Coupler
J4
J3
Figure 5.14: Block diagram showing the detection electronics of the 2D CP-FTMW
quadrature circuit. A 90° phase shift was induced on channel 3 by the quadrature coupler
and phase shifter. Two channels (ch1 and ch3) were simultaneously recorded by the
digital oscilloscope.
142
5.8 Future Applications of 2D CP-FTMW Spectroscopy
2D CP-FTMW spectroscopy has a variety of foreseeable applications. For
example the 2D technique could aid the fitting process of complex rotational spectra.
Using 2D CP-FTMW spectroscopy, coherences will propagate through connected
rotational energy levels that originate for the same molecular species. This would be
useful when seeking to identify molecular products in an electrical discharge spectrum
such as that presented in Figure 5.15. The spectrum is the result of the application of a
high voltage discharge to the sample molecule 2,3-dihydrofuran (DHF). This strong pulse
of energy fragments the 2,3-DHF, resulting in many smaller molecules which can be seen
from Figure 5.15. The rotational spectrum of this collection of molecules is shown in
black (top) and their predicted spectra are shown in assorted colors (bottom).11 Eight
unique isomers and conformers were identified in the discharge. Subsequent studies have
produced discharge spectra with over 15 isomers in a single spectrum.12
The identification process is currently quite tedious as extensive literature
searches are needed to build a database of suitable discharge candidates if the rotational
constants are previously known. When the rotational constants are not known, the
rotational spectrum of a potential candidate is recorded experimentally so the rotational
constants can be determined. This requires further data collection, and possibly synthesis
of the material if the sample is not commercially available.
The power of 2D CP-FTMW lies in its ability to identify transitions that share a
common energy level.13 This allows the researcher to group connected lines and therefore
isolate single molecular species. This is extremely useful for identifying exotic species
such as free radicals and ions, particularly because their rotational constants are seldom
143
known. 2D CP-FTMW spectroscopy may also have applications in quantum
computing14,15 and the rotational dependence of intramolecular vibrational redistribution.
Arbitrary Intensity
144
Trans CPCA
Cis CPCA
Trans CA
Trans Acrolein
Cis Acrolein
8000
10000
Formaldehyde
Propene
Propyne
Cyclopropenylidene
12000
14000
16000
18000
Frequency (MHz)
Figure 5.15: Dissociation products of 2,3-dihydrofuran measured by Chirped-Pulse
Fourier Transform Microwave spectroscopy (top). Predicted molecular spectra of
discharge products (bottom). Reproduced with permission from Karunatilaka et al.11
Copyright 2010 American Chemical Society.
145
5.9 References
(1)
Brown, G. G.; Dian, B. C.; Douglass, K. O.; Geyer, S. M.; Shipman, S. T.; Pate,
B. H. Review of Scientific Instruments 2008, 79.
(2)
Reinhold, B.; Finneran, I. A.; Shipman, S. T. Journal of Molecular Spectroscopy
2011, 270, 89.
(3)
Xu, L. H.; Lovas, F. J. Journal of Physical and Chemical Reference Data 1997,
26, 17.
(4)
Pozar, D. M. Microwave Engineering; 3 ed.; John Wiley & Sons, Inc., 2004.
(5)
Nantista, C. D. In High Energy Density and High Power Rf; Gold, S. H.,
Nusinovich, G. S., Eds. 2003; Vol. 691, p 263.
(6)
Huang, Y.-T.; Hotopp, K. M.; Dian, B. C.; Chappell, W. J. Submitted, 2012.
(7)
Wang, Y. Electronics Letters 1991, 27, 2396.
(8)
Huang, Y.-T.; Hotopp, K. M.; Dian, B. C.; Chappell, W. J. In International
Microwave Symposium Montreal, Quebec, Canada, 2012.
(9)
Redfield, A. G.; Kunz, S. D. Journal of Magnetic Resonance 1975, 19, 250.
(10)
Lambert, J. B.; Mazzola, E. P. Nuclear Magnetic Resonance Spectroscopy: An
Introduction to Principles, Applications, and Experimental Methods; 1st ed.;
Prentice Hall: Upper Saddle River, 2004.
(11)
Karunatilaka, C.; Shirar, A. J.; Storck, G. L.; Hotopp, K. M.; Biddle, E. B.;
Crawley, R.; Dian, B. C. Journal of Physical Chemistry Letters 2010, 1, 1547.
(12)
Shirar, A. J., Determination of Discharge Products Using Chirped-Pulse Fourier
Transform Microwave Spectroscopy. Purdue University, 2011.
(13)
Wilcox, D. S.; Hotopp, K. M.; Dian, B. C. Journal of Physical Chemistry A 2011,
115, 8895.
(14)
Golze, D.; Icker, M.; Berger, S. Concepts in Magnetic Resonance Part A 2012,
40A, 25.
(15)
Wei, Q.; Kais, S.; Friedrich, B.; Herschbach, D. Journal of Chemical Physics
2011, 135.
APPENDIX
146
APPENDIX: LABVIEW PROGRAM FOR TWO-DEMENSIONAL CHIRPED-PULSE
FOURIER TRANSFORM MICROWAVE SPECTROSCOPY
In this section we show the user interface and the LabVIEW code for the TwoDimensional
Chirped-Pulse
Fourier
Transform
Microwave
(2D-CP-FTMW)
spectroscopy program that was developed as part of this work. The screenshots in the
first three figures show the graphical user interface that is displayed during the operation
of the program. The subsequent unlabeled figures are representations of the visual
LabVIEW code that make up the program itself. National Instruments LabVIEW version
8.5 was used to create this program.
147
Figure A 1: Screen shot of the 2D program’s Hardware Configuration user interface tab. GPIB addresses are selected from
the drop down menus (left) and communication is opened with the instruments by pressing Connect (right). The 200 W
amplifier and electronic switch must be connected to the proper channels of the DG535, as indicated.
148
Figure A 2: Screen shot of the 2D program’s Pulse Parameters user interface tab. The user types in values for the Index
Number, Step Size, and Initial Loop Count for each dynamic delay of the pulse sequence. These values must match the
pulse sequence programmed into the arbitrary waveform generator.
149
Figure A 3: Screen shot of the 2D program’s Scan Parameters user interface tab. The user sets the timing of the DG535
channels which trigger the 200 W amplifier and the electronic switch. The user also specifies the Source (oscilloscope
channel), Number of Steps (or iterations), File Name, and File Path for the data. Pressing Start (right) begins the data
collection process. The current step and approximate time remaining are displayed while the program is acquiring data.
LabVIEW code 2D Program.vi
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VITA
189
VITA
Kelly M. Hotopp has been pursuing a Doctor of Philosophy degree at Purdue
University in the Department of Chemistry since August, 2006. Kelly graduated with
honors from Huntington University in May, 2006 with a Bachelor of Science in
Chemistry Education and a Minor in Physics. Her research is related to broadband
rotational spectroscopy using chirped-pulse Fourier transform microwave systems. Kelly
has also served as a Teaching Assistant for a number of courses, such as Physical
Chemistry Lecture (CHM 370), Physical Chemistry Lab (CHM 376), General Chemistry
(CHM 115, CHM 116), and Undergraduate Level Remedial Chemistry (CHM 226). She
was the Course Supervisor for General Chemistry (CHM 126) and a Grading Assistant
for graduate level Introduction to Lasers (ECE 552). While at Huntington University,
Kelly completed an independent study in radio astronomy and seismology.
Kelly’s Purdue experience includes advanced digital electronic systems such as
arbitrary waveform generators, microwave circuit construction and diagnostics, large
bandwidth/high sampling frequency oscilloscopes, digital filtering, quadrature detection,
and signal filtration/amplification. She has performed a large amount of data processing
through the use of programs such as Mathcad, Origin, and SPFIT/SPCAT spectral fitting
programs. Kelly also coordinated a complex, interdepartmental research project with the
190
School of Electrical and Computer Engineering of Purdue University. She developed the
project from the early design stages all the way through to successful completion.
Kelly’s professional activities are widely varied. She has a Teaching License for
High School Chemistry and Junior High Science in the State of Indiana and is member of
a number of professional societies, including the American Chemical Society and the
American Physical Society. Kelly is a recipient of the Bryan Scholarship, the American
Cancer Society Scholarship, and a Huntington University Trustee Scholarship in addition
to being listed on the Huntington University Dean’s List and a member of Kappa Delta
Phi (the Educational Honor Society).
Kelly has been active as a volunteer and member of Iota Sigma Pi, the national
honor society for women in chemistry, serving as the outreach coordinator on the Purdue
chapter Board of Directors. Her volunteer work included the planning of chemistry
demonstrations for 2500 elementary students and organizing over 200 volunteers for
National Chemistry Week. Kelly served on the Purdue Chemistry Department Lab Safety
Committee and has volunteered as a prospective graduate student mentor. Kelly has
authored or co-authored four peer-reviewed publications with one more currently in
preparation. She has also presented her work in conference talks at the International
Symposium on Molecular Spectroscopy (Columbus, Ohio). Keeping true to her roots,
Kelly is still a current member of the Wells County, Indiana Historical Society.
PUBLICATION
191
Reproduced with permission from Wilcox, D. S.; Hotopp, K. M.; Dian, B. C. Journal of
Physical Chemistry A 2011, 115, 8895. Copyright 2011 American Chemical Society.
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