close

Вход

Забыли?

вход по аккаунту

?

Hyperfine structure in the microwave spectra of the iodine fluorides iodine heptafluoride and iodine pentafluoride and of the weakly bound complex hydrochloric acid ... nitrous oxide

код для вставкиСкачать
INFORMATION TO USERS
The most advanced technology has been used to photo­
graph and reproduce this manuscript from the microfilm
master. UMI films the text directly from the original or
copy submitted. Thus, some thesis and dissertation copies
are in typewriter face, while others may be from any type
of computer printer.
The quality of this reproduction is dependent upon the
quality of the copy submitted. Broken or indistinct print,
colored or poor quality illustrations and photographs,
print bleedthrough, substandard margins, and improper
alignment can adversely affect reproduction.
In the unlikely event that the author did not send UMI a
complete manuscript and there are missing pages, these
will be noted. Also, if unauthorized copyright material
had to be removed, a note will indicate the deletion.
Oversize materials (e.g., maps, drawings, charts) are re­
produced by sectioning the original, beginning at the
upper left-hand corner and continuing from left to right in
equal sections with small overlaps. Each original is also
photographed in one exposure and is included in reduced
form at the back of the book. These are also available as
one exposure on a standard 35mm slide or as a 17" x 23"
black and white photographic print for an additional
charge.
Photographs included in the original manuscript have
been reproduced xerographically in this copy. Higher
quality 6" x 9" black and white photographic prints are
available for any photographs or illustrations appearing
in this copy for an additional charge. Contact UMI directly
to order.
University Microfilms Internationa!
A Bell & Howell Information Company
300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA
313/761-4700 800/521-0600
Order Number 1339059
Hyperfine structure in the microwave spectra of the iodine
fluorides IF7 and IF5 and of the weakly bound complex HCL
...NNO
Shea, James Christopher, M.S.
The University of Arizona, 1989
UMI
300 N.Zccb Rd.
Ann Arbor, MI 48106
HYPERFINE STRUCTURE IN THE MICROWAVE SPECTRA OF
THE IODINE FLUORIDES IF? AND IFg AND OF
THE WEAKLY BOUND COMPLEX HC1...NN0
by
James Christopher Shea
A Thesis Submitted to the Faculty of the
DEPARTMENT OF CHEMISTRY
In Partial Fulfillment of the Requirements
For the Degree of
MASTER OF SCIENCE
In the Graduate College
THE UNIVERSITY OF ARIZONA
19 8 9
STATEMENT BY AUTHOR
This thesis has been submitted in partial fulfillment
of requirements for an advanced degree at The University of
Arizona and is deposited in the University Library to be
made available to borrowers under rules of the Library.
Brief quotations from this thesis are allowable
without special permission, provided that accurate acknow­
ledgement of source is made. Requests for permission for
extended quotation from or reproduction of this manuscript
in whole or in part may be granted by the head of the major
department or the Dean of the Graduate College when in his
or her judgement the proposed use of the material is in the
interests of scholarship. In all other instances, however,
permission must be obtained from the author.
SIGNED:
APPROVAL BY THESIS DIRECTOR
n the date shown below:
I -2
STEPHEN G. KUKOLICH
Professor of Chemistry
Date
3
TABLE OF CONTENTS
LIST OF ILLUSTRATIONS
Page
4
LIST OF TABLES
5
ABSTRACT
6
I.INTRODUCTION
II.EXPERIMENTAL
1.Sample Handling
2.Instrumental
3.Data Treatment
III.RESULTS AND DISCUSSION
1.Iodine Heptafluoride
2.Iodine Pentaflouride
3.HC1...NNO
7
13
13
16
22
27
27
33
37
APPENDIX: FITTING PROGRAM
40
REFERENCES
55
LIST OF ILLUSTRATIONS
Figure
I.Gas Manifold
II.Diagram of Spectrometer
III.Timing Diagram of Pulse Sequences
IV.Example FID Signal
V.Fourier Transform of Example Signal
VI.Distorted Structure of IF7
Page
14
17
21
23
25
28
VII.FID Signal From IF7 Spectrum
30
VIII.Fourier Transform of IF7 FID
31
IX.Structure of IF5
34
LIST OF TABLES
Table
I. Instrumental Operating Parameters
Page
18
II. Measured and Calculated Transition Frequencies for IF7
• * • . • 32
III. Comparison of IF5 Constants With Previous Studies
35
IV. Measured and Calculated Transition Frequencies for IF5
36
V. Transition Frequencies for HC1...NN0
38
VI. Transition Frequencies for Unknown Trimer Species
38
ABSTRACT
A pulsed-beam fourier transform microwave spectrometer
was used to measure the rotational spectra of iodine
heptafluoride, iodine pentafluoride, and the weakly bound
complex, HC1...NNO.
For IF7, only five rotational
.transitions were observed, and no resolvable hyperfine
structure was detected.
Based on this data, the A, B,
and c rotational constants were determined to be
1746(3) MHz, 1732.0(8) MHZ, and 1553.0(2) MHZ,
respectively.
The existence of a pure rotational
spectrum confirms that this molecule undergoes polar
distortions.
Twenty-two hyperfine components of the IF5
spectrum were recorded.
The B rotational constant for this
molecule was determined to be 2727.421(3) MHz, and the
quadrupole coupling constant was found to be 1069.35(13)
MHz.
Though the work is still in progress on HC1...NN0,
nine transitions have been recorded.
In addition, five
transitions have been recorded for an apparent trimer
species composed of HC1, NNO, and an as yet unidentified
third species.
CHAPTER I: INTRODUCTION
Microwave spectroscopy is used to determine the rota­
tional energy of molecules.
The rotation referred to is the
end over end motion of a molecule, and not internal bond
rotation.
Such a rotating molecule, if it possesses a
dipole moment, can couple to an oscillating electric field.
The rotation is quantized, and the energy differences be­
tween rotational states of the molecule correspond to fre­
quencies in the microwave range of the electromagnetic
spectrum.
Thus microwave spectroscopy can be used to deter­
mine the energy of the rotational levels for certain
species.
The magnitudes.of these energies are determined by
rotational constants, and it is these constants which are of
interest.
A molecule has three rotational constants (A,B, and C)
corresponding to the three molecular axes (a,b, and c,
respectively).
The constants are all defined analogously:
A = h / 8*2Ia
(1)
Where Ia is the moment of inertia about the molecule's "a"
axis.
If a molecule's two larger rotational constants (A&B)
are equal, it is termed an "oblate symmetric top", or simply
an oblate top.
The molecule IF5 is an oblate top, and IF7
is very nearly so.
The energy for a rotational level of an
oblate top is given by:
E = BJ(J+l) + (C-B)K2 - Dj[J(J+l)]2
(2)
- DjkJ(J+1)K2 - DkK4
Where the quantum number J is the total rotational angular
momentum of the molecule, and the quantum number K is the
r>
•
projection of the angular momentum on the molecule's sym­
metry axis.
above.
B and C are rotational constants as described
Lastly, the constants Dj, DJK, and DK represent
centrifugal distortions of the molecule due to its rotation.
When an atom is present which possesses a nuclear spin
(I) of greater than 1/2, the resultant quadrupole moment
must be considered.
The nuclear spin (I) can couple with
the molecule's rotational angular momentum (J), giving a new
total angular momentum (F).
F is given by the formula:
F = J+I, J+I-l, J+I—2 f , |J-I|
(3)
So for a molecule such as IF5, containing iodine (1=5/2), in
the J=1 rotational state, the allowable values of F are:
F = 1 + 5/2
= 1 + 5/2 - 1
= 7/2
= 5/2
= 1 + 5/2 - 2 = |1 - 5/2| = 3/2
Of course these splittings of J states become more numerous
at higher values of J, as can be seen in table III.
The exact energy of each of these states is dependent
upon the strength of the quadrupole coupling.
The quad-
rupole coupling constant, eqQ, is a product of the fundamen­
tal charge, e; the potential field gradient, q, due to a
non-symmetrical distribution of the electrons and other
charges about the nucleus of interest; and the nuclear quad­
rupole moment for the given atom, Q.
Thus the splitting for
IF5 and IF7 would be expected to differ because of differing
molecular symmetries (C4v and C2, respectively) and differ­
ing electronic charge distibutions.
When quadrupole coupling is considered, the energy level
expression (equation 2) becomes:
E = BJ(J+l) + (C-B)K2 - Dj[J(J+l)]2
(4)
- DjkJ(J+1)K2 - DkK4
+ {eqQ [3K2/J(J+l) - 1] Y(I,J,F)}
Where Y(I,J,F) is Casimir's function:
Y(I,F,J) = [3C(C+1) - I(1+1)J(J+l)] /
(5)
[81(21-1)(2J-1)(2J+3)]
In equation 5, the symbol, C, is not the c-axis rotational
constant, but a quantity known as Casimir's coefficient,
given by:
C = F(F+l) - 1(1+1) - J(J+1)
(6)
The above energy expression actually represents only a first
order correction for the quadrupole coupling, though the
fitting program used in this research (see appendix) calcu­
lated the energy to second order.
The calculation of second
order corrections entails a considerably longer equation, so
for the sake of brevity, I leave its format to a reference
text1.
The energy of a transition between two rotational levels
is given (in terms of J, K, I, and F of the lower state) by:
2B(J+l) - 4Dj(J+l)3 - 2DJK(J+1)K2
AE =
(7)
+ eqQ {[3K2 /(J+l)(J+2) - 1] Y(I,F',J+l)
- [3K2 /J(J+l) - 1] Y(I,F,J)}
(Again, this shows only first order correction even though
the calculations were done to second order.)
So, by deter­
mining several transition frequencies, and assigning them
the correct quantum numbers, one can fit the rotational and
quadrupole coupling constants of a molecule to satisfy the
above equation.
Microwave spectroscopy is commonly used to obtain struc­
tural information about molecules.
As seen in equation 1,
measurement of the rotational constants, in essence, deter­
mines the moments of inertia.
A molecule's moments of iner­
tia are functions of the masses of the atoms (which are
known precisely), and the distribution of these atoms (bond
lengths and angles) with respect to the center of mass.
Thus three precise rotational constants may be sufficient
data to solve for the variables of a molecule's structure.
Often, though, there are more bond lengths and angles than
can be solved for with three data points, and it is neces­
sary to use isotopic substitution.
Since changing only the
mass of one atom will result in new moments of inertia this
gives an extra set of data points for each substitution.
This additional data is usually enough to solve for all the
variables (bond lengths and angles) in a molecule's struc­
ture.
In the case of the iodine fluorides, isotopic sub­
stitution was not possible, hence the study was only taken
as far as rotational and quadrupole coupling constants.
In
addition, as a true symmetric top, IF5 has a dipole along
only one axis, which means only one rotational constant
value can be found.
Another application of microwave systems like the one
used here is the study of weakly bound complexes (WBC's).
Weakly bound complexes are species such as van der Waal's
complexes.
The binding force in these cases is much, much
weaker than the force of the normal chemical bond.
This
means that the typical dissociation energy of a WBC is low
enough that they have negligible lifetimes at room tempera­
ture.
However, due to the rotational cooling that results
in the pulsed-beam, weakly bound complexes will form with
enough longevity to be observed.
The high sensitivity of
the instrument also aids in the study of such species.
The
complex HC1...NN0 is a WBC, the study of which is still in
progress, due to complications which are discussed below.
CHAPTER IX: EXPERIMENTAL
Sample Handling
The gas manifold is shown in figure I.
stainless steel.
All parts are of
The manifold is pumped out by a rough pump
through the lowermost port, and the remaining four ports are
used for gas input.
These four ports all have swagelock
fittings to accommodate lecture bottles or the carrier gas
line.
One port is commonly used for a line which connects,
by means of a simple "T", to either an Argon or a Neon
cylinder.
For work where weakly bound complexes are
studied, a lecture bottle of each constituent is attached to
an available port.
The system contains both a one liter
side tank and a half liter tank in line to the pulsed valve
(not shown).
The two tanks are wrapped in heating tape to
aid in working with less volatile species, and when pumping
out the system.
A pressure gauge is used to guide the making of gas mix­
tures.
For the iodine fluorides, a mixture of slightly less
than one percent in carrier gas (Argon was used) was found
to give a better signal strength than a more concentrated
mixture.
For complexes, a one to two percent mixture of
each component in the carrier gas is common.
The pressure
in the manifold is usually raised to one atmosphere or
•TD PULSED VALVE
1 UTER TANK
CARRIER GAS
<Ar OR Ne)
GAS A
GAS 8
slightly higher with the carrier gas.
However, the mixture
is introduced into the system until the manifold pressure
drops to approximately four hundred torr.
Furthermore, the
mixture is usually diluted with Ar back up to the starting
pressure two or three times.
No loss of signal strength is
commonly observed with these dilutions.
When the signal
finally falls off, a new mixture is made.
Between studying
different gases, the system is pumped down and heated at
least several hours, if not overnight.
The pulsed valve sends the gas pulses into the resonant
microwave cavity, inside a vacuum chamber.
The vacuum cham­
ber is evacuated to the microtorr range by a ten inch diffu­
sion pump with a mechanical backing pump.
After passing
through the chamber gases are exhausted through the
building's fume hood system.
There is one other aspect of the gas handling system,
which becomes important when complexes are being studied.
Since the gas mixture for a typical complex contains con­
stituent A, constituent B, and the carrier gas, any combina­
tion of these three species may complex and add to the ob­
served transitions.
Considering that species have been ob­
served containing four constituents (though this is statis­
tically unlikely), the possible complications can be great.
To help alleviate this problem, each recorded signal is gas
tested.
This process involves putting in mixtures of A and
B with a different carrier gas (Ne is usually used for this,
while Ar is used for scanning); and also putting in mixtures
of only one constituent at a time with the carrier gas.
If
the signal is still present in the former case, it provides
evidence (though not conclusive) that the signal belongs to
the complex of interest.
If the signal is still present in
the latter case, it generally proves that the transition
belongs to a different species.
Instrumental
The instrument used for this work was a pulsed-beam,
fourier transform, microwave spectrometer.
Its basic set up
is shown in figure II; instrumental operating parameters are
listed in table I.
The operating range of the instrument is
four to eighteen gigahertz.
This range is divided into
three bands: four to eight GHz (C-band); eight to twelve GHz
(X-band); and twelve to .eighteen GHz (Ku-band).
The oscil­
lators and waveguide used in the system are band specific,
so to change between bands requires switching these com­
ponents.
To facilitate this procedure, the necessary com­
ponents are mounted on sections of plywood, one for each
band.
Changing bands can be accomplished in about fifteen
minutes.
Operation of the spectrometer is as follows.
The frequency of interest is generated by the stimulat­
ing oscillator ("stimul. osc" in illustration).
This is a
YIG tuned Gunn diode oscillator for X- and Ku-bands, and a
YIG tuned transistor oscillator for C-band.
The stimulating
oscillator is phase locked twenty megahertz above the har-
STIMUL.
DSC.
PIN1
IBM PC
SCDPE
PIN2
MOLECULAR
FREQUENCY
LOCAL
OSC.
20MHz +/FID
AMP
FID
(0-1
MHz)
20 MHz REFERENCE
AMP
TWR
Table I
INSTRUMENTAL OPERATING PARAMETERS
Operating Range
4 - 1 8 GHz
Resolution
10 - 30 kHz
Precision
+/- 5 kHz
Bandwidth
1 MHz
Optimal Scan Rate
3 0 MHz/hr.
Sensitivity(per rotational state)
1 x 1014 molecules
Gas Pulse Rate
0.5 - 5 HZ
Rotational Temp in Beam
<20 K
Digitizing Rate
20 MHz
monic of a stable frequency which is generated by a program­
mable, crystal source frequency synthesizer (not shown).
The frequency from the stimulating oscillator is sent to
three locations: a frequency counter (not shown), to monitor
it precisely; the resonant cavity (discussed later); and a
second phase lock loop with another oscillator of the same
type ("Local osc").
Part of the signal from this local os­
cillator is mixed with the stimulating frequency to produce
a twenty megahertz reference signal which will be important
later.
The part of the stimulating frequency that was sent to
the sample cavity goes through a diode switch ("PINl"), and
then a circulator which sends it to an antenna inside a
Fabry-Perot cavity.
The cavity is tuned by moving the mir­
ror opposite the antenna.
Before the signal coming out of
the cavity gets to the main detection system, part of it is
split off and sent to a monitoring oscilloscope (not shown).
Using the signal on this scope, it is possible to tune the
cavity to produce the least reflection of signal.
Once the cavity is tuned, the actual experiment begins.
The instrument is controlled by an adjustable pulse genera­
tor.
The pulse time sequence is shown in figure III.
The
first of four pulses goes to the gas valve that lets the gas
into the chamber from the manifold.
The backing pressure on
this nozzle is approximately one atmosphere.
The chamber is
evacuated to the microtorr range by a ten inch diffusion
pump.
pulse.
This results in a supersonic expansion of the gas
The resultant cooling achieves a rotational tempera­
ture of less than twenty Kelvin.
After the gas pulse has had time to reach the central
region of the cavity (seventy-five microseconds to three
milliseconds), the second control pulse is sent to the diode
switch, PIN1.
This lets in a pulse of microwaves from the
stimulating oscillator lasting from one tenth to ten
microseconds.
A delay of from one tenth to fifteen
microseconds exists before the next microwave pulse, so that
the initial stimulating pulse can die down.
The third of the four pulses goes to the diode switch,
PIN2.
This lets the emission signal from the cavity (less
ten percent that goes to the oscilloscope used for tuning)
through to the detection system.
If the stimulating fre­
quency was within a few hundred kilohertz of a transition
frequency for the sample, the outgoing signal will be the
original stimulating frequency plus or minus the offset from
the exact transition frequency.
If no transition was near
the stimulating frequency, the signal out will be the same
as the signal in.
After passing through the PIN2 switch,
the signal is mixed with the local oscillator frequency,
which results in a twenty megahertz signal plus or minus any
offset from a possible transition.
is more easily amplified.
This new lower frequency
After amplification, it is mixed
once again, this time with the twenty megahertz reference
21
LJLJ
Ld
CxD 1
CD
LDQ_
00
z:i
£L
Figure III: Timing Diagram of Pulse Sequences
signal generated earlier.
The result is that only the off­
set frequency (if any) remains.
This is amplified and
detected, then sent to a transient waveform recorder("TWR").
The fourth and final control pulse triggers the TWR to
receive the signal.
The TWR sends the analog signal to an
oscilloscope for viewing, and also digitizes the signal to
be sent to an IBM PC for signal averaging and recording.
Data Treatment
When a transition occurs in the sample, a superposition
of rotational states has been created by the stimulating
radiation.
The excited molecules relax, and the emission
signal decays with time.
The signal is referred to as a
free induction decay (FID).
An example of one of the FID
signals found for IF5 is- shown in figure IV.
This signal
was digitized by the TWR and sent to the IBM PC, where it
was averaged.
The actual signal was averaged for about two
minutes to achieve the signal to noise ratio shown.
The gas
valve is opened only on every other pulse sequence, and the
computer subtracts the alternate signals to improve the sig­
nal to noise ratio.
This signal represents fifty gas
pulses, therefore it is approximately seven times stronger
than the original emission.
This signal (figure IV) shows the interesting feature of
a second signal superimposed on the first.
If one tran­
sition were present, the signal would be an exponentially
damped sinusoidal curve.
Close examination of the illustra-
*T1
<>q
n
a
£
I
—1
t
fD
bd
i—i
tn
w
H'
<ra
3
fa
0
8
16
X
JJ_
24
32
40
TIME IN MICROSECONDS
48
ro
tri
tion will show a second sinusoidal curve of lower intensity
superimposed upon the main FID.
This indicates a second
transition frequency lies slightly further away from the
stimulating frequency, but still within the bandwidth of the
instrument.
After a reasonable signal to noise ratio is achieved,
the signal is recorded on a floppy disk.
Once a number of
signals have been compiled, they are, in turn, run through a
fast fourier transform (FFT) program.
This converts the
signal from the time domain, as it is recorded, to the fre­
quency domain.
figure V.
The FFT of the example signal is shown
in
It does indeed show the two transitions indicated
by the FID.
The two transitions were assigned the quantum
numbers shown in accord with prior predictions (see chapter
III, section 2).
It can be seen that the frequency scale on the horizon­
tal axis of figure V is rather low.
This is because the
frequencies shown are the offset frequencies with respect to
the stimulating oscillator rather than the absolute fre­
quencies of the transitions.
This is due to the fact that
the FID signal is independent of whether it is above or
below the stimulating frequency.
To alleviate the uncer­
tainty, once a transition is found, the stimulating oscil­
lator is stepped up or down a few hundred kilohertz.
By
comparing a few FFT's from nearby frequencies, it is easy to
decide upon the location of the transition.
Figure V: Fourier Transform of Example Signal
The next step in the analysis is to assign quantum num­
bers to the transitions, based on spectral predictions.
These assignments are used as data points for a least
squares fitting program (see appendix).
The new values for
rotational constants output from the fitting program are
used to refine the spectral predictions.
This is an itera­
tive process, which becomes increasingly refined as more
transitions are located and recorded.
CHAPTER III: RESULTS AND DISCUSSION
Iodine Heptafluoride
The initial vibrational investigation^ of iodine hep­
tafluoride concluded that the molecule possessed D5tl sym­
metry.
For a seven-coordinated molecule such as this, a
pentagonal bipyrimidal structure would indeed be expected.
«•>
However, results of an electron diffraction study
suggested
that the equatorial fluorines were not exactly coplanar,
giving a distorted Dg^ symmetry.
This latter determination
was refuted by a later electron diffraction study4 which
supported the D5h symmetry model.
Another vibrational
study5 was done which also concluded Dg^ symmetry.
This was
not the end of the controversy, as yet another electron dif­
fraction paper6 returned to the distortion theory, and
reported angles of distortion for both the axial and
equatorial fluorines (see figure VI).
Furthermore, a subse­
quent vibrational study7 also agreed with the distortion
model, based on observed violations of selection rules for
vibrational combination bands.
In addition to these structural studies, a study was
done which confirmed the existence of slight polar
distortions®.
been obtained.
To date, though, no rotational spectrum had
Any dipole existing as a result of the above
28
Figure VI: Distorted Structure of IF^
mentioned distortions would be small, and the added com­
plications of hyperfine splitting might well have resulted
in signals too weak to be found.
As is shown by the FID
signal in figure VII, a weak signal can be observed.
This
FID signal was averaged for a much longer time than the IFg
example shown in the previous chapter.
Whereas the IF5 sig­
nal is shown approximately seven-fold enhanced, figure VII
shows an IF7 signal that has been enhanced twenty-fold.
corresponding fourier transform shown in figure
The
VIII is a
similarly weak but discernable signal.
The A, B, and C rotational constants for IFy were found
to be 1746(3) MHz, 1732.0(8) MHz, and 1553.0(2) MHz, respec­
tively.
The standard deviation for the fit was 0.459 MHz.
Table II gives the observed and calculated frequencies for
IF7.
Two comments need to be made regarding table II.
The
first is in regard to the number of transitions observed.
A
great deal of time was spent searching for additional tran­
sitions, but the search was eventually abandoned.
The dif­
ficulty in finding more than five signals was attributed to
the sample being used up.
IF7 is not currently commercially
available, and the special equipment necessary for fluorine
synthesis was unavailable to this author.
The second comment regards the two different measured
frequencies listed for the third transition.
an impurity in the IF7 sample used.
IFg exists as
A transition frequency
belonging to iodine pentafluoride lies very close to one
Figure VII: FID Signal From IF^ Spectrum
a
r»CM
CD
rv.
CD
LU
ZD
CJ
LU
ce
Lu
ui
CNJ
no
D
cn
Figure VIII: Fourier Transform of IFy FID
32
Table II
MEASURED AND CALCULATED TRANSITIONS FOR IF?
Calc. fMHzl
M-CCMHz}
J
9504.338(11)
9503.748
0.590
9504.372(5)
9504.507
10951.517(3)
10951.568(3)
10951.545
Measured(MHz!
Kn
J' K ' K '
2
E
1
2
-0.135
2
0
Tl
-0.028
0.023
2
12610.003(3)
12610.170
-0.167
12610.033(3)
12610.197
-0.164
Kn
3
E
1
3
2
3
0
3
0
2
3
2
1
3
1
3
4
1
4
3
0
3
4
0
4
belonging to iodine heptafluoride.
observed and resolved.
Both transitions were
Unfortunately, my predictions were
not precise enough to assign either to one or the other
molecule.
This transition was left out of the IF5 fit, but
was due to lack of data, no fit was done for IF7.
There are conclusions which can be drawn from this
study, however.
It is further confirmation that IF7 does
distort to a slightly polar configuration.
Also, consider­
ing the agreement between the data and the predictions based
on the work of Adams et al.6, it gives additional support to
their structure.
Finally, note should be made that these
predictions included no quadrupole coupling.
Again, con­
sidering the agreement with the data, it is possible that
the high symmetry of the molecule produces an extremely
small potential field gradient, q.
This would result in an
analogously small quadrupole coupling constant, eqQ, which
could produce splitting too small to be observed.
Iodine Penatfluoride
As mentioned above, iodine pentafluoride existed as an
impurity in the IF^.
Unlike IF7, however, IFg has a strong
dipole moment (see figure IX), and has been the object of
two previous microwave studies9'10.
As summarized in table
III, these two studies showed some disagreement, as well as
limited resolution in determining the quadrupole coupling
constant.
The results of this study agree more closely with
the results of the later of the two previous studies, though
in
o\
o
Figure IX: Structure of IFg
Table III
COMPARISON OF IF5 CONSTANTS WITH PREVIOUS STUDIES
CONSTANT:
Bp(MHz)
eaO fMHz)
Bradley et al.
2727.551(46)
1056.6(4.9)
Truchetet
et al.
2727.4217(10)
1067(10)
Present Work
2727.421(3)
1069.35(13)
36
TABLE IV
MEASURED AND CALCULATED TRANSITIONS FOR
MEASURED fMHz)
CALCULATED f MHz ^
M-C(MHz)
IF 5
F
F'
K
(J: 0-1 transitions)
5402.600
.042806
5627.491
.000179
5/2
5/2
7/2
5/2
0
0
10887.256(2)
10868.576(4)
10845.688(3)
10846.056(3)
10730.954(5)
10817.854(33)
10923 .636(8)
10960.881(8)
10983 .124(4)
11034.903(4)
11042.716(4)
11062.809(1)
(J: 1-2 transitions)
10887.208
.047903
10868.543
.032462
10845.734
-.046507
10846.008
.047952
10731.007
-.053618
10817.895
-.041179
10923.703
-.067212
10960.938
-.057061
10983.140
-.016164
11034.918
-.015770
11042.786
-.070807
11062.771
.037552
7/2
5/2
3/2
7/2
3/2
5/2
7/2
5/2
3/2
5/2
7/2
5/2
9/2
7/2
1/2
9/2
1/2
5/2
5/2
3/2
3/2
5/2
5/2
7/2
0
0
0
1
1
0
1
1
0
1
0
1
16293.898(1)
16332.344(5)
16336.401(6)
16341.737(8)
16343.116(6)
16352.022(3)
16378.802(7)
16406.845(10)
(J: 2-3 transitions)
16293.928
-.030318
16332.366
-.022708
16336.350
.050043
16341.703
.033183
16343.153
-.037983
16351.969
.052429
16378.756
.045795
16406.814
.030151
5/2 5/2
5/2 5/2
9/2 11/2
7/2 9/2
7/2 7/2
9/2 11/2
7/2 9/2
5/2 7/2
0
1
1
0
0
0
1
1
5402.643(6)
5627.492(5)
with much better resolution of eqQ.
The observed and calcu­
lated transition frequencies are listed in table IV.
The
overall standard deviation of the fit is .046 MHz.
HC1...NNO
The final species studied in this thesis is the weakly
bound complex of hydrogen chloride with nitrous oxide.
As
explained in chapter I, WBC's are transitory species at room
temperature, but are fairly long-lived in our vacuum chamber
where the molecular beam is expanding.
The work on this
complex is part of a collaborative effort of the Kukolich
research group at the University of Arizona.
The transi­
tions which have been observed so far are listed in table
V.
No definite assignments have been made for these transitions
as of yet.
The difficulty arises from two factors, both due
to the chlorine atom.
The first is that the isotope
fairly abundant with respect to
35 C1
37 C1
is
(approximately a 1:3
ratio). This produces a second set of transitions for the
") —t
H CI...NNO complex which are difficult to distinguish from
close-lying H35C1...NN0 transitions.
is the quadrupole moment of the
The second difficulty
chlorine atom.
This
produces splittings which make the assignment of quantum
numbers to the observed transitions extremely difficult.
An interesting side note to this study is the discovery
of what appears to be a trimer species.
When the gas test
procedure described in chapter II was applied to the transi­
tions listed in table VI, the initial results indicated they
Table V
OBSERVED TRANSITIONS IN THE SPECTRUM
THE COMPLEX HC1...NNO (MHz^
11426.421(5)
11771.343(10)
11773.655(3)
11776.468(25)
11777.858(2)
11784.271(16)
11785.373 (3)
11800.000(17)
11801.793(8)
Table VI
OBSERVED TRANSITION FREQUENCIES
OF UNKNOWN TRIMER fMHz)
7695.748(4)
7695.896(3)
7700.700(10)
11471.613(6)
15312.304(10)
15375.462(6)
recquired HC1, NNO, and Ar to be present.
Later tests with
high purity argon did not show a transition, yet the signal
returned when the initial argon cylinder was used.
Multiple
attempts with HC1, NNO, and high purity argon revealed no
signal.
Yet the signal was present when a small amount of
air from the lab was allowed into the mixture.
This result
is reasonable, considering that Ar is distilled from liquid
air, and could likely contain other atmospheric components.
The transitions listed in table VI seem to definitely belong
to a trimer of HC1, NNO, and a third constituent.
APPENDIX: FITTING PROGRAM
This program is adapted from the fitting program that
the our group uses for asymmetric tops.
There are
only minor changes in the main program.
The important dif­
ference is in the subroutines which provide the calculated
energies.
These, too, are modifications to existing
software.
I am unsure as to the origins of the various
pieces of programs used.
I have adapted and configured
them to do the job of fitting the hyperfine structure
of a symmetric top molecule with only one nuclear spin.
The actual code is fairly well commented.
$DEBUG
$LARGE
$NOFLOATCALLS
C
THE FOLLOWING PROGRAM WILL FIT THE HYPERFINE STRUCTURE
OF A
C
SYMMETRIC TOP (ONE NUCLEAR SPIN); IT WAS CREATED BY
MODIFYING
C
THE PROGRAM "FITSPEC" (USED FOR ASYMMETRIC TOPS)
IMPLICIT REAL*8(A-H,0-Z)
REAL*8 JACOB
CHARACTER*79 TITLE1,TITLE2,TITLE3
CHARACTER*15 PNAMES,VNAMES
CHARACTER*1 HOW,IFPROP,IHOW
DIMENSION
ALPHA(21,1),DELTAA(21,1),Y(150),Y0(150),YP(150),
1JAC0B(150,21),TJAC0B(21,150),W(150),XINV(21,21),PNAM­
ES(21),
2AINC(21),HOW(21),EVECT(150,1),TEMP(21,150),V(21,21),ASAVE(21),
3 DSAVE(21),IQNUMS(150,5),C0RRM(21,21),ALLVAR(21),VNAM­
ES(21), 4IFFIT(21)
C THIS VERSION ALLOWS 21 PARAMETERS AND 150 DATA PT. MAX.
C PROGRAM TO PERFORM GENERALIZED NON-LINEAR LEAST SQUARES
FIT BY THE JACOBIAN
C METHOD. SEE HYUNYONG KIM, J. CHEM. ED., VOL.47, pp. 120122 (1970).
C ALLVAR IS THE MATRIX OF VARIABLES SENT TO THE SUBROUTINE
FSUB FOR
C CALCULATION OF THE Y VALUES. ALPHA IS THE MATRIX OF
PARAMETERS OUT OF
C ALLVAR WHICH ARE ACTUALLY BEING FIT, DELTAA IS THE MATRIX
OF CORRECTIONS
C TO THE PARAMETERS, Y IS THE MATRIX CONTAINING THE DATA AS
READ IN, YO
C IS THE MATRIX CONTAINING THE CALCULATED VALUES COR­
RESPONDING TO Y, WITH
C THE CURRENT VALUES OF ALPHA, YP IS THE MATRIX CONTAINING
CALCULATED Y'S
C FOR USE IN CALCULATING THE DERIVATIVES, JACOB IS THE
JAC0BIAN MATRIX
C CONTAINING THE DERIVATIVE OF EACH Y WITH RESPECT TO EACH
PARAMETER,
C TJACOB IS JACOB'S TRANSPOSE, W IS THE MATRIX CONTAINING
THE WEIGHTS OF
C EACH Y, XINV IS A MATRIX USED FOR STORING THE INVERSE OF
• JACOB*TJACOB
C PNAMES IS A MATRIX CONTAINING THE NAMES OF THE PARAMETERS
IN ALPHA, AINC
C IS THE MATRIX CONTAINING THE INCREMENTS TO USE ON ALPHA
WHEN CALCULATING
C THE DERIVATIVES, HOW IS A MATRIX TO INDICATE HOW TO CAL­
CULATE AINC,
C EVECT IS THE ERROR VECTOR ORC Y-YO, TEMP IS A TEMPORARY
MATRIX NEEDED IN
C THE CALCULATIONS, V IS THE VARIANCE-COVARIANCE MATRIX AND
CORRM IS THE
C MATRIX OF CORRELATION COEFFICIENTS.
C LAST MODIFIED 4/21/88 TO GET WEIGHTING CORRECR FOT CAL­
CULATION OF STD.
C DEVIATIONS OF PARAMETERS. LAST MODIFIED 7/29/89 TO
OPERATE WITH
C HYPERFINE STRUCTURE FOR A SYMMETRIC TOP.
C
C SET MAX. NUMBER OF PARAMETERS AND DATA PTS. POSSIBLE W/
ABOVE DIMENSIONS
MAXPS=21
MAXDPS=150
OPEN(5,FILE='SYMFIT.IN',STATUS='OLD')
OPEN(6,FILE='SYMFIT.OUT',STATUS='NEW')
C INITIALIZATION
C
SSOLD=l.0D16
KOUNT=0
Z=O.ODO
DO 30 1=1,MAXPS
DSAVE(I)=Z
ASAVE(I)=Z
10
20
30
ALLVAR(I)=Z
IFFIT(I)=0
ALPHA(I,1)=Z
DELTAA(1,1)=Z
AINC(I)=Z
DO 10 J=1,MAXPS
CORRM(I,J )=Z
V(I,J)=Z
XINV(I,J)=Z
DO 20 J=1,MAXDPS
TEMP(I,J)=Z
JACOB(J,I)=Z
TJACOB(I,J)=Z
CONTINUE
DO 40 J=1,MAXDPS
W(J)=Z
EVECT(J,1)=Z
Y(J)—Z
Y0(J)=Z
YP(J)=Z
DO 40 1=1,10
IQNUMS(J,I)=0
40
C
C INPUT SECTION
C DATA FILE SHOULD CONSIST OF THE FOLLOWING:
C LINES 1-3 TITLE LINES .79 CHARS OR LESS EACH
C LINE 4: THE NUCLEAR SPIN IN UNITS OF 1/2
C LINE 5: THE NUMBER OF CYCLES THE FIT SHOULD RUN - INTEGER
FREE FORMAT
C LINE 6: THE NUMBER OF VARIABLES TO BE FIT,"NVARS" - IN­
TEGER FREE FORMAT
C
NOTE- THIS INCLUDES BOTH THE FIXED AND FIT VARI­
ABLES.
C
C NVARS LINES
C EACH LINE CONTAINING FIVE ITEMS;
C
1) THE PARAMETER NAME (15 CHARS OR LESS),
C
2) THE INITIAL VALUE OF THE PARAMETER - REAL FREE FOR­
MAT;
C
3) HOW TO INCREMENT THE PARAMETER - IF AN P IS HERE,
THE PARAMETER WILL
C BE INCREMENTED A PROPORTIONAL AMOUNT FOR TAKING THE DERVIVATIVE. IF AN F
C IS HERE, THE PARAMETER WILL BE INCREMENTED BY A FIXED
AMOUNT. 1 CHARACTER.
C
4) THE FRACTION OR FIXED AMMOUNT TO INCREMENT THE
PARAMETER WHEN
C CALCULATING DERIVATIVES. REAL - FREE FORMAT.
C
5) A 1 TO INDICATE THAT THIS VARIABLE WILL BE FIT.
OTHERWISE, VARIABLE
C WILL BE HELD FIXED TO THE VALUE INPUT - INTEGER FREE FOR­
MAT
C
C THE NUMBER OF DATA PTS. "NDPTS" AND THE NUMBER OF QUANTUM
NUMBERS "NQNUMS"
C FOR EACH DATA POINT - 2 INTEGERS FREE FORMAT (THIS VER­
SION OF THE PROGRAM
C IS DESIGNED FOR FIVE QUANTUM NUMBERS: J,J',F,F',K
C
C NDPTS LINES
C EACH LINE CONTAINS FOUR ITEMS;
C
1) THE DATA POINT - REAL FREE FORMAT
C
2) NQNUMS MANY QUANTUM NUMBERS (F IN UNITS OF 1/2)- IN­
TEGERS FREE FORMAT
C
3) A 'Y' IF PROPORTIONAL FITTING IS DESIRED - 1 CHAR.
FREE FORMAT
C
4) A WEIGHT OF THE DATA PT. - REAL FREE FORMAT
C
READ( 5,*)TITLE1
READ(5,*)TITLE2
READ( 5,*)TITLE3
WRITE(6,1)TITLE1,TITLE2,TITLE3
READ(5,*)ISPIN
WRITE(6,*)'THE NUCLEAR SPIN INVOLVED IS: ',ISPIN,'/2'
WRITE(6,*)
WRITE( 6 , * ) ' THE FOLLOWING VARIABLES WERE FIXED DURING THE
FIT 7
WRITE(6,51)
READ(5, *)KMAX
READ(5,*)NVARS
NPARMS=0
C READ IN VARIABLES AND ASSIGN FIT ONES TO ALPHA
DO 50 1=1,NVARS
READ(5,*) VNAMES(I),ALLVAR(I),IHOW,AINCR,IFFIT(I)
IF( IFFIT(I).EQ.1) THEN
NPARMS=NPARMS+1
PNAMES(NPARMS)=VNAMES(I)
ALPHA(NPARMS,1)=ALLVAR(I)
HOW(NPARMS)=IHOW
AINC(NPARMS)=AINCR
ELSE
WRITE(6,61) VNAMES(I),ALLVAR(I)
ENDIF
50 CONTINUE
WRITE(6,*)
READ(5,*) NDPTS,NQNUMS
DO 60 1=1,NDPTS
READ(5,*) Y(I),(IQNUMS(I,J),J=1,NQNUMS),IFPROP,W(I)
60
IF(IFPROP .EQ. 'Y') W(I)=W(I)/Y(I)
C CALCULATE YO
65 CALL
ASSIGN(MAXPS,ALLVAR,ALPHA,VNAMES,PNAMES, NVARS,NPARMS,
1IFFIT)
CALL
SYMFTSUB(MAXPS,MAXDPS,NDPTS,NPARMS,ALLVAR,YO,IQNUMS,ISPIN)
C CALCULATE JACOBIAN MATRIX "JACOB" AND ITS TRANSPOSE
DO 80 J=l,NPARMS
IF(HOW(J).EQ.'F') THEN
DELA=AINC(J)
ELSE
DELA=AINC(J)*ALPHA(J,1)
ENDIF
IF(DELA.EQ.O.ODO) DELA=1.0D-6
ALPHA(J,I)=ALPHA(J,1)+DELA
, CALL
ASSIGN(MAXPS,ALLVAR,ALPHA,VNAMES,PNAMES,NVARS,NPARMS,
1
IFFIT)
CALL
SYMFTSUB(MAXPS,MAXDPS,NDPTS,NPARMS,ALLVAR,YP,IQNU
MS,ISPIN) ALPHA(J,1)=ALPHA(J,1)-DELA
DO 70 1=1,NDPTS
JACOB(I,J)=(YP(I)—Y 0(1))/DELA
70
TJACOB(J,I)=JACOB(I,J)*W(I)
80 CONTINUE
C CALCULATE ERROR VECTOR
DO 90 1=1,NDPTS
90
EVECT(I,1)=Y(I)-YO(I)
C
C DO PRESCRIBED MATRIX OPERATIONS
C123456789123456789212345678931234567894123456789512345678
CALL
MMULT(MAXPS,MAXDPS,MAXDPS,MAXPS,MAXPS,MAXPS,NPARMS,N
.DPTS,
1NPARMS,TJACOB,JACOB,XINV)
CALL MTRXIN(MAXPS,XINV,NPARMS)
CALL
MMULT(MAXPS,MAXPS,MAXPS,MAXDPS,MAXPS,MAXDPS,NPARMS,NPARMS,
1NDPTS,XINV,TJACOB,TEMP)
CALL
MMULT(MAXPS,MAXDPS,MAXDPS,1,MAXPS,1,NPARMS,NDPTS,1,TE
MP, 1EVECT,DELTAA)
C CALCULATE VARIANCE OF OVERALL FIT
SS=0.0D0
WNDPTS=0.0D0
DO 100 1=1,NDPTS
WNDPTS=WNDPTS+W(I)
100
SS=SS+(Y(I)-YO(I))*(Y(I)-YO(I))*W(I)
SS=SS/(DBLE(NDPTS)-DBLE(NPARMS))
SDEV=DSQRT(SS)
C CALCULATE THE VARIANCE-COVARIANCE MATRIX.
45
DO 110 1=1,NPARMS
DO 110 11=1/NPARMS
110
V(I,II)=SS*XINV(I,II)
C CHECK FOR DIVERGENCE
IF(SS.GT.SSOLD) GO TO 1000
C RESET NO DIVERGENCE SWITCH
IDIV=0
C THIS IS CONVERGING BUT NOT YET DONE
SSOLD—SS
CALL
OUTPUT(Y,YO,ALPHA,KOUNT,SDEV,V,MAXDPS,MAXPS,NDPTS,NPARMS,
1PNAMES,IQNUMS,NQNUMS,W)
C CORRECT ALPHAS BUT SAVE ALPHA'S AND CORRECTIONS IN CASE A
DAMPENED FIT
C IS DESIRED ON NEXT CYCLE
DO 120 1=1,NPARMS
ASAVE(I)=ALPHA(I,1)
DSAVE(I)=DELTAA(1,1)*0.1D0
120 ALPHA(1,1)=ALPHA(1,1)+DELTAA(1,1)
C CHECK FOR TOO MANY ITERATIONS
IF(KOUNT.EQ.KMAX) GO TO 1200
KOUNT=KOUNT+1
C RE-ITERATE FOR NEW ALPHAS
GO TO 65
C
C SECTION FOR DIVERGENCE - WILL ATTEMPT DAMPENED FIT
C CHECK TO SEE IF DAMPENED FIT HAS BEEN ATTEMPTED ON PREVI­
OUS CYCLE
1000 IF(IDIV.NE.0) GO TO 1300
IDIV=1
WRITE(6,*)
WRITE(6,*) 7 ***** CAUTION ATTEMPTING DAMPENED FIT!
***** ' DO 1010 1=1,NPARMS
1010
ALPHA(1,1)=ASAVE(I)+DSAVE(I)
GO TO 65
C
C TOO MANY ITERATIONS SECTION
C
1200 WRITE(6,31) KMAX
GO TO 1500
C
C DIVERGENT EVEN AFTER DAMPENED FIT
C
1300 WRITE(6,*) ' FIT STOPPED DUE TO DIVERGENCE EVEN THOUGH
r
1'DAMPENED FIT HAS BEEN TRIED.'
WRITE(6,*)
C
C ALL DONE SECTION
C
C CALCULATE AND OUTPUT CORRELATION MATRIX
1500 DO 1505 1=1,NPARMS
DO 1505 J=1,NPARMS
CORRMfl,J)=0.0D0
1505
CORRMfl,J)=DSQRT((V(I,J)*V(I,J))/(V(I,I)*V(J,J)))
WRITE(6,*)
WRITE(6,*) ' CORRELATION MATRIX '
WRITE(6,*)
DO 1507 1=1,NPARMS
1507 WRITE(6,11)PNAMES(I),(CORRM(I,J),J=1,NPARMS)
WRITE(6,*)
WRITE(6,41)
DO 1510 1=1,NPARMS
DO 1510 J=l,NDPTS
1510
WRITE(6,21)Y(J),ALPHA(I,1),JACOB(J,I)
1 FORMAT(/A79,/A79,/A79/)
11 FORMAT(IX,A15,15F8.4)
21 FORMAT(IX,F20.10,IX,G20.10,IX,F15.5)
31 FORMAT(IX,/' FIT STOPPED BECAUSE',13,' ITERATIONS
HAVE BEEN', 1' COMPLETED. FIT MAY NOT',/' YET HAVE
CONVERGED TO THE BEST', 2' POSSIBLE VALUES.')
41 FORMAT(8X,'DATA PT.',12X,'PARAMETER',12X,'DERIVATIVE')
51 FORMAT(//' VARIABLE',15X,' FIXED AT ')
61 FORMAT(IX,A15,3X,G20.10)
END
SUBROUTINE
OUTPUT(Y,YO,ALPHA,KOUNT,SDEV,V,MAXDPS,MAXPS,NDPTS,
1NPARMS,PNAMES,IQNUMS,NQNUMS,W)
IMPLICIT REAL*8(A-H,0-Z)
CHARACTER*15 PNAMES
DIMENSION
Y(MAXDPS),Y0(MAXDPS),ALPHA(MAXPS,1),V(MAXPS,MAXPS)
DIMENSION PNAMES(MAXPS),IQNUMS(MAXDPS,10),W(MAXDPS)
WRITE(6,1) KOUNT
DO 10 1=1,NPARMS
SDA=DSQRT(V(I,I))
10
WRITE(6,11)1,PNAMES(I),ALPHA(1,1),SDA
WRITE(6,21)SDEV
WRITE(6,31)
DO 20 1=1,NDPTS
RESID=Y(I)-YO(I)
20
WRITE(6,41)Y(I),W(I),Y0(I),RESID,(IQNUMS(I,J),J=1,NQNUMS)
1
FORMAT(IX,'***********************************************—
**' f
******************************'
2//' ITERATIVE CYCLE # ',12//'
3 'STD. DEV.')
#
PNAME',20X,'VALUE',15X,
11 FORMAT(IX,I2,2X,A15,2X,G20.10,2X,G20.10)
21 FORMAT(//IX,' WEIGHTED STD. DEV. OF OVERALL FIT=
',G30.5//) 31 FORMAT(//6X,'DATA POINT',IX,'
WT.
',7X,'CALC,15X,'RESID', 16X,'QUANT. NOS.')
41 FORMAT(IX,F15.6,IX,F8.3,IX,F15.6,IX,F15.6,10I3)
RETURN
END
C
C
SUBROUTINE
ASSIGN(MAXPS,ALLVAR,ALPHA,VNAMES,PNAMES,NVARS,NPARMS
1IFFIT)
C SUBROUTINE TO ASSIGN THE FIT VARIABLES "ALPHA" TO THE
VARIABLES USED
C IN THE FUNCTION (OR CALLED BY ) FSUB.
IMPLICIT REAL*8(A-H,0-Z)
CHARACTER*15 VNAMES,PNAMES
DIMENSION VNAMES(MAXPS),PNAMES(MAXPS),ALLVAR(MAXPS)
1ALPHA(MAXPS,1),IFFIT(MAXPS)
NUMP=0
DO 10 1=1,NVARS
IF(IFFIT(I).EQ.1) THEN
NUMP=NUMP+1
ALLVAR(I)=ALPHA(NUMP,1)
ENDIF
10 CONTINUE
RETURN
48
This part of the program is the subroutine that outputs
the transition frequencies according to the assignments of
the input data points (measured transitions).
$LARGE
$NOFLOATCALLS
SUBROUTINE
FSUB(MAXPS,MAXDPS,NDPTS,NPARMS,ALLVAR,Y,IQNUMS)
IMPLICIT REAL*8(A-H,0-Z)
INTEGER EINDEX,OFFSET
DIMENSION ALLVAR(MAXPS),Y(MAXDPS),IQNUMS(MAXDPS, 10)
DIMENSION E(452)
AEFF=ALLVAR(1)
BEFF=ALLVAR(2)
CEFF=ALLVAR(3)
DELTJ=ALLVAR(4)
DELTJK=ALLVAR(5)
DELTK=ALLVAR(6)
DELJ=ALLVAR(7)
DELK=ALLVAR(8)
HJ=ALLVAR(9)
HJK=ALLVAR(10)
HKJ=ALLVAR(11)
HK=ALLVAR(12)
SHJ=ALLVAR(13)
SHJK=ALLVAR(14)
SHK=ALLVAR(15)
JMIN=20
JMAX=0
DO 10 1=1,NDPTS
IF(JMIN.GT.IQNUMS(1,1)) JMIN=IQNUMS(1,1)
IF(JMIN.GT.IQNUMS(1,4)) JMIN=IQNUMS(1,4)
IF(JMAX.LT.IQNUMS(1,1)) JMAX=IQNUMS(1,1)
10
IF(JMAX.LT.IQNUMS(I,4)) JMAX=IQNUMS(1,4)
IF(JMIN.LT.1) JMIN=1
OFFSET=(JMIN)*(JMIN)-1
WRITE(*,*) ' CALLING DASYME '
CALL
DASYME(JMIN # JMAX,AEFF,BEFF,CEFF,DELTJ,DELTJK,DELTK,DELJ,
1DELK,HJ,HJK,HKJ,HK,SHJ,SHJK,SHK,E,ME)
DO 20 1=1,NDPTS
J=IQNUMS(1,1)
KP=IQNUMS(1,2)
K0=IQNUMS(1,3)
EINDEX=(J+1)**2-J+KP—KO-OFFSET
EG=E(EINDEX)
J=IQNUMS(I,4)
KP=IQNUMS(1,5)
K0=IQNUMS(1,6)
EINDEX=(J+1)**2-J+KP—KO-OFFSET
EU=E(EINDEX)
Y(I)=DABS(EU—EG)
RETURN
END
This last part of the program is the subroutine which
calculates the energies of the specified levels.
it is a
modified version of the program, "symtop.for", which can be
found in the Kukolich lab.
Again, I do not know how many
modifications to the original code that "symtop.for" repre
sents.
I have deleted all extraneous I/O statements, and
completely eliminated the section that calculated transi
tion frequencies.
It is more efficient to have the
preceeding subroutine calculate only the specified transi
tions, as opposed to all within a given range.
$DEBUG
$STORAGE:2
$NOFLOATCALLS
$LARGE
SUBROUTINE
FTSYMNRG(B,DELTJ,DELTJK,DELTK,EQQ,DXZ,DXX,SA,SB,IS PIN,
1FMAX,KMIN,KMAX)
C PROGRAM TO CALCULATE ENERGIES FOR A SYMMETRIC TOP
MOLECULE WITH 1 NUCLEUS
C HAVING A SPIN BY EXACT DIAGONALIZATION OF THE HAMILTONIAN
MATRIX.
C INCLUDES DISTORTION,QUADRUPOLE,DISTORTION OF THE QUADRUPOLE AND SPIN ROT.
C H IS THE HAMILTONIAN MATRIX,EIGEN IS THE MATRIX OF EIGEN­
VECTORS,
C E IS THE MATRIX WHERE THE ENERGIES ARE STORED IN THE
E(J+1,2*F+1,K+1)
C FORMAT ( I.E. THE ENERGY FOR J=0,F=5/2,K=0 IS AT E(l,6,l)
),T IS A MATRIX
C CONTAINING THE TRANSITION FREQUENCIES AND IQN CONTAINS
THE CORRESPONDING
C QUANTUM NUMBERS IN THE ORDER J,J',F,F',K. ROGER BUMGARNER
AUG.,85.
C MODIFIED FOR K-LOOP 3-23-88 R.B.
IMPLICIT REAL*8(A-E,G-H,0-Z)
IMPLICIT INTEGER(F)
DIMENSION
H(12,12),EIGEN(12,12),E(40,40,6),IQN(200,5),T(200)
ISW1=0
MDIM=12
LDIM=40
1002
1003
1005
1004
JDIM=200
DO 1002 I=1,MDIM
DO 1002 J=1,MDIM
EIGEN(I,J)=0.ODO
H(I,J)=0.ODO
DO 1003 1=1,LDIM
DO 1003 J=l,LDIM
DO 1003 K=l,6
E(I,J,K)=0.ODO
DO 1004 I=1,JDIM
T(I)=0.ODO
DO 1005 J=l,5
IQN(I,J)=0
CONTINUE
XI=DBLE(I)/2.ODO
DO 2000 KI=KMIN,KMAX
KIND=KI+1
XK=DBLE(KI)
K=2*KI
FMIN=1
ITEST=(-1)**I
IF(ITEST.EQ.1) FMIN=0
DO 40 F=FMIN,FMAX,2
FIND=F+1
XF=DBLE(F)/2.ODO
JMIN=ABS(F-I)
IF(JMIN.LT.K)JMIN=K
JMAX=F+I
M=0
DO 20 J=JMIN,JMAX,2
XJ=DBLE(J)/2.ODO
M=M+1
MP=M-1
DO 10 JP=J,JMAX,2
XJP=DBLE(JP)/2.ODO
MP=MP+1
H(M, MP)=HAMIL( XI,XF,XJ,XJP,XK,B,DJ,DJK,DK,XA,DXZ,DXX,
1
SA,SB,ISW1)
H(MP,M)=H(M,MP)
10
CONTINUE
20
CONTINUE
IF(M.EQ.l) GO TO 25
CALL HDIAG(H,M,MDIM,0,0,EIGEN)
M=0
25
DO 30 J=JMIN,JMAX,2
JIND=J/2+l
M=M+1
E(JIND,FIND,KIND)=H(M,M)
WRITE(6,31) J,F,KI,H(M,M)
30
CONTINUE
31
FORMAT(IX, ' J=',12,'/2',3X,' F=',12,'/2',3X,7
K=',I3,3X,
1
' ENERGY(MHZ)= ',F15.5)
DO 35 L=1,MDIM
DO 35 LL=1,MDIM
35
H(L,LL)=0.0D0
40 CONTINUE
2000 CONTINUE
M—0
C CALCULATE TRANSITIONS FOR DELTA J=+l, DELTA F=-1,0,+1
,DELTA K=0
DO 3000 K=KMIN,KMAX
KIND=K+1
DO 60 F=FMIN,FMAX,2
FIND=F+1
FLIND=FIND-2
FUIND=FIND+2
FU=F+2
FI>F-2
JMIN=IABS(F-I)
IF(JMIN.LT.K)JMIN=K
JMAX=F+I
DO 50 J =JMIN,JMAX,2
IJ=J/2
IJP=IJ+1
JIND=J/2+l
JPIND=JIND+1
C DELTA F=0 TRANSITIONS
IF((E(JIND,FIND,KIND).EQ.0.0D0).OR.
1
(E(JPIND,FIND,KIND).EQ.0.0D0)) GOTO 45
M=M+1
T(M)=DABS(E(JPIND,FIND,KIND)-E(JIND,FIND,KIND))
IQN(M,1)=IJ
IQN(M,2)=IJP
IQN(M,3)=F
IQN(M,4)=F
IQN(M,5)=K
C DELTA F-+1 TRANSITIONS
45
IF((E(JIND,FIND,KIND).EQ.0.0D0).OR.
1
(E(JPIND,FUIND,KIND).EQ.0.0D0)) GO TO 46
M=M+1
T(M)=DABS(E(JPIND,FUIND,KIND)E(JIND,FIND,KIND))
IQN(M,1)=IJ
IQN(M,2)=IJP
IQN(M, 3)=F
IQN(M,4)=FU
IQN(M,5)=K
C DELTA'F-—1 TRANSITIONS
46
IF(FLIND.LT.l) GO TO 50
IF((E(JIND,FIND,KIND).EQ.O.0D0).OR.
1
(E(JPIND,FLIND,KIND).EQ.0.ODO)) GO TO 50
M=M+1
T(M)=DABS(E(JPIND,FLIND,KIND)E(JIND,FIND,KIND))
IQN(M,1)=IJ
IQN(M,2)=1JP
IQN(M, 3)=F
IQN(M,4)=FL
IQN(M,5)=K
50
CONTINUE
60 CONTINUE
3 000 CONTINUE
CALL ORD(JDIM,5,T,IQN,M)
END
C COMMENT FUNCTION TO CALCULATE HAMILTONIAN MATRIX ELEMENT
FUNCTION
HAMIL(XI,XF,XJ,XJP,XK,B,DJ,DJK,DK,X,DXZ,DXX,SA,SB,
1 ISW1)
C XI,XF,XJ,XJP,XK ARE THE REAL VALUES OF THE I,F,J,JP AND K
QUANTUM NUMBERS.
C B IS THE ROT. CONST, DJ IS THE DISTORTION CONST, X IS THE
QUADRUPOLE
C CONST, DXZ IS THE PARALLEL DISTORTION IN X, DXX IS THE
PERP. DISTORTION
C IN X AND A AND B ARE SPIN ROT CONSTS. ISW1 IS A SWITCH TO
CALCULATE
C ENERGIES TO FIRST ORDER ONLY. THIS IS JUST IN HERE AS A
LEARNING TOOL
IMPLICIT REAL*8(A-rH,0-Z)
IF(XJ.LT.XK)GOTO 3 0
S=XJ*(XJ+1.ODO)
C CALCULATE XA THE EFFECTIVE DISTORTED QUADRUPOLE STRENGTH
XFACT=1.ODO
IF((XJ.NE.0.0D0).AND.(XJ.EQ.XJP))XFACT=1.ODO3.0D0*XK*XK/S
XA-XFACT*(X+DXX*(S-XK*XK)+DXZ*XK*XK)
ER0T=0.ODO
EQUAD=0.ODO
ESPROT-O.ODO
C CALCULATE DISTORTED ROTOR ENERGY (DIAG IN J)
IF(XJ.EQ.XJP) EROT=B*S-DJ*S*S-DJK*S*XK*XKDK*XK*XK*XK*XK
XJTEST=DABS(XJ-XJP)
IF((XJTEST.NE.2.ODO).OR.(ISW1.EQ.1)) GO TO 10
C CALCULATE QUADRUPOLE ENERGY OFF DIAG BY 2 IN J
Y=3.0D0*XA/(16.ODO*XI*(2.0D0*XI1.ODO)*(2.0D0*XJ+3.ODO))
Z — (XI+XJ+XF+3.ODO)*(XI+XJ+XF+2.ODO)*(XI+XJ-XF+2.ODO)
Z=Z*(XI+XJ-XF+1.ODO)*(XJ+XF-XI+2.ODO)*(XJ+XFXI+1.ODO)
Z=Z*(XI+XF-XJ)*(XI+XF-XJ-
1.ODO)/(2.0D0*XJ+1.ODO)/(2.0D0*XJ+5.ODO)
XKSQ=XK*XK
XJ1=(XJ+1.ODO)*(XJ+1.ODO)
XJ2=(XJ+2.ODO)*(XJ+2.ODO)
Z=Z*(1.ODO-XKSQ/XJ1)*(1.0D0-XKSQ/XJ2)
EQUAD=EQUAD+Y*DSQRT(Z)
10 IF((XK.EQ.0.ODO).OR.(XJTEST.NE.1.ODO).OR.(ISW1.EQ.0))
GO TO 15
IF (XJ.EQ.O.ODO) GO TO 15
C CALCULATE QUADRUPOLE ENERGIES OFF DIAG IN J BY 1 FOR K'S
.NE. 0
C (SEE TOWNES AND SCHAWLOW PAGE 157)
EQUAD=3.ODO*XA*XK*(XF*(XF+1.ODO)-XI*(XI+1.ODO)XJ*(XJ+2.ODO))
EQUAD=EQUAD/(8.0D0*XI*(2.0D0*XI-1.ODO)*XJ*(XJ+2.ODO))
QSTUFF=(1.0D0(XK*XK/((XJ+1.ODO)*(XJ+1.ODO))))*(XI+XJ+XF+2.ODO)
QSTUFF=QSTUFF*(XJ+XF-XI+1.ODO)*(XI+XF-XJ)*(XI+XJXF+l.ODO)
QSTUFF=QSTUFF/( (2.0D0*XJ+1.ODO)*(2.0D0*XJ+3.ODO) )
QSTUFF=DSQRT(QSTUFF)
EQUAD=EQUAD*QSTUFF
C CALCULATE QUADRUPOLE AND SPIN ROTATION ENERGIES DIAG IN J
15 IF(XJ.NE.XJP)GO TO 20
S2=XI*(XI+1.ODO)
S3=XF*(XF+1.ODO)
C=S3—S2-S
C (C IS CASIMR'S COEF.)
S4=C*(C+1.0D0)
Z=(3.0D0/4.ODO)*S4—S2*S
Z=Z/(2.ODO*XI*(2.0D0*XI-1.ODO)*(2.ODO*XJ1.0D0)*(2.0D0*XJ+3.ODO))
EQUAD=-XA*Z
XPROD=Z*XFACT
WRITE(8,11)XJ,XF,XK,Z,XFACT,XPROD
11 FORMAT(IX,'J=',F3.1,' F=',F3.1/' K=',F3.1,/
COEFF=',
1F11.8,' QUAD FACT=/,Fll.8,' PROD'/F12.8)
C LET CSEFF = THE EFFECTIVE SPIN ROT STRENGTH
CSEFF=SA
IF(S.NE.0.ODO) CSEFF=CSEFF+(SB-SA)*XK*XK/S
ESPR0T=C*CSEFF/2.ODO
20 HAMIL=ER0T+EQUAD+ESPROT
RETURN
3 0 HAMIL=0.ODO
RETURN
END
REFERENCES
1. C.H.Townes and A.L.Schawlow, Microwave Spectroscopy
(McGraw-Hill, New York, 1955).
2. R.C.Lord, M.A.Lynch, W.C.Schumb, and E.J.Slowinski, J.
Am. Chem. Soc. 72., 522 (1950).
3. R.E.LaVilla and S.H.Bauer, J. Chem. Phys. 33., 182 (1960)
4. H.B.Thompson and L.S.Bartell, Trans. Am. Crystal Assoc.
2, 190 (1966).
5. H.H.Claassen, E.L.Gasner, and H.Selig, J. Chem. Phys. 49,
1803 (1968).
6. W.J.Adams, H.B.Thompson, and L.S.Bartell, J. Chem. Phys.
53, 4040 (1970).
7. H.H.Eysel and K.Seppelt, J. Chem. Phys. 56, 5081 (1972).
8. E.W.Kaiser, J.S.Muenter, and W.Klemperer, J. Chem. Phys.
53. 53 (1970).
9. R.H.Bradley, P.N.Brier, and M.J.Whittle, Chem. Phys.
Lett. 11, 192 (1971).
10. F.Truchetet,R.Jurek, and J.Chanussot, Can. J. Phys. 56,
601 (1978).
Документ
Категория
Без категории
Просмотров
0
Размер файла
1 473 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа