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High Resolution Spectroscopy below the Doppler Width.

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High Resolution Spectroscopy below the Doppler Width
By Hans Jiirgen Neusser * and Edward William Schlag
Microscopic insights into elementary molecular processes are only feasible through the observation of unique quantum states and the study of their couplings and time-dependent behavior.
In the case of larger chemically relevant molecules, the corresponding transitions lie so close
that they mostly overlap and lead to band structures. For example, electronic band spectra of
large molecules cannot be resolved into single lines even by high resolution UV-spectrometers.
The reason for this is the Doppler broadening, arising from the random velocity of the
molecules in the gas phase. In this article, we want to demonstrate that modern laser spectroscopic methods make it possible to overcome this “Doppler barrier” and to resolve the line
structure in band spectra. The selective excitation of unique quantum states yields precise
information on the mechanisms responsible for energy redistribution in molecules. Energy
redistribution processes represent a crucial first step preceding chemical reactions, which they
influence decisively. Very high resolution spectroscopy elucidates the influence of molecular
rotation on the energy redistribution. Through Coriolis forces in rotating molecules, vibrations
can couple, causing a flow of energy from the selectively excited vibrations to the many other
vibrational degrees of freedom. Weak interactions, namely van der Waals interactions and
hydrogen bonding, determine the structure of large molecules (biomolecules) and supermolecular systems. Weak intermolecular interactions, given their selectively resolved quantum states,
can be analyzed and understood at the microscopic level. “Doppler-free spectroscopy” with
its resulting line spectra furnishes information on the structure, including bond lengths, of van
der Waals complexes. With this information, Doppler-free spectroscopy provides the model
parameters indispensable for the quantitative description of complex systems.
1. Introduction
The general goal of chemical spectroscopy is the investigation of the positions of the quantum states of microscopic
systems, such as atoms or molecules. On the one hand, the
exact energetic position of these states when collated with
predictions of theoretical models pins down the electronic
arrangement, the bond strengths, and the structure of the
nuclear frame in molecules. On the other hand, the line
widths of the transitions yield information on the lifetimes of
the excited states and thus about dynamical processes in the
molecule. In this way spectroscopy has, up to now provided
the key information for an understanding of the physical and
chemical properties and the reactivity of elements and compounds.
In ultraviolet spectroscopy the absorbed photons excite
electrons of the molecule. Typically, this electronic excitation
proceeds according to the Franck-Condon principle, exciting, in addition. vibrations of the molecule. Furthermore,
before the excitation, the molecules are in various rotational
and vibrational states, as given by the Boltzmann distribution at the appropriate gas temperature. This rotational state
distribution is preserved or changed insignificantly in the
excitation. Unambiguous spectroscopic information can be
expected only if unique quantum states can be excited, i.e.
states for which all of the quantum numbers are fixed. This
means that along with the electronic and the vibrational
quantum number, the rotational quantum number must also
be distinctly defined.
[*] Prof. Dr. H. J. Neusser, Prof. Dr. E. W. Schlag
Institut fur Physikalische und Theoretische Chernie
der Technischen Universitat Miinchen
Lichtenbergstrasse 4, D-W-8046 Garching (FRG)
Angrw. Chew Inr. Ed. Engl. 31 (1992) 263-273
In the case of large polyatomic molecules, single rotational
lines in electronic or vibrational-electronic transitions (vibronic transitions) are so densely packed that they can no
longer be resolved by conventional spectroscopic methods.
This explains the broad band spectra with no line structure
typically reported for large molecules. The culprit is the
Doppler broadening of the transition, caused by the random
velocity of the molecules in the gas phase. A typical value for
the Doppler width of a molecule of the rough size of benzene
(C,H,) is in the case of the S, +So transition at about
40000 cm-’, 1.7 GHz or 0.05 cm-’ at room temperature.
Before discussing the possible methods of overcoming the
Doppler barrier in order to achieve line structure in spectra,
we enter briefly into the chemically relevant problems whose
clarifications demand the separation of single rotational
transitions in electronic or vibronic spectra. These are namely inquiries of the precise structure of molecules and extremely unstable weakly-bound van der Waals complexes (treated
in the second half of this article). Using Doppler-free spectroscopy, quantities such as van der Waals bond lengths and
potential parameters can be experimentally obtained which
lead to a quantitative understanding of the weak intermolecular interactions inherent in complex systems.
Essential for an understanding of elementary chemical reactions are insights into the reaction dynamics, or the study
of the course of reactions at the microscopic level. The study
of reaction mechanisms is not only essential for an understanding of chemical processes, but could have a tremendous
practical use if successfully applied to block, accelerate, or
initiate selective chemical reactions.
For an understanding of the reactions of polyatomic molecules at the microscopic level, statistical theories, in particular the Rice-Ramsperger-Kassel-Marcus (RRKM) theory1’]
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or Quasi-Equilibriums theory,['] are at present very popular
and useful. For many chemical reactions occurring along
bound potential curves, these theories are able to explain the
observed reaction course and its rate constant. The crucial
assumption of these theoretical models is that the total energy of the molecule before the reaction is statistically distributed over all of the degrees of freedom of the molecule.
In many cases a good agreement with experimental results is
achieved with this hypothesis. Consequently, over the last
decade and at present, the focus of studies in reaction dynamics is: How does a statistical distribution of energy in a
molecule come about? Is the distribution complete or limited
to certain vibrational states?
The process responsible for the redistribution of energy is
the intramolecular vibrational redistribution (IVR) occurring within a molecule.131Precise information on the IVR
process can only be obtained if distinct quantum states of the
molecule are prepared and the intramolecular vibrational
redistribution observed.
The states of polyatomic molecules lie so dense that stateselective excitation demands Doppler-free studies. Initiating
such studies, the dye
with its very sharp frequency
width, can be finely tuned over the molecular transitions.
This in turn has led in the last decade to the development of
various experimental methods such as saturation spectroscopy, optical double-resonance spectroscopy and twophoton absorption spectroscopy, which in principle serve to
reduce or to eliminate the Doppler width of an optical traniti ion.[^] These methods therefore hurdle a natural barrier to
the spectral resolution. The use of collimated atomic or
molecular beams should be included here, as this technique
also reduces the Doppler width, in this case through geometric selection of molecules of the same velocity. However,
application of the molecular beam technique for high resolution spectroscopy first became possible through the use of
extremely narrow-band tunable lasers; examples of high
resolution UV-spectroscopy on van der Waals complexes is
presented in the second half of this article.
The various methods mentioned above were mainly developed for studying fine structure in atomic spectra. Extension
to large molecules is not possible for every one of these methods. In a series of studies, our group has established that
two-photon spectroscopy represents a practical method of
obtaining Doppler-free high resolution spectra of large molecuIes.16,71
2. Doppler-free Two-Photon Spectroscopy
of Molecules and Intramolecular Energy
2.1. Concepts of Doppler-free Two-Photon Absorption
At the microscopic level, energy is transferred to atoms
and molecules in the smallest energy units, called photons.
As early as 1930, Maria Goppert-Mayer postulated that not
only one photon could be transferred, but rather that two
photons could also participate in one elementary absorption
step.[81Not until 1960, through the discovery of the laser
with its very high light intensity, could two-photon absorption be experimentally proved.Igl In two-photon absorption,
absorption of two photons excites the molecule to a state
whose energy is given by the summed photon energy. In this
manner, it is possible for example to excite UV absorption
bands of benzene with visible blue light. Moreover, as the
selection rules for one- and two-photon absorption differ,['']
spectroscopic information on previously unknown vibrational"
and electronic states[131is
selection rules complement each other in a way analogous to
those of infrared and Raman spectroscopy, both of which
Edward W Schlag was born in 1932 in Los Angeles. He studied chemistry at the Occidental
College, Los Angeles. He gained his doctorate at the University of Washington in Seattle in 1958
under the supervision of Professor B. S. Rabinovitch for work on the unimolecular isomerization
of cyclopropanes. Since t971 Edward Schlag has held a professorial chair for Physical Chemistry
at the Technical University of Munich. Several honors have been conferred on him for his diverse
research activities, which have been reported on in more than 250 original papers and books: Since
1978 Schlag has been afull member ofthe Bavarian Academy of Sciences, andsince 1984 afellow
of the American Physical Society. In 1988 he was made an honorary Doctor of the Hebrew
University in Jerusalem. His main interests currently focus on the investigation of the structure
and dynamics of molecules and molecular complexes using high-resolution spectroscopic methods.
Hans Jiirgen Neusser was born in 1943 in Troppau (Czechoslovakia). He studiedphysics at the
Technical University ( T U ) in Munich, where he was awarded his doctorate in 1971for work with
Professor W Kaiser. Subsequently, he worked for seven years with K E. Schlag and gained his
habilitation in Physical Chemistry for work on the two-photon spectroscopy of molecules in the
gas phase. In 1979 Neusser was appointed Professor of Physical Chemistry at the T U Munich.
In 1983 he was awarded the Chemistry Prize ofthe Academy ofSciences, Gottingen, for his work
in thejkld of Two-Photon Spectroscopy, Multiphoton Ionization and Doppler-free High-Resolution Molecular Spectroscopy. At present his main interests focus on the laser spectroscopy of
molecules and molecular complexes, intramolecular dynamics, and the kinetics of ionic decomposition.
Angew Chrm. Int. Ed. Engl. 31 (1992) 263-273
supplement spectroscopic information on the electronic
ground state.
If both absorbed photons stem from one light bundle or
from two different light bundles traveling in the same direction, then the spectral resolution of the two-photon absorption is limited, as that in one-photon absorption, by the
Doppler broadening. The Doppler width of a specific transition arises from the individual molecular absorption lines
from molecules with differing velocities; the shifts of their
absorption frequencies, depending on their speed and velocity vector, vary in accordance with the first order Doppler
effect. In the above absorption case, the resultant shift is the
sum of that from light frequencies v1 and v2. The averaging
over the differing Doppler shifts yields an inhomogenouslybroadened Gaussian-shaped absorption line, as illustrated in
Figure 1 (top).
vo= y + v*
v= v1 + v2-(v,+v2)vx/c
cv, =v$
to observe a transition's homogeneous line width. As we will
see later, the homogeneous line width is of special significance in studies of intramolecular relaxation processes, as it
supplies very important additional information on the dynamic behavior of the molecule. To summarize, Dopplerfree two-photon absorption should enable, even for large
molecules with very densely packed absorption lines, the
excitation of unique rotational states in vibronic quantum
states (unique rovibronic states), and consequently the precise monitoring of relaxation processes.
2.2. The Experimental Technique of Doppler-free
Two-Photon Absorption
Doppler-free two-photon absorption was first realized in
1974 on atoms.['61 Attempts at extending this technique to
large polyatomic molecules faced nontrivial experimental
difficulties. Firstly, in molecules the oscillator strength of the
two-photon transition is divided among many vibronic transitions. Secondly, about 103-1 O4 rotational states are populated, as if having to work with an effective low molecular
number density. And, in addition to these difficulties, twophoton absorption is inherently a weak higher order effect,
whose observation requires high light inten~ities."~]
A possible experimental setup to achieve sufficient signal
strengths to observe the weak two-photon absorption is
illustrated in Figure 2." 'I A continuous-wave single-mode
dye loser
v= vl+
Kr' loser
- vz)vx/c
b y ( v1
Fig. 1. Schematic representation of Doppler-limited (above) and Doppler-free
(below) two-photon absorption processes. If both photons approach the absorbing molecule from the same direction, their Doppler shifts are added, resulting in a broadened transition with a Gaussian line shape. If, however, the
two photons approach the absorbing molecule from opposite directions, the
Doppler shifts are subtracted and thus compensate each other; this eliminates
the Doppler broadening and reveals the sharp homogeneous line shape of the
transition (after [ 141).
In 1970, Chebotayev et aL1"] suggested the application of
two-photon absorption of two antiparallel light bundles of
an extreme monochromatic laser to avoid Doppler broadening. The principle of this method is illustrated schematically
in Figure 1 (bottom). Note that now the Doppler shifts of the
two light frequencies are subtracted. Whereas the light wave
approaching from the left experiences a red shift, the frequency of the light wave approaching from the right is blueshifted. If the two antiparallel light bundles have the same
frequency, the two shifts compensate each other exactly,
eliminating the Doppler shift for each and every velocity
component, so that the transition is free from any Doppler
broadening. Naturally, the transition frequency can then be
determined with considerably higher accuracy, and transitions which were perhaps concealed under the Doppler
broadening can be resolved. Furthermore, it is now possible
Angebc. f'hcJm.I f z t . Ed. Engl. 31 (lPY2) 263-273
......external ..._; high-voltoge
Fig. 2. Schematic diagram of the experimental setup for measurement of
Doppler-free molecular spectra with high resolution. Elimination of the
Doppler broadening proceeds by absorption of two photons, traveling in opposite directions, from the narrow-band standing light waves in the external resonator. PZT is a piezoelectric transducer.
ring dye laser, pumped by a Kr' laser, supplies very narrrowband light (Av = 1 MHz = 3 x lo-' cm-'). A "wavemeter"
measures the absolute laser frequency, while an interferometer records very precisely the relative frequency. The molecular gas under study is contained in a fluorescence cell at the
low pressure of less than 1 Torr so as to avoid molecular
interactions through collisions. This cell is placed in an external resonator, so that the Doppler-free two-photon absorption occurs through a standing light wave composed of two
antiparallel light bundles. If now a molecule absorbs one
photon from each of the oppositely-traveling light bundles,
the Doppler shift of the transition frequency for each mole265
cule, regardless of its velocity, will be compensated, and a
Doppler-free spectrum at the sum of the two photons' energies will be observed. The use of the external resonator is
crucial, as this can immensely amplify the light intensity,
which in turn increases the two-photon signal intensity with
its quadratic dependence on the light intensity by several
orders of magnitude.
The resulting two-photon absorption is detected through
the emitted UV fluorescence with the help of a photomultiplier tube. Scanning the laser light frequency requires synchronous fine tuning of the external resonator using a piezoelectric transducer (PZT); this ensures that the resonance
conditions in the external cavity for the particular wavelength in question are constantly fulfilled. A data processing
system facilitates the signal storage and the plotting of the
Doppler-free two-photon spectrum on the desired scale.
2.3. Doppler-free Two-Photon Spectra of Benzene
To illustrate the potential of Doppler-free spectroscopy,
Figure 3 displays a part of the S, t So spectrum of benzene
at various spectral resolutions. The topmost trace shows the
tional band (14;)[*] at a resolution limited by the Doppler
broadening. This represents the highest resolution achievable through conventional one-photon spectroscopy, even
with the help of a high-resolution spectrometer. The observed structure represents the overlapping of many rotational lines. The individual rotational lines become visible
only after the introduction of a technique of elimination of
the Doppler broadening and an increase in the resolution by
a factor of 50. The lowermost spectrum, recorded using
Doppler-free two-photon spectroscopy, displays single rotational lines. The frequency scale is now given in GHz instead
of cm- ', since the interferometer which measures the exact
relative frequency is calibrated in GHz (1 cm-' x 30 GHz).
This spectrum represents the blue edge and thus only a small
fraction of the complete vibrational band. Evidently thousands of rotational lines, hidden under the Doppler broadened vibrational band, first manifest themselves after elimination of the Doppler broadening.
The resulting rotational line spectrum can be unambiguously analyzed to yield extremely precise rotational and centrifugal distortion constants of the molecule in its electronic
ground state (So) and in its electronic excited state (S,). The
accuracy is a factor of 100 larger than in conventional highresolution (Doppler-limited) UV spectroscopy. A typical result for the rotational constants of the S, state with accompanying excitement of one quantum of C-C ring vibration
u14 of b,, symmetry is['*l B,, = 0.181284 and C;, =
0.090711 cm-', accurate to
cm-'. The rotational constants B and C are given by the rotational energy level formula for an oblate symmetric top molecule [Eq. (a)].['9]
ERo,= BJ(J
Fig. 3. The two-photon spectrum of the electronic S, + S, transition in benzene at various spectral resolutions (after [14]). Top: Vibrational structure of
the S, +So transition. Center: Q-branch of the strongest (14;) band at
Doppler-ltmited resolution. Bottom: After elimination of the Doppler broadening. single rotational lines appear which were hiding under the Doppler
width. 6v gives the resolution.
two-photon spectrum at a spectral resolution of 1 cm-'.
(The structure of the one-photon spectrum of benzene is in
principle similar, although due to the differing selection
rules, different vibrational bands are observed.) The middle
spectrum shows the central portion of the strongest vibra266
+ 1 ) - (B
J is here the quantum number of the total rotational angular momentum. K is also a good quantum number for a
symmetric top molecule and describes the projection of the
total angular momentum on the spinning top axis.
The accurately determined rotational constants and measurements on isotopomers (e.g. C6D6)allow exact determination of the bond lengths in the molecule and the changes
in bond length upon electronic excitation. For benzene in its
electronic ground state, an average C-C bond length of
1.397 8, and an average C-H bond length of 1.079 A are
determined. In the S, excited electronic state, the C-C bond
length increases to 1.432 A, whereas the C-H bond length
decreases slightly to 1.075 A. As anticipated, promotion of a
electron to an antibonding n* state is accompanied by a
decrease in binding energy, evoking an expansion of the
benzene ring.
The accurately determined rotational and centrifugal distortion constants suffice to reproduce the measured rotational line structure with respect to the line positions and
heights. A good agreement between the reproduced and
measured line positions implies in this case that the excited
rovibronic states are not coupled to other vibrational states,
so that no energy transfer to other vibrational modes can
take place.
The superscript denotes the number of excited quanta of a particular vibration (here No. 14) in the final state of the transition (here S, state), while the
subscript denotes the number of quanta of this vibration in the initial state
(here So state).
Angew. Chem. In[. Ed. Engl. 31 (1992) 263-273
2.4. The Model of Intramolecular Energy Redistribution: a Primer
Before evidence of intramolecular energy redistribution in
a Doppler-free spectrum is discussed, an introduction to the
theoretical model of this process should be presented.
In the description of molecules, one assumes that electronic,
vibrational, and rotational states can be considered as separated in the Born-Oppenheimer approximation. Theory designates such states as zeroth-order states. In reality, zerothorder states are not isolated from each other, but are often
coupled to other zeroth-order states of the molecule. This
coupling can occur, e.g., between states of the same or differing multiplicities, resulting in internal conversion (IC) or intersystem crossing (ISC), two well-known processes of radiationless decay. In the case of intramolecular energy redistribution preceding a chemical reaction, the pertinent coupling
is between different vibrational states of the same electronic
potential (intramolecular vibrational redistribution, IVR).
A more precise formulation of intramolecular coupling is
possible with the help of the theory of nonradiative processes.‘201The two limiting Cases depicted in Figures 4 and 5
are the most intuitively clear. Figure 4 shows the situation
zeroth-order states
I i9
Fig. 4. Schematic representation of a nonradiative process at the statistical
limit. The coupling of a molecular state lie) to a quasicontinuum of denselypacked states {Ino)>;leads to a broadened Lorentzian-shaped line.
present at the “statistical limit.” Here a large number of
states In”) lie within the width of the coupling matrix element V,{,, of a zeroth-order state li”). The manifold of states
{In”)} form a quasicontinuum to which the zeroth-order
state 1 i”) is coupled. The case of coupling to a continuum is
of course well-known for ionization and dissociation processes, but can also arise as a limiting case for the process of
intramolecular vibrational redistribution in large molecules,
due to the strongly increasing density p of vibrational states
with increasing excess energy in the electronic state. In the
simplest case, only state li”) carries oscillator strength and
therefore can be optically populated or is, in spectroscopy
jargon, “light”, whereas the manifold of states {(no)>is
“dark”. If we now carry out an experiment with a low coherence width (such as with continuous-wave narrow-band laser
light), we can expect for this coupling limit, a Lorentzianbroadened line shape of width y = V z p, arising from the
projection of the fragmented oscillator strengths or “light”
zeroth-order states
Fig. 5. Schematic representation of the coupling of two zeroth-order states,
11”) and In”). yielding a mixing and repulsion of the eigenstates li) and In).
Angekt Chm? I n t . Ed. Ennl. 31 (1992) 263-273
fractions on the eigenstates. On the other hand, using a large
coherence width, such as short-time pulsed laser excitation,
it is feasible to excite the “light” zeroth-order state li”),
which due to the high state density evolves exponentially and
irreversibly with time. Under these conditions, we are dealing with what we call “dynamics”.
The situation is entirely different when the density of
states is so low that the only coupling is between the two
zeroth-order states li”) and Ino) (Fig. 5). This is the natural
case for small molecules or for very low excess energies in the
electronic states of large molecules. As is well known in spectroscopy, such a coupling leads to repulsion of the states and
mixing of the wave functions of the two states. The repulsion
of the zeroth-order states leads to an “avoided crossing” of
the energy level curves of the eigenstates, which is observable
in the spectrum (static perturbation).
This short introduction to the theoretical description of
nonradiative processes demonstrates that the intramolecular
dynamics can reduce to the case of static coupling well
known in spectroscopy at the low density of states typical for
low excess energies. Unresolved questions and thus topics of
current research are the following points:
When does the statistical limit begin? What is the nature
of the transitional region from static perturbations to dynamics at the statistical limit?
Which coupling mechanisms are responsible for IVR? Are
only the anharmonic couplings between the vibrational
states of importance, or does the molecule’s rotation in the
form of rotational-vibrational coupling also play a role?
Is the coupling selective? Does the redistribution occur
only within a particular group of states?
With the example benzene, we are able to study a molecule
at increasing total excitation energy and so to analyze diverse
regions of the spectrum exhibiting strongly differing densities of vibrational states: as will be demonstrated below, the
benzene molecule with its 30 vibrational degrees of freedom
is especially suitable. Both limiting cases described above can
be reached if, on the one hand, one excites a low excess
energy up to 2000 cm-’, and on the other, the excess energy
within the optically-accessible region of the S, state is increased to about 4000 cm- ; additionally, the excitation of
unique states can be guaranteed by the Doppler-free twophoton spectroscopy. Concrete studies of the 14; vibrational
band and the 14A1: and 14A1: progressions of this band at
higher excess energies were carried out. These vibrational
bands correspond to totally symmetric two-photon transitions originating in the ground
with one quantum
each of the v14 (b2J vibration with 1570cm-’ of energy
excited in the S, state. The progressions arise from addition
of quanta of the totally symmetric C-C stretching vibration
v1 (a,,) amounting to excess energies of 2492 (14l1’) and
3412 cm-’ (14’12). With regards to Figures 4and 5, the final
states of these three transitions correspond to “light” zerothorder states in the S, state. The density of zeroth-order states
increases from 1.2 (14l) to 17 (14’1’) to 165 (14’1’) per
cm- These background states are not, however, directly
visible in the spectrum, as they carry negligible oscillator
strength for the two-photon transition. Nevertheless,
through their interaction with the 14’, 14’1 and 14’1’ excited states, they have a characteristic influence on the spectrum as described below. Around 3000 cm-’, the electronic
relaxation behavior of the molecule changes, as concluded
by early measurements from the abrupt drop in the fluorescence quantum yield.IZz1The cause of this behavior was tentatively attributed to a fast nonradiative relaxation channel
(“Channel Three”) whose origin was at the time unknown.
Using several selected examples, we shall explain in the
following section the spectral effects of a strongly increasing
density of background states with increasing excess energy
and how these observations fit into the theory of intramolecular vibrational redistribution. With such information, a clarification of the mechanism of “Channel Three” is possible.
2.5. Information on the Mechanism of Intramolecular
Energy Redistribution
A careful examination of the spectrum of Figure 3 (bottom) at higher rotational energies reveals irregular, seemingly
unsystematic deviations between the measured and predicted
(using the experimentally determined rotational constants) rotational structure, which cannot be consistently clarified by a
new set of rotational or centrifugal distortion constants.[’*’231
This is a signature ofperturbations in the spectrum, denoting
interaction with a “dark” background state.
Figure 6 demonstrates such isolated perturbations in two
sections of the spectrum. Below are two calculated sections
of the spectrum of the 14; band: above, for collation, are the
corresponding measured spectral sections. A collation of the
calculated and measured spectra for each section yields good
agreement for the majority of rotational lines. Nevertheless,
there are lines (marked by an arrow) in the experimental
Jw=Zl17 ;
-- 92
- 82
Av [GHzl
Fig. 6. Comparison of a section of the experimental (above) and calculated
(below) spectrum of the 14; vibrational band; low excess energy in the S,
electronic state of benzene. The lines tagged in the theoretical spectrum are
absent in the experimental spectrum: instead, two nearly symmetrically shifted
lines appear, analogous to the coupling case described in Figure 5 (after [23]).
spectrum with no direct match in the calculated spectrum
and vice versa. Instead two smaller lines appear in the experimental spectrum which are nearly symmetrically shifted
about the calculated line position. We are obviously witnessing here the coupling case described by Figure 5, namely the
coupling of two states, leading to a repulsion of the two
resulting eigenstates and to a mixing of the two coupled
zeroth-order states. This coupling is selective since an energy
resonance between a “light” and a “dark” state is rare with
the low density of states of 1.2 states/cm-’ at the excess
energy of 1570 cm-’. The mixing of states results in two
observable eigenstates (rather than the one anticipated
“light” state) which share the oscillator strength of the one
‘‘light’’ state. These eigenstates are direct proof of the coupling of two normal vibrational states, which finally leads to
an energy redistribution in the molecule.
A closer analysis of such perturbations in the spectrum
indicates a value of the coupling matrix element of the order
of a few 100 MHz. Moreover, a dependence of the coupling
matrix element on the rotational quantum numbers J and K
is found. This result can in no way be clarified through an
anharmonic interaction of the coupled vibrations, rather it
must follow that Coriolis coupling plays a crucial role. Coriolis forces appear in rotating molecules and can cause the
coupling of vibrational states through the rotation of the
This result, fundamental to the understanding of intramolecular energy redistribution, was obtained for the
spectral region of low excess energy, but can just as well be
confirmed at high excess energies. The region of high excess
energy is particularly interesting since the reactive region of
the potential of an electronic state is in general first reached
at high energies. Figure 7 displays results from the high resolution spectroscopy of the 14A1; vibrational band at an
excess energy of 3412cm-’. Here the line shapes (under
extremely high resolution) of the three rotational lines
JK = 2,, 6,, and 14, of the 14;l; vibrational band are pre~ented.[’~]
For clarification, we emphasize that this spectral
structure lies well below the Doppler width; the Doppler
width of the transition in Figure 7 is namely 1.6 GHz or four
times larger than the complete frequency range displayed in
Figure7. It is obvious here that the measured line width
increases strongly with J, namely from 12.7 to 53.2 MHz as
J increases from 2 to 14. In addition, the measured line shape
corresponds with high accuracy to a Lorentzian line. (The
solid lines represent Lorentzian lines fitted to the data
points.) In contrast to the results at low excess energies, here
the line widths rather than the positions depend strongly on
the molecule’s rotation. This rotational dependence cannot
be attributed to an electronic relaxation process but rather
must arise from coupling within S, . The Lorentzian shape of
the lines indicates moreover an irreversible vibrational relaxation at the statistical limit as given in Figure 4. A quantitative analysis of these results[24]establishes that even at these
high excess energies, or even in the “Channel Three” region,
Coriolis coupling produces an interaction of vibrational
states within S, and decisively influences the IVR process.
the rotationally-dependent line broadening directly demonstrates that Coriolis coupling to particular “dark” vibrational states represents the primary process of “Channel
Three”. These results, with respect to the intramolecular enAn,qew. Chem. Int. Ed. Engl. 31 (1992) 263-273
14; 1:
-1 \-
JK= 60
26.3 MHz
- -.
JK= 20
12.7 MHz
. i
’ <
A u CMHzl
Fig. 7. Three rotational lines from the 14A1: vibrational hand; high excess
energy in the S , electronic state of benzene. The Lorentzian line shapes and the
strong increase in line width with increasing rotational quantum number J
indicate that the rotation of the molecule plays a crucial role in the intramolecular vibrational relaxation via Coriolis coupling (after [24]).
ergy redistribution and the coupling mechanism, should in
principle be transferable to the electronic ground state, since
the S, and So states behave similarly with respect to couplings and density of states.
Using selected examples from the spectrum of benzene, we
have shown in this section that Doppler-free spectroscopy
enables the excitation of uniquely defined quantum states
even for large molecules with densely-lying transitions. Line
splittings and homogeneous line widths present below the
Doppler width have proven that rotation plays a decisive
role in the energy redistribution in molecules. Couplings between individual normal vibrations of a molecule are not
only generated through anharmonicities, but also through
Coriolis forces in a rotating molecule. Selection rules apply
to this coupling which determine the nature and symmetry of
the coupled “dark” state. In such a way, we have gained an
understanding of microscopic physical processes fundamental to energy redistribution. In conclusion, the basic mechanics of the energy redistribution process in a chemically relevant molecule has been presented for the first time.
3. Doppler-free Ultraviolet Spectroscopy of
Weakly Bound van der Waals Complexes
3.1. Introduction
Interest in the spectroscopy of weakly-bound complexes
has grown immensely in the last ten years. Such complexes or
clusters result from clustering of molecules or atoms, made
Angew. Chem. Int. Ed. Engl. 31 (1992) 263-273
possible by long-range, but weak electrostatic forces, such as
dipole-dipole interaction or induced dipole-dipole interacti~n.[’~I
With weak binding energies of the order of a few
kJ/mol, these complexes are generally unstable at room temperature. The increasing number of cluster studies can be
attributed to the convenient method of producing isolated
gas phase atomic and molecular clusters in cooled supersonic
beams.[261The general goal of these studies is the quantitative microscopic understanding of van der Waals bonding,
intrinsic to solvation processes and the structure and properties of the liquid phase and thus critically influencing chemical processes in the liquid phase. This goal in turn necessitates investigation of the exact structure of the complex, its
binding energy, the shape of the van der Waals potential, and
its dynamic behavior, i.e. the examination of its energy redistribution and its dissociation.
For complexes involving large organic molecules, the discussion of the previous section on polyatomics molecules
applies to an even larger extent: the desired information can
first be obtained when the spectral resolution is high enough
to resolve individual rotational lines within the Doppler
width. Particularly instructive are studies on complexes involving spectroscopically well-studied molecules. It is therefore natural to produce complexes containing the benzene
molecule. Moreover, with the distinct planar ring structure
of benzene, one expects a complexation behavior typical for
the large class of aromatic molecules, thus acquiring important basic information for the description of solvation processes at the microscopic level. In the simplest case, noble gas
atoms or small molecules are complexed with benzene. Here
we can expect relatively minor changes in the well-known
spectrum of benzene as the complexation entails no new
chemical bonds, thus minimally influencing the molecular
electronic structure.
This section presents results of the Doppler-free spectroscopy of complexes of benzene with noble gas atoms or
small molecules such as N,. As in the case of benzene itself,
Doppler-free spectroscopy provides a resolution of the rotational structure below the Doppler width, enabling precise
statements to be made on the structures and dynamic behavior of these clusters.
3.2. Experimental Techniques for the Preparation and
Spectroscopy of van der Waals Complexes
Due to their small binding energies, isolated van der Waals
complexes are not stable at room temperature. Such complexes are thus frequently prepared in cooled supersonic
molecular beams.[261Hereby a gas at a high pressure of a few
atmospheres is expanded into a vacuum through a small
orifice.[”’ During the expansion process, the thermal energy
of the gas particles is converted into translational expansion
energy, resulting in a gas beam with a highly directed velocity
and a low temperature of translational, rotational and vibrational degrees of freedom. In the cooling process, condensation of the gas can occur, leading to formation of van der
Waals complexes of various sizes.
Figure 8 shows the experimental setup for the high resolution spectroscopy of van der Waals complexes. The core of
the setup is the cooled molecular beam. Benzene at its natu269
rally-occurring vapor pressure of about 60mTorr is mixed
with a noble gas (e.g. Ar) at the high pressure of about 5 atm
and then expanded through a small orifice ca. 0.3 mm in
diameter into the first vacuum chamber. The gas throughput
is limited by the short pulsed opening of a valve, which
proceeds synchronously with the arrival of the laser light
pulses. Due to the cooling upon expansion, various homoand heteroclusters of benzene and Ar are formed. A conicalshaped skimmer peels away the outer shell of the molecular
beam, enabling the expansion of the central part into a second vacuum chamber with a lower background pressure
where the interaction with the light occurs. The skimmer
contributes substantially to the realization of a Doppler-free
spectrum, as its small opening selects exactly the molecules
that have the smallest velocity components perpendicular to
the direction of propagation of the molecular beam. Thereby
the Doppler broadening amounting to ca. 0.05 cm-' in a
bulk gas is reduced to 0.001 cm- *.This suffices for the resolution of rotational lines in the UV spectrum, so that the
method of Doppler-free two-photon spectroscopy becomes
superfluous here and, moreover, would not lead to a better
resolution due to the limiting frequency width (ca.
0.0025 cm-') of the exciting laser light.
moss spectrometer
Fig. 8. Schematic diagram of the experimental setup for obtaining high resolution Doppler-free UV spectra of van der Waals complexes (after [31]). Van der
Waals complexes of benzene and Ar are produced by expanding a gaseous
mixture of benzene and Ar at high pressure through an orifice into vacuum.
After a skimmer selects the central portion of the molecular beam, reducing the
Doppler broadening, the complexes are excited to the S, state by a pulsed,
narrow-band laser light and finally ionized by a second pulsed laser. The
nascent ions are mass-analyzed in a time-of-flight mass spectrometer. To obtain
spectra of the particular complex, free from obscuring overlaps with spectra of
other species, only the current from ions of a selected mass is observed and
In the present experiments, the narrow-band light of the
single-mode ring dye laser already described in Section 2.2
is pulsed-amplified to a high peak power in a three-stage
excimer-laser-pumped amplifier setup. The generated visible
blue-green light pulses have for their pulse length of 10 ns the
best possible frequency sharpness of 80 MHz. In this case,
the pulse length and the frequency width are linked to each
other by a Fourier transform. The amplification and the use
of pulsed laser light with its high peak intensities enable
Fig. 9. Energy level scheme for resonance-enhanced two-photon ionization of
molecules or van der Wads complexes. The efficiency of the ionization process
is extremely enhanced when the energy of the first photon is resonant with a
rovibronic transition in the complex (resonance-enhancement). As the frequency v1 of the narrow-band laser light is continuously scanned, the signal (ion
current) is modulated due to the spectrum of the intermediate state. In this
manner, Doppler-free rotationally-resolved spectra of mass-selected van der
Waals complexes can be measured. I.P. = ionization potential.
frequency-doubling of the blue-green light into the ultraviolet spectral region, which in turn allows excitation of the
S, +So transitions in the benzene-containing van der Waals
complex through the absorption of one photon of energy hv,
as depicted in the energy scheme of Figure 9. The subsequent
absorption of a further UV photon (hv,) stemming from a
relatively broad-band dye laser, simultaneously pumped by
the excimer laser, brings the excited (to S, state) complexes
into the ionization continuum. The total excitation process
corresponds to a two-photon ionization which is enhanced
by the resonant state at the energy of the first absorbed
narrow-band photon hv,: each time the energy of the narrow-band photon agrees with a rovibronic transition of the
cluster, the probability of a two-photon ionization is drastically enhanced. If the frequency of the narrow-band light hv,
is tuned while monitoring the ion current, this will be modulated according to the spectrum of the intermediate state and
consequently reflects this spectrum. The principal advantage
of resonant two-photon ionization is that the created ions
can be registered separately according to their mass in a mass
spectrometer. This property of resonance-enhanced twophoton ionization was recognized at an early dateLz8]and is
quite essential to the spectroscopy of van der Waals complexes. This was first demonstrated in several experiments with
relatively low resolution just sufficient to resolve the vibrational structure in the spectra,[291and is also essential for the
high-resolution spectroscopy of the van der Waals complexes
described here. Namely, a mixture of complexes of different
composition and size whose spectra often overlap is produced in a cooled supersonic beam, as mentioned above. The
mass-selective recording of the spectra facilitates the measurement of the spectrum of a selected complex in the mixture without interference by the presence of complexes of a
different mass. In the experiment the mass separation proceeds in a simple time-of-flight mass spectrometer in which
all cluster ions are accelerated to the same kinetic energy and
subsequently separated in time in a field-free flight tube due
to their mass-dependent flight times. Channel plates at the
Angen'. Chem. h t . Ed. Engl. 31 (1992) 263-273
end of the flight tube serve as the ion detector, delivering an
ion current each time an ion bundle of the chosen mass
arrives. The remaining units of the experimental setup facilitate the monitoring of the exact frequency of the exciting
laser light and the recording and processing of the ion signal.
described in Section 2.3) to the hitherto unattainable high
accuracy of 10- cm - l .
This spectral information is transposable into structural
information. From the fact that the observed spectrum is
that of a symmetric top, it follows that the sixfold rotational
axis of the benzene is preserved even after complexation;
consequently the Ar atom must sit on this axis (see Fig. 11).
3.3. Structure and van der Waals Bond Lengths
of Benzene-Noble Gas Dimers
Using the experimental method described in the previous
section, the rotational lines of vibronic transitions in benzene-noble gas dimers were successfully resolved. In this
section, we will show that analysis of the high-resolution
spectrum allows the determination of the structure and van
der Waals bond length to a high precision. The vibrational
structure of the transition in benzene is only minimally perturbed by the weakly-bound Ar atom. Accordingly, the 6;
band of the benzene-Ar complex is shifted by only 21 cm-’
to longer wavelength relative to the corresponding band in
pure ben~ene.1~~1
This red shift denotes that the complex is
more strongly bound in the S, state than in its electronic
ground state. Whereas the vibrational structure of the
S + So transition changes negligibly through complexation,
the rotational structures of the 6; band of benzene and the
benzene-Ar complex, which were resolved by Doppler-free
spectroscopy, no longer show any similarities. This can be
traced back to the fact that two inertial moments of the
system are altered by the addition of a noble gas atom. Figure 10 unequivocally demonstrates the high sensitivity of the
rotational line positions to changes in the mass and structure. The high-resolution spectrum of the 6; band of the
benzene-Ar complex is here contrasted with the corresponding band of benzene.[311The spectral analysis proves that the
complex, despite its completely altered moments of inertia, is
to high accuracy, like benzene itself, a symmetric top. Moreover a temperature distribution of the rotational degrees of
freedom of ca. 1.5 K can be derived and the rotational constants can be determined (by a procedure similiar to that
Fig. 11. The average structure of the benzene-Ar complex resulting from the
high-resolution spectrum displayed in Figure 10. The Ar atom sits on the sixfold axis of benzene at a distance of 3.58 8, from the benzene ring. This distance
decreases to 3.52 A when the benzene is excited to the S , state (see text) [31].
v,-38606.1 cm-’
\6=38585.1 cm-’
A V lGHzl
Fig. 10. Measured rotational structure of the 6; vibronic bands in the UV
spectrum of benzene (above) and the benzene-Ar complex (below). The arrangement of the rotational lines differs completely, and indeed allows a precise
determination of the structure of the complex by means of its inertial moments [31].
Angen. Ch1.m Inr. Ed. Engl. 31 (1992) 263-273
The average van der Waals distance (Ar from the benzene
plane) follows from the rotational constants. It is 3.58 A in
the ground state and decreases by 60 mb; upon electronic
excitation to the S, state. This behavior, in contrast to normal chemical bonds which typically expand upon electronic
excitation, is thereby characteristic for van der Waals bonding. Since benzene and obviously the Ar atom as well have no
permanent dipole moment, the induced dipole moments and
hence the polarizabilities of each unit constitute the attractive van der Waals forces. The electron cloud expansion, in
particular that of the n-orbital of benzene after an electronic
excitation into the S, (nn*)state, increases the polarizability
and thus the attractive forces. The resulting decrease in the
van der Waals bond distance is in addition supported by the
expansion of the benzene ring accompanying electronic excitation (see Section 2.3); owing to the stronger attractive
forces, the Ar atom can approach the expanded benzene ring
more closely before the repulsion through overlap of the
electron clouds dominates.
Similar results have been found for other benzene-noble
gas complexes1321:the van der Waals bond distance in the
electronic ground state for the Ne atom complexed with
benzene is 3.46 A and increases gradually from Ar (3.58 A)
to Kr (3.68 A) to Xe (3.81 A). This moderate increase in the
van der Waals bond distance is caused by the increase in
atomic radius with increasing mass number along the row of
noble gases. This effect, responsible for the repulsive part of
the potential, is partially compensated by the strong increase
in polarizability and hence attractive interaction from Ne to
Xe. Experimental values of comparable accuracy on the benzene-He complex have not yet been obtained, as the complexation process is so inefficient that, for example, no detectable concentration of complexes is observed in the
present experiment. Values for the van der Waals bond distance of benzeneeHe are at present only known from experiments with lower spectral resolution,r331and, due to their
lower accuracy, cannot be instructively compared with the
data presented in this work.
3.4. The Structure of a Larger Benzene-Noble Gas
After the exact position of the first clustered noble gas
atom is known, a natural question concerns the subsequent
complexation behavior, i.e. at which positions do further
noble gas atoms attach. With the help of the technique described in Section 3.2 it is also possible to mass-selectively
measure the spectra of such larger complexes, despite their
lower concentrations and hence reduced signal strengths. In
addition, however, the moments of inertia become larger and
consequently the rotational lines in the spectrum become
denser, making their resolution more difficult. Furthermore,
it is not definite that further noble gas atoms are strongly
enough bound to exclude isomerization processes, i.e. fast
migration of the Ar atom about the benzene ring, at the vibrational temperature achieved in the cooled supersonic beam.
The first actual experiments yielded a rotationally resolved spectrum at mass 158 a.m.u., i.e. for the C,H,-Ar,
complex.f341Analysis of this spectrum yields a structure in
which the Ar atoms are located on the sixfold axis, one on
each side of the benzene ring (see Fig.12). From the precise
experimental rotational constants, a bond distance of 3.58 A
is derived, exactly that in the benzene-Ar complex (with one
Ar atom). This implies that the benzene ring completely
screens any possible van der Waals interactions between the
two Ar atoms. Such a behavior is typical for complexation
processes in planar aromatic molecules.
At this point we must ask if the structure in Figure 12 is
the only existing structure or do other stable structures of the
benzene-Ar, complex also exist. Recent experiments with
lower resolutionr35]point to the stability of at least one additional structural isomer in which both Ar atoms lie on the
same side of the benzene ring. Only the rotationally resolved
Doppler-free spectrum can provide an unambiguous clarification of this problem. Such experiments will be possible in
the near future.
Fig. 12. The experimentally determined structure of the benzene-Ar, complex.
The Ar atoms sit 3.58 %, from the benzene plane; a distance identical with that
found for benzene-Ar (see Fig. 11). This signifies that the benzene ring effectively screens the long-range van der Waals interactions between the two Ar
spond to a symmetric rotor structure, there appear lines
which can only be accounted for in terms of the internal
rotation of the N, molecule about the C, axis of benzene.
The distance of the center of mass of the N, molecule from
the benzene plane is 3.50 8, and decreases by 45 m8, upon
electronic excitation of the benzene to the S, state. Despite
the spectroscopic complexity presented by the internal rotation of the N, molecule, this phenomenon is nevertheless of
particular interest for future studies. Namely, this internal
rotation serves as a probe of the anisotropy and wavelike
1 3.50A
3.5. Benzene-Molecule Complexes
The two previous sections were concerned with complexes
formed by the absorption of noble gas atoms with isotropic
polarizabilities to the benzene molecule. The next step is the
absorption of simple diatomic molecules with anisotropic
polarizabilites to the benzene surface. The benzene-N, complex has been studied by Doppler-free spectroscopy.[361.The
rotationally resolved spectrum yields the structure shown in
Figure 13, in which the N, molecule is adsorbed parallel to
the benzene surface. Besides the transitions which corre272
Fig. 13. The experimentally determined structure of the benzene-N, complex.
Lying in the plane parallel to the benzene ring at a distance of 3.50 A, the
nitrogen molecule internally rotates about the sixfold rotational axis of the
Angew. Chem. Int. Ed. Engl. 31 (1992) 263-273
curvature of the van der Wads binding potential with respect
to rotation about the sixfold axis, which is caused by the
periodic change in electron density along the benzene ring.
larger and differently bound complexes will lead in the near
future to a deeper understanding (at the microscopic level) of
intermolecular bonds, such as the hydrogen bond, and of
complexation and solvation processes integral to chemical
and biological processes in the liquid phase.
4. Summary and Outlook
Through the rapid development of new methods in laser
spectroscopy it is possible, even for large molecular systems,
to observe spectroscopic fine structures which are hidden by
Doppler broadening in conventional high resolution spectroscopy. Elimination of the Doppler broadening allows the
spectroscopic study of such systems with a precision previously possible only for atoms or small molecules; thus, access is provided to the domain of high resolution spectroscopy within the Doppler width. In this manner, more
and more chemically relevant issues which are typical for
large systems can be addressed.
Intramolecular energy redistribution, as the primary process preceding chemical reactions, is of fundamental importance in reaction kinetics. With a detailed understanding of
this process, the influence or even control of chemical reactions should be possible. For this reason it is understandable
that there has been substantial activity in the last two
decades in the field of intramolecular vibrational redistribution. Whereas a general theoretical understanding of intramolecular vibrational redistribution through the theory
of radiationless processes is available, precise experimental
results to serve as critical tests of the theoretical models are
seemingly scarce. In this article, using a test molecule we
have proven the power of high resolution spectroscopy in
this respect. Resolution of the band structure of the benzene
spectrum into many individual rotational lines enables monitoring of the development of vibrational redistribution from
the situation typical for small molecules to that for large
molecules with their high level densities. Analysis of these
initial results furnishes the surprising new finding that not
only anharmonic coupling must be considered as the coupling mechanism, but rather that rotational-vibrational interaction in the form of Coriolis coupling also plays an essential role. The results thus obtained also permit a quantitative
comparison with theoretical models and give a deeper insight
into the coupling mechanisms.
The second part of this article demonstrated that Dopplerfree spectroscopy furnishes detailed spectroscopic information on the large field of weakly-bound van der Waals complexes. The rotational line spectrum of selected complexes in
the mixture of many clusters produced in the cooled molecular beam can be measured by the combination of Dopplerfree excitation with mass-selective two-photon ionization.
Initial experiments have yielded the structures and precise
van der Waals bond distances for benzene-noble gas dimers
and trimers and complexes of benzene with small molecules.
These results demonstrate the precision and unambiguity of
the statements regarding structure made possible by
Doppler-free spectroscopy.
Doppler-free spectroscopy of van der Waals complexes is
a very young field of research. For this reason Doppler-free
spectra currently exist for only a few prototype systems.
These few examples nevertheless outline the full scope of
applications of this new spectroscopic method. Studies of
Angen. Chem. lnt. Ed. Engl. 31 (1992) 263-273
The authors would like to thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie forfinancia1 support of this research. We thank Drs. Riedle, Schubert,
Sieber and Weberfor invaluable collaboration with the experiments and interpretation of the results. We also wish to thank
Dr. Alice M . Smith for the English translation of this article.
Received: December 3, 1991 [A 857 IE]
German version: Angew. Chem. 1992, 104, 269
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