Download Dependence of Intramolecular Vibrational Relaxation on Central

8282
J. Phys. Chem. 1991,95, 8282-8293
Energy (e")
Flgm 3. Sticking probability (logarithmic scale) vs the incident collision
energy (in electronvolts) for different f a c e of a pt crystal. The real part
of the optical potential takes full cognizance of the atomic arrangement
at the different faces. The imaginary part of the optical potential is the
same for all three computations,with L = 1.0 eV, zo = 2.0 bohr, and Y
= 0.1 bohr. For the (1 11) face the O2molecule can approach the surface
closer in than for the other two. Hence at higher energies its sticking
probability begins to decrease with increasing energy that is the generic
behavior for nonactivated chemisorption.
much simplifies the interpretation of the resulting energy dependence. It implies that only part of the imaginary potential
V l ( r ) ,which is in the classically accessible region, z > z,, can
influence the removal of molecules from the direct channel. The
turning point z, defined by E = Vo(z,)occurs at lower values of
z as the energy is increased.
At low collision energies the imaginary potential is de facto
inaccessible. The Gaussian form of V l ( z )means that 7 is never
exactly zero. However, at low energies 7 is itself exponentially
small so that P is zero for all intents and purposes. The initial
exponential increase of 7 with E leads to the apparent threshold
in P seen in Figure 1. We reiterate that results indistinguishable
from Figure 1 are obtained using the first-order perturbation
approximation for q so that the post threshold increase in P is here
entirely due to the behavior of the scattering wave function in the
classically allowed region. Why is tunnelling into the forbidden
region unimportant in our model? The answer is that at lower
energies when tunnelling will be most important, 7 is exponentially
small itself, so that P is essentially negligible. At higher energies
the tunneling contribution to 7 remains small yet 7 itself is larger,
so that P is determined primarily by the classically allowed
contributions to 7.
Figure 3 shows the calculated dissociation probability of O2
on three different faces of R. Our purpose was not to reproduce
any particular experimental results but to demonstrate that the
model can exhibit considerable structure sensitivity. The real
potential Vo(z)was calculated as described earlier by summation
of pair potentials with respect to all surface atoms over a particular
site. To make a direct comparison between scattering from three
different faces of the same crystal, an -atop" site was chosen in
each case to calculate the real potential Vo(z).The same Gaussian
functional form for V,(z)is used throughout.
The differences between the calculations for the three different
faces are entirely due to the distances of closest approach. For
the (1 11) face the molecule can approach closer and thereby
sample more of the imaginary part of the potential. It is interesting
to note that the same order of reactivity of the three faces is
observed experimentallyBfor N2on Fe. Other things being equal,
the model predicts that the most important parameter is the
distance of closest approach.
Conclusion
The optical model is based on the distinction between those
molecules that are scattered promptly off the surface and those
that are not. The sticking probability is computed in terms of
an imaginary component of the molecule-surface potential. In
this quantitative study we have established that the activated
adsorption can be represented by an imaginary potential that is
localized at short molecule-surface distances. There is then no
strict energy threshold for adsorption, but there is a de facto
threshold above which the sticking probability increases exponentially with collision energy. The sensitive dependence of the
probability on the distance of closest approach can explain the
significant differences in reactivity exhibited by different faces
of the same crystal.
Registry No. N2,7727-37-9; Re, 7440-15-5; 02,7782-44-7; Pt,
7440-06-4.
Dependence of Intramolecular Vibrational Relaxation on Central Atom Substitution: v1
and 2v, Molecular Beam Optothermal Spectra of (CH3)&C=CH and (CH,)3SIWH
E. R. Tb. Kentel, K. K. Lehmann,* T. F. Mentel, B. H. Pate, and G. Stoles*
Department of Chemistry. Princeton University, Princeton, New Jersey 08544 (Received: February 25, 1991)
Using the optothermal detection method for molecular beam infrared spectroscopy, we have measured, with rotational resolution,
All spectra
the fundamental and first overtone of the acetylenic C-H stretch in (CH3),CC=CH and (CH3)@=H.
show homogeneous broadening due to intramolecular vibrational energy relaxation (IVR), which results in Lorentzian line
shapes for the individual R(J)and P(J)transitions. From the homogeneous line widths we are able to determine the lifetime
of the initial vibrational excitation. For (CH3)3CC=CH the lifetimes in the fundamental and first overtone are 200 and
110 ps respectively. For (CH3)pSiC=CHthe lifetimes are 2 and 4 ns for the fundamental and first overtone. All of these
lifetimes are long compared to values typically given for IVR lifetimes. Despite the fact that the silicon compound has a
higher density of states at both levels of excitation, the line width of the silicon compound is much narrower than that of
(CH3)3CCWH. Furthermore, the density of states of the silicon compound increases by more than a factor of IO00 in
going from the fundamental to the overtone, and yet the line width of the overtone is narrower than it is in the fundamental.
Although we consistentlyfind that the IVR lifetime of the molecule with the heavier central atom is longer, a simple heavy-atom
effect for the inhibition of IVR does not appear to fully explain the data.
Introduction
The study of intramolecular vibrational energy relaxation in
isolated molecules is of central importance in physical chemistry.
In particular, the great success of standard statistical reaction rate
0022-3654/91/2095-8282S02.50/0
theory (RRKM)'v2suggests that vibrational energy redistribution
is rapid on the time scale of typical chemical reactions. Studies
(1) Oref. I.; Rabinovitch,
B. S.Acc. Chem. Res. 1979, 12, 166.
0 1991 American Chemical Society
Intramolecular Vibrational Relaxation
of vibrational relaxation, in both the fmt excited electronic state>-'
and the ground electronic state: have shown that the onset of IVR
occurs at quite low energies for larger polyatomic molecules. Often
extensive IVR is observed in the energy region of the high-frequency vibrational fundamentals. For the ground state it has been
seen that the onset of IVR occurs when the density of background
rovibrational states reaches about 100 ~tates/cm-'.~ This
threshold level predicts the onset of IVR for a very large number
of molecules for excitations in a number of different chromophores.
Although there is general agreement that the onset of IVR
occurs at low energies, there is still very little information on the
true homogeneous lifetime of vibrational excitations. Estimation
from the contour of gas-phase vibrational bands has been one
experimental method used to provide lifetime information.
However, evaluations from gas-phase measurements can greatly
overestimate the rapidity of the energy relaxation process since
the rotational and hot-band congestion can cause extensive inhomogeneous broadening in the measurement. For example, the
gas-phase photoacoustic spectra of benzene suggest that IVR is
very rapid in the overtones of the C-H stretches.* Molecular
beam double-resonanceexperiments, which provided some rotational selectivity, later showed that the homogeneous IVR lifetime
of the first overtone was significantly longer than suggested by
the gas-phase result^.^
There is inherently some ambiguity about what is meant by
the homogeneous lifetime of an isolated molecule. The homogeneous spectrum is clearly defined as the set of transitions arising
from a single, well-defined initial state (a single rotational state
in the vibrational ground state, for example). Under experimental
conditions allowing ultimate resolution (determined by the radiative line width), such a spectrum will consist of a series of sharp
transitions as long as the density of states is low enough that only
a single state lies within the radiative line-width profile.IO A short
laser pulse (short on the time scale of the intramolecular vibrational
relaxation) will create a unique nonstationary state (the bright
state) due to the excitation of the set of molecular eigenstates lying
within the frequency bandwidth of the laser pulse. The Fourier
transform of the autocorrelation of the homogeneous spectrum,
denoted &,b(t),'l is then equal to the probability of the molecule
being in the initially created bright state at time t. Thus such
a frequency-resolved homogeneous spectrum directly provides the
probability of being in the bright state but does not provide direct
information about what other states are populated by the dynamics. &,(I) will always have recurrences on the time scale of
the density of states, leading to sharp eigenstates in the spectrum
when the resolution is greater than the spacing between background states. For experimental cases where the homogeneous
spectrum consists of a large number of eigenstates (intermediate
or statistical case IVR) the initial decay of Pbb(t)will be approximately exponential.IO The time scale of this initial decay
is given by the inverse full width of the homogeneous spectrum
in the frequency-resolvedexperiment. It is often the case that
P b ( t ) will have recurrences at one or more times between these
two limits reflecting multiple time scales over which the vibrational
excitation is transferred between different modes in the molecule.
It is certainly overly simplistic and even a little misleading, to
describe such rich dynamics in terms of a single "lifetime". In
certain cases, however, Pb(t) decays rapidly compared to the long
time limit imposed by the density of states, and recurrences do
not occur until this time. As discussed by Heller," in this case
(2) Subds, A. S.; Schulz, P. A.; Grant, E. R.; Shen, Y. R.; Lee, Y. T. J .
Chem. Phys. 1979, 70, 912.
(3) Parmenter, C. S. J . Phys. Chem. 1982.86, 1735.
(4) Parmenter, C. S. Faraday Discuss. Chem. Soc. 1983, 75, 7.
(5) Smalley, R. E. Annu. Rev. Phys. Chem. 1983, 34, 129.
(6) McDonald, J. D. Annu. Rev. Phys. Chem. 1979, 30, 29.
(7) Kim, H. L.; Kulp, T. J.; McDonald, J. D. J . Chem. Phys. 1987,87,
._.-.
A116
(8) Rcddy, K. V.; Heller, D. F.; Berry, M. J. J . Chem. Phys. 1982, 76,
28 14.
(9) Page, R. H.; Shen, Y. R.; Lee, Y. T. J . Chem. Phys. 1988.88,4621.
(10) Freed, K. F.; Nitzan, A. J . Chem. Phys. 1980, 73.4765.
( I 1 ) Heller, E. J. Faraday Discuss. Chem. Soc. 1983, 75, 141.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8283
the molecular motion has sampled the energy shell almost ergodidly and calling the decay a "relaxation" agrees with common
usage of the word. We believe that this situation describes the
spectra we report in this paper. It must be remembered that any
spectroscopic experiment is sensitive only to recurrences over some
window of time determined by the spectral window explored on
the one hand (giving the shortest time) and the effective resolution
on the other (giving the longest time). Our experimentsare only
sensitive for long times up to about 20 ns (determined by residual
Doppler broadening, which limits our experimental resolution).
For the molecules we are studying, this long time limit is less than
the time scale imposed by the density of states. Thus we can
rigorously interpret our spectra only as implying a homogeneous
relaxation that is effectively irreversible for a time of 20 ns or less.
The presence of recurrences on a time scale longer than our
experimental limit would imply relaxation processes much slower
than those reported herein, which are already the slowest IVR
rates that have ever been reported.
Recently, high-resolution measurements of the vibrational
spectra of larger polyatomic molecules in molecular beams have
been performed with the goal of studying the IVR process.l2-I8
In this paper we are interested in these frequency domain experiments and their interpretation in the context of IVR. There
has also been much progress in time domain measurements of the
IVR process in both the ground electronic state19 and the first
excited electronic state;mhowever, we limit the scope of this paper
to the results obtained from high-resolution spectroscopy. In these
spectra the presence of IVR is indicated by extensive perturbations
to the expected zero-order spectrum. These perturbations occur
when vibrational states, which otherwise would have no transition
strength (the so-called dark states), couple to the optically active
vibrational state being studied (the bright state). This coupling
allows the vibrational energy to redistribute over the entire
molecule since the coupled states often involve the motion of a
number of different atoms in the molecule. Through the study
of these perturbations the high-resolutionspectrum provides information on the vibrational dynamics of the molecule. The
information is often obtained with full-state (J,K) resolution, and
so the dynamical information obtained is truly homogeneous.
The high-resolution studies reported to date have all shown the
presence of several very weak perturbation^.'^-'^ The states that
appear in the spectrum due to these vibrational couplings to a
single zero-order state are termed the molecular eigenstates.
Typically, as the background density of states increase, the number
of molecular eigenstates observed will also increase. When the
number of molecular eigenstates reaches about 10, the molecule
is said to be in the "intermediate regime" of IVR.'O It has been
shown that in this regime the lifetime of the initial excitation can
be determined by calculating the time evolution of a coherently
excited superposition of the eigenstatessZ1 When the exciting
optical pulse is short compared with this lifetime, the initial decay
of the prepared state is approximatelyexponential at early times
with a decay rate given by a Fermi Golden Rule formula.lOJ
Since it is often possible to assign the high-resolution spectrum
with rotational quantum numbers, this calculation can be performed homogeneously; that is, only the eigenstates with the same
(12) deSouza, A. M.; Kaur, D.; Perry, D. S. J . Chem. Phys. 1988,88,
4569.
(13) Go, J.; &hardy, G.A.; Perry, D. S. J . Phys. Chem. 1990,94,6153.
(14) Bethardy, G. A.; Perry, D. S. J. Mol. Specfrosc. 1990, 144, 304.
(15) McIlrov, A,; Nesbitt, D. J. J . Chem. Phvs. 1989. 91. 104.
(16) McIlrG, A.; Nesbitt; D. J. J . Chem. Phs. 1990; 92; 2229.
(17) Lehmann, K. K.; Pate, B. H.; Scoles, G. J . Chem. Soc., Faraday
Trans. 1990. 86. 2071.
(18) Lehmann, K. K.; Pate, B. H.; Scoles, G. J. Chem. Phys. 1990, 93,
2 152.
(19) Stewart, G. M.; Ensminger, M. D.; Kulp, T. J.; Ruoff, R. S.;
McDonald, J. D. J. Chem. Phys. 1983, 79, 3190. Stewart, G.; Ruoff, R.;
McDonald, J. D. J. Chem. Phys. 1984,80,5353. Kulp, T.; Ruoff, R.; Stewart,
G.; McDonald, J. D. J . Chem. Phys. 1984,80, 5359,
5359.
(20) Felker, P. M.; Zewail, A. H. J . Chem. Phys. 1985,82, 2961. Felker,
P. M.; Zewail, A. H. J . Chem. Phys. 1985,82,2975. Felker, P. M.; Zewail.
A. H. J. Chem. Phys. 1985,82,2994. Felker, P. M.; Lambert, W. R.; Zewail,
A. H. J . Chem. Phys. 1985.82, 3003.
(21) Lahmani, F.; Tramer, A.; Tric, C. J . Chem. Phys. 1974, 60, 4431.
8284 The Journal of Physical Chemistry, Vol. 95, No. 21, 199‘1
good quantum numbers, typically the rotational quantum numbers,
are included in the calculation. In this way the homogeneous
lifetime of a few molecules have been calculated.’= The reported
lifetimes have ranged from a few hundred picoseconds to a few
nanoseconds. These homogeneous lifetimes are longer than the
few picosecond lifetimes often assumed for IVR.
When the density of states is very high, the molecule enters
the statistical regime of IVR.’O In this case there is irreversible
flow of the energy out of the initially excited mode. This decay
takes the form of an exponential decay and a Lorentzian lineshape
will be observed in the spectrum. We have recently observed true
Lorentzian broadening due solely to IVR in the fundamentals of
(CH3)$CWH and (CH3)$iC=CH.18 In other studies the
spectra have been fit to convolutions of Lorentzian line shapes
with a predicted rigid-rotor spectrum.I6 The observed lifetimes
have been on the order of a few picoseconds to a few nanoseconds.
The question of the homogeneous IVR line width for vibrational
excitations is of obvious importance for the prospects of performing
laser-enhanced, mode-specific, chemistry of large molecules: a
longstanding goal of experimental physical chemistry. It has
recently been shown that direct overtone excitation of HOD leads
to a great enhancement of a mode-specific reaction with H atoms.23
However, HOD is a molecule that is too small to show IVR at
the level of excitation used in the experiment, so the energy must
remain localized until a collision occurs. For larger molecules
a prerequisite for similar mode-specific reactions becomes that
the IVR rate be slower than the collision rate, so that the energy
will still be localized in the reaction coordinate when a possible
reactive collision occurs. Since for typical gas pressures (- 1 atm)
there will be about 10’O collisions/s, IVR lifetimes on the order
of a few hundred picoseconds or longer are required.
In the early 198h chemical activation studies on molecules with
heavy central atoms showed non-RRKM reaction rates suggesting
that the presence of a heavy atom could serve to localize energy
in one of the ligand^.^^,^^ These initial results led to a number
of additional experimental ~ t u d i e s ~and
~ * ~to’ much theoretical
directed toward determining if a “heavy-atom effect”
operates in these systems to decrease the IVR rate. However,
both the experimental and theoretical results were somewhat
ambiguous. Part of the problem is separating the effect of simply
changing the mass from the chemical effects that accompany the
substitution of a larger atom, such as reduced bond strengths and
longer bond lengthsDJ5 Possible evidence of a heavy-atom effect
for reducing IVR has also come from gas-phase photoacoustic
studies of the overtones of molecules containing heavy
A study of the relaxation rates of alcohols and silanols in solution
also showed a longer lifetime for the heavier species.38 Still, the
question of whether heavy-atom substitution inhibits IVR, as well
(22) Pate, B. H.; Lehmann, K. K.; Scolcs, G. To be published in J. Chem.
Phys.
(23) Sinha, A.; Hsiao, M. C.; Crim, F. F. J . Chem. Phys. 1990,92,6333.
(24) Rogers, P.; Montague, D. C.; Frank, J. P.; Tyler, S.C.; Rowland, F.
S . Chem. Phys. Lett. 1982,89,9.
(25) Rogers, P. J.; Selco,J. I.; Rowland, F. S.Chem. Phys. Lett. 1983,97,
313.
(26) Wrigley, S.P.; Rabinovitch, B. S.Chem. Phys. Lett. 1983,98, 386.
(27) Wrigley, S.P.; Oswald, D. A.; Rabinovitch, B. S.Chem. Phys. Lett.
1984, 104, 521.
(28) Lopez, V.; Marcus, R. A. Chem. Phys. Lett. 1982, 93, 232.
(29) Swamy, K. N.; Hase. W. L. J . Chcm. Phys. 1985, 82, 123.
(30) Lopez, V.; Fairen, V.; Lederman, S. M.; Marcus, R. A. J . Chem.
Phys. 1986,84, 5494.
(31) Lederman, S.M.; Lopez, V.; Voth, G. A.; Marcus, R. A. Chem. Phys.
Lett. 1986, 124, 93.
(32) Lederman, S.M.: Lopez, V.; Fairen. V.: Voth, G.A,; Marcus, R. A.
Chem..Phys. 1989. 139, 171.(33) Uzer. T.; Hynes, J. T. Chem. Phys. 1989, 139, 163.
(34) Uzer, T.; Hynes, J. T. J. Phys. Chem. 1986, 90,3524.
(35) A discussion of these results can be found in Faraday Discuss. Chem.
Soc. 1983, 75, 155 (General Discussion Section).
(36) Manzanares, I. C.; Yamasaki, N. L. S.;Weitz, E.; Knudtson, J. T.
Chem. Phvs. Lett. 1985. 117. 411.
(37) Manzanares, I. C.;Yamasaki, N. L. S.;Weitz, E. J . Phys. Chem.
1989, 93, 4133.
(38) Heilwcil, E. J.; Casassa, M. P.; Cavanagh, R. R.; Stephenson, J. C.
J . Chem. Phys. 1986.85, 5004.
~
Kerstel et al.
as which physical properties actually define the heavy-atom effect,
are open problems.
In this paper we report homogeneous lifetime data for isolated
molecules using high-resolution, molecular beam optothermal
spectroscopy. We have measured both the fundamental and first
overtone of the acetylenic C-H stretch in 3,3-dimethylbutyne
(tert-butylacetylene) and (trimethylsilyl)acetylene, where the
central atom is substituted by silicon. The ability to measure the
lifetime at two levels of excitation allows us to see if a mass
dependence alone can account for our results or whether other
mechanisms are important in determining the IVR lifetime of the
vibrational excitation.
These molecules provide a convenient model system for studying
the vibrational energy relaxation of molecules containinga heavy
central atom. Most of the background states involve motions of
the trimethyl end of the molecule since most of the vibrational
modes related to the acetylene chromophore have high frequencies.
For the vibration to kinetically reach these modes it must pass
through the central atom. Since we are exciting a low-lying
vibrational motion that is localized in the terminal C-H end of
the acetylene, we expect that central atom substitution will cause
only small differences in the nature of the motion initially excited.
Since the central atom is on the symmetry axis and near the center
of mass of the molecule, there are only small changes in the
rotational constants. The symmetry of the two molecules is also
the same. Therefore, direct comparison of the spectra can be
made, allowing us to clearly determine the effect of central atom
substitution.
Experimental Section
The molecular beam infrared spectrometer uses the technique
of optothermal bolometric d e t e ~ t i o n . ’ ~ .In~ short, a well-collimated molecular beam, of a carrier gas (He) seeded with the
molecule that is to be studied, is crossed with infrared laser radiation. A bolometer detector placed further downstream detects
changes in the internal energy of the molecular beam. Using two
color center lasers, the tuning range comprises both the fundamental and the first overtone vibrational excitation region of
(among others) acetylenic C-H stretches.
In this section we will describe first the molecular beam machine, followed by the laser and data acquisition systems. Because
of the particular advantages offered by this technique for overtone
spectroscopy, we will conclude this section by comparing it in some
detail to other methods.
Molecular Beam Machine. The molecular beam machine,
showing in Figure 1, consists of two vacuum chambers, each
pumped by a 5000 L s-’ oil-diffusion pump, backed by a single
rotary/Roots combination. In one chamber the sample gas is
expanded through a 30-pm diameter nozzle (a Structure Probe,
Inc., electron microscope aperture) at a typical backing pressure
of 10 bar, with dilution ratios in the range 0 5 1 % . The molecules
used in this study were obtained from Aldrich Chemical Co. The
vapor phase was used without further purification. The beam
source and gas-inlet line assembly can be heated, to approximately
400 K at the nozzle, in order to prevent excessive clustering, while
maintaining high throughput rates. For the study of van der Waals
molecules, for which the machine was originally designed, the
source is also equipped with a cryogenic cooler. A 0.5-mm-diameter conical skimmer, located 12 mm downstream, collimates
the polecular beam, which enters the second chamber and is
detected by a liquid helium cooled (1.5 K) composite-type silicon
bolometer (Infrared Laboratories) located 44 cm from the nozzle.
Measurement of the dc current through the bolometer as a
function of its bias voltage revealed a noise-equivalent power of
5 X
W Hz-II2 and a sensitivity of 5.5 X IO5 V W-I. The
W Hz-’/’
manufacturer’s (measured) specifications are 3 x
and 7.7 X lo5 V W-I, respectively. The 3-dB point in the fre(39) Gough, T. E.; Miller, R. E.; Scoles, G. Appl. Phys. Lett. 1977, 30,
338.
(40)Miller, R. E. In Atomic and Molecular Beam Methods; Scoles, G.,
Ed.; Oxford University Press: Oxford Vol. 2, Chapter 6, in press.
Intramolecular Vibrational Relaxation
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8285
,wF=-\--[ n
quency response curve occurs near 400 Hz. The detector “sees”
the molecular beam through a 1.5 X 3 mm slit in its liquid helium
cooled shielding. To further reduce the amount of black-body
radiation and scattered laser light, a second aperture, measuring
1.5 X 4 mm and held at liquid nitrogen temperature, is placed
approximately 65 mm in front of the bolometer. Even with these
measures in place, the output power level of our overtone (1.5 pm)
laser is sufficiently high to produce an appreciable background
signal, on the order of 10 times the noise level. Changes in the
baseline, sometimes observed in overtone spectra, therefore reflect
changes in the output power as the laser is scanned.
The infrared laser radiation is crossed with the molecular beam
by weakly focusing it into a plano parallel mirror multipass arrangement, thereby increasing the detection sensitivity by 1 order
of magnitude over a single-pass crossing. Due to the slightly
nonorthogonal crossings, the resolution is limited by a residual
Doppler broadening amounting to 10 MHz at 3 pm and 20 MHz
at 1.5 pm. The laser is amplitude modulated at 280 Hz, in a
window in the noise spectrum. The detector signal is preamplified
and fed into a lock-in amplifier (Stanford Research 510). Typical
root-mean-squared noise levels in a 1-Hz bandwidth are around
60 nV. Expanding 1% acetylene in helium at a stagnation pressure
of 10 bar, we achieve a S / N ratio of lo4 on the P(l) transition
for the fundamental (the 3-pm v 3 band) and about 5 X lo3 for
overtone (the 1.5-pm v, v3 band) excitation. However, taking
into account that in this particular case the fundamental transition
is saturated, the overall sensitivity for overtone excitation is about
8 times below that of fundamental excitation. This is consistent
with the number calculated considering the two transition dipoles
and the available laser power.
Laser System and Data Acquisition. Infrared laser radiation
is provided by two commercial color-center lasers. The first, a
Burleigh FCL- 120, relies on laser action in the 1.5-pm region of
TIo(1) color centers in a KCl host. It is pumped with the fundamental output at 1.064 mm and 1.9 W of a Spectra-Physics
3460, continuous-wave(CW) Nd:YAG laser. Mode locking of
the pump laser and an optical isolator both provide protection
against relaxation oscillations caused by optical feedback. This
+
0
color center laser is tunable, single-mode, from 1.45 to 1.58 pm
and provides about 150 mW of power at 1.53 pm, measured at
the machine. Its free running line width is estimated to be 6 MHz
(from a molecular beam acetylene absorption with a single orthogonal laser crossing) and is believed to be caused mainly by
pump laser power fluctuations. The second laser, the more
common Burleigh FCL-20, uses three crystals to achieve a combined single-mode tuning range from 2.3 to 3.45 pm. In the region
of the fundamental acetylenic C-H stretch, around 3.0 pm, we
obtain 18 mW (again measured at the machine) when pumping
the RbC1:Li-F,(II)-crystal with 2 W from the 647.1-nm line of
a Spectra-Physics Model 171 Kr+ laser. The free-running line
width is on the order of 1 MHz.
The singlemode scanning of these lasers is completely computer
controlled. To ensure lasing on the proper cavity mode in the
course of a scan, it is essential that the intracavity etalon, and
to a lesser extend the grating, accurately track the scanning cavity
mode. To this end, both etalon and grating are advanced in a
feed-forward manner. In addition, the etalon transmission is
actively locked to the lasing cavity mode with a feedback loop,
as described previously by Kaspar et al.4’
One aspect of the operation of our lasers that deserves to be
described in detail is the way in which the scans are linearized
in frequency. This is an important issue for high-resolution
spectroscopy, as tuning of the intracavity elements can cause
frequency jumps of which the exact magnitude is unknown but
that are of the same order of magnitude or larger than the desired
spectral precision (Le., typically 1 order of magnitude better than
the experimental line width). When, for example, the Littrow
mount grating is advanced, an associated small change in cavity
length generally causes the laser to rescan anywhere from 0 to
20 MHz of the spectrum. The exact step size is unpredictable,
due to the finite mechanical accuracy of the sine-drive/grating
combination. A common solution to this problem has been to scan
the laser to a nearby transmission of a long, temperature-stabilized
(41) Kaspar, J. V. V.;Pollock, C. R.;Curl, Jr., R. F.;Tittel, F.K. Appl.
Opt. 1982, 21, 236.
8286 The Journal of Physical Chemistry, Vol. 95, No. 21, 199'1
etalon, so the scan can be resumed at exactly the same point after
the grating has been advanced." A similar procedure then has
to be followed when the end mirror and intracavity etalon piezo
ramp voltages need to be reset. This makes the necessary software
rather complicated and slow. To overcome these problems, we
continuously monitor the laser frequency with two scanning etalons
(spectrum analyzers), using an electronic circuitry, originally
designed and built by W. S.Woodward for the laboratory of R.
E. Miller.'2 A 150-MHz FSR etalon (Burleigh CFT 500) serves
as the frequency reference, while an 8-GHz etalon is used to
correctly identify the 150-MHz etalon order. The electronic
circuitry receives the piezo ramp and the scanning etalon detector
signals. It produces as its output for each scanning etalon the
piezo ramp voltage for which (the first) transmission occurred.
In this way, a continuous frequency map of the scan is obtained
and stored with the data (bolometer signal and gas-cell transmissions). The linearity of the spectrum now only depends on
the linearity of the I50-MHz etalon piezo scanning over one FSR
and the frequency stability of the etalon. The etalon is therefore
temperature stabilized to 0.01 OC and hermetically sealed. A
nonlinearity in the response of the 150-MHz etalon piezo can be
made very small by adding an independent quadratic term to its
ramp voltage.
This frequency monitoring scheme allows for a relatively simple
and efficient programming of the loop that controls the singlemode scanning and can achieve scan speeds up to 10 cm-'/h.
When the scan is completed, the discontinuities in the frequency
spectrum are removed by (partially interactive) software routines.
The data are subsequently transferred to the spectral fitting
program D E C O M P ~to~ extract the linepositions and lineprofile
(Voigt) parameters.
Comparison with Other Methods. It is only recently that
high-resolution spectroscopic studies of larger molecules have been
carried out under sub-Doppler molecular beam conditions with
the explicit purpose of studying IVR in the ground electronic state.
The experimental challenges are substantial: especially in the
sparse and intermediate regimes, ultimate resolution and sensitivity
are required to observe all states (perturbation) that appear in
the spectrum and that are often due to very weak high-order
couplings. Furthermore, an accurate determination of the rotational constants (in particular the aA*sand aB's) is useful in
determining the character of the perturbing state@). Therefore,
even though extreme cooling of the intermolecular degrees of
freedom can greatly reduce the spectral congestion and improve
the S/N on low-J and low-K lines, it is actually desirable to obtain
as "warmwa spectrum as the S / N and resolution will permit.
With the above in mind, we will discuss hereafter the factors
that are important in evaluating the two related experimental
techniques employed to date in these high-resolution IVR studies:
direct absorption and energy deposition. In approximate order
of importance, for high-resolution studies of stable molecules, these
factors are as follows:
(i) Sensitivity. In the direct absorption method, the laser is
passed (in a multipass arrangement) through the high-density
region of an unskimmed, free-jet expansion. Molecular absorption
is measured by the resulting attenuation of the laser beam. Since
the optical density of the free jet is very low, extreme demands
are placed on the detection system and in particular the laser
amplitude stability. It is immediately seen that the sensitivity in
this case does not depend on the available laser power (as generally
the noise level is limited by laser amplitude noise, rather than the
NEP of the detection system). The sensitivity is ultimately limited
to the laser shot-noise level. With a carefully designed twebeam
detection system Nesbitt and -workers obtained a near shot-noise
limited minimum detectable absorption of 1.4 X lod Hz-'IZ for
their difference-frequency, slit-jet spectrometer.u This figure
may seem low compared to the sensitivity of a color-center laser
(42) Circuit designed by W.S. Woodward,Digital Specialties, 1702 Allard
Rd., Chapel Hill, NC.
(43) DeCOMP was provided by P.Bernath and was originally written by J.
Brault, National Optical Astronomy Observatory, Tuscon, A Z 85719.
(44) Lovejoy, C. M.; Nesbitt, D. J. J . Chcm. Phys. 1987, 86, 3151.
Kerstel et al.
(output power = 10 mW in the 3-pm region) optothermal spec~.~
the
trometer that can be better than 1O-Io H Z - ~ / However,
beam flux in an optothermal apparatus is limited by the requirement of a well-collimated beam and by the degrading of the
bolometer responsivity together with an increase in its noise level
that would accompany a very large beam intensity. In contrast,
the density-length product appearing in the Lambert-Beer absorption law can be made very large in the pulsed slit-jet expansion,
direct absorption, experiment. This is of particular concern when
the species under study are van der Waals molecules, the production of which is highly favored by expanding large quantities
of gas. Recently, Bevan and co-workers reported on a CW slit-jet
spectrometer using a frequency modulated diode laser in the 5-pm
region4swith a sensitivity comparable to that of the pulsed slit-jet,
difference frequency, spectrometer of Nesbitt and co-workers.
However, when the transition dipole matrix element of the
molecular excitation is much smaller, as is the case for overtone
excitation (typically by a factor of 40-100), the sensitivity of the
direct absorption method is irrevocably reduced by the same factor,
while in an optothermal spectrometer this loss can be compensated
for by an increase in the power of the laser source (when this is
available). The spectrum of the 2ul band of the HCN dimer,&
obtained with our spectrometer, as well as later overtone studies
of acetylenic mole~ules,~~'
which have shown excellent S/N ratios,
serve to prove this point.
(ii) Resolution. Pioneering studies of the kind as those discussed
here were camed out with a 3-pm color-center laser in combination
with a pulsed, free-jet, pinhole expansion in the laboratory of D.
S. Perry.'2I4 In these experiments the expansion was not skimmed
to form a collimated molecular beam. Instead the laser was
multipassed through the free-jet, close to the pulsed valve opening,
to maximize the absorption density-length product. Without
further measures, the experimental resolution is entirely determined by the Doppler broadening (approximately 300 MHz for
1-butyne12),due to the stream lines fanning out in two dimensions.
The same laboratory demonstrated that a resolution of 12 MHz
can be achieved, with a sliced-jet pinhole expansion, without
seriously reducing the s e n ~ i t i v i t y . In
~ ~this
~ ~ simple and elegant
approach to the problem of Doppler broadening, a narrow metal
blade was inserted in the center of the expansion, just before the
laser crossing, to deflect molecules from the center line of the
expansion that absorb with near-zero Doppler shift (as opposed
to retaining only this group of molecules by beam collimation).
The result is a spectrum in which the Doppler broadened lines
show a narrow dip in the center.
In the slit-jet expansion method the residual Doppler broadening
is reduced to about 30 MHz (for heavier molecules), when the
laser beam propagates parallel to the long axis of the slit. This
results from the tendency of the one-dimensional expansion to
strongly narrow the velocity distribution in the direction of the
laser beam.
In the case of optothermal detection, the contribution to the
overall line broadening from the frequency instabilities of the laser
source, the Doppler effect, and transit-time broadening can be
made very small (on the order of 100 kHz or less, by stabilizing
the laser with the help of an external cavity, by seeding in a heavier
carrier gas to reduce the beam velocity, by further collimation
of the molecular beam, and by increasing the size of the molecular
beam-laser interaction region). However, in most practical situations it is difficult, though not impossible, to reduce the observed
line width to much less than 1 M H Z . ~
(iii) Cooling of Internal Degrees of Freedom. McIlroy and
Nesbitt found that their linear jet produces a nearly perfect
(45) Wang,Z.; Eliadcs, M.; Carron, K.;Bevan, J. W.Rev. Scf. Instrum.
1991,62, 21.(46) Meyer, H.; Kerstel, E.R.Th.; Zhuang, D.;Scoles, G. J. Chem. Phys.
1989, 90,4623.
(47) Kerstd, E. R.T.;Lchmann, K.K.;McIlroy, A.; Nesbitt, D. J.; Pate.
B. H.;Scoles, G., manuscript in preparation.
(48) Mercorelli, L. R.; Hammand. S. A.; Perry, D. S. Chem. Phys. Lett.
1989, 162, 277.
(49) Kaur. D.: dcSouza. A. M.: Wanna. J.: Hammand. S.A.: Mcrcorelli.
L.;Pe&y, D.'S.
Appl. Opi. 1990,.29, 119.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8287
Intramolecular Vibrational Relaxation
equilibrium in the rotational (J as well as K ) state po ulations
and the (parallel) translational temperature of the jet.' The K N
= 0 and 1 (J" = 1-7) intensities of the P and R branch of the
u2 transition in pmpyne are well described by a single temperature,
indicative of Boltzmann statistics.
It is generally accepted that the pinhole expansion tends to
produce J and K state distributions that are not equilibrated. The
higher J levels are relatively overpopulated, whereas J and K
'temperatures" (assuming that the population of the corresponding
levels can be characterized with one temperature) are different,
the K temperature generally being higher. As pointed out before,
this is not necessarily a disadvantage. In fact, we have recorded
spectra (of propyne), while deliberately raising the rotational
'temperature" by expanding a very rich mixture (10%) against
a high background pressure, with the explicit purpose of observing
as high J states as possible. Moreover, given a sufficiently high
spectral resolution, the ability to accurately predict intensities based
on Boltzmann statistics is relatively unimportant, since then the
spectral assignment can almost entirely rely on the matching of
ground-state combination differences. Where intensities are of
crucial importance, as in the evaluation of anharmonic coupling
matrix elements via a Lawrence-Knight deconvolution scheme
or a calculation of a lifetime from the time evolution of eigenstates,
all states in question belong to the same zero-order 'bright" state
and have the same quantum numbers J and K.16 On the other
hand, the study of the methyl stretches of I-butyne by Perry and
co-workers convincingly shows the advantages of being able to
cool the sample to rotational temperatures as low as I K in a
pinhole expansion." The lowest temperature reported for a slit-jet
is about 5 K. The effect of this difference in temperature, in terms
of spectral congestion, is best appreciated when realizing that the
partition function scales with PI2.
(iv) Experimeetal Considerations. The vacuum requirements
for a pulsed pinhole expansion direct absorption experiment are
very modest compared to both the Roots-blower pumped slit-jet
direct absorption experiment and the CW, differentially pumped,
pinhole expansion in an optothermal apparatus. On the other
hand, Stark spectroscopy and separated fields (Ramsey fringes)
type of experiments are more easily carried out in a collimated
molecular beam a p p a r a t u ~ . ~ The
* ~ ~same is true for doubleresonance experiments that require more space and could be
compromised when the interaction region is not entirely collision
free. The CW linear jet, because of its large gas consumption
(10L103 times that of a pinhole expansion), is unattractive when
expensive or difficult to obtain and/or handle samples are to be
studied.
The very modest demands for laser power in a direct absorption
experiment allowed Nesbitt and co-workers to build a difference-frequency laser that is tunable over a wide range (2.2-4.2
pm), covering most fundamentalexcitations of interest. The price
paid for the increased tuning range is the complexity of the laser
system. The work of several groups shows that is has become
possible to overcome the limited sensitivity of earlier diode laser
system^."^"^ Given the rapid and ever-evolving progress in diode
laser (single-mode) tunability, frequency coverage, ease of handling, and the lowering of their cost, this technique holds good
promise for the near future.
We conclude that, certainly at the overtone excitation level,
the optothermal spectrometer, combined with the high-power (150
mW) 1.5-pm oolor-center laser, is superior to the direct absorption
technique. But even at the fundamental excitation level our
technique appears to offer some advantages. This is perhaps best
illustrated by the u I 1-butyne spectrum. Perry and co-workers
P
(50) Gough, T. E.; Orr, B. J.; Isenor, N. R.;Scoles,G . J. Mol. Spctrosc.
1983, 99, 143.
(51) Adam, A. G.; Gough, T. E.; Isenor, N. R.;Scoles, 0. Phys. RN.1985,
A33, 1451.
(52) Hodge, J.; Havman. G.D.: Dvkc T R * H n w a d R 1 I r h p m %P
Faradav Trans. 2 1'
. . --
. ...
(54) Sncls, M.; Meerts, W. L. Appl. Phys. 1988. B45,27.
were able to identify in their sliced-jet spectrum s K statts belonging
=
to the P(2) transition and sharing the same upper state
McIlroy and Nesbitt observed seven states belonging to the
same lo, 202transition.Is Recently, in our laboratory we have
been able to identify 22 components of this transition in a 0.2-cm-'
frequency region. The transitions were assigned by combination
differences with R(0). The weakest assigned features had a
signal-to-noise of about 3:l. The strongest transitions were
measured with a signal-to-noise of about 80:l.
-
Expected Features of the Observed Spectra
Before presenting the experimental results, it is useful to discuss
the type of spectra that we expect to observe. Both the fundamental and overtone excitations of the acetylenic C-H stretch
produce parallel-band, symmetric-top spectra.5s These spectra
are characterized by a central Q branch with P and R branches
to the low- and high-frequency sides, respectively. Each individual
P(J) or R(J) transition also has a set of K components. For the
P branch each P(J) consists of K components with K = 0 to (J
- 1). In the R branch the R(J) transitions include K components
for K = 0 to J. For a rigid rovibrator the transition frequencies
for these lines are given bySS
V ~ , ~ ( J ,=Kv0) + ( B f+ B")m + ABm2 + (AA - AB)P (1)
Here centrifugal distortion terms, which generally produce only
small corrections at low J,K values, have been neglected. For
P-branch transitions m = -J, and for R-branch transitions m =
J 1. The intensities of the individual K components are given
by the Honl-London factors and the ground-state populations.ss
In this paper we are most interested in the structure of the
individual P(J) and R(J) transitions since lifetime information
is available from the line width of these transitions. Within the
individual P(J) or R(J)transitions the individual K components
will be spaced according to the final term in eq 1. Physically,
the acetylenic C-H stretch primarily involves motion of the H
atom along the symmetry axis of the molecule. This motion is
expected to produce only a small, negative change in the B rotational constant. Since the uI normal mode involves only parallel
motion of atoms on the symmetry axis, the magnitude of L 4 is
expected to be much less than that of AB. These physical notions
are borne out by the constants of CF,CCH, which has a very
similar mass distribution. For this molecule AB = -4.320 MHz
and AA = -0.26 MHz." For the compounds studied here, the
ratio of (d'/aB) should be smaller still. Therefore, the K structure
in the R(J)and P(J) transitions will degrade to the high-frequency
side of the transition. The degradation of intensity arises from
the fact that the low-K components have greater Hbnl-London
factors and larger ground-state populations.
The transition frequencies of the Q branch are given byss
VQ(J,K) = yo + ABJ(J 4- 1) + (AA - AB)@
K # 0 (2)
Under the same assumptions for AA and AB as above, the Q
branch will degrade to the low frequency side. According to the
second term in eq 2, the Q-branch lines move toward lower frequencies as J increases and their intensity decreases due to reduced
population and intensity factors. As K increases, these J series
move further out to the low-frequency side due to the second and
third terms in eq 2 since a K progression begins with the J = K
term.
The molecular symmetry group of these molecules, allowing
for torsional motion of the methyl groups, is Glb2. We have
recently reported the character table for this group and the statistical weights of the torsional levels.% The presence of torsional
motion has a large effect on the observed spectrum. Indeed, in
our preliminary report on the acetylenic C-H stretch fundamentals
of (CH,),CC=CH and (CHJ3SiC=CH we showed that the
spectra are quantitatively Lorentzian with no observed eigenstates.** However, the classification of these molecules in the C,
+
~
( 5 5 ) Herzberg, G . Molecular Spctro and Molecular Structure II. Infrared and Raman Spectra of Polyotomic Molecules; Robert E. Krieger
Publishing Co., Inc.: Malabar, FL, 1945; Chapter IV.2.
(56) Lchmann, K. K.;Pate, B. H.J . Mol. Spectrosc. 1990, 144, 443.
8288 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
point group, which corresponds to the neglect of torsional motion,
does not provide a sufficient density of states to explain the lack
of individually resolved eigenstates. In the C3, classification of
( C H 3 ) 3 C m H ,the average spacing of AI eigenstates, which
is the manifold that can couple to the acetylenic C-H stretch via
anharmonic interactions, is 51 MHz, and so a fairly resolved
spectrum would be expected, especially considering the expected
Thomas-Porter fluctuations in the intensities of the individual
eigenstate~.~’The effect of including torsional states is that the
ground state is 27-fold degenerate and consists of six different
symmetry species. This means that we measure the superpasition
of six different spectra. The spectrum is then expected to have
a density of lines that, in the absence of vibration-rotation
splittings (for example, the 1-type doubling of E vibrational states),
is 24 times the density of states. If vibrational-rotation splittings
are large, the number of lines observed can be as much as 122
times the density of A, states. This factor accounts for the observation of ‘filled-in” rotational profiles for both ( C H 3 ) 3 C m H
and (CH3),SiC=CH, Clearly, to obtain smooth rotational
profiles, the bright state must be coupled to a sizable fraction of
the vibrational bath states that lie within the narrow homogeneous
line width.
Our goal in this study is to obtain homogeneous lifetimes for
the vibrational energy relaxation following excitation of the
acetylenic C-H stretch. However, in light of the previous discussion it is obvious that there is potential for extensive inhomogeneous broadening in our measurements. First of all, each
individual P(J) and R(J) transition definitely contains inhomogeneity due to the presence of many K components. This
inhomogeneous component should increase with J as additional
K components are included with a spacing that goes as P.
However, we will show that for tert-butylacetylene the widths of
the P(J) and R(J) transitions are independent of J. The conclusion
then is that the homogeneous IVR broadening is much greater
than the K structure inhomogeneity. When the line width increases
with J, as occurs for the silicon-substituted compound, we can
estimate the K structure inhomogeneity using the measured
spectroscopic constants and the assumptions discussed above. In
this way we hope to be able to distinguish the effect of inhomogeneous broadening due to the K structure from the possibility
of rotationally mediated IVR mechanisms (Coriolis effects).
Inhomogeneity due to the different torsional levels should also
be considered. It is conceivable that the transitions from the six
different torsional symmetry species could have different center
frequencies. However, it is unlikely that we will observe such
effects. For trimethyl carbon compounds the barrier to internal
rotation is sufficiently large that microwave studies fail to observe
ground-state splittings even at the kilohertz leveL5* For the silicon
compound the barrier drops and torsional splittings may be
measurable. For example, the spectrum of (CH3)3Si-H has been
mentioned in a previous microwave study but was said to be left
unassigned due to the complex structure of the transitions, presumably due to torsional ~ p l i t t i n g s . ~Still,
~ to produce a measurable effect in our infrared spectra, it is necessary that the barrier
to internal rotation in the ground and excited vibrational states
be sufficiently different so that the splitting pattern changes
between the two states. Accordingly, we do not expect to have
torsional inhomogeneity in our spectra.
For the spectrum of (CH3)3SiCECHthe natural abundances
of the Si isotopes should be taken into account (there are two
heavier isotopes of about 4% natural abundance in addition to
the major isotope %i, which is in 92% abundance). A normal-mode calculation for the Si compound indicates that the
isotope shift for the acetylenic C-H stretch should be small even
compared with the observed line width. Since the major isotope
will dominate the spectrum, we expect at most to observe small
effects in the residuals to our fits.
(57) Engel. Y. M.; Levine, R. D. J. Chem. Phys. 1988,89,4633.
(58) Nugent, L. J.; Mann, D.E.: Lide Jr., D. R.J. Chem. Phys. 1%2,36,
965.
(59) Lide Jr., D. R.;Mann. D. E.J . Chem. Phys. 1958, 29, 914.
Kerstel et al.
TABLE I: Measured SpcetroscoPic Constantsa
( C H M m H
VI
3329.371 08 (94)
0.089 560 (43)
0.089 439 (48)
. .
-50.85
-0.000096 (20)
;
”
E’
XI I
an
2Vl
VO
E”
E’
6557.0247 (12)
0.090006 (46)
0.089865 (56)
(CH,),SiC=CH
“I
2‘E’‘
XI I
an
3312.462913 (64)
0.065 4848 (32)
0.065 4300 (38)
-52.30
-0.0000566 (18)
2Vl
‘;’
B’
6520.305 26 (IO)
0.0655171 (49)
0.065 400 4 (49)
“All values are in c d . Reported errors in the constants for the
vibrational levels are 20.
Last, hot-band transitions may also be present. For example,
the hot-band coming from the lowest frequency vibration is observed both in our spectrum of propyne4’ and trifluoropropyne.22
These hot bands appear at lower frequency. So we may possibly
observe small hot-band absorptions, probably to the low-frequency
side of the transitions.
By carefully considering all of the sources of inhomogeneity,
we aim at making reliable estimates of the homogeneous lifetimes
from our spectra. In the following section these considerations
will be used when assigning the homogeneous line width. This
line width is then used to obtain the dynamical lifetime information.
Experimental Results
Figure 2 shows the fundamental and first overtone spectra of
both (CHJ3CC=CH and (CH3)3SiC=CH. The parallel-band,
symmetric-top rotational structure is apparent; however, the K
structure of the individual R(J) and P(J) transitions is not resolved.
In spite of the fact that, for the sake of comparison, the full spectra
have been compressed to fit the size of the figure, it is obvious
that the width of the tert-butylacetylene compound is much larger
than that of the silicon-substituted compound. From the spectra
the band origin, rotational B constant, and change in rotational
constant upon vibrational excitation (AB) can be determined.
These spectroscopicconstants are listed in Table I. Also given
in Table I is the anharmonicity, XIl,calculated from the band
origins of the fundamental and first overtone. The value of about
-50 cm-I for this parameter is the same as the value previously
found for a number of symmetric-top terminal acetylenes from
photoacoustic spectroscopy data that included up to the fifth
overtone of the acetylenic C-H stretch.@
For interpreting our data in terms of the dynamics of the
vibrational motion, we are most interested in the line shape of the
spectral features. In the statistical limit of intramolecular vibrational relaxation a Lorentzian line shape is predicted.1° The
line width of the profile provides the relaxation rate. In our
previous preliminary communication of the fundamental spectra
of these two molecules we showed that the line shapes were
Lorentzian.l* The lifetimes reported in the previous publication
are a factor of 2 too long. The lifetime we gave was the correct
T2lifetime calculated from a Lorentzian profile. When spectral
broadening comes only from population relaxation of the upper
state
(3)
where T is the lifetime associated with the exponential IVR decay
of population and r is the full width at half-maximum (fwhm)
of the Lorentzian line shape.
The spectra reported here were taken with much colder expansions than were used in the previous measurements.’’*’* The
colder expansion has allowed us to measure the lower rotational
(60) Hall, R. R. Ph.D. Thesis, Rice University, 1984; University Microfilms International, 8416524.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8289
Intramolecular Vibrational Relaxation
V.1
.-Em
W
Y
-
,
3327.49
3328.49
~
~
3329.49
Wavenumber/cm- 1
.
~
3330.49
,
~
6555.45
-
~
6558.45
~
,
~
6557.45
Wavenumber/cm- 1
i
6558.45
v.2
.-E
.-E
C
C
-
Y
YC
-C
331
8516.90
transitions where the inhomogeneity from K structure is reduced,
providing better estimates of the homogeneous IVR lifetime of
these two molecules. The R(7) transitions of the fundamentals
and the R(5) transitions of the overtones are shown in Figure 3
along with the residuals from the best fit to a single Lorentzian.
The fit is performed by using a nonlinear least-squares algorithm.6l
For the terr-butylacetylene the fit runs from the midpoint between
two successive rotational transitions to the midpoint of the next
two transitions in order to provide as much baseline as possible.
For the overtone spectra a sloping baseline is used in the fit since,
due to the greater power of the 1.5-pm laser, a slowly variable
background signal due to scattered light is present. All four fits
include about 2000 data points each. All of the measured R
branch lines were fit, and the line widths are plotted in Figure
4. Generally the lowest J line width reported is not very well
determined due to low signal-to-noise.
We find that the line width of the silicon-substituted compound
is significantly narrower than that of tert-butylacetylene in both
the fundamental and first overtone. Combined with our previous
results for the fundamental of tert-butylacetylene,'* we find that
the line width remains nearly constant at about 800 MHz from
R( 1) to R( 18). The lack of J dependence of the width indicates
that the dominant mechanisms for IVR are anharmonic. Furthermore the K structure inhomogeneity is obscured by the IVR
broadening. We conclude that the homogeneous IVR lifetime
of rert-butylacetylene in the fundamental is 200 ps. This value
agrees very well with the lifetimes observed for other terminal
acetylenes at u = 1.16
The line widths of (CH,),SiC=CH in the fundamental show
a steady increase as a function of J. We believe that this increase
is due to unresolved K structure and not to Coriolis IVR mechanisms. Coriolis mixing matrix elements increase as [J(J + 1)
- K(K f 1)11/* for xy-axis interactions or as K for z-axis interactions.'j2 The observed line widths do not increase that rapidly
as J increases. Furthermore, at the higher J values the line shape
starts to develop a shoulder to the high-frequency side as expected
for K structure based on the measured AB value. The line widths
expected for K structure can be estimated through a simulation
of the data. Under the assumption that hA << AB the line shape
can be constructed by summing the contributions from each K
component. The K components are taken as Lorentzians with
a width estimated to be the homogeneous line width and a height
given by the HBnl-London factor. The resulting line shape is then
fit to a single Lorentzian. Using 75 MHz as the homogeneous
line width, the R(6) transition is expected to be 87 MHz. The
measured value is 94 MHz. Therefore, since the J dependence
is well accounted for by the K structure, we conclude that anharmonic couplings are probably dominant in the vibrational
relaxation process.
We note that the R(0) transition consists of only a single K
component, so its line width should be the homogeneous line width.
However, due to signal-to-noise limitations for this transition the
(61) Res, W.H.;Flannery, B. P.;Teukolrky, S.A.; Vetterling, W.T.
Numerical Rccfpcs;Cambndge University h New York, 1986; Chapter
(62) Papousek, D.;Aliev, M. R. Molecular Vibrarionul-Rotational
Spectroscopy;Elsevier Scientific Publishing Co.: New York. 1982; Chapter
6519.90
6520.90
Wavenumber/cm- 1
Figure 2. Fundamental (left) and the overtone (right) rovibrationalspectra of the acetylenic C-H stretching vibration in 3,3-dimethylbutyne (above)
and in (trimethylsily1)acetylene (below). The comparison of the fundamental spectra on the left-hand side clearly indicates that the line width of the
rotational lines decreases dramaticallyon substitutionof the center C-atom in (CH3),CC=CH by silicon. Comparing the fundamental and the overtone
spectra (left-right), the line widths increase for the carbon compound (upper) in going from the fundamental to the overtone, while they decrease in
the case of the silicon compound (lower). (This decrease is less distinct on the scale of the figure.)
14.4.
111.18.3.
Kerstel et al.
8290 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
c
3330.0
I
3550.79
1
3330.89
I
6557.96
Wavenumber/cm- 1
I
3313.40
1
sJl3.50
I
6558.W
i
85%. 16
Wovenumber/cm- 1
1
3313.60
Wovenumber/cm- 1
I
6520.96
,
I
6521.Q3
i
6521.16
Wovenumber/cm- 1
Figure 3. Left-hand side: R(7)of the fundamental acetylenic C-H stretch rovibrational spectra of (CHd3COsCH (above) and (CH,),SiCrCH
(below).
(below). Right-hand side: R(5) of the overtone acetylenic C-H stretch rovibrational spectra of (CH3)$C=CH (above) and (CH,),Si=H
In all four cases the measured rotational line and a nonlinear least-squares fit to a single Lorentzian are shown in the upper traces, while residual of
the Lorentzian fit and the zero line are shown in the lower traces. (For the sake of clarity upper and lower traces are staggered.) The residuals indicate
a true Lorentzian line shape for the carbon compound as expected for the statistical regime of IVR. For the silicon compound the fit to a single Lorentzian
is not as exact. The small residuals at the low-frequency side for the Si compound (below) in both the fundamental and the overtone are likely due
to two isotopes of Si with 4.67% and 3.1% natural abundance or to a hot-band transition.
line width is not as well determined by the fit. In the case of the
fundamental of (CH3)3SiCWH, the line width of R(0) does
appear to fit in the smooth trend determined by the measurement
of the stronger R(J) transitions. We take the measured R(0) line
width of 75 MHz to be the homogeneous line width of (CH3)3Si-H
in the fundamental providing an IVR lifetime of about
2 ns, an order of magnitude longer than that found in (CH3)$CECH.
The line width of the overtone transitions of tert-butylacetylene
is approximately constant over the measured range of J. The value
at R(2) is not well determined by the fit, and so it was discarded.
Again the apparent independence of the line width on J suggests
that anharmonic interactions are dominant. The homogeneous
line width is about 1400 MHz. This correspondsapproximately
to a 110-ps lifetime, signifying that the overtone relaxation occurs
nearly twice as fast as the fundamental.
As dicussed above for the fundamental, the J dependence of
the line width for the overtone of the silicon compound is most
likely due to K structure inhomogeneity. Assuming a 50-MHz
homogeneous line width, the simulated width of the R(6) transition
is 87 MHz. The measured value is 76 MHz. The results of the
two simulations of ( C H 3 ) 3 S i m Hshow that near R(6) the line
widths of the fundamental and first overtone should be nearly
equal, and this is observed in our data. In general, the fits of the
data for ( C H 3 ) , S i W H are not exact, as demonstrated by the
residuals in Figure 3. Several effects could explain this. There
are two isotopes of Si that have about 5% abundance of the major
isotope. The transitions in these isotopic molecules likely occur
very near those of the major isotope. Hot bands from transitions
with small off-diagonal anharmonicitieswith the acetylenic C-H
stretch may also be present. These two s o u m of inhomogeneity
may produce the structure observed on the red side of the transition. For the overtone transitions with width of the K structure
is significant compared to the homogeneous line width and can
prevent a quantitative fit to a single Lorentzian. Last,the overtone
spectra have about 20-MHz residual Doppler broadening, so a
Voigt profile would describe the line shape more accurately.
We estimate the homogeneous line width in the overtone of
( C H 3 ) $ i W H by taking the R(0) full line width to be 50 MHz
based on the trend in the line widths in Figure 4. This line width
is assumed to be the Voigt profile line width. Using the measured
machine line width of 20 MHz as the Doppler component of the
Voigt rofile the Lorentzian component is calculated to be 40
M H z ~The corresponding4-11s
lifetime of the overtone of the
silicon compound is therefore nearly 40 times longer than the
lifetime of (CH,),C=H
at the same energy and is much longer
than lifetimes often given for IVR (typically a few picoseconds).
The ability to keep three-quarters of an electronvolt of energy
localized in the C-H stretch for a few nanoseconds may allow
mode-selective chemistry to be performed on this and, possibly,
similar systems.
In addition to the dramatic lengthening of the vibrational relaxation lifetime upon silicon substitution in rert-butylacetylene,
(63)Olivero. J. J.; Longbothum, R. L. J. Quanr. Sprctrosc. Radial.
Transfer 1977, 17, 233.
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8291
Intramolecular Vibrational Relaxation
.-b
m
P)
Y
-c
I
330 2420
3306.2720
I
Wovenumber/cm- 1
"1
Figure 5. P(2) of the fundamental acetylenic CH stretch rovibrational
spectrum of (trimcthylstanny1)acetylene (CH&hC=CH. The structure of the line contains inhomogeneity likely due to the different isotopes
of Sn (14.76, 7.796, 24.396, 8.696, and 32.4% natural abundance).
t'
0
3306.2570
(CHs)sS.C.C-H
I
I
I
I
I
I
I
1
(64)Mills, I. M. MolecularSpect"py: Modern Resear& Reo, K.N.,
Mathews, C. W.,Eds.; Academic Pres: New York, 1972; Chapter 3.2.
lifetimes determined for 1-butyne and the gauche and trans isomers
of 1-pentyne.l6 These results suggest that the IVR lifetime is also
a property of the chromophore. The observation of dramatically
different lifetimes in the silicon compound, involving substitution
at the fourth position of the linear acetylene frame, shows that
if the lifetime is chromophore dependent, then it is very sensitive
to long distance structure.
In their paper on terminal acetylenes, McIlroy and Nesbitt
propose that the lifetime is determined by the interaction with
a doorway state that is the acetylenic C=C stretch and two quanta
of the acetylenic C-H bend, that is, a resonance composed exclusively of motion of the acetylenic part of the molecule.16 This
resonance is known to be present in propyne with an anharmonic
matrix element of about 7 ~m-l!~ However, our data show that
this resonance cannot explain the observed behavior. In
(CH3),CC=CH this state lies near 3370 cm-I and in (CH,),S i C e H it lies near 3396 cm-I. The origin of these states is
calculated by using the measured gas-phase infrared frequencies
and neglecting anharmonicity.Since the resonance is closer
in tert-butylacetylene (about 42-cm-I detuning) than in the silicon
compound (about 83-cm-I detuning) for the fundamental, it could
conceivably explain the observation of a narrower spectrum in
the latter compound. However, in the overtone the large value
of the anharmonicity for the acetylenic C-H stretch would cause
the resonance to further detune for both molecules, resulting in
narrower lines for both compounds. Instead the terf-butylacetylene
broadens and (CH,),SiC=CH narrows.
The results actually suggest, in our opinion, the absence of any
single dominant doorway interaction. The fact that we observe
unstructured rotational transitions implies that the bright state
couples to a significant fraction of the background states.
Therefore, the states with large number of vibrational quanta in
low-frequency modes are coupled. These low-frequency modes,
especially the bending modes of the linear part of the molecules,
will have aAand aB values that are much larger than those of
the acetylenic C-H stretch. As a result, both the B and A rotational constants of a typical background state will be very
different from the constants in uI. This means that different
vibrational states will couple at different J values and different
K values, and yet the line width appears to be insensitive to the
exact identity of the coupled states.
As mentioned in the Introduction, the substitution of silicon
in terf-butylacetylene was motivated by the idea of looking for
(65) Duncan, J. L.; McKean, D. C.; Nivellini, G. D. J. Mol. Stnrct. 1976,
32, 255.
(66) Sheppard, N.J . Chem. Phys. 1949, 17,455.
(67) Durig, J. R.;Craven, S. M.;Bragin, J. Chem. Phys. 1970, 53, 38.
(68) von Puttkamer, K. M.Sc. Thesis. Laboratorium f6r Physikalische
Chemie der ETH,ZBrich, Switzerland.
Kerstel et al.
8292 The Journal of Physical Chemistry, Vol. 95, No. 21, 19
evidence of a heavy-atom effect in IVR. Such an effect may be
TABLE II: Density of A , States for ( C H , ) , C m H and
present. Both the fundamental and overtone of the silicon compound have longer lifetimes than the carbon species. We have
also recently measured the fundamental and first overtone of
level of excitationi
pAlb
(CH,),SnC=CH. The P(2) transition of the fundamental is
v=l
704
u=2
1.06 X 106
shown Figure 5. The overall line width of the transition is about
100 MHz; however, structure is present that shows much narrower
(CH3)3SiC=CH
line widths. Structure is observed in all transitions and is, we
level of excitation
PAI
believe, due to the presence of isotopes (there are 10 isotopes for
2.09 X 10‘
u=l
tin). We are currently working on quantitatively understanding
v=2
4.99 x 107
the line shape in both the tin and silicon compounds, and these
“This is the vibrational excitation level of the acetylenic C-H
results will be reported in a future publication. A preliminary
stretch. bThis is the number of states/cm-I of A I symmetry calculated
value for the homogeneous line width of (CH3),Sn=H
is about
by using the molecular symmetry designations of GI,> The full density
25 MHz (6 ns) in the fundamental.
of states is 162 times the density of AI states.
While for the fundamentals we do see a decrease in the line
width when the mass of the central atom is increased, a heavy-atom
a small matrix element controlling the relaxation since it would
effect alone does not appear to explain the data. First, the factor
most likely be greatly detuned in the overtone. We, therefore,
of 2.3 mass increase from C to Si narrows the line width by loOo%,
believe that our data imply that there is no single state (or small
while the factor of 4.2 mass increase from Si to Sn only narrows
set of states) that act as a doorway for the intramolecular vithe width by about 40%. Second, a mass effect cannot explain
brational relaxation.
why (CH3)3CC=CH broadens in the overtone but (CH3),SiIn conclusion we have no natural explanation of the trends in
C=--CH narrows. Again, although the mass of the central atom
line widths observed in these molecules. It must be cautioned that
may reduce the IVR rate, we cannot conclude that it is the
the tin results are only preliminary, and the lifetime may be
dominant effect in determining the IVR lifetime of these systems.
considerably longer than we estimate if other explanations are
Although the intent of our experiment was to simply increase
found for the observed line shape. Future double-resonance or
the mass of the central atom, the substitution of silicon (and tin)
time-resolved measurements may answer these questions.
causes other changes in the structure of the molecule. Perhaps
Methyl group rotation has been implicated in enhancing IVR
the greatest effects are related to the lengthening of the bond
in a few cases.”-73 In particular, the chemical timing experiments
between the methyl groups and the central atom. The distance
of Parmenter et al. on p-fluorotoluene and p-difluorobenzene
increase reduces the barrier to rotation of the methyl group. The
strongly suggest that the presence of the methyl group enhances
barrier for (CH3),CC=CH has been measured to be 1434 cm-I,
the IVR rate.’* However, time-resolved fluorescence experiments
and the barrier of (CH,),SiC=CH can be taken to be about the
of p-fluorotoluene in a free-jet expansion did not confirm this
same as that of (CH3),SiH which is 871 ~ m - I . 6The
~ barrier for
finding.74 Later theoretical work suggested that the thermally
(CH,),SnH has been calculated to be 217 ~ m - I . 6 A
~ questionable
populated torsions in pfluorotoluene made good acceptor modes
assignment for the methyl torsional mode fundamental in
.’~
these results suggest that the
in the IVR p r o c e s ~ . ~ ~Although
(CD ),Sn=H
(70 an-’)
implies a barrier almost identical with
freedom of the torsion is important, it is difficult to reconcile our
thisjO If we take the height of the torsional barrier to be represults with the previous work. First, pfluorotoluene has a leading
resentative of the strength of other steric interactions across the
v
6 Fourier term in the torsional barrier and so is only slightly
central bond, we predict a central-atom dependence to the rate
hindered; the measured barrier is 4.77 cm-’.” Second, our spectra
of energy relaxation similar to that predicted by the mass effect.
are taken in a molecular beam where the torsional states are, most
A simple heavy-atom effect, where the kinetic couplings are relikely, not thermally populated. Last, we find that a lower barrier
duced, would predict a line-width decrease proportional to (1/
results in a decreased IVR rate.
mcmtnlItm). For this mass effect the line widths are expected to
Clearly there is much work left to be done before achieving a
be in the ratio 104.3:l for central atoms C, Si, and Sn respectively.
detailed understanding of the factors that determine the intraThe ratios of the barrier heights are 6.6:4.5:1 and are very similar
molecular vibrational relaxation rate. However, our data do serve
to the ratio for the mass effect. Neither of these predictions is
to show that the total density of states has little importance for
in good agreement with the experimental data, which for the
the dynamics of vibrational relaxation. The normal modes of
fundamental have a ratio of about 303:l. Other estimates of the
( C H 3 ) 3 C m H 6 6 * 6and
7 (CH,),SiCbCH@’
have been assigned.
steric interactions could be made, but without knowledge of which
From these data and the barriers to methyl group rotation we have
modes are most important in coupling vibrational energy across
calculated the density of states for these two molecules in the
the central atom, it is difficult to choose between them.
fundamental and first overtone. In this calculation the energy
Another change that occurs as the mass of the central atom
levels of the methyl torsion are calculated separately?* The rest
increases is a lowering of the frequencies of many of the modes.
of the modes are treated as harmonic vibrations. The labels of
The central-atom substitution results in an increased mass and
the molecular symmetry group G162are used.56 In Table I1 the
longer bond lengths, and also a reduction in force constants of
results of this calculation are presented for the A, levels. The
modes involving motion of the central atom. Swamy and HaseZ9
density of states alone fails to explain any of the data. At the
have found that the ‘heavy-atom blocking” of vibrational energy
fundamental and first overtone the silicon compound has a much
transfer found in classical trajectory c a l c ~ l a t i o ndoes
s ~ ~not
~ ~ ~ ~ higher
~
density of states than does (CH3),C=H,
and yet a t
occur unless one changes the force constants as well as the mass
both levels of excitation (CH,),SiCWH has a longer IVR
of the central atom. If small, near-resonant mixing of some specific
mode or modes controls the vibrational energy transfer, then the
(71) Walters, V. A.; Colson, S.D.; Snavely, D. L.;Wiberg, K. B.; Jamison,
rate will strongly depend upon the mode frequencies. Examination
8. M. J . Phys. Chem. 1985,89, 3857.
of fundamental frequencies for all three molecules reveals no
(72) Parmenter, C. S.; Stone, B. M. J. Chem. Phys. 1986, 84, 4710.
low-order resonances that could provide a doorway for the energy
(73) Reid, S. A.; Kim. H. L.;McDonald, J. D. J . Chem. Phys. 1990,92,
relaxation. Furthermore, the small change in line width of the
7079.
(74) Baskin, J. S.; Rose, T. S.;Zewail, A. H.J . Chem. Phys. 1988,88,
overtone bands (where the detuning will change by 100 cm-I due
1458.
to anharmonicity) compared to the line width in the fundamental
(75) Moss,D. B.; Parmenter, C. S.;Ewing, G. E. J. Chem. Phys. 1987,
of the same molecule argues against a high-order resonance with
86, 51.
(76) Martens, C. C.; Reinhardt, W. P. J . Chem. Phys. 1990, 93, 5621.
(77) Ghosh, P. N. J. Mol. Spectrosc. 1990, 142, 295.
(78) The program for calculating the torsional energy levels for a V3hmer
(69) Ouellette, R. J. J . Am. Chem. Soc. 1972, 94, 7674.
was written by D. S. Perry, Department of Chemistry, University of Akron,
(70) Belyakov, A. V.; Bogoradovskii, E.T.; Zavgorodnii. V. S.; Apal’kova,
Akron, OH 44325.
G. M.; Nikitin, V. S.;Khaikin. L. S. J . Mol. Srruct. 1983, 98, 27.
~~
J. Phys. Chem. 1991, 95, 8293-8299
lifetime. For each individual compound there is a large increase
in the density of states in going from the fundamental to the first
overtone (more than a factor of IOOO), and yet (CH3),CC=CH
broadens only slightly (a factor of 2) and the silicon-substituted
compound narrows. The inability of the total density of states
to explain the lifetime trend of the data and the above-mentioned
insensitivity of the line width on the identities of the final states
of the full bath illustrate the minor role that the full density of
states plays in the dynamical process of vibrational energy redistribution in these molecules.
There is clearly a minimum density of vibrational states (about
100-1OOO per cm-') required for a vibrational energy relaxation
to occur since several coupled states lying within the frequency
region given by the homogeneous line width are required for a
true relaxation process. For lower state densities, the time evolution of the excitation will show negligible energy transfer
(small-molecule limit) or quantum beats with a few frequencies.
There is ample experimental evidence for substituted acetylene
compounds that the acetylenic C-H fundamental will relax into
all symmetry-allowed vibrational states (and perhaps rovibrational
states) that fall within the homogeneous width.12J6J8.22The
time-averaged state in this case is like a microconanical ensemble
and thus has a statistical distribution of vibrational energy among
the vibrational modes. Increasing the density of states beyond
this minimum will be expected only to increase the volume of phase
8293
space into which the molecular excitation decays.
In summary, using the optothermal technique, we have measured both the fundamental and first overtone spectra of
(CH,),C*CH
and (CH,),SiC=CH. All of the spectra show
broadened transitions that are Lorentzian, with some inhomogeneity in some cases. The four spectra show a wide variety of
interesting behavior with respect to the homogeneous IVR lifetime.
In all cases the lifetimes are rather long, ranging from 100 ps up
to about 4 ns. Lifetimes on the order of nanoseconds ensure that,
at reasonable pressures (about 1 atm), collisions with vibrationally
excited molecules can occur. These long IVR lifetimes may allow
mode-selective, laser-enhanced, bimolecular chemistry to occur.
More experimental and theoretical work is necessary to understand
in further detail the measured lifetimes in terms of the intramolecular forces and dynamics.
Acknowledgment. We thank D. S.Perry for providing us with
the program for the calculation of torsional energy levels. It is
a pleasure to thank Prof. J. Schwartz for his generous help in
synthesizing the tin-substituted compound. T.F.M. thanks the
Deutsche Forschungsgemeinshaft for research support. This work
was supported by the NSF under Grants CHE87-09572 and
CHE85-53757.
Registry No. (CH,),CC=CH, 917-92-0; (CH,),Si=H,
54-2; (CH,),SnC=CH, 11 12-00- 1.
1066-
Calculation of the Vibrational Levels of Electronically Excited Ar-OH(A2E+) Using a
Proposed Potential Energy Surface and Analytic Discrete Variable Representatlonst
Y. Guan and J. T. Muckelman*
Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973
(Received: December 27, 1990; In Final Form: April 16, 1991)
The vibrational levels of a potential energy surface recently proposed by Bowman et al. [ J . Phys. Chem. 1990, 94, 22261
for the electronically excited van der Waals complex Ar-OH(A2Z+) are calculated by using analytic discrete variable
representations. The results, together with those of previous calculationsand with experimental spectroscopic data on vibrational
band origins, are used to suggest further refinements in the potential energy function.
Introduction
Recently Bowman et al.' attempted to "invert" experimental
spectroscopicdata to obtain a potential surface for the electronically excited state of the van der Waals complex Ar-OH(A2Z+).
Their approach was to perform an exact calculation of vibrational
energy levels using a flexible functional form for the potential and
to search in the multidimensional parameter space for the optimum
set of parameters. The functional form of the potential they
employed was guided significantly by an ab initio calculation of
the surface by Degli Esposti and
The experimental data
to which the fit was carried out were the fluorescence excitation
spectra of Berry et al." and of Fawzy and Heaven,7J who also
reported spectra for Ar-OD(A*Z+). These data consisted of band
origin energies assigned to a series of van der Waals stretching
vibrations3 ("A" bands7a) and some unassigned band origins ("U"
bands7.*) which Fawzy and Heaven attributed to the excited
bending vibration. Berry et aL5 subsequently confirmed this
assignment through product state distributions following vibrational predissociation of the complex.
Using the van der Waals stretching assignments made by the
two experimental groups for the A bands, corresponding to energy
'This research was carried out at Brookhaven National Laboratory under
Contract No. DE-AC02-76CH00016 with the U S . Department of Energy and
supported by its Division of Chemical Sciences.
0022-3654/91/2095-8293$02.50/0
intervals v, to v, - 1 for v, from 2 to 6 for Ar-0H3g8 and A P O D ~ ~
and assigning most of the reported U band^^.^ to highly excited
van der Waals stretching states in the first excited bending state,
Bowman et al.' were able to vary selected potential parameters
and repeatedly diagonalize the matrix representation of their trial
Hamiltonian operator in a fairly large basis until reasonable
agreement with the experimental intervals and rotational constants
was obtained. The basis they employed was optimized to yield
reliable representations of states with the linear Ar-H-O configuration, the geometry believed to have the only substantial
Franck-Condon factors with the electronic ground state. In fact,
their variations of the trial potential affected only this region of
configuration space. Only energy intervals involving states as( 1 ) Bowman, J. M.; Gazdy, 9.;Schafer, p.; Heaven, M. C. J. Phys. Chem.
1990, 94, 2226; correction, 1990, 94, 8858.
( 2 ) Degli Esposti, A.; Werner, H.-J. J . Chem. Phys. 1990, 93, 3351.
(3) Berry, M. T.;Brustein, M. R.; Adamo, J. R.; Lester, M. I. J . Phys.
Chem. 1988, 92, 5551.
(4) Berry, M. T.; Brustein, M. R.; Lester, M. I. Chem. Phys. Lett. 1988,
153, 17.
(5) Berry, M. T.; Brustein, M. R.; Lester, M. I. J . Chem. Phys. 1989, 90,
5879.
(6) Berry, M. T.; Brustein, M. R.; Lester, M. I. J. Chem. Phys. 1990,92,
6469.
(7) Fawzy, W. M.; Heaven, M. C. J. Chem. Phys. 1988,89, 7030.
(8) Fawzy, W. M.; Heaven, M. C. J . Chem. Phys. 1990, 92,909.
(9) Lin, Y.; Kulkarni, S . K.; Heaven, M. C. Unpublished results.
0 1991 American Chemical Society