The rotationally resolved 1.5 pm spectrum
hydrogen-bonded
complex
of the HCN-HF
E. R. Th. Kerstel, H. Meyer,a) K. K. Lehmann, and G. Stoles
Department
of
Chemistry Princeton University, New Jersey 08544
(Received 15 May 1992; accepted 17 August 1992)
We have measured the overtone spectrum of the CH stretching mode in HCN-HF. The
vibrational predissociation rate is approximately twice that previously determined
for fundamental excitation, whereas the complexation induced frequency shift is only
marginally larger than that of the fundamental spectrum. These results are discussed in terms
of a first-order perturbation theory treatment as set forth by LeRoy, Davies, and Lam
[J. Phys. Chem. 95, 2167 (1991)]. We suggest that the frequency shift observed here might
not only be due to complexation, but also to a long-range anharmonic interaction.
INTRODUCTION
Over the past few years the HCN-HF van der Waals
heterodimer has emerged as a benchmark system for the
spectroscopic study of linear hydrogen-bonded complexes,
from the microwave to the (near) infrared regions of the
spectrum. rm3Microwave spectra of HCN-HF and its isotopically substituted derivatives, recorded in a gas-cell experiment or a pulsed nozzle Fourier-transform IR (FTIR)
spectrometer, have established its linear geometry (with
the HF unit hydrogen bonded to the N atom) and allowed
for the evaluation of ground-state rotational constants,4’5
electric quadrupole coupling constants,6 electric dipole moment,7’8 and the hydrogen-bond dissociation energy.’ Exploiting the wide spectral coverage of their FTIR spectrometer and the relatively high sample temperature in a
cooled static gas cell, Bevan and co-workers have been able
to assign all seven fundamentals and several combination
bands, hot bands, and overtones, including up to the 4~:
third overtone of the high-frequency intermolecular
bend,‘@19 and the first overtones of the CH and HF intramolecular stretching modes.20’21Of the 34 anharmonic
constants Xij and gii ( lQi<i<7)
22 are now known with
reasonable accuracy. For no other hydrogen-bonded complex is such an extensive vibrational database, including
anharmonicities, available for comparison with state-ofthe-art calculations, such as have been performed for
HCN-HF by Botschwina22 and Amos et ~1.~~Whereas the
gas-cell FTIR experiments have been instrumental in the
rovibrational characterization of the complex, their limited
spectral resolution, albeit sufficiently high to resolve the
rotational structure, has precluded the accurate measurement, from the observed spectral linewidths, of the vibrational predissociation lifetimes associated with highfrequency intramolecular vibrations. It is in this respect
that the much higher resolution afforded by a color-center
laser, molecular beam, optothermal spectrometer can be
applied to the further advancement of our knowledge of
this benchmark system. Using such a spectrometer operat‘)Present address: Universitit Bern, Institut ftir anorganische, analytische
und physikalische Chemie, Freierstrasse 3, CH-3000 Bern 9,
Switzerland.
ing in the 3 pm region Miller and co-workers have
uniquely determined the vibrational predissociation lifetimes of the vr (HF) (Ref. 24) and v2( CH) (Refs. 24 and
25) stretching fundamentals and of the associated combination band with the vi lowest-frequency bending mode.25
We have previously demonstrated the feasibility of extending these measurements into the region of the CHstretch first overtone, using a powerful commercial colorcenter laser operating near 1.5 ,um.26 In that study we
recorded the 2vt spectrum of the HCN dimer. As in the
study of the corresponding fundamental, the rotational linewidths, and therewith the vibrational predissociation lifetime, proved to be instrument limited. Here we report the
2v2 overtone spectrum of the CH stretching vibration in
HCN-HF. Since the observed linewidths are not instrument limited, their Lorentzian component gives a direct
measure of the predissociation lifetime of the excited complex at an energy of 6500 cm-‘, almost 4 times the dissociation energy. At the same time we can compare the complexation induced vibrational frequency (red-) shift for
fundamental and overtone excitation, for the two systems
HCN-HF and HCN dimer.
The HCN-HF complex, along with the HF dimer,27
are the first (hydrogen bonded) van der Waals systems for
which the vibrational predissociation lifetimes have been
determined for both fundamental and overtone excitation
of the same high-frequency intramolecular vibration (i.e.,
the CH and HF oscillators, respectively). The (NO) 2 molecule is to our knowledge the only other dimer for which
both fundamenta128-30 and overtone3’ vibrational predissociation (without simultaneous electronic excitation) data
exist. In this case, due to the open-shell nature of the NO
molecule, the dissociation process is believed not to occur
on the ground-state electronic potential only, but instead to
involve (at least) two electronic states, which are coupled
through spin-orbit interaction. It may therefore be difficult
to discuss this system in the same framework as used in
this paper for van der Waals systems.
EXPERIMENT
The spectrometer used in these studies is based on the
optothermal detection technique, an energy deposition
technique that has been described extensively in the liter-
J. Chem. Phys. 97 (12), 15 December 1992 0021-9606/92/248896-l
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@ 1992 American Institute of Physics
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Kerstel et al.: Overtone spectroscopy
ature.32’33 In short, a highly collimated molecular beam
containing the species of interest impinges on the cold (l-2
K) surface of a semiconducting bolometer detector, after
interaction with the IR laser radiation. Rovibrational energy deposited into the molecular beam by the laser is
registered by the bolometer in a phase-sensitive detection
scheme. If the excited molecules dissociate before reaching
the detector (as in the case of vibrational predissociation of
most weakly bound complexes) and most of their fragments leave the molecular beam, the resulting signal will
have the opposite sign of a signal resulting from absorption
by a stable molecule. This technique is particularly suited
to studies involving vibrational overtone excitation, since
the decrease in signal-to-noise ratio (S/N) resulting from
the reduced transition strength of the overtone transition
as compared to that of the fundamental transition (a difference of a factor of roughly 40 for most acetylenic CH
stretch excitations), can be compensated for by an increase
in laser power, if available. For a technique like direct
absorption on the other hand, a decrease in oscillator
strength translates directly in a proportional loss in S/N
(provided the dominant noise source is technical noise of
the laser system).
The above considerations and the experimental setup,
which combines an optothermally detected molecular
beam with a Nd:YAG laser pumped, 1.5 ,um, 150 mW
color-center laser (Burleigh FCL-120), have been discussed in detail in a previous publication (YAG denotes
yttrium aluminum garnet).34 Here we will limit ourselves
to discussing the experimental conditions specific to this
study. The molecular beam is extracted, using a conical
skimmer, from a room-temperature expansion of a 0.5%
HCN and 1% HF in helium mixture through a 50 pm
diameter nozzle, at a stagnation pressure of 4 bars. The gas
mixture was obtained by on-line mixing of pre-mixed 1%
HCN in helium (Matheson) with 2% HF in helium. Between the recording of the full HCN-HF 2v2 spectrum and
the measurements of the individual linewidths, we replaced
both the mirrors and the spacers (with precision ground
parallels) in the plano-parallel mirror multipass arrangement, to yield a slightly improved instrumental linewidth
of 15 MHz [full width at half maximum (FWHM)], and
improved S/N. We presently achieve a S/N of 2.5 x lo4 on
the P( 1) transition of the acetylene v1 +v3 band near 1.5
pm, expanding an approximately 1% acetylene in helium
mixture at 4 bars backing pressure. As the S/N ratio on the
corresponding fundamental transition is actually slightly
lower, this is a good indication of how efficiently we can
pump overtone transitions. In the case that both fundamental and overtone transition are saturated one would
expect the overtone signal to be twice as large due to the
larger photon size. The spectra were linearized in frequency using reference signals derived from two scanning
&talons of 8 GHz and 150 MHz free spectral range, as
described in Ref. 34. Absolute frequency calibration was
obtained from the P( 1) transition of the HCN 2v1 band.
Its frequency was determined by Smith et aL3’ to be
6516.649 25 cm-‘, in reference to O2 calibration lines,
whose accuracy we estimate at 4 to 5 x 10m4 cm-‘.
8897
of HCN-HF
-2.01
6516.0
I
6517.0
6516.0
Frequency
6519.0
6520.0
(cm-l)
FIG. 1. P(9) through R(6) of the 2~~ overtone spectrum of HCN-HF.
RESULTS
The spectrum of Fig. 1 shows the P( 9) through R (6)
transitions of the linear HCN-HF complex. The negative
features belong to the HC 14N and HC “N monomers
[P( 1) and R(O), respectively]. At the present S/N level no
hot band of the dimer is observed. The oscillations in the
base-line level are caused by changes in the amount of
scattered IR radiation received by the detector. The period
of the oscillations is consistent with them being due to
interference of overlapping laser beam paths occurring between the mirrors of the multipass (the mirror spacing is
25 mm). Realignment of the optical beam path indeed
made the oscillations disappear.
The R (6) through P( 9) transitions were fitted to the
standard expression for a rotating vibrator, with the
ground-state constants constrained to the microwave values of Legon, Millen, and Rogers.4 A list of the transition
frequencies is presented in Table I. The spectroscopic constants are given in Table II and include the values determined from the fundamental v2 spectrum by Dayton and
Miller,24 and the FTIR gas-cell overtone spectrum of Bevan and co-workers.2’ The standard deviation of the fit is
TABLE I. Observed transition frequencies and residuals for the 2vz band
of HCN-HF. The standard deviation of the fit is 5.4 MHz.
OBS
(cm-‘)
R(6)
R(5)
R(4)
R(3)
R(2)
R(l)
R(O)
P(l)
P(2)
P(3)
P(4)
P(5)
P(6)
P(7)
P(8)
P(9)
65 19.973 40
6519.738 81
6519.503 55
65 19.267 27
65 19.030 07
6518.792 29
6518.554 06
6518.075 54
6517.835 54
65 17.594 79
6517.353 33
6517.111 07
6516.867 89
65 16.624 42
6516.380 05
6516.134 96
OBS-CALC
(IO-” cm-‘)
15.4
9.34
24.7
17.8
-6.27
- 19.0
-9.76
-9.30
9.63
15.9
15.7
1.89
-32.8
-20.8
-17.0
4.52
J. Chem. Phys., Vol. 97, No. 12, 15 December 1992
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Kerstel et al.: Overtone spectroscopy
8898
TABLE II. Spectroscopic constants for the HCN-HF
v=o
Ref. 4
B (cm-‘)
0.119 181
0.11973(S)
0.119 787b
0.119 817
AB (10-s
cm-‘)
D (lo-’ cm)
v=l
Ref. 31
v=2
Ref. 21
0.11958(5)
IOOOc
.2
3
800
f
z
600-
-
.r"
0.119 478(7)
0.119 489
15(l)
1 zoor
vz vibration.8
v=2
This work
of HCN-HF
,u
2
400 -
_c
33
31(l)
-900
I.
17
22(b)
-60I.
-40*.
-20I.
0I.
Frequency
16(h)
17b
25
-60I.
20I.
408.
608.
80*.
100
1
(MHz)
63(11)
26
v. (cm-‘)
3310.3271(30)
6518.3152(l)
6518.3208
Av,, (cm-‘)
-1.149(3)
-1.2905(S)
- 1.291
FL (MHz)
9.9(3)
W2)
r W
16.1(5)
9( 1.5)
FIG. 2. Comparison of the experimentally observed (squares) rotational
line shapes for the HCN P( 1) and the HCN-HF R( 3) lines. The solid
lines give the results of a Gaussian line-shape fit to the monomer line, and
of a Voigt profile fit to the HCN-HF line.
< 45oE
‘The errors in parentheses represent one sigma.
bConstrained to the microwave value of Ref. 4.
‘Gas-cell FIIR data (pressure is 5 Torr, temperature -31 “C).
5.4 MHz. The results of the fit are in good agreement with
the FIIR spectrum. The linewidths of the 5 Torr, - 3 1 “C
gas-cell spectrum are approximately 450 MHz, which naturally limits the accuracy of the constants obtained from
this spectrum. It should also be noted that in general the
distortion constant D and the rotational constant B are
highly correlated. For our fit the correlation between B’
and D’ is given by cos-’ (correlation) = 17”. In terms of a
simplistic ball-and-stick model of the molecule, the AB’s
for the fundamental and overtone spectrum can be entirely
attributed to the extension of the excited CH bond, without
the necessity of invoking a shortening of the hydrogen
bond upon CH stretch excitation. The 2~~ band of the
complex is observed to be shifted by only 1.2905 cm-’ to
the red of the corresponding band in the HCN monomer.
This redshift Av( U’= 2, u” =O) is not only small when
compared to the shifts observed for similar small
hydrogen-bonded systems, like the HCN dimer, but also
when compared with the redshift of the fundamental spectrum (1.149 cm-1).24
The linewidths observed in the overtone spectrum are
clearly broader than dictated by the residual Doppler
broadening in the laser multipass. This is illustrated in Fig.
2, which shows both the HCN-HF R( 3) and the HCN
monomer P( 1) transition. The monomer is well represented by a Gaussian of width 15.3 MHz (FWHM), which
is taken as the instrumental line profile. The approximation
that the monomer line shape represents the Gaussian contribution to the Voigt-shaped diameter lines is valid if both
monomers and complexes have essentially the same velocity distribution. Since we expand rather dilute mixtures, we
expect the velocity slip of the complexes with respect to the
carrier gas to be small, and the approximation to be very
good indeed.36 In order to fit a Voigt profile to the
HCN-HF
line an additional Lorentzian component of
18(2) MHz (FWHM) was needed, which corresponds to
an excited-state lifetime r of about 9 ns. The accuracy
quoted for the Lorentzian width reflects the distribution in
widths obtained from three different scans over the R (3)
line. Also, within the experimental accuracy of the spectrum of Fig. 1, there is no indication of a J dependence of
the linewidths. The absence of a Lorentzian component to
the monomer line shape rules out a significant power
broadening component to the linewidth of the complex,
since no significant enhancement of the CH vibrational
transition moment is expected upon hydrogen bonding to
nitrogen.
DISCUSSION
It is interesting to discuss the present results for
HCN-HF in the light of the data available for the HCN
dimer, so far the only similar system for which a CH
stretching overtone, sub-Doppler spectrum has been recorded. For HCN dimer both the v1 fundamental37 and the
2vi overtone26 spectrum of the “outside” CH stretch show
linewidths that are instrument limited. Together with the
observation that the excited dimers do dissociate before
reaching the detector, these IR studies confined the HCN
dimer vibrational predissociation lifetime to the range from
140 ns to 0.3 ms for fundamental,37 and to the range from
11 ns to 90 ps for overtone26 excitation. Recently, in our
laboratory we have carried out microwave-infrared doubleresonance experiments on (HCN)2 with the goal of narrowing the gap between the bounds for the fundamental
(u= 1) vibrational predissociation lifetime.38 In a preliminary experiment we observed rotational transitions in the
vibrational upper state with a 220 kHz (FWHM) Lorentzian component, indicating a U= 1 predissociation lifetime
of approximately 1.5 ps.
It has been argued before37*39that the long lifetime of
the v1 excited HCN dimer is consistent with the observations that the hydrogen bond does not contract measurably
and that the complexation induced redshift is rather small
(3.16 cm-t for the fundamental, 6.39 cm-’ for the overtone) when compared to the redshift caused by excitation
of the “inside” CH stretch (70 cm-’ for this fundamental
J. Chem. Phys., Vol. 97, No. 12, 15 December 1992
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Kerstel et al.: Overtone spectroscopy
8899
of HCN-HF
~2 band, which shows a lifetime of “only”
6 ns), since all of
these observations can be attributed to the “outside” CH
bond being decoupled to a much larger extend from the
hydrogen bond than the inside CH bond participating in
the hydrogen bonding. In fact, observations such as these
for a wide range of weakly bound complexes have led
Miller to propose his predissociation rate vs redshift correlation law:40
-r-la
(Av)~.
(1)
Even though the plot of log( 7-l) vs log( Av) presented by
Miller, and containing data on over 20 systems shows substantial scatter in a band nearly half an order of magnitude
wide, around the proposed slope-equals-two line, the vibrational predissociation rates observed for HCN-HF (u= 1,
as well as v=2) are at least 1 order of magnitude larger
than the plot would suggest on the basis of the observed
redshifts for the v2 and 2v2 bands. The results for ( HCN)2,
on the other hand, are much more in line with the predictions of the correlation law.
The correlation law of Eq. ( 1) was rationalized by
LeRoy and co-workers41 in a first-order perturbative treatment (including the use of Fermi’s golden rule to calculate
the vibrational predissociation rate) for a hypothetical system involving only one internal degree of freedom (the
initially excited intramolecular high-frequency mode). For
example, their model would treat HCN-HF as the linear
quasitriatomic H-( CN) v* * (HF), and also ignores vibrational modes associated with the van der Waals bond, as
well as rotations of the complex or dissociation products.
The authors showed that extension of their model to more
than one internal degree of freedom (associated with other
intramolecular modes in the monomer unit(s), or with the
van der Waals bond, including motions that correlate with
rotations of the free monomer units) leads to, the conclusion that the correlation law is no longer expected to hold.
That it persists (as Miller’s observations show) is then
taken as evidence for a two-step impulsive predissociation
mechanism, in which the initial, rate-determining step involves only one internal degree of freedom. The redistribution over the product internal degrees of freedom of the
energy released would then be decided during the process
of fragment separation. It appears therefore that the preconditions for LeRoy’s theory are fulfilled for a series of
systems in which the strength of the coupling function,
which drives the vibrational predissociation process, varies
over more than 2 orders of magnitude. LeRoy describes
these preconditions as “all-else-being-equal” (if strictly applied this would limit the applicability of the theory to a
single case), but in effect implying that the functional form
of the coupling potential function be very similar for the
systems considered. Since many of these systems involve
the same type of monomer vibrational mode (e.g., the triply bonded CH stretch), it seems reasonable to expect that
at least the dependence of the coupling functions on the
intramolecular (CH stretching) coordinate be very similar.
The question now arises whether “all-else” can be considered equal when comparing overtone and fundamental ex-
FIG. 3. Schematic representation of the one-dimensional intra- and intermolecular potential-energy curves, and their wave functions, as discussed in the text. The potential U,(r) is the one-dimensional representation of the CH stretching potential in the complex, whereas U,(r)
represents the corresponding potential in the isolated monomer. Note that
the lowest vibrational levels (n=O) of the vibrationally averaged intermolecular (van der Waals) potentials correlate with the CH stretch energy levels in the complex, while their asymptotic values at large separation (R + m ) correlate with the monomer energy levels.
citation of the same mode in the same complex. To answer
this question, we will first proceed with introducing LeRoy’s formalism.
The starting point of LeRoy’s4i analysis is the Hamiltonian for the van der Waals molecule with only one intramolecular mode, which can be written as follows:
fMr,R)
=H,,,(r) - (h2/8Gp)(d2/dR2)
+ VoWI +AV,(r,R).
(2)
Here H,(r) describes the intramolecular vibration of the
free monomer: H,@,(r) =E,( u) @J r) . The overall interaction potential is the sum of a “frozen” monomer potential V,(R) and a potential coupling term AV,(r,R). Introducing a crude adiabatic separation of variables, the total
wave function becomes
\I’tot,v(r,R)=~,(r)~v(R),
(3)
where the wavefunctions $,(R) are associated with the
radial van der Waals motion on the vibrationally averaged
effective adiabatic potential ( V( R ) >uv (see Fig. 3) :
(V(R)),,=
IAVJr,R)
v~(R)+(%(r)
I%,(r)).
(4)
The next approximation is to expand the potential coupling
term in a suitably chosen basis set:
AV,(r,R)=
c
k= 1,m
h(r)VdR)
and to retain the leading term only:
AV,(r,R) z&(r)
VI(R).
(5)
If we take 4k( r) = (r- re) k, the expression corresponds to a
Taylor expansion in the small-amplitude intramolecular vi-
J. Redistribution
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12, 15
December
1992
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or copyright,
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8900
Kerstel et
a/.:Overtone
brational coordinate, an obvious approximation. At this
point we follow LeRoy in allowing for a more general
formulation.
In the following paragraphs we will discuss, in light of
the above considerations, first the vibrational frequency
shift Av that accompanies complexation, then the vibrational predissociation lifetime r, and finally we will return
to the issue of the correlation law as represented by Eq. ( 1)
The vibrational
frequency
shift
Referring again to Fig. 3, it is easily seen that the
vibrational frequency shift due to complexation is the
quantity:
Av”,“,, = [Ec(v’) -mu”)
I - [&Au’)
-&(u”)
I
=(D”m-DUt).
(6)
It can be shown that within first-order perturbation theory
one can write the shift as
Avury,,= (4,(4)“~“4$“~(R)
-(d,(T))u~‘u~‘(~,r,(R)
I V,(R) I$,r(R))
I v,(R)
IZC1”4R)).
(74
The notation (&(T))~~ is short for (Q”(r) [d,(r) (Q,(r)).
We now make the simplifying assumption that the radial
averages of Vi (R) do not significantly depend on the vibrational quantum number u, and obtain the result
Av,, “,, =
,
[(~l(r))u~u~-(~1(T))u”v”l
x (tCIP(R)I v,(R) I$“4R)).
0)
For HCN-HF the approximation made above is supported
by the experimental redshifts and the dependence of the
rotational constant on v. Since D,, = Dutt - Av~,~,,, the
small redshifts indicate that the (hydrogen bond) dissociation energy, and consequently the van der Wards potential
well depth, do not change significantly with excitation of
the CH stretch. Also, the rotational constant B, does not
indicate a vibrational dependence of the van der Waals
bond length. Therefore, the radial van der Waals potential
of our linear quasitriatomic complex appears not to change
shape, or to shift position with respect to R, upon CH
stretch excitation. Consequently, the same should be true
for the wave functions supported by these potentials, and
for the diagonal expectation values as they appear in Eq.
(7b).
If the dependence on the intramolecular coordinate r
of the interaction potential is assumed to be linear, &(r)
=s (r-Q,
we obtain for the ratio of vibrational frequency shifts:
Av,dAv,o=((r),,-((r),)/((r),,-(r),)
=2.029.
(8)
Since in the above expression the matrix elements are evaluated by integration over the monomer wave functions, the
result is independent of the nature of the (ground state)
partner in the complex. Consequently, we would predict
the same ratio of u= 2 to u= 1 shifts for HCN-HF as for
( HCN)2. To obtain the numerical result the (T)“” matrix
spectroscopy
of HCN-HF
elements were evaluated from the HCN monomer rotational constants, B, [i.e., the (r),, were approximated by
( ( (r) -2) ,“) - 1’2]. For the HCN dimer the ratio of the experimentally observed overtone and fundamental shifts is
2.024, in excellent agreement with the above result. It
should be noted that the result of Eq. (8) is exactly what
would be obtained from the electrostatic theory of Liu and
Dykstra,42 when it is assumed that the effect of complex
formation can be represented by the addition of an interaction potential linear in the CH stretching coordinate r to
the intramolecular CH stretching potential. Liu and Dykstra have performed high-level ab initio calculations of the
interaction potential for several systems containing HF
that show that, within the limits of only considering the
electrostatic forces, the approximation of a linear interaction potential is a very good one. Even for a strong interaction system such as the HF dimer with the inside HF
stretch excited, the potential is certainly locally very nearly
linear. For our case, where a nonbonded CH stretch is
excited that is only slightly perturbed by the other molecule in the complex, the approximation should be even
more valid.
Using wave functions constructed to closely correspond to those of the CH oscillator in HCN,43 we have
evaluated the expression on the right-hand side of Eq. (8))
replacing the matrix elements with ( ( r>2),, to obtain a
numerical value of 2.18. Therefore, even if the secondorder term had an appreciable magnitude, we would not
expect the ratio of vibrational frequency shifts to change
dramatically. Moreover, we expect Eq. (8) to be rather
accurate since, to first order, the strength of the coupling
function will cancel in the ratio of redshifts, eliminating the
need to evaluate the absolute value of the coupling
strength. It is therefore somewhat of a surprise to find the
experimental value of the overtone redshift for CH excited
HCN-HF to be only marginally larger than the fundamental shift: ( Av~,,/Av,,,)~~~ = 1.124.
We propose that the discrepancy is caused by the overtone band (or both fundamental and overtone bands) being displaced by a long-range anharmonic vibrational interaction. We do not see any evidence of J-dependent,
local, near-resonant perturbations: there appears to be no
correlation in the residuals of transitions connecting the
same upper state-P( J” + 1) and R (J” - 1)-nor
are
there irregularities in their intensities. Also, a Coriolis mediated interaction will not shift the band origin, but in
general will effect the rotational constants (a Coriolis interaction can therefore not be positively ruled out because
of the large difference in D” and D’ values of our fit).
However, a long-range, low-order anharmonic perturbation, like a Fermi resonance, could be shifting the 2v2 state
up by an amount equal to the predicted overtone redshift
[based on Eq. (S)] minus the observed shift, i.e., 2.029
X 1.149- 1.2905=1.0 cm-‘. Together with the fact that
we observe the HCN-HF spectrum at approximately the
same S/N as the HCN dimer spectrum and that we have
failed to observe the perturber in the region scanned, this
leads to the estimate that the perturbing state must be at
least 5 cm-’ below 2v2, and that the interaction matrix
J. Chem. Phys., Vol. 97, No. 12, 15 December 1992
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Kerstel et
aL:Overtone
TABLE III, Calculated frequencies for transitions from the ground state,
for the HCN-HF vibrational states of A, symmetry, that appear in a 300
cm-’ wide window directly below the 2v2 state (0,2,0,0,0c,00,00). Also
listed is their energy difference AhEwith the 2vs state. The labeling of the
normal-mode vibrations follows that used by Bevan and co-workers
(Refs. 19 and 20). The total number of A, states in this region is 12 (16
when l-type doubling would be taken into account).
State
AE(cm-‘)
Energy (cm-‘)
w,o,o,oqoq~)
(o,1,1,1,00,2°,00)
6519.22
6511.65
6478.50
6435.63
6397.88
6375.40
6361.16
6327.07
6325.75
6318.88
6227.02
6225.77
(1,0,1,0@,1’,1’)
(10003’
91,)
*,1’00)
(0,0,3,1,~,~,~)
w,Lo,~,2°,~)
(0 t0 , 3 ,0 ,00,00,2e)
( 1,0,1,3,0c,0e,0?
(0,1,1,1,1’,00,1’)
( 1,0 I0 ,0 92’,22,00)
(0 90 93 ,0 Ioo,@,$)
( wNv2,22,@v
0.00
7.57
40.72
83.59
121.34
143.82
158.06
192.15
193.47
200.34
292.20
293.45
spectroscopy
there is potential for a vibrational interaction of the kind
we are looking for to occur, even at this density of states,
e.g., transferring one quantum from the CH stretch to one
quantum in the CN stretch and two quanta in the highfrequency HF bend (and possibly one quantum in the van
der Waals stretch). We are, however, hesitant to choose
any one state with certainty, especially due to the uncertainties in the anharmonic cross terms, and because a 144
cm-’ detuning as for the (O,l, 1,0,0,2,0) state would require a rather large interaction matrix element of 12 cm-‘.
As one last note here, we would like to mention that
we recently observed the fundamental and overtone spectra
associated with CH stretch excitation in HCN-BF3.44 Both
spectra (vi and 2vi) appear very regular, showing no signs
of short-range (Coriolis mediated) perturbations. The fundamental spectrum is shifted by 0. lO( 1) cm-’ to the red of
the corresponding monomer band. However, the overtone
is observed approximately 0.65 ( 1) cm- ’ to the blue, presumably also due to a vibrational perturbation.
The vibrational
element is larger than roughly 2 cm-‘, since the frequency
shift yields ( Wi”,)‘/AE=
1 cm- ‘, while the intensity argument leads to ( B’i”,/AE)2 < 0.2. As mentioned above, there
exists of course also the possibility that both the fundamental 5r2and the overtone 2v2 levels are shifted (presumably
both up from their unperturbed positions, thus only increasing the required size of the interaction matrix element). We note too, that for a weak, long-range perturbation it is reasonable to consider the change in linewidth
insignificant, unless the perturber is intrinsically much
broader (shorter lived).
We have attempted a direct count of the density of
states of HCN-HF using the harmonic frequencies and
anharmonicities determined for the complex by Bevan and
co-workers, supplemented with those of the HCN monomer and assuming those that are not (yet) available to be
zero. Only states of A, symmetry, which can couple to 2v2
via an anharmonic interaction, were counted. The total
number of quanta in the molecule was (arbitrarily) limited
to 5, while we searched in a 300 cm-’ window below 2v2.
The results are summarized in Tables III and IV. Clearly
TABLE IV. The harmonic frequencies and anharmonicities (in units of
cm-‘) as used in the calculation of the HCN-HF vibrational energy
levels (Refs. 10-20).
1
wi
XI,
Xl/
X3/.
x4j
XSJ
1
2
3891.80 3440.94
-116.9
0
-51.355
3
4
5
2127.71 190.22
726.95
0
8.025
0
- 14.85 -0.161 -19.352
- 10.224 0
-3.107
-4.341
2.61
-2.497
xbj
xlj
gsJ
gbj
g7J
5.23
6
7
611.72
75.0
54.1
4.214
0
-0.409
0
-0.61
- 17.231
0.015
0
0
-32.717 -7.701
0
0
18.047
0
0.8
0
8901
of HCN-HF
predissociation
rate
We will attempt to predict the ratio of u=2 to U= 1
vibrational predissociation rates within the same framework. The Fermi’s golden rule formula yields the following
expression for the rate:
r-‘=2rK
c
I @&9>“QJ12
U<U’
x I (&E(R)
I VI(R) lb(R))
12.
(9)
The “free” wave function @“JR) is associated with the
dissociation channel with v < U’ and a kinetic-energy release E= [E,( v’) - EC(u”)] -Do- E,( 0). The density-ofstates factor usually present in the expression for the
Golden rule45 is implicit in the summation over all energetically allowed dissociation channels and the normalization of the wave functions.46 In general, a strong preference
for the v = v’- 1 dissociation channel is observed.4749 We
will therefore drop the summation from Eq. (9) and obtain
for the ratio of overtone to fundamental rates:
=( I (h(r))2,l/l
(hW)ml
j2
x ( I Ww2,(R)I VI(R)1$2(R))
x I %,E,~(R)
I V,(R) IA(R))
I
I -‘12.
(10)
If the vibrationally averaged van der Waals potentials
( V(R)),, do not depend strongly on the vibrational quantum number U, then both the free and the bound (metastable) wave functions appearing in Eq. (10) will be fairly
similar for U= 0 and u= 1, respectively, for U= 1 and U= 2.
Consequently, the rightmost factor in Eq. ( 10) reduces, in
a first approximation, to unity:
J. Chem. Phys., Vol. 97, No. 12, 15 December 1992
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8902
Kerstel et
a/.:Overtone
This approximation can of course be justified with the
same arguments presented earlier to justify the approximation made to arrive at Eq. (7b) from Eq. (7a).
We have numerically evaluated [see the discussion following Eq. (8)] the matrix elements appearing in Eq. ( 11)
and find for the linear term, #r(r) =s* (r-rc),
that
~-‘(u’=~)/T-~(u’=
1) =2.03, while for the quadratic
term, f$i(r)=t*(r-ra)*,
we calculate r-l(0’=2)/
r-‘(v’=1)=8.42.
This compares to a ratio of 1.8 (0.3)
observed experimentally.
The correlation
law
That the correlation law of Eq. ( 1) can be misleading
when comparing overtone with fundamental vibrational
predissociation is easily seen by combining the estimates of
Eqs. (8) and ( 11)) with a linear approximation for & (r),
into
x
(~)~*-(r)~)/((r),~-(r)~))*=2.03.
(12)
If the correlation law of Eq. ( 1) could be applied as implied above, the ratio on the left-hand side in Eq. (12)
should be unity. Clearly then, when comparing v=2 to
v = 1 predissociation, “all-else” is not equal in the same
sense as one needs to assume to make Eq. ( 1) valid. However, if it can be assumed that the monomer vibrational
wave functions Q’,(r), and therefore the matrix elements
(4t (r) ), are not much affected by complexation, the factors containing the matrix elements (+t (r) ) in Eqs. (7)
and (9) can be treated as constants, for a given seriesof
complexes involving the same intramolecular vibrational
excitation (from v” to v’). In this case the correlation law
relies on the coupling function having very much the same
shape for all members of this series, so that in first approximation one can assume a simple scaling of the coupling
function with a constant factor. In contrast, when comparing overtone and fundamental vibrational predissociation
in the same complex, the coupling function is naturally
unchanged, but the monomer vibrational wave functions,
and thus the matrix elements (+t (r) ), change dramatically
with the vibrational quantum number.
As we have already pointed out, the validity of the
correlations derived for this case [specially the one formulated in Eq. ( 1 1 )] now depends on changes with the quantum number v in the radial van der Waals wave functions
being negligible, in both the metastable and the unbound,
dissociative state. This appears to be a reasonable assumption for the case of the metastable wave function r&(,,(R):
since it is presumed that the initial excitation does not
involve a hot band or combination band transition associated with the van der Waals mode(s), the function r,&(R)
has the smooth shape without nodes, characteristic of the
lowest vibrational level (with quantum number n =O).
However, the wave function $JR)
associated with the
dissociation products is a rapidly oscillating function and
its exact behavior could depend strongly on the dissocia-
spectroscopy
of HCN-HF
tion channel considered. Especially when one (or both) of
the dissociation products has more than one internal degree of freedom, it is possible that the vibrational predissociation following overtone excitation shows a very different redistribution of the excitation energy over the internal
degrees of freedom of the products than the predissociation
following fundamental excitation. But even in the case of
only one internal degree of freedom, the degree of rotational excitation of the products may be quite different.
Indeed, the beautiful work of Miller’s group on HF dimer
has clearly demonstrated the importance of near-resonant
channels in the vibrational dissociation process.50 Therefore, even if the Au= - 1 preference holds rigidly, the
1c11,~~~
CR1 and $o,.Q~(R1 wave functions might not just be
simply displaced by AE=E,(v=2) -EJv= l), but also be
of rather different shape and displaced along the van der
Waals coordinate.
In conclusion, the requirement that the diagonal radial
matrix elements appearing in the expression for the frequency shifts [Eq. (7a)] do not depend strongly on v is
more easily satisfied than the corresponding requirement
for the off-diagonal coupling matrix elements in the expressions for the predissociation rate [Eqs. (9) and (lo)]. The
first-order description of the predissociation rate behavior,
and therewith the correlation law, is potentially much
more troublesome than the frequency-shift prediction
within the same framework.
This may very well be the main reason for the faster
predissociation of the overtone, “free” HF-stretch excited
HF dimer, compared to the corresponding fundamental
case, as observed very recently by Nesbitt and coworkers.*’ The linewidths in their 2~~ spectrum are indicative of predissociation rates that are sensitively dependent
on the rotational quantum numbers (including the interconversion tunneling symmetry of the levels), and that are
generally about 1 order of magnitude faster than for the
fundamental. Due to the small moment of inertia of HF
and the highly anisotropic hydrogen bond (resulting in a
strong mixing of the rotational states), rotational excitation of the fragments is expected to result in efficient vibrational predissociation of the HF dimer. However, as for
our HCN-HF system, the number of accessible dissociation channels for (HF), is not expected to increase dramatically from fundamental to overtone excitation, in view
of the harmonic preference for Au = - 1. Still, it should not
surprise us if the HF dimer, with its more strongly anharmanic HF oscillator and nonlinear hydrogen bond, defies
treatment in such a simple model as presented here. Already its overtone frequency redshift is larger than approximately twice the fundamental shift (71 vs 30 cm-‘); the
experimental ratio of redshifts is 2.37, whereas an evaluation of Eq. (8), with as input the monomer rotational
constants of HF,51 yields a predicted ratio of 2.033.
King and co-workers have observed the NO stretching
v1 + v5 combination band and the 2v5 overtone of the NO
dimer.3 ’ The vi and v5 fundamentals were previously recorded in both time29 and frequency28*30 domain experiments. For the present discussion the v5 (antisymmetric
NO stretches) measurements are the most interesting. For
J. Chem. Phys., Vol. 97, No. 12, 15 December 1992
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Kerstel et
a/.:
Overtone spectroscopy
this mode, the fundamental and overtone frequency redshifts are -87 and - 165 cm-‘, respectively (i.e., Av2d
Avlo= 1.9), whereas the lifetimes were determined to be
39(8) and 20(3) psec, respectively [yielding a ratio
r-‘(u’=2)/r-l(v’=
1) =2.0]. Both the ratio of redshifts
and the ratio of the lifetimes agree remarkably well with
the predictions based on Eqs. (8) and ( 1 l), especially
when taking into account that the large redshifts suggest a
relatively strong potential coupling. However, there exists
strong evidence that the predissociation of the NO dimer
evolves, at least partially, through a nonadiabatic spinorbit coupling mechanism which involves the electronic
ground state ( ‘A 1) and the repulsive surface of a low-lying
electronically excited state. As already pointed out in the
Introduction, this level of agreement might well turn out to
be fortuitous as our understanding of the (NO), dissociation mechanism increases.
Predissociation
8903
of HCN-HF
TABLE V. Direct count of the accessible dissociation channels following
excitation of the “outside” CH stretch. The maximum kinetic-energy
release is 200 cm-‘. The dimer is assumed to be prepared in the predissociative state with J=O. The spectroscopic data for the HCN monomer
was taken from Ref. 54, that of HF from Ref. 51. D, (HCN-HF) = 1737
cm-‘. Do (HCN-HCN) = 1330 cm-‘.
HCN-HF
(a) No rotational excitation
of the products
(b) Only Au= - 1 channels,
with no vibrational
excitation of the partner;
bc0.3 8,
(c) Same as (b), except that
b<lti
(d) Same as (b), no limit to
the impact parameter b
(HCNh
u=l
v=2
lJ=l
v=2
2
3
0
0
20
17
0
0
48
35
6
14
55
49
81
83
rate vs density of exit channels
The last issue we would like to discuss is the much
shorter lifetime of the HCN-HF complex, compared to the
HCN dimer, for both fundamental and overtone excitation. While the total density of dissociation channels is
undoubtedly much larger for the HCN dimer, many of
these channels are not likely to play an important role for
reasons explained below. For the sake of simplicity, we will
assume for the following discussion that the complex is
excited to the J=O level of the predissociating state. This is
not a serious restriction in view of the very low rotational
temperatures attained in molecular-beam experiments.
Conservation of angular momentum then requires that
J,-tJ2+Jort,=O,
(13)
where J, and J2 are the internal angular momenta associated with the fragments, while Jorb represents the orbital
angular momentum associated with the reduced mass p,
relative velocity g, and impact parameter b (i.e., the shortest line segment between the asymptotic straight-line trajectories of the fragments at large separation) of the separating fragments. Similarly, conservation of energy
requires that
hv=Do-Einit+
C (EY+ER+ET)i,
i= I,2
(14)
where hv represents the energy of the photoexcitation, Einit
the internal energy of the complex before excitation (relative to the zero-point energy), and E, ERt and ET the
vibrational, rotational, and translational energy of each
fragment. The total number of energetically allowed dissociation channels is obtained from Eq. ( 14), given the energy levels of the monomer fragments, as the number of
ways in which we can combine the energies deposited into
vibrational and rotational motions of the fragments under
the condition that the kinetic-energy release is zero or positive (the ratio of ET1 to En is determined by conservation
of linear momentum).
The larger number of energetically accessible channels
for the HCN dimer is mostly a result of the additional
internal degrees of freedom in the nonexcited HCN mole-
cule and the rotational constant being much smaller for
HCN than for HF. However, the additional channels associated with the intramolecular vibrational modes of the
nonexcited HCN partner in the HCN dimer are rather
remote from the excited, outside CH stretching mode. That
is to say that in this case the overlap between the metastable and the free wave functions appearing in the Golden
rule expression of Eq. (9) is expected to be small. It can
therefore be argued that their excitation in the vibrational
predissociation process is unlikley, as we also expect the
excitation of the HF stretch to be unlikely. In both cases,
the energy leaking out of the excited CH stretch would
have to pass through the van der Waals bond. But even
when we consider only those dissociation channels that
leave the other molecule in the vibrational ground state,
the HCN dimer has, in principle, many more channels at
its disposal by virtue of the much smaller rotational level
spacing in HCN than in HF. However, again it can be
anticipated that these are not very effective in accelerating
the dissociation process. Indeed, in order to dispose of the
same amount of energy, the HCN fragment would have to
be excited to much higher angular momentum states than
the HF fragment. It is generally accepted that V-R energy transfer processes are much less efficient than V- V
processes.49Moreover, the large-amplitude zero-point motion of the internal hydrogen atom in HCN-HF, correlating with HF free rotation, allows the HCN-HF complex to
access dissociation channels with, for a linear complex,
remarkably different angular momenta, whereas for the
much more rigid HCN dimer we expect both fragments to
have very nearly the same angular momentum (the “impact parameter” is at every instant close to zero, corresponding to zero orbital angular momentum associated
with the separating fragments).
For the above reasons we have tabulated in Table V
(for both fundamental and overtone excitation, and for
both systems) the number of energetically accessible dissociation channels (with an upper limit to the kineticenergy release of 200 cm-‘) for the following cases: (a)
counting only the vibrational channels, i.e., excluding ro-
Chem. Phys., Vol.
97, No.
12, license
15 December
1992
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subject
to AIP
or copyright,
see http://ojps.aip.org/jcpo/jcpcr.jsp
8904
Kerstel et a/.: Overtone spectroscopy
tational excitation of the products, (b) counting only the
Av= - 1 channels that leave the partner molecule in the
vibrational ground state and with the range of product
angular momenta limited such that the maximum impact
parameter b is limited to 0.3 A, (c) ditto, but with the
impact parameter b < 1 A, and (d) including all rotational
channels. The expectations based on the above arguments
are clearly born out. The large difference in the number of
available vibrational (rotationless) channels for the two
systems can be attributed to the different dissociation energies (Da=1737 cm-’ for HCN-HF,9 while Da=1330
) . For HCN dimer, for which the
cm - ’ for HCN dimer52V53
energy to be redistributed after dissociation is larger, the
energy is still not sufficient to excite the second overtone of
the bend. The remaining energy, however, is now much
larger than can be accommodated by the next lower vibrational state, the first overtone of the bend. Necessarily, this
amount of excess energy has to be disposed of in the form
of rotational and kinetic excitation of the fragments, both
in themselves rather inefficient processes. Note too, that
the increase in density of dissociation channels from fundamental to overtone excitation is at most very modest. In
conclusion, we can state that a reasonable constraint on the
number of channels that are considered accessible by the
system, such as the kinetic constraint of limiting the range
of impact parameters, suffices to rationalize the observed
trends in the vibrational predissociation rates for these systems.
CONCLUSIONS
We have observed the spectrum of HCN-HF involving
overtone excitation of the CH stretch. The vibrational predissociation lifetime is about a factor of 2 shorter than for
the corresponding fundamental spectrum. This result is not
inconsistent with a simple picture based on first-order perturbation theory, if we assume the dependence on the intramolecular CH stretching coordinate of the coupling potential function to be linear. This appears to be a
reasonable choice for a system in which the CH stretching
potential is only slightly affected by the formation of the
complex. It is then disconcerting to see that the vibrational
frequency shift for the overtone spectrum is very different
from that predicted by the same model. We have therefore
proposed that the experimentally observed frequency shift
reflects not only the effect of complexation, but also the
effect of a long-range vibrational interaction that shifts the
relevant energy levels in the complex. Perhaps isotopic substitution, by selectively shifting the vibrational energy levels in the complex, will allow us to assessthe correctness of
our proposed vibrational interaction. A good understanding of the driving forces behind the complexation induced
vibrational frequency shift is important, so the measured
shift can be reliably used as a sensitive test for the effects of
electron correlation in ab initio calculations. Another issue
is that calculations of dimer properties often neglect the
effects of anharmonicities. Overtone data should allow us
to decide whether observed discrepancies with experiment
are due to this simplification or to other factors (such as
basis-set errors).
of HCN-HF
ACKNOWLEDGMENTS
We are grateful to Professor R. LeRoy for sending a
preprint of his publication (Ref. 41), for discussing his
work with us, and for his critical reading of this manuscript under difficult circumstances, and to Professor J. W.
Bevan for sharing with us a manuscript of Ref. 19 and the
unpublished FTIR spectrum of the HCN-HF 2~~ band.21
This work was supported by the NSF under Grant No.
CHE-901649 1.
‘A. C. Legon and D. J. Millen, Faraday Discuss. Chem. Sot. 73, 71
(1982); Chem. Rev. 86, 635 (1986).
‘J. W. Bevan, in Structure and Dynamics of Weakly Bound Molecular
Complexes, edited by A. Weber, Vol. 212 in NATO ASI Series C (Reidel, Dordrecht, 1986); W. Klemperer, ibid.
‘D. J. Nesbitt, Chem. Rev. 88, 843 (1988).
4A. C. Legon, D. J. Millen, and S. C. Rogers, Proc. R. Sot. London Ser.
A 370, 213 (1980).
‘Z. Kisiel, A. C. Legon, and D. J. Millen, Proc. R. Sot. London Ser. A
381, 419 (1982).
‘A. C. Legon, D. J. Millen, and L. C. Willoughby, Proc. R. Sot. London
Ser. A 401, 327 (1985).
‘A. C. Legon, D. J. Millen, and S. C. Rogers, Chem. Phys. Lett. 41, 137
(1976).
s A. C. Legon, D. J. Millen, and S. C. Rogers, J. Mol. Spectrosc. 70, 209
(1978).
9B. A. Wofford, M. E. Eliades, S. G. Lieb, and J. W. Bevan, J. Chem.
Phys. 87, 5674 (1987); 88, 6678 (1988).
“B A. Wofford, J. W. Bevan, W. B. Olson, and W. J. Lafferty, J. Chem.
Phys. 83, 6188 (1985).
“B. A. Wofford, J. W. Bevan, W. B. Olson, and W. J. Lafferty, Chem.
Phys. Lett. 124, 579 (1986).
“B. A. Wofford, M. W. Jackson, J. W. Bevan, W. B. Olson, and W. L.
Lafferty, J. Chem. Phys. 84, 6115 (1986).
13E Kyro, M. Eliades, A. M. Gallegos, P. Shoja-Chagervand, and J. W.
Bkvan, J. Chem. Phys. 85, 1283 (1986).
14M W. Jackson, B. A. Wofford, J. W. Bevan, W. B. Olson, and W. J.
Lafferty, J. Chem. Phys. 85, 2401 (1986).
“D Bender, M. Eliades, D. A. Danzeiser, M. W. Jackson, and J. W.
Bevan, J. Chem. Phys. 86, 1225 (1987).
16M. W. Jackson, B. A. Wofford, and J. W. Bevan, J. Chem. Phys. 86,
2518 (1987).
“B A. Wofford, M. W. Jackson, S. G. Lieb, and J. W. Bevan, J. Chem.
Phys. 89, 2775 (1988).
‘*B A Wofford R. S. Ram, A. Quinonez, J. W. Bevan, W. B. Olson, and
w. J: Lafferty: Chem. Phys. Lett. 152, 299 (1988).
IsA. Quinones, R. S. Ram, G. Banderage, R. R. Lucchese, and J. W.
Bevan, J. Chem. Phys. (submitted).
“B. A. Wofford, S. G. Lieb, and J. W. Bevan, J. Chem. Phys. 87, 4478
(1987).
“J. W. Bevan (private communication).
22P. Botschwina, Structure and Dynamics of Weakly Bound Complexes,
edited by A. Weber, Vol. 212 in NATO ASI Series C (Reidel,
Dordrecht, 1987).
23R. Amos T. Gaw, N. Handy, E. Simandiras, and K. Somasundram,
Theor. dim. Acta 71, 41 (1987).
24D. C. Dayton and R. E. Miller, Chem. Phys. Lett. 143, 181 (1988).
“D. C. Dayton and R. E. Miller, Chem. Phys. Lett. 150, 217 (1988).
26H Meyer, E. R. Kerstel, D. Zhuang, and G. Stoles, J. Chem. Phys. 90,
4623 (1989).
*‘M. A. Suhm, J. T. Farrel, A. McIlroy, and D. J. Nesbitt (unpublished).
28Ph. Brechignac, S. De Benedicts, N. Halberstadt, B. J. Whitaker, and S.
Avrillier, J. Chem. Phys. 83, 2064 (1985).
29M P Casassa, J. C. Stephenson, and D. S. King, J. Chem. Phys. 89,
1966’(1988).
“Y. Matsumoto, Y. Ohshima, and M. Takami, J. Chem. Phys. 92, 937
(1990).
“J R. Hetzler, M. P. Casassa, and D. S. King, J. Phys. Chem. 95, 8086
(‘1991).
“T. E. Gough, R. E. Miller, and G. Stoles, Appl. Phys. Lett. 30, 338
(1977).
J. Chem. Phys., Vol. 97, No. 12, 15 December 1992
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp
Kerstel et al.: Overtone spectroscopy
“M Zen, in Atomic and Molecular Beam Methods, edited by G. Stoles
(dxford University, New York, 1988), Vol. 1.
UE. R. Th. Kerstel, K. K. Lehmann, T. F. Mentel, B. H. Pate, and G.
SC&S, J. Phys. Chem. 95, 8282 (1991).
“A. M. Smith, S. L. Coy, W. Klemperer, and K. K. Lehmann, J. Mol.
Spectrosc. 134, 134 (1989).
I’D. R. Miller, in Atomic and Molecular Beam Methods, edited by G.
Stoles (Oxford University, New York, 1988). Vol. 1.
“K. W. Jucks and R. E. Miller, J. Chem. Phys. 88, 6059 (1988).
‘*E. R. Th. Kerstel, X. Yang, K. K. Lehmann, and G. Stoles (to be
published).
‘sR. E. Miller, in Dynamics of Polyatomic van der Waals Complexes,
edited by N. Halberstadt and K. C. Janda, Vol. 227 in NATO AS1
Series B (Plenum, New York, 1990).
‘OR. E. Miller, Science 240,447 (1988).
” R. J. LeRoy, M. R. Davies, and M. E. Lam, J. Phys. Chem. 95, 2167
(1991).
of HCN-HF
8905
“S. Liu and C. E. Dykstra, J. Phys. Chem. 90, 3079 (1986).
43K. K. Lehmann and A. M. Smith, J. Chem. Phys. 93, 6140 (1990).
“E. R. Th. Kerstel, X. Yang, and G. Stoles (to be published).
45See, e.g., A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York,
1975).
46R. J. LeRoy, Comput. Phys. Commun. 52, 383 ( 1989).
47D. H. Levy, Adv. Chem. Phys. 47, 323 (1981).
48J M. Skene, J. C. Drobits, and M. I. Lester, J. Chem. Phys. 85, 2329
(‘1986).
49G. E. Ewing, J. Chem. Phys. 91,4662 (1987).
%D. C. Dayton, K. W. Jucks, and R. E. Miller, J. Chem. Phys. 90, 2631
(1989).
“G. Guelachvili, Opt. Commun. 19, 150 (1976).
‘*H. D. Mettee, J. Phys. Chem. 77, 1762 (1973).
53L. W. Buxton, E. J. Campbell, and W. H. Flygare, Chem. Phys. 56, 399
(1981).
54W. Quapp, J. Mol. Spectrosc. 125, 122 (1987).
J. Chem. Phys., Vol. 97, No. 12, 15 December 1992
Downloaded 18 Mar 2002 to 128.112.83.42. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp