Vibrational predissociation dynamics in the vibronic states of the aniline-neon van der Waals complex: New features revealed by complementary spectroscopic approaches

Article abstract of DOI:10.1063/1.478869

We report two independent sets of experimental spectroscopic data which both contain information about the vibrational dynamics occurring in the aniline-neon van der Waals complex in its S₁ electronically excited state. The high resolution excitation spectra of the three vibronic bands, 6a₀¹ I₀², and 1₀¹, of the S₁←S₀ transition, exhibit lifetime broadening with respect to transitions to the corresponding states in the aniline monomer. The dispersed emission spectra taken under excitation of the same three vibronic bands give access to both the distribution of aniline monomer states produced by vibrational predissociation of the complex and to the rates at which this dynamics proceeds. The overall results are discussed in a consistent way, with emphasis being given to the role of the coupling between the intramolecular and the intermolecular vibrational states. In the case of I₀² excitation, it is shown that this coupling is reflected in the shape of the van der Waals wavefunction, as accessed through the analysis of the high resolution spectra [M. Becucci, G. Pietraperzia, N. M. Lakin, E. Castellucci, Ph. Brechignac, Chem. Phys. Lett. 260, 87 (1996).].

Full text of DOI:10.1063/1.478869

Vibrational predissociation dynamics in the vibronic states of the aniline–neon van der
Waals complex: New features revealed by complementary spectroscopic approaches
M. Becucci, N. M. Lakin, G. Pietraperzia, E. Castellucci, Ph. Bréchignac, B. Coutant, and P. Hermine
Citation: The Journal of Chemical Physics 110, 9961 (1999); doi: 10.1063/1.478869
View online: http://dx.doi.org/10.1063/1.478869
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 110, NUMBER 20
22 MAY 1999
Vibrational predissociation dynamics in the vibronic states
of the aniline–neon van der Waals complex: New features
revealed by complementary spectroscopic approaches
M. Becucci,a) N. M. Lakin,b) G. Pietraperzia, and E. Castellucci
`
European Laboratory for Non-Linear Spectroscopy (LENS), Universita di Firenze, Largo E. Fermi 2,
I-50125 Firenze, Italy
`
and Dipartimento di Chimica, Universita di Firenze, via G. Capponi 9, I-50121 Firenze, Italy
´
Ph. Brechignac, B. Coutant, and P. Hermine
´
´
ˆ
Laboratoire de Photophysique Moleculaire-CNRS, Universite de Paris-Sud, Batiment 210,
F91405 Orsay Cedex, France
͑Received 29 October 1998; accepted 3 March 1999͒
We report two independent sets of experimental spectroscopic data which both contain information
about the vibrational dynamics occurring in the aniline–neon van der Waals complex in its S1
electronically excited state. The high resolution excitation spectra of the three vibronic bands, 6a10,
I20, and 101, of the S1←S0 transition, exhibit lifetime broadening with respect to transitions to the
corresponding states in the aniline monomer. The dispersed emission spectra taken under excitation
of the same three vibronic bands give access to both the distribution of aniline monomer states
produced by vibrational predissociation of the complex and to the rates at which this dynamics
proceeds. The overall results are discussed in a consistent way, with emphasis being given to the
role of the coupling between the intramolecular and the intermolecular vibrational states. In the case
of I20 excitation, it is shown that this coupling is reflected in the shape of the van der Waals
wavefunction, as accessed through the analysis of the high resolution spectra ͓M. Becucci, G.
´
Pietraperzia, N. M. Lakin, E. Castellucci, Ph. Brechignac, Chem. Phys. Lett. 260, 87 ͑1996͒.͔.
© 1999 American Institute of Physics. ͓S0021-9606͑99͒01020-X͔
I. INTRODUCTION
In the present work we have studied the first electronic
transition in the aniline–neon vdW complex in the near-
ultraviolet using the complementary techniques of laser ex-
citation spectroscopy at high resolution and dispersed emis-
sion spectroscopy. These methods provide jointly a fairly
complete description and understanding of the dynamical be-
havior of the molecular system when the intramolecular vi-
brational modes in the first electronically excited state of the
vdW complex are excited. On the one hand, the measure-
ment of the linewidths in the high resolution excitation spec-
tra give direct information on the excited states lifetimes. On
the other hand, the measurement of the branching ratios for
the various final states following vibrational excitation in
dispersed emission spectra give the vibrational predissocia-
tion rates, thanks to the internal molecular clock provided by
the natural lifetime of the free molecule. In addition, high
resolution excitation spectroscopy provides information
about the molecular structure of the complex in the states
involved in the transition. This structure reflects the averag-
ing of the inertial tensor over the vibrational motions of the
complex in a particular vibronic state. In cases of favorable
symmetry it has been used to provide a measure of the quan-
tum mechanical extension of the large amplitude internal
motions in the complex.2 In particular a measure of the am-
plitude of the vdW bending motion of aniline–neon in the
lowest vibrational levels of the S0 and S1 electronic states
was reported in a previous article.3 Consequently the high
resolution spectroscopy of higher-lying excited vibronic
What governs the outcome of intramolecular dynamics
in a large system has been a central question in chemical
reaction dynamics for many years. The search for evidence
of mode specificity has known little success, in spite of many
efforts to interrogate molecular systems by spectroscopic
techniques, both in the frequency and in the time domain.1
The study of van der Waals ͑vdW͒ clusters is of funda-
mental interest for the understanding of detailed intramolecu-
lar dynamics, as these species can be considered as model
systems in which the reduction in magnitude of both the
binding strength and vibrational frequencies induces a gen-
eral reduction of the dynamical rates, without preventing ef-
ficient unimolecular reactions from taking place. The times-
cale of these internal processes may reach the nanosecond
range, making them particularly accessible to study using
high resolution spectroscopic techniques. Over such time in-
tervals, the internal dynamics competes with radiative pro-
cesses in the excited states of many molecules. This situation
can be turned into a means to measure reaction rates by
comparing the relative intensities which can be observed in
the various reactive channels to that in the main radiative
channel.
a͒
Author to whom correspondence should be addressed. Electronic mail:
becucci@lens.unifi.it
b͒
¨
¨
Present address: Institut fur Physikalische Chemie, Universitat Basel, Klin-
gelbergstrasse 80, CH-4056 Switzerland.
0021-9606/99/110(20)/9961/10/$15.00
9961
© 1999 American Institute of Physics
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9962
J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
states of this vdW complex offers a unique way to interro-
gate the heart of the quantum reaction dynamics.
The use of various excitation energies, as resulting from
allowed intramolecular vibronic transitions in aniline, opens
the possibility to explore a wider range of the vdW potential
energy surface than was allowed from the spectra of the ori-
gin transition3 only. Indeed the vdW surface associated with
an excited intramolecular vibration lies above the vdW sur-
face associated with the 00 state, and due to the coupling
between intermolecular and intramolecular modes both sur-
faces affect the wavefunction. This coupling is responsible
for a time-dependent vibrational dynamics, whose rate is
even more sensitive than the wavefunction to the relative
shapes of these surfaces at the common excitation energy.
When the excitation energy exceeds the vdW binding energy
vibrational predissociation may proceed towards the ener-
getically allowed product channels. The relative partial rates
determine the branching ratios.
FIG. 1. High resolution fluorescence excitation spectrum of the 6a10 vi-
bronic band of the S1←S0 electronic transition of the aniline–neon van der
Waals complex in a continuous supersonic molecular beam.
Three different vibronic bands of aniline, namely the
6a10, I20, and 110 bands, have been used to investigate in detail
the vibrational dynamics induced by the preparation of the
corresponding vibrational states in the aniline–neon cluster.
The rate for vibrational predissociation ͑VP͒ exhibits a
marked sensitivity to the exact nature of the intramolecular
mode that is prepared. Of particular interest is the observed
correlation between the enhancement of the predissociation
rate, when the inversion mode of aniline is excited, and the
extension of the corresponding quantum wavefunction re-
vealed by the high resolution excitation spectroscopy.
The layout of this paper is as follows: Sec. II summa-
rizes the main aspects of the experimental procedures, Sec.
III describes the results obtained independently by the two
techniques, and Sec. IV compares, discusses, and interprets
these data on the basis of the present knowledge of intramo-
lecular dynamics.
perature stabilized, Fabry–Perot interferometer of 150 MHz
free spectral range ͑this value was treated as an experimental
observable which was accurately determined using the spec-
trum of the aniline monomer taken immediately after each
scan on the vdW complex͒. The UV laser power was also
monitored for the signal normalization. The overall instru-
mental resolution is 15 MHz, mainly limited by residual
Doppler broadening.
The experimental apparatus which has been used in Or-
say to spectrally analyze the emission following vibronic ex-
citation of the aniline–neon complex consists of a supersonic
free jet crossed by the beam of a pulsed, frequency-doubled,
tunable dye laser, pumped by a Q-switched Nd-YAG laser.5
The laser induced fluorescence ͑LIF͒ was collected at right
angles by a system of optics which imaged the central part of
the jet onto the entrance slit of a grating monochromator
͑Jobin et Yvon, Fϭ320 mm) and the light emerging from
the exit slit was detected by a photomultiplier. The dispersed
emission spectra of the species present in the jet ͑free aniline
molecules and vdW complexes͒ were recorded as a function
of wavelength as the stepping motor driving the rotation of
the grating was scanned by a microcomputer.
II. EXPERIMENT
The high resolution fluorescence excitation and the dis-
persed fluorescence experiments were performed, respec-
tively, at the LENS laboratory in Florence and at the LPM in
Orsay. Both experiments have already been described
elsewhere;4,5 here we will give only a short summary.
III. RESULTS
The high resolution spectrometer at LENS is formed by
the combination of a collimated supersonic molecular beam
and a cw single mode ring dye laser ͑with intracavity dou-
bling of the fundamental frequency to reach the near-UV͒.
The gas mixture ͑0.1% aniline in pure neon͒ was expanded
into the first chamber at a backing pressure of 600 kPa
through a 50 ␮ nozzle. The central core of the expansion was
collimated by a 400 ␮ conical skimmer, placed at 10 mm
from the nozzle. The crossing of the resulting molecular
beam with the laser beam occurred at 34 cm downstream the
skimmer, where the total undispersed fluorescence was im-
aged onto a cooled photomultiplier ͑EMI 9893Q/350͒ and
the signal was recorded by photon counting. The absolute
frequency of the laser source was monitored ͑on the funda-
mental wave͒ by a wavemeter ͑Burleigh PWA͒. The relative
frequency shift was calibrated against a pressure-sealed, tem-
A. High resolution spectroscopy
We report in Figs. 1 and 2 the spectra of the 6a10 and the
I20 vibronic bands of the S1←S0 electronic transition of the
aniline–neon vdW complex. Both spectra, as well as the
spectrum of the 110 vibronic band ͑not shown͒ are extremely
similar to the already published spectrum of the 000 vibronic
band of the complex.3 The major difference is the presence
of a significant line broadening in the I20 band, which is the
signature of enhanced relaxation in the excited state. All
three spectra consist of a superimposition of two different
components, which correspond to the two neon-20 and
neon-22 isotopic forms of the complex.3
All rotational assignments were obtained by simulation
and least-squares ͑LSQ͒ fits using a rigid rotor Hamiltonian.6
The number of assignments made for each vibronic band
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J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
9963
TABLE I. Rotational constants on the ground state of the aniline–neon
complex obtained in fits of different vibronic bands.
000
6a10
101
Averaged values
Aniline–20Ne
a
A
͑cmϪ1
͒
0.061 81͑3͒
0.061 88͑3͒
0.057 44͑20͒ 0.057 50͑9͒
0.043 78͑20͒ 0.043 59͑9͒
0.061 84͑3͒
0.057 53͑15͒
0.043 48͑15͒
0.061 84͑2͒
0.057 50͑13͒
0.043 59͑13͒
Љ
B
C
Љ
Љ
Aniline–22Ne
0.060 98͑3͒
0.055 33͑19͒ 0.055 40͑28͒ 0.055 38͑17͒
0.041 70͑19͒ 0.041 90͑28͒ 0.041 88͑17͒
0.061 00͑3͒
0.061 00͑2͒
0.061 00͑2͒
0.055 37͑13͒
0.041 82͑13͒
A
B
C
Љ
Љ
Љ
aNumbers given in parentheses represent one standard deviation of the pa-
rameter in units of the last quoted decimal place.
linewidth and the resulting lower signal-to-noise ratio. We
were able to fit for the neon-20 complex only 24 transitions
belonging to the lower J ‘‘clumps of transitions’’ and 13
transitions for the neon-22 complex with a 20 MHz standard
deviation. Table II reports the u.s. rotational constants for the
000, 6a10, 101, and I20 vibronic bands of the two isomeric forms
of the aniline–neon vdW complex.
The rotational constants determined from an experiment
are determined by the inertial properties of the molecular
system. Unfortunately the direct inversion of the rotational
constants to give the molecular geometry is not always pos-
sible, especially in such a loosely bound system as a vdW
molecule. In complexes involving an aromatic monomer the
weak binding between the rare gas atom and the aromatic
ring allows a large freedom for the motion of the rare gas
atom in a plane parallel to the ring. The rotational constants
of the complex therefore reflect an effective value of the mo-
lecular geometry and not just the average values of the atom
positions.7
In order to properly discuss the problem of the aniline–
neon complex it is necessary to define a suitable axis system
to describe the inertial tensor of the complex. We will as-
sume that the aniline molecule is a rigid body whose geom-
etry is unchanged upon complexation. The reference frame,
as already discussed in a previous paper,8 is attached to the
center of mass of the aniline–neon complex so that the axes
͑x,y,z͒ are parallel to the principal inertial axes (a0 ,b0 ,c0) of
the monomer. The inertial tensor is then given by
FIG. 2. High resolution fluorescence excitation spectrum of the I20 vibronic
band of the S1←S0 electronic transition of the aniline–neon van der Waals
complex in a continuous supersonic molecular beam.
depends upon the linewidth of the isolated transitions: this
determines both our ability to resolve single eigenstates and
the effective signal-to-noise ratio. The I20 band was the most
difficult to analyze due to the large linewidth and the pos-
sible presence of spectral perturbations. In a first stage of
analysis we independently determined both the ground state
͑g.s.͒ and the upper state ͑u.s.͒ rotational constants for the
000, 6a10, and the 110 bands. The values determined for the g.s.
were found to be equal within the error of the measurements
͑see Table I, in which the standard deviation is reported in
parentheses, in units of the last digit͒. To minimize the num-
ber of free parameters we have taken advantage of the fact
that all these transitions share a common vibronic ground
state: we therefore averaged over the three sets of g.s. con-
stants obtained in the independent fits and then fixed them to
this new set of values in final LSQ fits of the three bands.
The typical deviation between the calculated and the experi-
mental line positions was ca. 8 MHz. The same set of g.s.
constants was then used for the analysis of the I20 vibronic
band, under the assumption that this transition shares the
same ground state as the others. The number of assignments
we were able to make for the I20 band was limited due to the
k/A ϩ␮ Y2ϩZ2͒
͑
0
Ϫ␮XY
Ϫ␮XZ
Ϫ␮YZ
k/A
0
0
0
k/B
0
0
0
k/C
k/B ϩ␮ Z2ϩX2͒
Ϫ1
Ϫ␮XY
Ϫ␮XZ
͑
ϭM=
M=
,
͑1͒
0
ͭ
ͮ
ͭ
ͮ
Ϫ␮YZ
k/C ϩ␮ X2ϩY2͒
͑
0
=
constants of the complex; and M is the unitary transforma-
tion matrix between our frame and the principal axes of the
complex.
where A0 , B0 , and C0 are the rotational constants of the
aniline monomer in the corresponding vibronic state; X, Y,
and Z are the coordinates of the neon atom with respect to
the aniline principal axes; ␮ is the reduced mass of the com-
plex and the proportionality constant kϭh/(8␲2c) ͑in units:
cmϪ1 amu Å2͒; A, B, and C are the calculated rotational
The above tensor was used to derive effective coordi-
nates for the neon atom, Xeff , Yeff , and Zeff , for each vibronic
state using the experimentally determined rotational con-
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9964
J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
TABLE II. Rotational constants on the S1 excited states of the aniline–neon
complex obtained in fits of different vibronic bands.
TABLE III. The effective coordinate sets obtained from the experimental
rotational constants for all the vibronic states of aniline–22Ne.
a
000
6a10
I02
101
S0
S1
00
00
6a1
I2
11
Aniline–20Ne
a
͑cmϪ1
͒
0.061 38͑3͒
0.061 36͑3͒
0.056 71͑3͒
0.044 30͑9͒
0.061 57͑8͒
0.056 84͑9͒
0.043 32͑9͒
0.061 39͑3͒
0.056 72͑3͒
0.044 30͑9͒
A
Ј
b
Xeff
Yeff
Zeff
0.209͑2͒
0.249͑39͒
3.399͑1͒
0.218͑1͒
0.203͑14͒
3.378͑1͒
0.216͑1͒
0.227͑10͒
3.372͑1͒
0.187͑11͒
0.586͑44͒
3.373͑6͒
0.220͑1͒
0.311͑18͒
3.375͑1͒
B
C
0.056 72͑3͒
0.044 32͑9͒
Ј
Ј
Aniline–22Ne
0.060 43͑2͒
0.054 78͑3͒
0.042 51͑9͒
0.060 34͑3͒
0.054 83͑3͒
0.042 49͑9͒
0.060 40͑10͒
0.054 73͑20͒
0.041 83͑20͒
0.060 45͑3͒
0.054 78͑3͒
0.042 51͑9͒
A
B
C
aDetermined from averaged values of rotational constants.
Ј
Ј
Ј
bNumbers given in parentheses represent the range of acceptable solutions in
units of the last quoted decimal place.
aNumbers given in parentheses represent one standard deviation of the pa-
rameter in units of the last quoted decimal place.
all the acceptable sets of coordinate values. The calculated
values of Xeff , Yeff , and Zeff and the range of acceptable val-
ues, for each vibronic level and for the ground state, are
reported in Table III. For reasons which were discussed in
Ref. 3 ͑i.e., the proximity of the aniline–20Ne complex to a
symmetric top and the resulting interchange of inertial axes
occurring along the vdW stretching coordinate͒, only the val-
ues for aniline–22Ne are significant for our analysis and will
be used in the forthcoming discussion.
stants. These effective coordinates involve some combina-
tion of the vibrationally averaged coordinate value and the
amplitudes of the vibrational motion. Nevertheless in some
special cases, when symmetry makes the mean value of a
coordinate equal to zero, or when the mean value of a coor
dinate is, in absolute terms, very much larger than its vibra-
tional amplitude, it is possible to determine one or the other
of these quantities. Both symmetry considerations ͑all of the
Once the spectra were fully assigned it was possible to
measure the linewidth for each single rovibronic transition
and to determine the line center position. We fitted the ex-
perimental lineshape using a Voigt profile. The Gaussian
component was fixed to our known instrumental resolution4
while the Lorentzian part was a free parameter. Table IV
contains the fitted Lorentzian widths, ␥j , together with their
standard deviations for each of the vibronic bands of the
complex, and the Lorentzian widths, ␥0 , for the correspond-
ing vibronic bands in the aniline monomer, already measured
in our laboratory.10 The linewidth is independent of the
excited vibronic states are of A type in C group͒ and the
Ј
S
shape of the potential well for the rare gas atom demand that
the mean value of Y is zero. Therefore we have direct access
with Yeff to a measure of the root-mean-square deviation of
the vibrational motion along this coordinate, denoted ⌬Y.
The mean distance between the neon atom and the aromatic
8
ring ͑typically ca. 3.4 Å͒ is much larger than the expected
amplitude of the vibrational wavefunction in this direction
͑typically ca. 0.1 Å͒,9 so that the value Zeff we determine ͑for
Z͒ basically reflects the former value. Finally the yz plane is
not a symmetry plane of the complex and therefore the mean
value of X will be nonzero, so it is almost impossible to
separate in Xeff the contributions from the mean value of X
and from the vibrational amplitude ⌬X.
eigenstate rotational quantum number in the region from J
Љ
ϭ0 to 3. The I20 band represents a special case: due to the
low S/N ratio and the large linewidth, the analysis was lim-
ited to the R(1) ‘‘clump’’ ͑see Fig. 3͒. The lines with higher
rotational quantum numbers are strongly superimposed and a
line profile analysis was not possible. Table IV also contains
the positions, ␯j , of both the vdW complex and the
monomer10 vibronic bands, and the pure vibrational vdW
shifts, ␦j . The latter are defined as the changes of the vibra-
In order to calculate the effective coordinates, Xeff , Yeff
,
and Zeff , from the experimental rotational constants we built
a grid of values for X, Y, and Z. We then calculated for each
possible set of values the rotational constants via Eq. ͑1͒ and
we accepted only those values that reproduced the rotational
constants to within tolerable limits. Finally we averaged over
TABLE IV. Band origins and linewidths ͑FWHM͒ measured for the vibronic bands of the S1←S0 transition of
aniline–neon compared to their values in the free molecule. The pure vibrational vdW shifts are also given.
000
6a10
I02
101
Vibronic band
a
Band origins ␯ ͑cmϪ1
͒
j
b
vdW complex ͑this work͒
monomer ͑Ref. 10͒
340 24.17͑3͒
340 29.26͑3͒
345 16.76͑3͒
345 21.70͑3͒
347 85.60͑3͒
347 90.06͑3͒
348 22.52͑3͒
348 27.15͑3͒
Vibrational shifts ␦j
0.0
0.15͑4͒
0.63͑4͒
0.46͑4͒
͑cmϪ1
͒
FWHM ͑MHz͒
vdW complex ␥j ͑this work͒
monomer ␥0 ͑Ref. 10͒
18͑2͒
18͑2͒
39͑3͒
18͑2͒
138͑10͒
18͑2͒
48͑4͒
18͑2͒
aMeasured for the aniline–20Ne vdW complex. The corresponding transition for the aniline–22Ne vdW complex
is shifted by Ϫ0.040 cmϪ1 with respect to that of aniline–20Ne.
bNumbers given in parentheses represent one standard deviation of the parameter in units of the last quoted
decimal place.
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J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
9965
Figure 4 also shows how the branching ratios of the
various final states are quantitatively determined by compari-
son of the experimental spectrum with a reconstructed spec-
trum obtained by summing up the properly weighted indi-
vidual emission spectra expected from the directly excited
complex state and from the observed monomer states. Some
of these emission spectra can be directly measured, i.e., those
originating from all the excited monomer states that can be
reached by laser excitation ͑Franck–Condon and symmetry
allowed vibronic bands͒. This is indeed the case for two of
the states produced following excitation of the 6a1 level of
the complex, namely the state 00 and the 10b2 states. Unfor-
tunately many open product channels, especially those ac-
cessed when the excitation energy is larger, do not corre-
spond to laser accessible monomer states. The I1 state,
prominent in Fig. 4, or states like 10b1,16a1,16b1 S1, which
are formed in the predissociation following the I2 or l1 ex-
citations fall into this category. Such states usually appear in
sequence bands in the room temperature spectra, and compi-
lation of the literature data allows us to obtain frequencies
and intensities that can be used to build a synthetic stick
spectrum ͑see Appendix͒.
FIG. 3. The ‘‘R(1) clump of rotational components’’ in the S1←S0 000, 101,
and I20, vibronic transitions of the aniline–neon complex. The Lorentzian
linewidth was determined only after deconvolution with a 15 MHz instru-
mental function.
tional separations induced by the vdW binding ͑for more
information see Sec. IV͒.
For the final comparison with the experimental spec-
trum, the stick spectrum is convoluted at the actual experi-
mental resolution, which depends on the width of the mono-
chromator slits used for the measurements. Visual
comparison of the two spectra is used because the spectral
congestion becoming rather strong when extending far to the
red of the excitation band can cause automated fitting proce-
dures to give unphysical results. We estimate the accuracy of
the branching ratios obtained in this way to be of the order of
0.03 for the weak features, and of 10% for the main features.
This means that some of the product states formed with low
efficiency and responsible for the weakest bands can only be
tentatively identified. It is, however, very important in the
context of this paper which aims at comparing the total re-
laxation rate as measured by the lifetime broadening in the
high resolution spectra with that deduced from the branching
ratios obtained by measuring the dispersed emission spectra,
to realize that only the branching ratio for the fluorescence
out of the initially excited state matters. For all the bands
investigated here, this branching ratio is large, and thus well
determined ͑to about 10% relative accuracy͒.
B. Dispersed emission experiment
Figure 4 shows the dispersed emission spectrum ͑bottom
trace͒ recorded after excitation of the 6a1 level of the vdW
complex, together with the assignments of the main bands. It
can be seen that in addition to bands corresponding to tran-
sitions from the 6a1 state of the vdW complex to excited
vibrational levels in the ground state of this complex, other
features are observed which can be assigned to fluorescent
emission involving monomer states. The bands assigned to
emissions of the vdW complex are the dominant contributors
to the overall emission intensity, which indicates that predis-
sociation proceeds at a slower rate than radiative emission in
the complex. One of the most prominent progressions is built
upon the I1 monomer state, which appears to be the preferred
fragment channel. The other final fragment states which can
be identified are the ground state 00 and the 10b2 states.
The results thus obtained for the branching ratios for
fluorescence arising from the initially excited states and of
all the final states are summarized in Table V. Measurements
were made using excitation through the same three vibronic
bands for which high resolution, rotationally resolved spectra
had also been recorded, namely 6a10, I01, and I02. Only three
final product states were found in the case of 6a1 excitation
and of these, the I1 and 10b2 states, which lie within a few
tens of wavenumbers of the initially excited complex state
͑see Fig. 5͒, represent about 85% of all fragments. The lower
lying states 10b1 and 16a1 should be very weak, if at all
present, while the ground 00 state accounts for the remaining
15% of fragments. The fact that neither the 16a2 state, nor
the 10b116a1 combination state, which lie very close to the
10b2 state, were found tends to suggest that either their cou-
pling to the initially prepared state is much weaker than that
FIG. 4. Dispersed emission spectrum ͑bottom trace͒ recorded under excita-
tion through the 6a10 band of the aniline–neon complex, and example of the
reconstruction of this spectrum as a weighted sum of spectra due to various
individual excited states ͑see text͒.
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9966
J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
TABLE V. Branching ratios for vibrational predissociation of the aniline–neon complex. Summary of the branching ratios for fluorescence out of the initially
excited and all the final states, as derived from the dispersed emission spectra taken under excitation on the 6a10, I02, and 101 bands, respectively. All the
energies have been referred to the 00 monomer state. The value D0ϭ142 cmϪ1 for the dissociation energy was used to set the energies of the complex states
relative to this reference.
State
Energy
00
I1
10b2
6a1
350
0
334
348
Branching ratio
0.61
0.06
0.23
0.09
I2
State
10b1
16a1
I1
10b2
6a1
I1 10b1
I1 16a1
S1 10b1
10b3
16b1 10b1
Energy
Branching ratio
618
0.22
174
0.028
177
0.032
334
0.034
348
0.042
492
0.078
508
0.140
511
514
0.102
522
561
0.106
0.117a
0.085b
State
11
10b1
41
6a1
I1 10b1
S1 10b1
Energy
Branching ratio
656
0.74
174
0.09
365
0.07
492
0.03
508
0.03
514
0.05
aPart of this intensity may be shared with the S1 state lying at 340 cmϪ1
.
bPart of this intensity may be shared with the 16b1 state lying at 387 cmϪ1
.
of the other nearby states, or that they are energetically for-
bidden. Since the 10b and 16a modes have already be found
to be strongly mixed together and with the vdW modes
around 350 cmϪ1,5 the latter condition is much more plau-
sible, and would set a lower bound for the dissociation en-
periments, involving different techniques and different
setups, must first be compared to one another, before they
can then be commented upon in the framework of the theo-
retical background specifically available for vibrational pre-
dissociation ͑VP͒ and intramolecular vibrational redistribu-
tion ͑IVR͒ in vdW complexes.
ergy at 142 cmϪ1
.
The 10b1 is the strongest product channel in the case of
I1 excitation, but predissociation proceeds about as slowly as
in the case of 6a1 excitation. On the contrary it is much more
efficient in following I2 excitation. In this case the fragments
are distributed among a large number of final states, and the
most populated of these product states lie predominantly at
high energy ͑80% of the products are found in states lying
above 492 cmϪ1͒. Also remarkable is the fact that, in spite of
a larger excitation energy these highest lying states were not
present or were too weakly populated to be observed in the
predissociation out of the I1 level.
In the case of the dispersed emission experiment, the
branching ratio Rj for emission from the initially excited
state ͉j͘ is a direct measure of the efficiency of the relaxation
from this state through IVR and/or VP. We have
Rjϭk / k ϩKj͒,
͑2͒
͑
0
0
in which k0 is the intrinsic relaxation rate of the free mol-
ecule resulting from both radiative and nonradiative transi-
tions ͑known to be dominated by intersystem crossing in
aniline͒, and Kj is the additional relaxation rate introduced
by the vdW dynamics ͑IVR and/or VP͒. The value of k0 will
be taken as the inverse of the lifetime of the S1 00 level in
aniline. Indeed previous studies have established that the
lifetimes for several other vibronic states of the aniline
molecule10 as well as for the 000 state of the neon-complex3
are almost identical ͑see Table IV͒. As a matter of fact, both
IVR and direct VP channels are open for the relaxation of the
vibronically excited (S1 state͒ vdW complex, and it is of
interest to consider the possible competition between the two
processes. For the IVR channel to be effective it needs some
‘‘dark’’ states within the observed linewidth. Such states can
be divided into bound and unbound states. If bound dark
states would be formed, it would affect the dispersed emis-
sion spectrum, which has not been seen. If unbound dark
states would be formed, they would very quickly ͑on a pico-
second timescale͒ decay into continuum states, as shown by
classical trajectory calculations.11 However this is very un-
likely because the density of states is too small. Indeed a
realistic evaluation of the density of vdW states in the
ground intramolecular state of S1 , done by direct count us-
ing results of 3D quantum calculations for the frequencies,12
shows that it cannot exceed 100 states per cmϪ1 at the high-
est excitation considered in this work, and the bound dark
IV. DISCUSSION
The results presented in the above section need to be
discussed in the light of present understanding of intramo-
lecular dynamics and unimolecular processes. More specifi-
cally the sets of data originating from the two different ex-
FIG. 5. Scheme of the energy levels involved in the predissociation pro-
cesses studied in this work.
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J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
9967
complex by Nimlos et al.13 The most striking feature is that
the variation of the rate with excitation energy is not mo-
notonous. This is a strong indication that the vibrational dy-
namics in these vdW complexes is not governed only by the
energetics. On the contrary the specific character of the ini-
tially excited mode is essential. In particular the VP/IVR
relaxation rate, Kj, of the I2 state is almost one order of
magnitude larger than that of the 6a1 state, or even that of
the 11 state. A similar behavior was reported by Zhang
et al.14 in the case of the aniline–argon complex. Thus the
coupling of the inversion mode to the various vdW modes
should be much larger than for the in-plane symmetric ring
modes. This is not physically surprising since both the vdW
bending modes and the inversion mode of the aniline mono-
mer involve large amplitude atomic motions that are known
to accelerate the IVR process in many molecular
systems.15–18 The amplitude with which the hydrogens of the
amino group oscillate along a direction orthogonal to the
plane of the ring increases, upon excitation of the inversion
mode, from about 0.6 Å in the ground state to 1.1 Å in the I2
state. Consequently even if its average position is a long
distance away from this group, the neon atom should be
significantly affected by the resulting change in their mutual
interaction. Indeed the degree to which this inversion motion
is hindered by the rare gas atoms in the small
TABLE VI. Summary of the data about relaxation rates out of the various
vibronic levels of the aniline–neon complex.
000
6a10
I02
101
Vibronic band
Excitation energy ͑cmϪ1
͒
0
492
760
798
Rj a
1.00
1.00
0
0.61͑6͒
0.46͑10͒
0.113
0.22͑3͒
0.16͑3͒
0.693
0.74͑8͒
0.38͑9͒
0.168
␥0 /␥j
Kj ͑nsϪ1
͒
aNumbers given in parentheses represent one standard deviation of the pa-
rameter in units of the last quoted decimal place.
states are even sparser. Very likely VP proceeds in aniline–
neon prepared in the 6a1, I2, and I1 states, through the direct
mechanism, which involves coupling of the initially prepared
state with the continuum states.
In the case of the linewidth measurements from high
resolution excitation spectra the total relaxation rate for an
excited state ͉j͘ is given by
kjϭ1/␶jϭ2␲␥j .
͑3͒
Assuming that the increase of the relaxation rate from its
value k0 for the 00 S1 state is entirely due to the IVR and/or
VP processes, we have
kjϭk0ϩKj, or, equivalently ␥jϭ␥0ϩKj/2␲,
where ␥0 is the FWHM of rotational lines in the aniline 000
band. Finally, we obtain
aniline–͑argon͒ clusters has recently been the subject of a
n
theoretical investigation.19 From this study we can then ex-
pect that the spatial dependence ͑on X,Y,Z͒ of the wavefunc-
tion for the vdW ground state associated to the intramolecu-
lar I2 excitation should look different from that of the
corresponding vdW state without intramolecular excitation
͑i.e., the 00 intramolecular state͒.
Rjϭ␥0 /␥j .
͑4͒
Table VI contains the independently obtained values of the
branching ratios Rj and the ratios ␥0 /␥j for the three initially
prepared excited states of aniline–20Ne which have been
studied in both experiments. The overall agreement is satis-
factory; it is within the experimental uncertainties for the
6a1 and I2 excitations. However, the relaxation out of the I1
state seems to proceed at a slower rate, as measured by the
dispersed emission compared to the linewidth measurements.
A possible difference between the two kinds of measure-
ments, rather than a mere discrepancy, could result from the
influence of a dark channel which depopulates the I1 state.
Two possibilities can give rise to this situation. In the first
one an actual physical process, such as a relaxation to a
nonfluorescent state opens up at an excitation energy slightly
smaller than the 11 state energy. The second, more plausible
possibility is that the dispersed fluorescence experiment is
not capable of detecting all the final states. Indeed, because
of spectral congestion which makes data reduction very dif-
ficult, not all the spectral range over which fluorescence can
be seen has been recorded, but instead preferentially the high
frequency side where isolated bands can be unambiguously
identified.
As discussed in the previous section, high resolution
spectroscopy gives a kind of direct access to these vdW
wavefunctions through the way the instantaneous inverse in-
ertia tensor is averaged over the amplitude of the vdW mo-
tions. The relevant results are those of Table IV, giving the
values of the effective parameters, Xeff , Yeff , and Zeff for the
various vibronic states. An interesting trend appears from the
values of Yeff for the aniline–22Ne complex: it increases as
the linewidth increases ͑compare Table III and IV, or see the
correlation in Fig. 6͒. We have already commented in Ref. 3
that, among the three effective coordinates, Yeff , is the one
which provides a measure of an amplitude of the vdW mo-
tion. Although the approximation made in using the inertia
tensor ͑1͒ to reproduce the experimental rotational constants
means that a precise physical significance cannot be attached
to this coordinate, its value appears to provide a useful indi-
cation of the degree of coupling of a particular intramolecu-
lar vibrational state to the set of vdW modes.
The question of the relation of this coupling strength to
the details of intramolecular dynamics has been widely de-
bated in the literature. In the particular context of the vibra-
tional dynamics of vdW molecules, the connection of relax-
ation rates to the pure vibrational vdW shifts was first made
ten years ago by Weber and Rice.20 These authors, with the
benefit of experimental evidence for a limited IVR process
͑energy transfer from intramolecular to vdW modes without
The first remark concerning Table VI is that the relax-
ation rates Kj ͓which are equivalent to the increase in the
rotational linewidth on complexation, 2␲(␥jϪ␥0)] are all
small, i.e., the lifetimes remain in the nanosecond range. No
other direct measurement of lifetime with which these results
may be compared has been reported for aniline complexes
with neon, but the values measured here are of the same
orders of magnitude as measured for the aniline–argon vdW
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9968
J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
V͒ and the partial rates obtained for each fragment state, the
deviations from this simple law are likely to result from the
role of the other important factors, namely the energy gap,
⌬E, and the density of states.
Indeed the exponential energy gap law,25 or its adapta-
tion as the momentum gap law,26 represents the first solid
theoretical background for the description of VP in vdW
molecules. Although its application to the case of aromatic
molecules is not an easy task because of the large number of
intramolecular modes which can be involved, it is important
to consider the role of the energy gap parameter ⌬E. It ap-
pears that the final states involving a small ⌬E seem to be
preferred in the present data. This is very clear in the case of
the 6a1 excitation, where the two main fragment states I1
and 10b2 ͑representing 85% of all fragments͒ lie within 20
cmϪ1 of the exact resonance ͑if the vdW binding energy is
taken to be 142 cmϪ1, in agreement with the discussion at the
end of Sec. III B͒. It is also the case for the I2 excitation,
where the fragment states lying above the 6a1 state ͑i.e.,
within 130 cmϪ1 of resonance͒ represent 80% of all frag-
ments. In contrast, in the case of the 11 excitation no frag-
ment state is available very close to resonance ͑see Fig. 5͒,
which may explain the less efficient relaxation. It may be
concluded that the size of the coupling element between the
initial state and the vdW coordinates is only one of the fac-
tors controlling the VP in the observed states of aniline–
neon, and that the specific characteristics of the final states
must also be taken into account to provide a consistent un-
derstanding of the data.
FIG. 6. Correlation between the linewidth, large amplitude motions, and
frequency shift ͑squared͒ for the different vibronic bands in the aniline–
neon van der Waals complex.
fragmentation͒ in the s-tetrazine–argon complex,21 were able
to justify on a theoretical basis a proportionality relationship
between the IVR rate and the vibrational shift. Let us recall
that the pure vibrational vdW shift, ␦j , of the intramolecular
vibrational state ͉j͘ is defined as the change induced by com-
plexing to a partner in the energy separation between the
position of this state and the position of the ground state. It is
given by the difference in the vdW shifts of the vibronic
transition to level ͉j͘ in S1 with respect to that of the 000
transition:
␦jϭ⌬␯jϪ⌬␯0 .
͑5͒
A much better correlation is found between the line-
width, ␥, and the effective coordinate, Yeff ͑correlation coef-
ficient 0.98͒. The vibrational vdW shift is basically a quan-
tity specific to the initially excited state, without any
dependence on the final fragment states. Obviously nothing
is more characteristic of the initially excited state than its
wavefunction. We have demonstrated the ability of the high
resolution spectra to give information about this wavefunc-
tion, through the effective vdW coordinate space ͑X,Y,Z͒.
Thus, if a correlation between the relaxation rates and the
shifts is present, we may also expect a correlation between
the Yeff parameter, measuring purely the amplitude of this
wavefunction in the y-direction, and the other two param-
eters. The occurrence of such correlations among the three
sets of data is shown in the 3-dimensional plot of Fig. 6. The
overall quality of these correlations is striking. This demon-
strates clearly that preparation of the large amplitude inver-
sion mode I2 state both induces the largest rate for IVR/VP
dynamics, and reveals a vdW wavefunction containing the
largest admixture of other perturbing states. Although the
exact nature of these perturbing states is unknown, scattering
wavefunctions outgoing in the y-direction are suggested by
the present results, which is consistent with the direct VP
mechanism that predicts Lorentzian lineshapes, as observed.
This graph nicely illustrates the intrinsic connection of the
two findings recalled above, as classically recognized in ei-
ther the time-dependent approach of nonradiative transitions
or the time-independent approach of true molecular eigen
states. To our knowledge this is the first time that such a
correlation has been experimentally demonstrated.
Miller22 suggested a different form for the correlation that
exists between the VP lifetimes and the vibrational shift, ␦,
for a number of vdW molecules. He empirically showed that
the VP lifetime goes as the inverse of the square of the vi-
brational shift, or equivalently for the VP rate:
Kϰ␦2.
͑6͒
Le Roy et al.23 later demonstrated that this relationship could
be theoretically rationalized for a direct VP mechanism on
an ‘‘everything else being equal’’ basis. This phrase must be
understood in the sense that both VP dynamics and the fre-
quency shift are supposed to be controlled by the same cou-
pling factors. Although this assumption is not obviously
valid in every practical case, it is an interesting justification
for this correlation. Nonetheless, as recently noted by Oude-
jans et al.,24 the derivation of relation ͑6͒ also implicitly as-
sumes that the density of product states is large enough to
prevent energy gap considerations from dominating the dy-
namics.
It is of interest to examine to what degree this correlation
is satisfied by the present data ͑which seem to demonstrate
the importance of the coupling factor͒. Figure 6 shows the
3-dimensional correlation diagram obtained for ␦2 versus the
linewidth, ␥, and versus Yeff . The correlation coefficient be-
tween ␦2 and ␥ is 0.93, indicating that, although relation ͑6͒
reproduces the general trend in the spectra, it does not accu-
rately represent the details of the IVR/VP dynamics at work
in this vdW molecule. Considering the distribution of final
states revealed by the dispersed emission experiment ͑Table
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J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
TABLE VII. Franck–Condon factors of the vibronic bands of the S1←S0 transition in aniline.
Becucci et al.
9969
000
I20
6a01
0.45
110
0.43
1201
0.28
I026a01
0.51
1201
0.28
18a01
0.17
6a02
0.11
I02101
0.48
1301
0.17
Transition
FC
1.00 0.71
I11 I116a01
1.22 0.72
I31
0.29
I11101
0.49
I111201
0.38
I111801
0.32
I116a02
0.30
I136a01
0.18
I111301
0.38
Transition
FC
6a10 6a01I20 6a11 6a10101 6a11I02 6a101201 6a0118a01 6a21 6a10I02110 6a011301
Transition
FC
0.67 0.51
0.31
0.40
0.40
0.28
0.17
0.88
0.31
0.13
I20 I22
0.28 0.75
I206a01 I20101
I226a01
0.60
I201201
0.28
I2018a01 I206a02
0.09 0.11
I42
0.42
Transition
FC
0.41
0.34
110 110I02 1106a01
0.62 0.28 0.42
111
0.26
110I206a01 1011201
0.31 0.18
11018a01 1106a02
0.18 0.13
111I02
0.51
1116a01
0.34
Transition
FC
V. CONCLUSION
the amplitude of the vdW wavefunction in the bending coor-
dinate, and the relaxation rate, is a feature of remarkable
beauty.
Further investigation of the internal vibrational dynamics
of this interesting vdW system by appropriate quantum mul-
tidimensional theoretical approaches is needed to confirm the
conclusions which have been asserted on a mostly experi-
mental basis.
We have reported new, original results revealing the ef-
ficiencies of VP in three vibronically excited states of the
aniline–neon vdW molecule. These data are the high resolu-
tion ͑LIF͒ excitation spectra of the 6a10, 101, and I02 vibronic
bands of the S1←S0 transition in this complex, and the dis-
persed emission spectra recorded when the same bands are
excited.
From the analysis of the excitation spectra the rotational
constants of the vdW molecule are determined, as well as the
band origin frequencies and the linewidths of the transitions.
These linewidths exhibit a contribution from the relaxation
in the excited state, which depends on the nature of the mode
being excited. The rotational constants characterize the effec-
tive inertia tensor, which contains information not only on
the vibrationally averaged position of the neon atom with
respect to the aniline frame, but also on the amplitude of the
wavefunction along one vdW bending coordinate in the cor-
responding state.
ACKNOWLEDGMENTS
We wish to thank D. Pratt for sending us the preprint of
his work on the aniline–Ar vdW complex. We are grateful
also to P. Parneix, D. Consalvo, and H. Dreizler for useful
discussions. Support from the EC ͑under Contract No. TM-
RERBFMGECT950017͒ and Italian MURST are gratefully
acknowledged. One of us ͑N.M.L.͒ wishes to thank the EC
for the fellowship ERBFMBICT961046.
From the analysis of the emission spectra the branching
ratios for the final states which are populated by the relax-
ation in the excited state have been derived. Vibrational pre-
dissociation takes place on a timescale which is comparable
or longer than the normal radiative lifetime. From the value
of this lifetime, and by comparison between fluorescence in-
tensities from the initial and final states, the predissociation
rates have been obtained. A tendency to favor final states at
small energy separations from the initial state has been ob-
served.
These results obtained from two independent experimen-
tal sources have been compared and found essentially con-
sistent. They demonstrate a clear evidence of actual mode
specificity: the predissociation proceeds much faster when
the out-of-plane large amplitude inversion motion of aniline
is excited at 760 cmϪ1, while excitation of the in-plane sym-
metric ring vibration mode 1 at 798 cmϪ1 only shows the
normal general increase of the rate k(E) versus energy. This
finding is recognized to be connected to the unusual strength
of the coupling of this out-of-plane mode with either the bath
of the vdW modes or the density of the continuum states
built upon each final state channel. Indeed, under the as-
sumption that this coupling strength is reflected by the value
of the so-called pure vibrational vdW shift, the triple corre-
lation, which has been found between the coupling strength,
APPENDIX: CONSTRUCTION OF SYNTHETIC
SPECTRA AND FRANCK–CONDON FACTORS
We present here some details of the intermediate proce-
dures which were used to recover the branching ratios for the
initially excited complex state and the various VP-populated
monomer final states by reconstruction of a synthetic spec-
trum and its comparison with the experimental spectrum.
First it should be noted that relation ͑2͒ can be fully
justified from a rate equations analysis under the assump-
tions that the excitation laser pulse is rectangular in shape,
and that the time integrated fluorescence is measured ͑this
was achieved thanks to the boxcar integrator͒. Second the
relationship between the fluorescence intensity Inm , mea-
sured for a given band
͉
n →
͘
͉m , and the population of the
͘
upper state responsible for this band involves both experi-
mental factors, such as the efficiency of collection, the trans-
mission of the optical arrangement ͑lenses and monochro-
mator͒, the overall gain of the detection system, and physical
factors like the partial spontaneous emission rate constant
characteristic of the transition, the fluorescence quantum
yield, and the purely radiative lifetime of the upper state.
Considering that the spectral region which was actually used
is rather narrow, it is a good approximation to assume that all
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9970
J. Chem. Phys., Vol. 110, No. 20, 22 May 1999
Becucci et al.
the experimental factors are spectrally independent. The par-
tial spontaneous emission rate is proportional to the Franck–
Condon factor of the transition, and its spectral dependence
can be neglected over the narrow region. Since we have seen
that the lifetimes of the upper states are all the same, it im-
plies that the fluorescence quantum yield and the radiative
lifetime are state independent. Thus, finally, the time-
integrated fluorescence intensity of a given band appears
simply as proportional ͑with always the same proportionality
constant, C͒ to the Franck–Condon factor of the band under
measurement, and of course to the population of the upper
state:
4 E. R. Th. Kerstel, M. Becucci, G. Pietraperzia, and E. Castellucci, Chem.
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B. Coutant and Ph. Brechignac, J. Chem. Phys. 91, 1978 ͑1989͒; 100,
5
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7087 ͑1994͒.
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8 M. J. Ondrechen, Z. Berkovitch-Yellin, and J. Jortner, J. Am. Chem. Soc.
103, 6586 ͑1981͒.
9
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11 P. Parneix ͑private communication͒.
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2
I
nmϭCNn
n
͉
m
.
͗
͘
14 X. Zhang, J. M. Smith, and J. L. Knee, J. Chem. Phys. 97, 2843 ͑1992͒.
15 C. S. Parmenter and B. M. Stone, J. Chem. Phys. 84, 4710 ͑1986͒.
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Only the relative Franck–Condon factors are needed. The set
2
that we used is given in Table VII, in which 00 ϭ1 is
͗
͘
taken as reference. The first line corresponds to the 00 upper
state. The numbers are averaged over data in Refs. 27–29.
The third, fourth, and fifth lines corresponds to the 6a1, I2,
and 11 upper states, respectively. The numbers were ob-
tained by remeasuring the corresponding transitions with our
setup. These lines were scaled with respect to each other
using the data in Ref. 30 ͑LIF excitation spectrum͒ and Ref.
31 ͑photoacoustic absorption spectrum͒. The second line cor-
18 G. A. Bethardy, X. L. Wang, and D. S. Perry, Can. J. Chem. 72, 652
͑1994͒.
19
´
P. Parneix and Ph. Brechignac, J. Chem. Phys. 108, 1932 ͑1998͒.
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22 R. E. Miller, Science 240, 447 ͑1988͒.
23 R. J. LeRoy, M. R. Davies, and M. E. Lam, J. Phys. Chem. 95, 2167
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responds to the I1 upper state. The numbers have been ob-
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25 J. A. Beswick and J. Jortner, Chem. Phys. Lett. 19, 13 ͑1977͒; J. Chem.
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2
tained from Ref. 27, and scaled relative to 0
͉
0
using the
͗
͘
data in Refs. 32 and 33. For all the states which usually
appear in sequence bands, like 10b11, 16a11, S11, and so on, we
have assumed that they give rise to progressions in emission
with the same relative Franck–Condon factors as the 000
band. The Nn are the weighting factors which are used to
build up the synthetic stick spectrum.
26 G. E. Ewing, Chem. Phys. 29, 253 ͑1978͒; J. Chem. Phys. 71, 3143
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1 Many examples of such studies can be found in Chapters 1–10 in Jet
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͑1984͒.
2 W. L. Meerts, W. A. Majewski, and W. M. van Herpen, Can. J. Phys. 62,
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1293 ͑1984͒.
3
´
M. Becucci, G. Pietraperzia, N. M. Lakin, E. Castellucci, and Ph. Brechig-
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