Energy disposal in the two-photon laser-assisted reaction in xenon and chlorine gas mixtures

Article abstract of DOI:10.1063/1.1324976

The two-photon laser assisted reaction in a low pressure xenon and chlorine gas mixtures is studied to characterize the role of the entrance channel in determining the vibrational state distribution. A high degree of vibrational excitation in the XeCl product is measured. The measurements are in contrast with the vibrationally cold excimer observed following laser excitation in molecular beam experiments. The mean vibrational energy in the XeCl excimer depends upon the laser wavelength. As the laser is tuned toward shorter wavelength, an increasing fraction of the available energy from the reaction is observed.

Full text of DOI:10.1063/1.1324976

Energy disposal in the two-photon laser-assisted reaction in xenon and chlorine gas
mixtures
J. Kohel and J. W. Keto
Citation: The Journal of Chemical Physics 113, 10551 (2000); doi: 10.1063/1.1324976
View online: http://dx.doi.org/10.1063/1.1324976
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 113, NUMBER 23
15 DECEMBER 2000
Energy disposal in the two-photon laser-assisted reaction in xenon
and chlorine gas mixtures
J. Kohela) and J. W. Keto
Department of Physics, The University of Texas at Austin, Austin, Texas 78712
͑Received 31 May 2000; accepted 22 September 2000͒
The two-photon laser assisted reaction ͑LAR͒ in low pressure xenon and chlorine gas mixtures has
been studied over a broad range of excitation wavelengths in order to characterize the role of the
entrance channel in determining the vibrational state distribution of the reaction products. We
*
measure a high degree of vibrational excitation in the XeCl product, confirming observations from
previous studies of the LAR of XeϩCl2 collision pairs ͓Ku et al., J. Phys. Chem. 87, 2989 ͑1983͔͒,
and in distinct contrast with the vibrationally cold excimer observed following laser excitation in
molecular beam experiments ͓Boivineau et al., Chem. Phys. Lett. 128, 528 ͑1986͔͒. The mean
vibrational energy in the XeCl excimer depends strongly on laser wavelength, increasing with
decreasing wavelength. Moreover, an increasing fraction of the available energy from the reaction
*
is observed as vibration in the XeCl product as the laser is tuned toward shorter wavelengths. The
reaction outcomes are interpreted in terms of a selectivity of initial conditions on the ionic potential
surface that mediates the reactive collision. © 2000 American Institute of Physics.
͓S0021-9606͑00͒71447-4͔
I. INTRODUCTION
2h␯ is not necessarily resonant with either reagent as an
unperturbed species, and the tuning range of the excitation
can be very broad. The excitation in Xe/Cl2 gas mixtures, in
particular, is characterized by a broad continuous tuning
range between approximately 288–316 nm.3,11
The two-photon excitation in ͑1͒ provides a large exoer-
gicity ͑1.3–2.2 eV͒ for the reaction; this excess energy will
be shared between the translational, rotational, and vibra-
tional degrees of freedom of the reaction products. A signifi-
cant fraction of the available energy can be expected to ap-
pear as internal energy ͑i.e., vibration and/or rotation͒ in the
The two-photon laser-assisted reaction ͑LAR͒ of Xe
with Cl2 can be classified under a general category of laser-
induced ‘‘harpoon’’ reactions. A common feature of the har-
poon reactions between rare gas atoms ͑Rg͒ and halogen
molecules (X2) is the presence of an intermediate charge
transfer complex RgϩXϪ . This charge transfer state ͑CTS͒
͕
͖
2
leads to formation of the RgX(B,C) exciplex with near unit
probability. The RgϩX2 harpoon reactions have been the
subject of considerable research interest as useful systems for
fundamental studies of bimolecular reaction dynamics, and
are also of practical interest due to the role of the RgϩXϪ
*
excimer product XeCl . In this work, a large variation in the
͕
͖
2
vibrational energy distributions in the excimer product has
been directly measured for the first time as the excitation is
tuned through this range. This variation is interpreted in
terms of the role of initial conditions in the entrance channel
to the reaction. The present experiment is thus of interest as
a demonstration of the coherent control of a chemical reac-
tion.
CTS in neutral channels contributing to formation of the ex-
cimer states involved in rare gas–halide ͑excimer͒ lasers and
UV lamps.
The LAR of rare gases with halogens has previously
been demonstrated using one- or two-photon excitation in
experiments involving transient ‘‘collision pairs’’ in the gas
phase,1–8 van der Waals ͑vdW͒ complexes formed in super-
sonic expansions,9–11 as well as liquid or solid rare gas/
halogen mixtures.12–17 The entrance channel to the XeϩCl2
LAR is unique from other laser-induced reactions between
Xe and Cl2 in that it involves a coherent two-photon excita-
tion of the transient Xe–Cl2 collision pair ͑or bound vdW
complex͒ to the XeϩClϪ CTS,
II. EXPERIMENTAL APPROACH
In these experiments, we seek to observe the nascent
vibrational distributions in reaction products resulting from
the two-photon laser-assisted reaction. By monitoring the
*
bound–free fluorescence of the XeCl reaction product, the
͕
͖
degree of vibrational excitation can be characterized as a
function of excitation energy. Detailed analysis of the extent
and nature of the diffuse emission spectra, moreover, should
ultimately provide an accurate characterization of the distri-
bution of quantum states from which the radiation originates.
The short radiative lifetime of the XeCl(B) product fa-
cilitates direct observation of nascent product state distribu-
tions in low pressure gas mixtures. Nevertheless, in order
that the radiating distribution reflect the nascent distribution,
we must ensure that the collision rate is sufficiently low so
that vibrational relaxation due to secondary collisions are
2
2h␯
*
*
XeϩCl ——
XeϩClϪ →XeCl ϩCl.
͑1͒
→
͕
͖
2
2
The above reaction is usually described as a cooperative pro-
cess, where the excitation involves a pair of chemical species
rather than a single chemical center.8 This reaction is distinct
from other harpoon reactions in that the two-photon energy
a͒
Present address: Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasa-
dena, California 91109-8099.
0021-9606/2000/113(23)/10551/9/$17.00
10551
© 2000 American Institute of Physics
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10552
J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
J. Kohel and J. W. Keto
improbable during the radiative lifetime of the product state,
i.e., ␯collϽ␯rad . This implies the need to work at the lowest
possible pressures (PϽ3 Torr). These low working pres-
sures also limit, however, the number of collision pairs seen
by the excitation laser—the number of collision pairs at a
specific collision radius is proportional to the square of the
total pressure—so that reaction rates and hence signal levels
are necessarily limited in our experiment.
Given the above limitation on the density of collision
pairs, it is especially important to maximize production rates
and detection efficiencies for the reaction products. Although
two photon transition rates scale quadratically with incident
laser powers, saturation effects, including stimulated emis-
sion and photoionization, effectively limit increases in useful
signal due to increasing laser intensities. We instead utilize a
long focal length lens to maximize focal volume, thereby
increasing the number of potential collision pairs in the in-
teraction region. We also employ high collection efficiency
optics and multichannel detection to improve sensitivity. In
addition, long integration times and averages of many spec-
tra are required to obtain acceptable signal to noise ratios.
We also note that, as the laser and continuum emission
occur in overlapping spectral regions, we are faced with the
technical problems associated with monitoring weak signals
in the presence of a strong background. Fluorescence signals
are monitored at right angles to the excitation laser beam,
and multiple apertures are employed to provide a high degree
of rejection of scattered laser light from windows and sur-
faces. And, most importantly, we employ background sub-
traction techniques to effectively remove the narrow Ray-
leigh background signals from the spectra.
FIG. 1. Fluorescence spectra as a function of excitation wavelength for the
two-photon LAR in 2.7 Torr Xe/Cl2 ͑10% Cl2͒ gas mixtures. Laser scatter
peaks have been subtracted, and peak fluorescence signals have been nor-
malized to the same height for comparison.
was resolved by an optical multichannel analyzer ͑OMA͒
with a UV-enhanced, intensified diode array detector
͑EG&G PARC 1420R-1024-HQ͒ mounted on a 0.64 m spec-
trometer ͑Instruments SA HR640͒ with f/5.5 imaging optics.
The spectrometer includes a 300 g/mm grating blazed for
500 nm in first order. This grating was used in second order
to gain greater detection efficiency in the spectral region of
interest near 300 nm. The measured quantum efficiency of
the diode array detector is 18% at 300 nm.
III. RESULTS AND ANALYSIS
A. Emission spectra
The diffuse emission spectra observed following excita-
tion of the Xe/Cl2 gas mixture for a range of laser excitation
energies are illustrated in Fig. 1. The excitation laser wave-
length was tuned from 286 to 313.5 nm in 2.5 nm incre-
ments, and the dispersed fluorescence was recorded between
approximately 240 and 320 nm for the reaction at each laser
wavelength. The recorded spectra were corrected for the
measured spectral response of the combined OMA/
spectrometer system ͑using a D2 UV radiance standard͒ as
well as the measured ‘‘flat field’’ response18 of the diode
array detector. The Rayleigh scattered laser light was re-
corded immediately afterward using pure xenon; this peak
and a dark noise background were then subtracted from the
corresponding LAR spectrum.
A. Experimental apparatus
The xenon and chlorine gas mixtures were prepared by
first introducing xenon ͑Spectra Gases, Inc. 99.999%͒ into a
gas handling system, then cryogenically pumping the gas
into a mixing bottle. Chlorine ͑Matheson Gas Products, re-
search grade͒ was next released into the same volume in the
gas handling system, then also condensed into the mixing
bottle. The gas mixture was allowed to thermalize at room
temperature within the mixing bottle, and then released into
the sample cell.
Excitation of Xe/Cl2 gas mixtures was provided by the
frequency-doubled output of an Nd:YAG-pumped tunable
pulsed dye laser system. The laser output was tunable be-
tween the range 280–340 nm ͑using various Rhodamine and
DCM laser dyes͒ with pulse energies up to 7 mJ/pulse. Pulse
lengths were 6–7 ns. The UV beam was focused by a 175
mm lens and entered the detection cell via a sapphire win-
dow. To avoid the nonlinear effects due to the high laser
intensities discussed above, the fluorescence was collected
five Rayleigh lengths from the focus of the laser. At this
position the beam waist was approximately 240 ␮m and the
intensity 8–10 MW/cm2. A series of three apertures were
positioned inside the sample cell both before and after the
detection region to reject scattered laser light from the en-
trance and exit windows.
The fluorescence spectra were acquired in Xe/Cl2 gas
mixtures at the lowest possible pressures ͑Ptotϭ2.6 Torr, or
nϭ8.4ϫ1016 cmϪ3͒ in order to minimize collisional relax-
ation of the nascent vibrational distributions in the reaction
products. In order to verify that vibrational relaxation is not
significant at this pressure, we consider the vibrational relax-
ation constant kRXe determined by Inoue et al.19 for ϭ2
v
Ј
→0,1 relaxation in XeCl(B). From analysis of the time-
resolved emission profiles following photoassociative excita-
tion to the XeCl(B, ϭ2) level, the authors assigned a
v
Ј
value kRXeϭ(2Ϯ1)ϫ10Ϫ10 cm3 moleculeϪ1 sϪ1. Using this
value we calculate
Fluorescence signals were monitored at right angles to
the excitation laser beam, and the broad excimer emission
Ϫ1
␯
relaxϭkR • Xe Ϸ 60 ns͒
.
͑2͒
͓
͔
͑
Xe
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J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
Reaction in Xe and chlorine gas mixtures
10553
1. Spectral simulations
In comparison, the radiative lifetime for the XeCl(B) state
has been measured as ␶ϭ11.1Ϯ0.2 ns.19 Hence, ␯radϭ1/␶
Ͼ␯coll , and vibrational relaxation can be assumed to be
small during the time the excimer fluoresces. The radiative
lifetime increases to ␶Ϸ30 ns for ϭ100,20 but the condi-
To accurately model the observed emission spectrum,
we have simulated the bound–free and bound–bound emis-
sion resulting from the XeCl(B, →X) transition. The
v
Ј
v
Ј
dominant contribution is from bound–free transitions due to
the largely repulsive character of the ground state potential.
The bound–free emission spectrum resulting from transitions
tion ␯radϾ␯
is still satisfied for these very high vibra-
relax
tional levels. The efficiency, furthermore, of V–T transfer is
relatively small for most atom–diatom collisions—103 or
more such collisions are typically required for V–T
transfer.21 We surmise that the rapid vibrational relaxation
rate observed by Inoue et al.19 ͑nearly equal to the collision
frequency͒ results from exchange and would not be expected
to increase significantly for higher vibrational levels. Con-
clusions from the above analysis were borne out by compari-
son of emission spectra from the LAR measured at 2.6 Torr
with that in 6 Torr gas mixtures: Vibrational relaxation was
minimal in the higher pressure spectrum.
between a single rovibrational state
͉
J
and all lower
Ј Ј
͘
v
states
͉
␧ J in the vibrational continuum is given by22
Љ Љ
͘
4
64␲
3h
bf
v J
Ј Ј
5
2
I
␭͒ϭ
␯
͉
␧ J
Љ Љ
͉
␮ R͉͒ J
v
Ј Ј
͉ .
͘
͑3͒
͑
͑
e
͗
The emission wavelength is a function of the continuum en-
ergy, ␭ϭ1/(Gv J ϩT Ϫ␧ ), where T is the energy differ-
Љ
e
e
Ј Ј
ence between the minima of the excited and ground state
potentials, and Gv J is the rovibrational energy in the ex-
Ј Ј
cited state. Similarly, the bound–bound contribution is cal-
culated as
The dependence of the laser-induced fluorescence on la-
ser fluence was also investigated. Integrated fluorescence sig-
nals were recorded at right angles to the incident laser as the
laser fluence at the focus in the optical cell was varied from
approximately 3 to 30 MW/cm2. The measured fluorescence
signals were found to be proportional to Iy, where y
ϭ1.7–1.8 for the current focus conditions. By further defo-
cusing the incident laser beam, the power dependence was
seen to approach I2, as is expected for two-photon transi-
tions. We note that our detection geometry is not sensitive to
stimulated emission, and so the measured deviation from
quadratic dependence at higher incident laser intensities is
consistent with the large cross section for stimulated emis-
sion in the upper XeCl state.6
4
64␲
bb
v J
Ј Ј
5
2
I
␭͒ϭ
␯
͉
J
Љ Љ
͉
␮ R͉͒ J
v
Ј Ј
͉ ,
͘
͑4͒
͑
v
͑
͗
e
3h
where ␭ϭ1/(TeϩGv J ϪGv J ). Therefore the total emis-
Ј Ј
Љ Љ
sion spectrum from a single rovibrational level is
Iv J ␭͒ϭIbf ␭͒ϩIbb ␭͒.
͑5͒
͑
͑
͑
v J
v J
Ј Ј
Ј Ј
Ј Ј
The above spectral distributions Iv J (␭) are expressed
Ј Ј
in terms of a quantum flux per wave number in order to
facilitate comparison to the experimental spectrum recorded
per unit wavelength. The wave functions ␺ (R)ϭ R͉ J
v
͘
͗
vJ
and ␺ (R)ϭ R͉␧J are normalized solutions of the radial
͗
͘
The gross trends in energy disposal are evident from
inspection of the spectra in Fig. 1. As the excitation laser is
tuned to shorter wavelengths, the blue wings of the emission
spectra are enhanced, indicating greater vibrational excita-
tion in the XeCl excimer. The excess energy from the reac-
tion ⌬H00 increases from 1.4 eV at an excitation wavelength
of 313.5 nm to 2.2 eV at 286 nm, and much of this energy
can be expected to appear as vibration in the excimer prod-
uct. In order to provide a more quantitative analysis of en-
ergy disposal in the LAR, we model the observed spectral
emission. The techniques used to simulate the emission spec-
tra and determine the corresponding vibrational distributions
are the subject of the following section.
␧J
¨
Schrodinger equation,
d2␺/dR2ϩ 2␮/ប2͒ EϪU R͒ ␺ R͒ϭ0,
͑6͒
͑
͓
͑
͔ ͑
J
where EϭGvJ (Eϭ␧) for the bound ͑unbound͒ states and
UJ are the effective potentials defined as
U R͒ϭV R͒ϩ ប2/2␮R2͒J Jϩ1͒.
͑7͒
͑
͑
͑
͑
J
V(R) are the rotationless potentials V (R) and V (R) asso-
Ј
Љ
ciated with the B( 12) and X( 12) electronic states of XeCl,
respectively, and ␮ is the reduced mass for the XeCl mol-
ecule. The potentials and dipole transition moment ␮e(R)
used in this work are described in the Appendix.
¨
The Schrodinger equation ͑6͒ is integrated numerically
using the Numerov finite difference method as described by
Cooley23 ͑see also Ref. 24͒ to obtain the eigenenergies and
normalized wave functions. The continuum wave functions
were energy normalized by matching the amplitude at large
R to the asymptotic solution
B. Simulation and analysis method
The vibrational distributions in the reaction products
were determined by simulation of the emission from the
*
XeCl excimer. Determining an unambiguous solution for
R→ϱ
the populations of the individual vibrational levels P( ) is
made difficult by the vast number of energetically accessible
v
2
ͱ2␮/␲ប k sin kRϩ␦͒,
Ј
␺
R͒ ——
͑8͒
͑
→
͑
␧
where kϭͱ2␮␧/ប and ␦ is a phase term dependent on the
form of the dissociative lower potential.
Once the wave functions have been obtained, the
Franck–Condon integrals ͑3,4͒ are evaluated for the dipole-
vibrational levels in the upper radiating state ͑up to
v
Ј
ϳ140͒ and the overlapping nature of the broad continua
emission to the repulsive ground state from each of these
rovibrational levels in the upper state. The simulation tech-
nique is described below, and the inversion approach is de-
tailed in Sec. III B 2.
allowed transitions ⌬JϵJ ϪJ ϭ0,Ϯ1 and over a range of
Ј
Љ
continuum energies ␧ .
Љ
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10554
J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
J. Kohel and J. W. Keto
P0
f
͉
R
fV͒ϭ 32 1Ϫg ͒1/2/ 1Ϫf ͒,
͑12͒
The observed spectra are modeled as superpositions of
the radiative transitions originating from all possible rovibra-
tional levels in the upper state, i.e.,
͑
͑
͑
R
V
where fV , fR are the reduced energies defined as fV
ϵEv /E, fRϵER /E; and gR is the reduced rotational energy
defined as gRϵfR /(1ϪfV). The summation over J in Eq.
͑11͒ was also approximated by including fewer than a dozen
levels ͑i.e., every 80th J͒ for computational expediency.
The sensitivity of the direct inversion method was first
tested by applying this procedure to the analysis of a simu-
lated spectra generated for a known vibrational distribution.
Toward this end, a three-body linear surprisal distribution,27
vЈ
JЈ (v )
Ј
max max
I ␭͒ϭ
͑
P
,J ͒ I
Ј Ј
␭͒,
͑
v J
Ј Ј
͑9͒
͑v
͚ ͚
v ϭ0 J ϭ0
Ј
Ј
where P( ,J ) is the population in the initial state
͉
J
v
Ј Ј
,
v
Ј Ј
͘
Ј
max is the maximum energetically allowed vibrational level,
v
and JЈ ( ) is the maximum allowed rotational level within
v
Ј
max
the vibrational manifold . As noted, the summations in Eq.
v
Ј
͑9͒ are over very large numbers of vibrational and rotational
levels due to the large reaction exoergicity in the laser-
assisted reaction.
P f ͒ϭP0 f ͒exp Ϫ␭ Ϫ␭ f
,
͔
V
͑13͒
͑
͑
͓
V
V
0
v
where fVϵEv /E, and P0(fV) is the vibrational prior distri-
bution
5
2
3/2
P0 f ͒ϭ 1Ϫf ͒
,
͑14͒
͑
͑
V
V
2. Inversion method
was chosen to represent a typical rovibrational distribution
involving very high vibrational levels. The inversion algo-
rithm quickly converged to a stable solution, independent of
Once the emission spectra Iv J (␭) have been calculated
Ј Ј
for all energetically accessible levels in the upper state, it
should be possible to determine the product state distribution
from which the observed spectra originates by directly solv-
¯
initial conditions, for the amplitudes Pi . The size and num-
ber of vibrational bins were varied to confirm the invariance
of the fit, and the self-consistency of this approach was also
verified by recalculating the simulated spectrum from the
derived population histogram.
ing Eq. ͑9͒ for the populations P( ,J ). This approach,
v
Ј Ј
however, is computationally expensive, and in practice is
also limited by the finite instrumental resolution and by the
presence of noise in the experimental spectrum. These limi-
tations make a unique determination of the individual popu-
lations P( ,J ) difficult if not impossible. A more expedi-
v
Ј Ј
C. Simulation and analysis of the LAR
ent and reliable approach is to seek
a
histogram
representation of the actual distribution, i.e.,
The series of emission spectra recorded following the
two-photon excitation in low pressure Xe/Cl2 gas mixtures
͑Fig. 1͒ were analyzed using the direct inversion technique
as described above to determine the vibrational distributions
N
¯
I ␭͒Ӎ
͑
P I ␭͒,
͑10͒
͑
͚
i
i
iϭ1
¯
*
in the XeCl reaction product. Each spectrum was analyzed
where Pi is the mean population number for the ith group of
rovibrational levels, N is the total number of bins of vibra-
tional levels, and Ii(␭) is the sum of the contributions to the
spectra from all rovibrational levels within the ith group,
using multiple combinations of vibrational bin size and num-
ber in order to confirm that the algorithm converges to a
consistent and physical result. Optimal results were obtained
using 5–7 bins containing between 15 and 21 vibrational
levels each—larger numbers of bins typically resulted in less
smooth histogram distributions and larger uncertainties.
Typical simulated and observed emission spectra are il-
lustrated in Figs. 2–4. The simulated spectra are seen to
reproduce the profile of the experimentally obtained spectra
well, particularly the oscillations at shorter wavelengths. Di-
rect inversion using the histogram representation gave quali-
tatively similar results to those obtained using a linear vibra-
tional surprisal representation ͑13͒ in which the vibrational
distribution is described by the single parameter ␭v—in fact,
in most cases the simulated spectra from the two methods
could not be distinguished although the direct inversion re-
sult indicated greater population in the highest vibrational
levels. A comparison of the simulated spectra obtained using
these two representations and the resulting vibrational distri-
butions is provided in Fig. 2. Differences in the population
numbers determined by these two representations were
within the fitting errors for the histogram amplitudes re-
turned by the direct inversion algorithm. We also noted prob-
lems in both methods in reproducing the sharpness of the
main peak in certain spectra. We were unable to determine
the reason for this discrepancy.
JЈ (v )
Ј
max
I ␭͒ϭ
P J
͑
͉
v
Ј Ј
͒ I
␭͒.
͑
v J
Ј Ј
͑11͒
͑
͚ ͚
i
v ෈i J ϭ0
Ј
Ј
P(J
͉
)ϵP( ,J)/P( ) is the conditional probability for
v v v
Ј Ј
the level J in the rotational manifold of the vibrational level
Ј
.
v
Ј
¯
The binned populations Pi were determined using a non-
linear regression technique25,26 in which the amplitudes were
constrained to non-negative values. The optimal size and
number of bins were determined through trial and error. Best
results were typically obtained using 5–7 equal sized bins
containing approximately 20 vibrational levels each—
smaller bin sizes resulted in less reliable histogram represen-
tations while larger bin widths resulted in obvious loss of
resolution and a degraded fit to the observed spectrum. The
simulated spectra Ii(␭) are largely insensitive to rotational
contributions—although the summation over J may include
a very large number of rotational levels, the effect of angular
momentum is largely to smooth out the highest frequency
͑noiselike͒ components in the generated spectrum. Hence the
rotational distributions P(J
͉ ) were adequately repre-
v
Ј Ј
sented by the rotational ‘‘prior distribution,’’ 27
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J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
Reaction in Xe and chlorine gas mixtures
10555
FIG. 2. Comparison of observed emission spectra from the Xe/Cl2 LAR for
excitation at 311 nm ͑crosses͒ to simulated spectra obtained by direct inver-
sion using histogram ͑solid line͒ and linear surprisal ͑dashed line͒ represen-
tations for the vibrational populations, as described in the text. The popula-
tions determined using each models are shown in the inset. The asterisk
above the wavelength axis indicates the two-photon laser excitation wave-
length for this reaction.
FIG. 4. Comparison of observed emission spectra from the Xe/Cl2 LAR for
excitation at 293.5 nm ͑crosses͒ to simulated spectra ͑solid line͒ obtained by
direct inversion. The asterisk indicates the two-photon excitation wave-
length for the reaction.
are the eigenenergies in the upper potential, and E is the
maximum energy available to the reaction products in the
LAR,
The vibrational population histograms returned by the
direct inversion method are shown in Figs. 5 and 6, and the
energy disposal trends determined by inversion of the ob-
served spectra using both the histogram and linear surprisal
representations of the vibrational distributions are summa-
rized in Table I. Vibrational energy disposal in the LAR was
characterized by the mean reduced vibrational energy
Eϭ⌬H0ϭ2h␯ ϪT XeCl͒ϪD Cl ͒.
͑16͒
͑
e
͑
e
ex
2
0
f
ϭ E /Eϭ
P
,J͒E /E,
͑15͒
͑v
͗
͘
V
͗
͘
͚
v
v
v,J
where P( ,J) is the normalized vibrational distribution de-
v
termined from the simulation of the observed spectrum, Ev
FIG. 3. Comparison of observed emission spectra from the Xe/Cl2 LAR for
excitation at 301 nm ͑crosses͒ to simulated spectra ͑solid line͒ obtained by
direct inversion. The asterisk above the wavelength axis indicates the two-
photon excitation wavelength for the reaction.
FIG. 5. Calculated vibrational distributions, as determined by direct inver-
sion of the emission spectrum recorded following excitation at ͑a͒ 313.5 nm,
͑b͒ 311 nm, ͑c͒ 308.5 nm, ͑d͒ 306 nm, ͑e͒ 303.5 nm, and ͑f͒ 301 nm.
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10556
J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
J. Kohel and J. W. Keto
FIG. 7. Mean vibrational energy E and mean fraction of available energy
͗
͘
v
*
in the XeCl reaction product as a function of the
͘
V
entering vibration
f
͗
available energy ⌬H00 from the LAR.
͑lowest ⌬H00͒ to over one-half at the shorter wavelengths.
The vibrational energies determined using the linear surprisal
representation were consistent with the direct inversion re-
sults. These energy disposal trends are illustrated in Fig. 7.
IV. DISCUSSION
A large degree of vibrational energy disposal character-
ized the LAR’s in Xe/Cl2 gas mixtures studied in this work.
The mean vibrational energy E in the excimer product
͗
͘
FIG. 6. Calculated vibrational distributions, as determined by direct inver-
sion of the emission spectrum recorded following excitation at ͑g͒ 298.5 nm,
͑h͒ 296 nm, ͑i͒ 293.5 nm, ͑j͒ 291 nm, and ͑k͒ 288.5 nm.
v
varied from slightly less than 0.5 eV for the LAR at 313.5
nm to greater than 1 eV for the reaction at 288.5 nm. Fur-
thermore, the average fraction of available energy entering
vibration
f
was also found to increase with decreasing
͘
͗
V
The analysis results ͑Table I͒ show that the mean vibrational
laser wavelength from an initial value of one-third for ␭
ϭ313.5 nm to over one-half for wavelengths ␭exр306 nm.
The mean reduced energy f is approximately constant for
excitation wavelengths below 306 nm. The mean vibrational
energy appears to be significantly less, however, for the LAR
in the current experiment than for the reactive quenching of
ex
energy in the excimer product E increases ͑from 0.48 to
͗
͘
v
1.13 eV͒ as the excitation laser is tuned from 313.5 nm to
288.5 nm. Moreover, the average fraction of the available
͗
͘
V
energy entering vibration f is seen to increase from ap-
͗
͘
V
proximately one-third at the longest excitation wavelengths
*
metastable Xe by Cl —compare, for example, f ϭ0.77
͗
͘
V
2
measured for the Xe(3P2)ϩCl2 reaction (⌬H00ϭ1.865 eV)
TABLE I. Summary of analyses results for energy disposal in the two-
photon laser-assisted reaction of Xe with Cl2. Fitting results using a linear
three-body surprisal model are also shown for comparison to direct inver-
sion results using histogram representations for the distributions of vibra-
tional levels. ͑See text for details.͒
͑Ref. 28͒ with the mean energy f ϭ0.56 for the LAR at
͗
͘
V
296 nm (⌬H00ϭ1.874 eV͒—although the quenching reac-
tions were investigated at substantially lower pressures ͑0.1
Torr vs 2.6 Torr in the current experiment͒.
Linear surprisal
Histogram
The entrance channel to the XeϩCl2 LAR, unlike the
quenching reaction, involves a direct two-photon excitation
to the XeϩClϪ CTS via a cooperative photoabsorption by
⌬H00
͑eV͒
␭
E
f
f
͗
͘
͗
͘
V
E
͘
v
͗
͘
␭
͑nm͒
͗
vmax
v
v
V
ex
͕
͖
͑eV͒
͑eV͒
2
the initial XeϩCl2 complex. One of the difficulties associ-
ated with demonstrating this cooperative excitation process
is in isolating this reaction from competing reaction path-
ways, particularly that of the photodissociation of Cl2 fol-
lowed by photoassociation of Xe with Cl,
286.0
288.5
291.0
293.5
296.0
298.5
301.0
303.5
306.0
308.5
311.0
313.5
2.167
2.092
2.018
1.946
1.874
1.804
1.735
1.667
1.601
1.535
1.470
1.407
138
131
123
116
110
104
98
92
87
83
78
¯
¯
¯
¯
¯
Ϫ2.87
Ϫ1.87
Ϫ2.12
Ϫ3.16
Ϫ2.71
Ϫ1.91
Ϫ2.64
Ϫ2.86
Ϫ0.32
Ϫ0.43
Ϫ0.41
1.02
0.86
0.86
0.94
0.85
0.73
0.77
0.75
0.50
0.49
0.46
0.49
0.43
0.44
0.50
0.47
0.42
0.46
0.47
0.33
0.33
0.33
1.13
0.99
1.03
1.05
0.98
0.97
0.92
0.87
0.60
0.55
0.48
0.54
0.49
0.53
0.56
0.54
0.56
0.55
0.55
0.39
0.37
0.34
h␯
Cl —— Cl A 1⌸ ͒→2Cl,
͑17͒
→
͑
2
2
u
h␯
XeϩCl —— XeCl B͒.
͑18͒
→
͑
This sequential or stepwise process was observed by Mc-
74
Cown and Eden29 in the excitation of high pressure ͑300
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J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
Reaction in Xe and chlorine gas mixtures
10557
The range of initial conditions probed on the reactive
V(Xeϩ;ClϪ2 ) surface as the laser is tuned from the minimum
transition energy is determined by gradients in both the
Xeϩ–ClϪ and Cl–ClϪ coordinates of the PES. The gradient
in the Cl–ClϪ coordinate ͓ץV/ץR(Cl–ClϪ)ϷϪ15.7 eV/Å at
R(Cl–ClϪ)ϭRe(Cl2)͔ ͑Ref. 33͒ is much larger than that in
the Xeϩ–ClϪ coordinate ͓ץV/ץR(Xeϩ–ClϪ2 )Ϸ0.8 eV/Å at
R(Xeϩ–Cl2Ϫ)ϭ4 Å͔, so the vibrational phase in the Cl2 re-
agent may have a large role in determining the excitation
range for the reaction. In fact, as noted by Setser,8 the width
of the excitation spectrum can be accounted for entirely by
the gradient in the Cl–ClϪ coordinate of the PES.
As the laser is tuned to more energetic wavelengths, we
consider two limiting cases: ͑a͒ the reaction proceeds from
collision pairs at larger Xe–Cl2 distances and typical Cl–Cl
distances R(Cl–Cl)ϷR (Cl ) ͑point B in Fig. 8͒, and/or
͓
͔
e
2
͑b͒ the reaction occurs for R(Xe–Cl2) near the vdW mini-
*
mum and for R(Cl–Cl)ϽRe(Cl2) ͑point B in Fig. 8͒. If we
follow a typical reactive trajectory originating from point
FIG. 8. Semiempirical representation of the reactive potential energy sur-
face for the XeϩCl2Ϫ system, assuming a C2v geometry. The trajectories
represent the classical evolution of the triatomic complex from initial con-
*
B , we see that any additional energy is also carried away as
*
translation between the XeCl and Cl products, so that the
*
ditions A, B, and B on the reactive surface. ͑See text for discussion.͒
degree of vibrational excitation in the excimer differs very
little from that resulting from the half collision originating at
point A.
Torr͒ Xe/Cl2 gas pressures. Previous researchers have argued
a lack of evidence for this sequential channel in the Xe/Cl2
reaction in low pressure gas mixtures,8 and detailed calcula-
tions show that this process is indeed negligible
If, on the other hand, the excitation at the shorter wave-
length occurs for an initial geometry corresponding to point
B on the ionic surface, the subsequent dynamics will exhibit
significant motion in the R(Xe–Cl) coordinate as the tri-
atomic complex flies apart, and thus the XeCl excimer will
be formed with a high degree of vibrational energy. This
interpretation appears to be more consistent with the obser-
vations in the current experiment, in which a significant de-
(␴seq /␴LARϷ10Ϫ4
)
under the current experimental
conditions.30
We note that the two-photon excitation in ͑1͒ can also be
considered as proceeding via the energy-resonant dissocia-
tive Cl2(A 1⌸u) intermediate state, as recognized by Setser
and co-workers.8 If the lifetime of this intermediate complex
is short, however, the initial conditions still determine the
reaction outcome.31 Recent two-photon femtosecond
studies17,32 suggest that this is in fact the case in the reaction
originating from collision pairs in low pressure gas mixtures.
In the latter study,32 Dedonder-Lardeux et al. also identified
a second entrance channel occurring some 500 fs after the
initial photon absorption in the reaction originating from
vdW complexes. This delayed entrance channel is also tran-
sient, and therefore is thought to occur within XenCl2 clus-
ters where cage effects allow a recoil of the dissociating Cl
atom.
gree of vibrational excitation was measured ( E ϳ1 eV)
͗
͘
v
for the LAR at short laser wavelengths.
The previous analysis assumes a C2v ͑T-shaped͒ geom-
etry for the collision pair or vdW complex, as suggested by
the spectroscopic studies of Janda et al.34 Recent studies of
Xe/Cl2 in Ar matrices imply that this assumption is not nec-
essarily valid, even for the vdW molecule: Their work gives
evidence for the existence of a linear ground state for
XeCl2.35 Similar arguments, however, can be presented, mu-
tatis mutandis, for the dynamics on a reactive PES appropri-
ate for a linear geometry.
The observed energy disposal trends support the qualita-
tive interpretation of dynamics in the LAR based on the role
of initial conditions on a reactive PES.11,31 For laser wave-
lengths above 306 nm, the direct excitation is predicted to
occur for Xe–Cl distances very near the minimum of the
‘‘exit seam’’ in the ionic potential surface ͓correlating to
XeCl(B) at large R(Cl–Cl)͔. Release of the repulsion in the
Cl–ClϪ bond leads to energy disposal largely as translation
between the XeCl and Cl products. This is illustrated in Fig.
8 by the trajectory originating from point A. The low fraction
of excess energy found as vibration in the excimer produced
V. SUMMARY AND CONCLUSIONS
The entrance channel to the Xe/Cl2 LAR is unique from
other laser-induced reactions between Xe and Cl2 in that it
involves a direct two-photon excitation to the XeϩClϪ
͕
͖
2
CTS. This excitation occurs via a cooperative photoabsorp-
tion by the transient Xe–Cl2 collision pair, and is character-
ized by a broad continuous excitation spectrum. The continu-
ous range of excitation in the LAR affords an aspect of direct
laser control of the reaction. The goal of the present work has
been to characterize the energy disposal as a function of
excitation wavelength, and thus to relate the measured trends
to the role of initial conditions in the entrance channel to the
LAR. Toward this end, we have analyzed the continua emis-
sion observed following the LAR for a broad range of exci-
by the LAR at this laser wavelength ( f Ϸ0.3) is consistent
͗
͘
V
with this interpretation, and implies that as much as 1.1 eV
of kinetic energy is shared between the atom and diatom
products.
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10558
J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
J. Kohel and J. W. Keto
tation wavelengths to determine the vibrational distributions
in the excimer product. Significant vibrational population in-
version is observed in the excimer resulting from the LAR.
From analysis of the measured XeCl(B–X) fluorescence
pears to be a significant feature of the LAR, even when ac-
counting for additional relaxation due to the higher pressures
in the current study. The exit channels in both the laser-
assisted and quenching reactions involve the XeϩClϪ CTS,
͕
͖
2
so this apparent difference in energy disposal was
previously8 attributed to the presence of different pathways
for the two reactions.
spectra we determined the mean vibrational energy E in
͗
͘
v
the newly formed Xe–Cl bond to be approximately 0.5 eV
(3900 cmϪ1) for the reaction resulting from laser excitation
wavelength of 313.5 nm.
E
increases to approximately
͘
͗
v
1.1 eV (9100 cmϪ1) for the reaction at 288.5 nm. Further-
more, we found an increasing fraction of the available en-
ergy from the reaction appears as vibration in the excimer
ACKNOWLEDGMENTS
This work was supported by the U.S. Department of
Education, Office of Basic Energy Sciences, Division of
Chemical Sciences and the Robert A. Welch Foundation.
*
product XeCl as the laser is tuned from redmost ͑ f
͗
͘
ex
V
Ϸ0.3 at 313.5 nm͒ to bluer wavelengths ͑ f Ϸ0.5 for ␭
͗
͘
V
р306 nm͒. As illustrated in Fig. 7, this transition is sudden
with increasing exoergicity for the reaction. This sudden in-
crease in vibrational energy disposal is also evident in the
sequence of spectra shown in Fig. 1.
APPENDIX: POTENTIAL REPRESENTATIONS
The upper and lower potentials used in the simulations
of the excimer emission were taken from Sur et al.37 and the
molecular scattering studies of Aquilanti et al.,38 respec-
tively, with slight modifications as necessary to accurately
simulate emission spectra from both thermal and highly ex-
cited vibrational distributions in the upper state. The
XeCl(X) ground state potential was unmodified, while the
vertical position of the XeCl(B) excited state potential was
The high degree of vibrational excitation observed in the
*
XeCl product in the current experiment is qualitatively con-
sistent with the previous observations by Setser and co-
workers for the LAR of XeϩCl2 collision pairs. The signifi-
cant variation in degree of vibrational excitation over the
wide range of excitation wavelengths, however, is clearly
demonstrated for the first time in the present work. We at-
tribute the increasing vibrational energy disposal to a varia-
tion of initial conditions on the reactive V(Xeϩ;Cl2Ϫ) poten-
tial energy surface, as discussed. We note, however, that
while this predicted trend toward greater vibrational energy
disposal with decreasing laser wavelength is clearly demon-
strated in the current experiment, the same trend may not
necessarily be exhibited in similar experiments in supersonic
jets or in solid matrixes, due to the restricted geometries and
cage effects in the in vdW complexes and in the solid matrix.
While gross dynamical trends may be inferred from the
present work, deconvolution of the data to reveal individual
reactive trajectories is far more difficult. A more detailed
analysis, furthermore, must consider complications due to a
distribution of initial ͑kinetic and internal͒ energies and ori-
entations in the reagents. Nonetheless, the above conclusions
are believed to be qualitatively correct. Numerical calcula-
tions of classical trajectories on the reactive PES using
Monte Carlo sampling techniques to integrate over a distri-
bution of initial conditions are also in reasonable agreement
with the observed product state outcomes.36 These conclu-
sions differ slightly from that of Setser and co-workers, who
calculate that the majority of collision pairs are found in
bound levels of the shallow vdW potential ͑nb /nfϭ0.86 at
300 K͒ and conclude that the width of the excitation spec-
trum ͑0.4 eV͒ is largely determined by the gradient in the
Cl–ClϪ coordinate of the PES.8 This interpretation, however,
would fail to account for the significant variation in energy
disposal observed in the present work or, for that matter, the
dramatic difference in energy disposal observed for the LAR
in gas phase studies and in molecular beam experiments
where the initial geometry may be more restricted.
determined by the XeCl(B–X) 00 transition energy ␯(00)
͓
ϭ32 495Ϯ1 cmϪ1 measured by Jouvet et al. in a free jet.39
͔
The upper potential was then shifted relative to the lower
potential along R in order to accurately simulate the
vibrationally-relaxed emission measured in high pressure
Xe/Cl2 gas mixtures ͑1430 Torr Xe, 10 Torr Cl2͒. And fi-
nally, the upper repulsive wall was adjusted slightly to give
agreement with the oscillations in the blue wing of vibra-
tionally excited low pressure emission spectra observed by
Setser and co-workers40 following the reactive quenching of
Xe(6s, 3P2) by Cl2. The modified upper potential was recast
in the form of a truncated Rittner potential,
V
R͒ϭa exp ϪR/b͒ϪC /RϪC /R4ϩd,
͑A1͒
͑
͑
Ј
1
4
and the shape of this potential was verified by comparing the
calculated eigenenergies to measured values37 for the lowest
dozen vibrational levels.
The XeCl(B–X) transition moment is a slowly varying
function of R with a maximum near RЈe . The ab initio tran-
sition moment of Hay and Dunning,41 however, required
slight modification for the best simulation of spectra origi-
nating from distributions including large vibrational quanta
͑which sample transitions at large R͒. The transition moment
was represented in this work by the function
exp Ϫ␥ RϪc ͒
͔
1
͓
͑
␮ R͒ϭc
.
͑A2͒
͑
e
0
1ϪR/c ͒2ϩc
͑
1
2
Parameters for the above transition moment function were
adjusted so that the overall ‘‘envelope’’ of the simulated
TABLE II. Parameters for the XeCl(B) Rittner potential function.
We have noted also that vibrational energy disposal in
the LAR appears to be significantly less in the current ex-
periment than that in the quenching reactions of metastable
C1
a
b
͑Å͒
C4
d
(105 cmϪ1 Å)
(107 cmϪ1
)
(105 cmϪ1 Å4)
(cmϪ1
)
2.185
0.387
1.177
5.456
68 987
Xe with Cl2 studied by Setser et al.28 This difference ap-
*
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J. Chem. Phys., Vol. 113, No. 23, 15 December 2000
Reaction in Xe and chlorine gas mixtures
10559
15 M. E. Fajardo et al., Laser Chem. 9, 1 ͑1988͒.
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͑A2͔͒.
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c0
͑Debye͒
c1
͑Å͒
c2
␥
͑ÅϪ1
͒
0.323
3.139
0.122
0.10
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