Laser spectroscopic excitation function and reaction threshold studies of the H + DCl → HCl + D gas-phase isotope exchange reaction

Article abstract of DOI:10.1021/jp054818o

The dynamics of the gas-phase hydrogen atom exchange reaction H + DCl → HCl + D were studied using the pulsed laser photolysis/laser induced fluorescence pump-and-probe method. Laser photolysis of H ₂S at 222 nm was used to generate nonequilibrium distributions of translationally excited hydrogen atoms at high dilution in a flowing moderator gas (Ar)/reagent (DCl) mixture. H and D atoms were detected with sub-Doppler resolution via Lyman-α laser induced fluorescence spectroscopy, which allowed the measurement of the line shapes of the moderated H atom Doppler profiles as well as the concentration of the D atoms produced in the H + DCl → HCl + D reaction. From the measured H atom Doppler profiles, the time evolution of the initially generated nascent nonequilibrium H atom speed distribution toward its room-temperature thermal equilibrium form was determined. In this way, the excitation function and the reaction threshold (E₀ - 0.65 ± 0.13 eV) for the H + DCl → HCl + D reaction could be determined from the measured nonequilibrium D atom formation rates and single collision absolute reaction cross-section values of 0.12 ± 0.04 A² and 0.45 ± 0.11 A² measured at reagent collision energies of 1.0 and 1.4 eV, respectively.

Full text of DOI:10.1021/jp054818o

J. Phys. Chem. A 2006, 110, 3273-3279
3273
Laser Spectroscopic Excitation Function and Reaction Threshold Studies of the H + DCl f
HCl + D Gas-Phase Isotope Exchange Reaction†
Almuth La1uter, Rajesh K. Vatsa,‡ Jai P. Mittal, Hans-Robert Volpp,* and Ju1rgen Wolfrum
Physikalisch-Chemisches Institut der UniVersita¨t Heidelberg, Im Neuenheimer Feld 253,
D-69120 Heidelberg, Germany
ReceiVed: August 25, 2005; In Final Form: December 8, 2005
The dynamics of the gas-phase hydrogen atom exchange reaction H + DCl f HCl + D were studied using
the pulsed laser photolysis/laser induced fluorescence “pump-and-probe” method. Laser photolysis of H2S at
222 nm was used to generate nonequilibrium distributions of translationally excited hydrogen atoms at high
dilution in a flowing moderator gas (Ar)/reagent (DCl) mixture. H and D atoms were detected with sub-
Doppler resolution via Lyman-R laser induced fluorescence spectroscopy, which allowed the measurement
of the line shapes of the moderated H atom Doppler profiles as well as the concentration of the D atoms
produced in the H + DCl f HCl + D reaction. From the measured H atom Doppler profiles, the time
evolution of the initially generated nascent nonequilibrium H atom speed distribution toward its room-
temperature thermal equilibrium form was determined. In this way, the excitation function and the reaction
threshold (E0 ) 0.65 ( 0.13 eV) for the H + DCl f HCl + D reaction could be determined from the
measured nonequilibrium D atom formation rates and single collision absolute reaction cross-section values
of 0.12 ( 0.04 Å2 and 0.45 ( 0.11 Å2 measured at reagent collision energies of 1.0 and 1.4 eV, respectively.
I. Introduction
from the reaction threshold up to Ec.m. ) 2.4 eV.11,12
H + DCl f HD + Cl
Since the pioneering experimental work of Bodenstein and
Dux on the photochemical kinetics of the hydrogen-chlorine
system,1,2 the elementary reactions
(3)
(4)
H + DCl f HCl + D
H + HCl f H2 + Cl
H + HCl f HCl + H
(1)
(2)
In a subsequent theoretical study, quantum mechanical
scattering (QMS) calculations were performed on the BW2 PES
in which reaction cross-sections for reactions 1 and 2 in the
collision energy range Ec.m. ) 0.1-1.4 eV were computed.13
On the experimental side, several reaction cross-section mea-
surements were performed for the abstraction reaction 1 in which
translationally excited H atoms were employed in combination
with state-resolved detection of H2 product molecules using
coherent anti-Stokes Raman scattering (CARS)14 and vacuum
ultraviolet laser induced fluorescence (VUV-LIF) detection of
ground-state Cl(2P3/2) atom products, respectively.12,15 The
results of the latter VUV-LIF absolute reactive cross-section
measurements, which agreed reasonably well with the results
of QCT calculations on the G3 PES,11,12 demonstrated that there
is no sharp increase in the reaction cross-section of reaction 1
in the collision energy range Ec.m. ) 1.0-1.7 eV, as was
suggested by the earlier CARS experiments.14 Experimental
studies of reaction 3, in which resonance-enhanced multiphoton
ionization (REMPI)16 and VUV-LIF spectroscopy17 were uti-
lized for ground-state Cl(2P3/2) atom product detection, yielded
reaction cross-sections which were found to be in good
agreement with the results of QCT calculations on the G3
PES.11,12 In further experiments, VUV-LIF spectroscopy could
be successfully applied for the detection of spin-orbit excited
Cl*(2P1/2) atoms formed via a nonadiabatic reaction pathway
in the H + HCl and H + DCl abstraction reactions 1 and 3.17
In these studies, it was found that the [Cl*]/[Cl + Cl*] spin-
orbit product branching ratio in reactions 1 and 3 increases from
6% to 19% and 16%, respectively, in the collision energy range
and the reverse reaction Cl + H2 (reaction -1) have played
seminal roles in the evolution of modern chemical kinetics and
reaction dynamics.3 Reaction 1 represents the H atom abstraction
channel, while reaction 2 represents the H atom exchange
channel of the HClH reactive system. Great efforts have been
made in recent years to construct an accurate global potential
energy surface (PES) required for the theoretical investigation
of reactions 1, -1, and 2.3-5
A large number of experimental thermal kinetics studies were
carried out for the reactions 1 and -1, resulting in quite accurate
Arrhenius parameters for the thermal rate coefficients in the
temperature ranges 195-1200 K and 199-3020 K, respec-
tively.6,7 The results of the latter kinetics studies were found to
be in generally good agreement with the results of rate constant
calculations8-10 on the G3 PES.4 The G3 PES was also
employed, along with the more recently developed BW1 and
BW2 PESs,5 in comparative quasi-classical trajectory (QCT)
studies in which reaction cross-sections for reactions 1 and 2
as well as for the hydrogen atom abstraction (reaction 3) and
hydrogen atom exchange (reaction 4) reactions of the isotopic
variant H + DCl were calculated for reagent collision energies
† Part of the special issue “Ju¨rgen Troe Festschrift”.
* Corresponding author. E-mail: aw2@ix.urz.uni-heidelberg.de.
‡ Present address: Novel Material and Structural Chemistry Division,
Bhabha Atomic Research Centre, Mumbai, 400085, India.
10.1021/jp054818o CCC: $33.50 © 2006 American Chemical Society
Published on Web 02/07/2006

3274 J. Phys. Chem. A, Vol. 110, No. 9, 2006
La¨uter et al.
Ec.m. ) 1.0-1.7 eV, demonstrating the increasing importance
of the nonadiabatic reaction pathways with increasing collision
energy.
corresponding ones obtained on the G3 PES. A comparison
between the QCT results11,12 and the experimental results16
obtained for Ec.m. < 2.4 eV is shown in the lower panel of figure
5 in ref 12, which reveals that the experimental values are not
reproduced by the calculations on either one of the PESs. As a
consequence, the available experimental data16 so far does not
allow for a definite assessment of the comparative quality of
the PESs employed in the theoretical dynamics studies of the
hydrogen exchange reactions 2 and 4.11-13,16
The influence of the Cl*(2P1/2) spin-orbit excited state on
the reactivity of the Cl + H2/D2/HD abstraction reactions was
investigated in the reagent collision energy range Ec.m. ) 0.1-
0.3 eV employing a crossed molecular beam apparatus.18-20 The
latter integral reaction cross-section measurements revealed an
exceptionally large reactivity for the reactions of Cl*(2P1/2
)
In the work presented in the following article, we applied
the moderated hot H atom pulsed laser “pump-and-probe”
method described in detail in ref 27, which allows, on the basis
of a combination of single collision reaction cross-sections, H
atom moderation and nonequilibrium D atom formation rate
measurements, to determine the reaction threshold and a global
representation of the excitation function for the H + DCl f
HCl + D hydrogen atom exchange reaction 4. The results
obtained in the present study can be directly compared with
the results obtained in previous theoretical dynamics stud-
ies.11,12,16
atoms, indicating a large extent of electronic nonadiabaticity in
these reactions. On the theoretical side, detailed state-of-the-
art electronic structure calculations were performed along with
exact multielectronic-state QMS calculations,21 which explicitly
allowed for the effect of electronic nonadiabaticity,22 to rational-
ize the experimental observations reported in refs 18-20. The
QMS calculations of ref 21 revealed an electronically nonadia-
batic effect in the Cl + H2 reaction, resulting in an reduction
of the reactivity of the ground-state Cl(2P3/2) atom via an
electronically nonadiabatic transition in the reactant entrance
valley which leads to nonreactive inelastic “backscattering” to
the Cl(2P3/2) + H2 reactants. However, for the elevated collision
energies as employed in the experiments,18-20 the QMS calcula-
tions did not yield any indication for the experimental observa-
tion of the Cl*(2P1/2) spin-orbit excited state being substantially
more reactive than the Cl(2P3/2) ground state, which is the one
which in the Cl + H2 reaction system correlates adiabatically
with the observed HCl + H products in their respective ground
II. Experimental Section
The present studies were performed using the pulsed laser
flash photolysis/laser induced fluorescence (LP/LIF) “pump-
and-probe” technique in a flow reactor system at room tem-
perature. The experimental arrangement and methodology
employed in the present experiments have been described in
detail elsewhere.27,28 Therefore, only specific details relevant
to the present investigations will be given in the following.
The measurements were carried out in a flow reactor made
of stainless steel, through which H2S (UCAR, electronic grade,
99.99%)/DCl (Sigma Aldrich, D > 99%) as H atom precursor/
reagent mixtures together with the bath gas Ar (99.998%) could
be continuously pumped, with a flow rate high enough to ensure
renewal of the gas mixture in the cell between two successive
photolysis (“pump”) laser shots. The flow rates of the H2S, DCl,
and Ar gases were regulated by calibrated mass flow controllers,
and the cell pressure was measured by a MKS Baratron.
In the single collision absolute reaction cross-section mea-
surements, no bath gas was used. Typical values for the [H2S]:
[DCl] ratios were between 1:2 and 1:3. These experiments were
carried out at low total pressure of ptot ) 40-100 mTorr and at
short pump-probe delay times of ∆t ) 90-200 ns to avoid
translational relaxation of the translationally “hot” H atoms. The
moderated hot H atom experiments were carried out in an excess
of Ar buffer gas. In these experiments, the total pressure was
typically 1.0-1.1 Torr with H2S and DCl partial pressures of
10 and 80 mTorr, respectively.
In the present studies, translationally excited H atoms with a
nonequilibrium velocity distribution were generated by pulsed
laser photolysis (with a laser pulse duration of 15-20 ns) of
H2S at two different excimer laser wavelengths of λpump ) 248
nm and λpump ) 222 nm. The photodissociation lasers were
operated without polarizing elements, and the analysis of the
H atom Doppler profiles generated confirmed that the nascent
velocity distributions were essentially spatially isotropic. An
aperture was used to skim off a homogeneous part of the
rectangular excimer laser profiles to provide photolysis beams,
which were slightly focused and directed through the flow cell.
Photolysis laser intensities employed in the experiments were
in the range 2-5 mJ/cm2. At these laser intensities, a linear
dependence of the photolytically produced H atom concentra-
tions on the intensity of the photolysis laser was observed, and
no secondary “high-energy” H atoms due to SH photolysis29
were detectable.
electronic states. In agreement with most recent Cl(2P3/2 1/2
, ) +
H2 crossed molecular beam measurements of differential cross-
sections at elevated23 and low24 collision energies, the multi-
electronic-state QMS calculations performed on the newly
developed CW PESs25 clearly demonstrated that at all but the
very lowest collision energies both integral and differential
cross-sections for the spin-orbit excited-state reaction Cl*(2P1/2
)
+ H2 are much smaller than those of the ground-state reaction
Cl(2P3/2) + H2.
In contrast to the number of experiments performed to
elucidate the dynamics of the abstraction reaction pathways,
up to now only one experimental study of the dynamics of the
hydrogen atom exchange reaction 4 has been reported, in which
absolute reaction cross-sections were measured as a function
of reagent collision energy in the range Ec.m. ) 1.0-2.4 eV.16
The latter experimental values, which exhibited a considerable
dispersion, indicated a flat dependence on collision energy with
a slightly decreasing tendency in the higher-energy regime. In
contrast to this behavior, results of QCT calculations on the
GQQ PES,26 which were also performed in the course of the
study reported in ref 16, showed a strictly monotonic increase
of the reaction cross-section as a function of collision energy
that leads, for the highest collision energy of 2.4 eV as employed
in the experiments, to considerably larger cross-sections than
experimentally observed. A similar discrepancy between experi-
ment and theory is observed if the experimental results of ref
16 are compared with the results of QCT calculations of the
excitation function, i.e., the collision energy dependence of the
absolute reaction cross-section σR(Ec.m.), obtained on the G3,
although (see, e.g., lower panel of figure 4 in ref 11) the G3
reaction cross-sections are considerably smaller (by a factor of
about 2) than the GQQ ones. Subsequent QCT studies12
performed on the BW1 and BW2 PESs for collision energies
up to Ec.m. ) 2.5 eV yielded excitation functions which also
indicated a strictly monotonic increase of the reaction cross-
section as a function of collision energy, with the absolute
reaction cross-section values being slightly higher than the

Dynamics of Gas-Phase H Exchange Reaction
J. Phys. Chem. A, Vol. 110, No. 9, 2006 3275
due to H2S and DCl “Lyman-R self-photolysis”. At this point,
it should be mentioned that, in measurements where only DCl
was present, no D atoms produced by the photolysis laser beams
could be detected. In the flowing H2S/DCl mixture, however,
we observed a D atom background (see section III) which we
attribute to direct photolysis of D2S or HDS formed by a
heterogeneous isotope exchange reaction at the walls of the
mixing part of the flow system. In separate experiments, this D
atom background was found to be independent of delay time
and to decrease slowly when the flow of DCl was stopped, but
on a time scale long enough to allow reliable determination of
the Doppler profile of reactively produced D atoms by deter-
mining the difference between D atom profiles recorded with
and without the presence of DCl. The D atom Doppler profile
line shapes recorded without DCl flow were evaluated to
determine the average kinetic energy, which was found to be
consistent with D atom generation via 248 and 222 nm
photolysis of D2S or HDS, respectively.
Figure 1. H atom reagent and D atom product Doppler profiles
obtained in the H + DCl f HCl + D single-collision reaction cross-
section measurements. H atoms with average collision energies of Ec.m.
)
1.4 eV (Figure 1a) and Ec.m. ) 1.0 eV (Figure 1b) were generated via
pulsed laser flash photolysis of H2S at photolysis laser wavelengths of
222 and 248 nm, respectively, in the presence of 75 mTorr of DCl. D
atom products were probed at a delay time of 120 ns. The centers of
the Doppler profiles correspond to the Lyman-R transition of the H
(82 259.1 cm-1) and D atoms (82 281.4 cm-1), respectively.
III. Results
A. Single Collision Absolute Reaction Cross-Sections.
Single collision cross-sections were obtained using the pulsed
laser pump/probe method, which we have employed previously
to measure absolute reaction cross-sections for the H +
D2O f D + HOD hydrogen atom exchange reaction.27,31 The
determination of absolute reactive cross-sections σR was based
on the following equation:31
H and D atoms were detected by means of Doppler-resolved
laser induced fluorescence spectroscopy via the respective (2p2
P r 1s2 S) hydrogen atom Lyman-R transitions. Tunable
narrow-band VUV-probe laser radiation (bandwidth ∆νprobe
≈
0.3 cm-1) was generated by resonant third-order sum-difference
frequency conversion (νprobe ) 2νR - νT) of pulsed dye laser
radiation (pulse duration ≈ 15 ns) in a phase-matched Kr/Ar
mixture.30 In the four-wave mixing process, the frequency νR
(λR ) 212.55 nm) is two-photon resonant with the Kr 4p-5p
(1/2, 0) transition. The frequency νT could be tuned from 844 to
848 nm to cover the H and D atom Lyman-R transitions
(λLR-H ) 121.567 nm, λLR-D ) 121.534 nm). The generated
VUV probe laser radiation was separated from the unconverted
laser radiation by a lens monochromator. The VUV probe beam
was aligned to overlap the photolysis beam at right angles in
the viewing region of an LIF detector. H and D atom LIF signals
were measured through a band-pass filter by a solar blind
photomultiplier positioned at right angles to both photolysis and
probe laser. The delay time ∆t between the photolysis and the
probe pulse was controlled by a pulse generator. The VUV-
probe laser beam intensity was monitored after passing through
the reaction cell with an additional solar blind photomultiplier.
The LIF signal, the VUV-probe beam intensity, and the
photolysis laser intensity were recorded with a boxcar system
and transferred to a microcomputer where the LIF signal was
normalized to both photolysis and probe laser intensities. To
obtain a satisfactory S/N ratio, each point of the H and D atom
Doppler profiles (Figure 1) was averaged over 30 laser shots.
All measurements were carried out at a repetition rate of 6 Hz.
As in our previous studies of the H + D2O f D + HOD
hydrogen exchange reaction,31 it was observed that the Lyman-R
probe beam itself produced D atoms via photolysis of the DCl
reagent alone. To distinguish these “background” D atoms from
the D atoms produced by the H + DCl reaction, an electronically
controlled mechanical shutter was inserted into the photolysis
beam path. At each point of the D atom line scan, the signal
was first averaged with the shutter opened and again averaged
with the shutter closed. A point-by-point subtraction procedure
was adopted to obtain on-line a signal free from background D
atoms. The background subtraction method described above was
also applied when H atom lines were recorded. Hence, all the
data presented in the following are free from any contribution
[D]∆t ) σR(Ec.m.)Vrel[DCl][H]∆t + [D]0
(5)
Here, Vrel is the relative velocity, Ec.m. ) 1/2µVrel2, of the reactants
where µ represents the reduced mass of the H-DCl collision
pair. Ec.m. and hence Vrel can be calculated from the photolysis
laser wavelength, the H-SH bond dissociation energy, and the
internal state distribution of the SH fragment29 as described in
detail in ref 32. ∆t stands for the time delay between the
photolysis and probe laser pulses, which was determined by
measuring the time difference between photolysis and probe
scattered light pulses observed on a fast oscilloscope. [x] denotes
the concentration of species x and [D]0 the constant D atom
background originating from the direct photolysis of D2S/HDS
formed by heterogeneous isotope exchange between H2S and
DCl as discussed in the previous section. After rewriting
eq 5 as
[D]∆t/[H] ) σR(Ec.m.)vrel[DCl]∆t + [D]0/[H]
(6)
it can be seen that by measuring D/H atom ratios at different
delay times ∆t under identical experimental conditions, σR can
be determined from the slope of a linear fit if the relative
velocity and the DCl concentration are known. In Figure 1, H
atom and D atom Doppler profiles observed when a room-
temperature mixture of H2S and DCl was irradiated by laser
light with a wavelength of 222 nm (Figure 1a) and 248 nm
(Figure 1b) are depicted. The H atom Doppler profiles shown
in Figure 1a,b correspond to translationally excited H atoms
with average collision energies of Ec.m. ) 1.4 eV and Ec.m.
)
1.0 eV, respectively. In a number of experimental runs,
integrated areas under the H and D Doppler profiles were
determined at various delay times. In Figure 2, a typical plot of
the measured D/H atom ratios versus delay time is shown.
Evaluation of the experimental data sets via eq 6 yielded
absolute reaction cross-sections of σR(1.4 eV.) ) 0.45 ( 0.11
Å2 and σR(1.0 eV.) ) 0.12 ( 0.04 Å2 for the H + DCl f
HCl + D exchange reaction.

3276 J. Phys. Chem. A, Vol. 110, No. 9, 2006
La¨uter et al.
the ratio of the integrated areas of the D atom products measured
at reaction time ∆t (see, e.g., Figure 3) and the nascent H atom
reagent Doppler profile measured at a reaction time close to
zero (before significant reaction could occur).
As described in detail in ref 27, the H atom Doppler line
shapes measured at different pump/probe delay times were
evaluated to determine the laboratory frame distribution f(Vz, t)
of the velocity component Vz of the absorbing H atoms along
the propagation direction of the probe laser beam. A symmetric
double sigmoidal function, eq 9, was used as a fitting function
to evaluate the measured H atom Doppler line shape, as it well
describes the Doppler line shapes at both short and long pump-
probe delay times (see Figure 3a). In eq 9, A is a normalization
Figure 2. Plot of measured D/H atom ratios against delay time ∆t
between photolysis and probe laser pulse. H atoms were generated via
pulsed 222 nm laser flash photolysis of H2S in a flowing mixture of
H2S and DCl at a total pressure of 100 mTorr. [D]0 stands for the
photolytically produced D atom background (for details, see text and
ref 31).
f(Vz, t) )
1
1
A
1 -
[Vz + ω1(t)/2]
[Vz - ω1(t)/2]
B. Excitation Function and Reaction Threshold Determi-
nation. If translationally excited H atoms are generated by
pulsed laser photolysis of H2S molecules in a large excess of a
moderator gas, the initially present nascent nonequilibrium H
atom velocity distribution evolves toward the thermal equilib-
rium distribution determined by the temperature of the moderator
gas. Therefore, the velocity distribution of the H atoms in the
laboratory frame has to be described by a time-dependent
distribution function (see, e.g., ref 33 and references therein).
When a reagent, such as DCl, is present, reactive collisions occur
in competition with the translational relaxation. In this case,
the nonequilibrium kinetics of D atom product formation in the
moderated hot H atom reaction H + DCl f HCl + D are then
described by the rate equation27
1 + exp -
1 + exp -
[
][
]
{
}
{
}
ω2(t)
ω2(t)
(9)
factor, while the two variables ω1(t) and ω2(t) are a measure
for the time-dependent width of the profile and the steepness
of its wings, respectively. To derive an empirical representation
of f(Vz, t), ω1 and ω2 were parametrized by the following
functions:
ω1(t) ) a1 + b1 exp(-c1t)
(10)
(11)
x
ω2(t) ) a2 + b2 t exp(-c2t)
In Figure 4, the solid lines represent the results of a least-
squares fit of the measured data, which was used to determine
the functional forms of ω1(t) and ω2(t) under the conditions of
the present experiments.
d[D]
t ) { ∞ σR(Vrel)Vrel f(Vrel, t) dVrel}[H]t[DCl] (7)
∫
0
dt
In Figure 3a, H atom Doppler profiles, which were simulated
using eq 9 as the empirical representation of f(Vz, t), are depicted
as solid lines and compared to the experimental ones (solid
circles). The corresponding time-dependent distribution function
f(Vrel, t) obtained from f(Vz, t) by differentiation followed by a
laboratory to center-of-mass transformation (for details, see refs
32 and 33) is depicted in Figure 3b. Doppler profiles of the D
atom reaction products are shown in Figure 3c. Values for the
reaction times at which the respective H and D atom Doppler
profiles were recorded are given in the figure.
In Figure 5, results of a D atom fractional product yield
measurement are plotted against the reaction time. The experi-
mental data were analyzed by assuming a model excitation
function given by eq 12 containing parameters a, b, and c to be
optimized.
Here, it has been assumed that DCl is present in excess over H
atoms so that its concentration remains constant in time.
f(Vrel, t) stands for the time-dependent distribution function of
the reagents’ relative velocities in the H-DCl collision frame.
In eq 7, the term in braces represents the reaction rate constant
which, under the translationally nonequilibrium conditions of
the present experiments, is time-dependent. After replacing [H]t
by [H]t)0 - [D]t and introducing the new variable øD(t) )
[D]t/[H]t)0, which represents the fractional yield of D atoms
produced, the following expression can be obtained as a solution
of eq 7 for the initial condition øD(t ) 0) ) 0:
øD(∆t) )
∆t
[DCl]
{
∞ σR(Vrel)Vrel f(Vrel, t) dVrel}[1 - øD(∆t)] dt (8)
0
∫ ∫
0
2
E
c.m. g E0
a + bEc.m. + cEc.m. for
In eq 8, the delay time ∆t between the pump laser pulse, which
generates the H atom reagents, and the probe laser pulse, which
detects the D atom products, corresponds to the reaction time.
To perform the integration in eq 8, one has to know the
excitation function, i.e., the reaction cross-section σR as a
function of the relative velocity, as well as the time dependence
of the relative velocity distribution function f(Vrel, t). On the
other hand, when øD(∆t) and f(Vrel, t) can be determined
experimentally, information about the actual form of the
excitation function can be obtained.
σR(Ec.m.) )
(12)
{
Ec.m. < E0
0
for
With the time-dependent parametrization of the H-DCl
reagents’ relative velocity distribution function f(Vrel, t), D atom
fractional yields predicted by the model excitation function could
be calculated via eq 8 for the conditions corresponding to each
measured data point øD(∆t). The integration over t in eq 8 was
performed numerically. A measure of the quality of a given set
of excitation function parameters could be obtained by comput-
ing the global mean-squared deviation of both the nonequilib-
rium kinetics data set and the single collision cross-sections from
the corresponding values calculated from the trial excitation
function. Optimization of the excitation function parameters a,
The pulsed laser pump/probe method employed in the present
work allowed the direct determination of both the D atom
product yield øD(∆t) and the time-dependent relative velocity
distribution function f(Vrel, t). øD(∆t) could be obtained from

Dynamics of Gas-Phase H Exchange Reaction
J. Phys. Chem. A, Vol. 110, No. 9, 2006 3277
Figure 3. (a) H atom Doppler profiles measured at different pump-probe delay times between 90 and 900 ns after 222 nm laser flash photolysis
of 10 mTorr of H2S in a flowing mixture of 80 mTorr of DCl and 1 Torr of Ar. Solid lines are results of a nonlinear least-squares fit analysis of
the measured Doppler profiles performed to determine the time evolution of the H atom laboratory velocity distribution f(Vz, t) as described in the
text. (b) Evolution of the corresponding time-dependent distribution function f(Vrel, t) of the relative velocity in the H-DCl collision frame. Shaded
areas represent 1σ statistical uncertainty determined by simple error propagation from the least-squares fit procedure employed to derive a continuous
analytical representation for the time evolution of the line shape parameters ω1(t) and ω2(t) (solid lines in Figure 4). The arrows mark the threshold
for the H + DCl f HCl + D reaction. (c) Doppler profiles of D atoms produced in the reaction H + DCl f HCl + D. The D atom signal at
900 ns corresponds to a D atom product yield of øD(900 ns) ) [D]900 ns/[H]t)0 ≈ 0.04.
Figure 4. Measured time dependence of the H atom Doppler profile
line shape parameters ω1 and ω2 (solid circles). Experimental conditions
are the same as in Figure 3. Solid lines are the results of a least-squares
Figure 6. Comparison between experimental and theoretical absolute
fit procedure used to derive a continuous analytical representation for
reaction cross-sections for the H + DCl f HCl + D hydrogen atom
exchange reaction. Open circles are experimental results obtained by
Polanyi and co-workers.16 The filled circles are the experimental results
of the present single collision reaction cross-section measurements,
where the widths of the boxes drawn around represent the spreads
(fwhm) in the collision energy distributions, and the heights of the boxes
represent the experimental uncertainties of the measurements. The solid
line is the excitation function σR(Ec.m.) derived in the present moderated
hot H atom experiments. The shaded area reflects the statistical
uncertainty (1σ) of the least-squares fit procedure used to determine
the optimum excitation function (for details, see text). Theoretical
excitation functions obtained in quasiclassical trajectory calculations12
performed on different potential energy surfaces (PESs): “dotted” curve,
BW2-PES; “dash-dot” curve, BW1-PES; “dash-dot-dot” curve,
G3-PES.
the two parameters ω1(t) and ω2(t). Shaded areas represent 1σ statistical
uncertainty of the respective fitting function.
Figure 5. Plot of the D atom product yield øD versus reaction time.
Filled circles represent experimental results. The solid line is the result
of a simulation of the experimental moderation conditions using the
measured velocity distribution f(Vrel, t) and the excitation function
σR(Ec.m.) reproduced in Figure 6 as a solid line.
IV. Discussion
b, and c was performed by a nonlinear least-squares fit to
minimize the sum of these two mean-squared deviations. The
latter procedure yielded a set of optimal values resulting in the
excitation function depicted in Figure 6 as a solid line, which
corresponds to a reaction threshold energy of E0 ) 0.65 ( 0.13
eV. The statistical uncertainty in each of the model parameters
allows estimation of the confidence region (1σ) of the excitation
function, which is shown as the shaded area in Figure 6.
In Figure 6, the global excitation function derived in the
present moderated hot H atom study of the H + DCl f HCl +
D reaction is depicted (solid line) along with the two single
collision reaction cross-sections σR(1.0 eV.) ) 0.12 ( 0.04 Å2
and σR(1.4 eV.) ) 0.45 ( 0.11 Å2 (filled circles) obtained in
the course of the present work. The width of the boxes drawn
around the latter quantities represents the spread (fwhm) in the
nascent collision energy distribution,32 and the height of the

3278 J. Phys. Chem. A, Vol. 110, No. 9, 2006
La¨uter et al.
boxes represents the experimental uncertainties in the reaction
cross-measurements.
the QCT approach of ref 12 the latter PES provides at present
the most accurate description of the dynamics of the H +
DCl f HCl + D exchange reaction 4.
For comparison with the experiments, results obtained in QCT
calculations12 on the G3 (dash-dot-dot curve) and on the BW1
(dash-dot curve) and BW2 (dotted curve) PESs are reproduced
in Figure 6. The latter two PESs represent two slightly different
versions of the PES of Bian and Werner,5 which is based on
extensive and high-quality ab initio calculations performed at
1200 geometries. The BW1 version is based on a global fit of
the original ab initio data points, whereas the BW2 version was
obtained by scaling the correlation energies at all geometries
with a constant factor chosen in order to more accurately
reproduce the HCl and H2 bond dissociation energies.5
Caution should be taken, however, to draw a final conclusion
about the comparative quality of the BW2 and G3 PESs in
regard to the ability to accurately describe the dynamics of both
the exchange and abstraction reactions in the low as well as
high collision energy regimes. The BW2 PES was particularly
successful in reproducing experimental results such as, e.g., the
collision energy dependence of the DCl/HCl branching ratio
for the Cl + HD reaction measured by Liu and co-workers,
which could not be reproduced in QMS calculations on the G3
PES.34 Because of the relatively low collision energies Ec.m
)
0.17-0.35 eV employed, however, only the barrier region and
the entrance valley features of the respective abstraction reaction
pathways on the BW2 and G3 PESs were probed in the latter
studies.
The theoretical excitation functions shown in Figure 6
represent rotationally averaged quantities. To account explicitly
for the experimental conditions of the present work, the reactive
cross-sections were averaged over a room-temperature Boltz-
mann distribution of the DCl reagent rotational levels in the
ground vibrational state.12 As discussed in refs 11 and 12, for
all three PESs employed in the QCT calculations the influence
of DCl reagent rotation on reactivity was found to be relatively
small for all DCl rotational levels significantly populated at room
temperature (see, e.g., Figure 2 in ref 11) resulting in virtually
temperature independent rotationally averaged reaction cross-
section values for Trot(DCl) e 300 K. Hence, a further comparison
of the QCT results with absolute reaction cross-sections obtained
by Polanyi and co-workers (depicted as open circles in Figure
6)16 in experiments with “cold” DCl reagent molecules with a
rotational temperature of ca. 30 K11 is possible. However, as
can be seen in Figure 6, the earlier experimental results, with
values between 0.25 and 0.75 Å2 for the depicted collision
energy range, did not reveal any clear trend in the collision
energy dependence of the exchange reaction cross-section. The
experimental values of ref 16 seem to indicate a moderate
decline of the excitation function for collision energies above
1.0 eV. Such a collision energy dependence of the reaction cross-
section would however be at variance with the QCT excitation
functions, all of which exhibit a strictly monotonic increase from
the reaction threshold to a value of ca. 1 Å2 at a collision energy
of Ec.m. ) 2.25 eV.12 The BW2 cross-sections are slightly larger
than the BW1 ones because of the slightly higher barrier for
the exchange reaction on the latter PES.5 The G3 excitation
function, although qualitatively similar in shape to the excitation
functions obtained on the BW surfaces, is significantly smaller
in absolute value for collision energies above ca. 0.9 eV.
In contrast to the previous experimental results,16 the excita-
tion function obtained in the present study (solid line in Figure
6) exhibits an energy dependence in accordance with theory.
In addition, the experimentally obtained reaction threshold
energy of E0 ) 0.65 ( 0.13 is in good agreement with the joint
theoretical threshold energy of E0 ≈ 0.65 eV reported in ref
12. A detailed inspection of Figure 6 reveals that for low
collision energies (Ec.m. < 1.0 eV) all three PESs yield cross-
sections which agree, within the experimental uncertainty
(represented by the shaded area in Figure 6), with the excitation
function σR(Ec.m.) derived in the present moderated hot H atom
experiments. For collision energies above ca. 1.0 eV, however,
the G3 cross-sections fall below the lower error limit of the
experimental excitation function, while both the BW1 and BW2
cross-sections continue to lie within the experimental error
bounds up to a collision energy of about 1.3 eV. For the highest
collision energies employed in the present experiments, however,
only the BW2 excitation function continues to agree with the
experimental one, demonstrating that within the framework of
Experimental investigations of the abstraction reactions 1 and
3, in which translationally excited H atoms were employed to
study the reaction dynamics in the higher collision energy regime
Ec.m ) 1.0-2.4 eV,12,15-17 yielded reaction cross-sections which
were considerably smaller than the respective reaction cross-
sections obtained in QCT calculations on the BW2 PES.12 In
particular, for the H + DCl f HD + Cl abstraction reaction 3,
the absolute values of the experimental reaction cross-sections
and their collision energy dependence16,17 were found to be in
good agreement with QCT results obtained on the G3 surface,11
which yielded cross-sections that were smaller than the BW2
cross-sections12 by a factor of about 2 (see, e.g., figure 4 of ref
17). A detailed discussion concerning the origin of the large
difference in reactivity observed in the QCT calculations on
the BW2 and G3 PESs at high H + DCl collision energies is
given ref 12, where, e.g., individual high-energy trajectories
were analyzed in combination with R-γ contour plots of the
two PESs (here, R denotes the distance between the incoming
H atom and the center-of-mass of the DCl reactant, and γ is
the Jacobi angle between R and the DCl internuclear distance).
In this empirical analysis, narrow “valleys” in the contour plot
centered at γ ≈ 30°, which are not present in the G3 PES, were
identified as the most probable origin of the too-high reactivity
of the abstraction reaction on the BW2 PES. In addition, it has
been noted that, because of the purely adiabatic character of
the QCT calculations,11,12 nonadiabatic effects, such as the
formation of spin-orbit excited Cl*(2P1/2) atom products via a
Born-Oppenheimer forbidden reactive pathway, which was
experimentally observed in the abstraction reactions 1 and 3 at
higher collision energies,12,17 could not be accounted for. Hence,
the need for more sophisticated reactive scattering calculations
beyond the single-surface approach of ref 12 is clearly obvious
for a more comprehensive description of the dynamical features
of the abstraction reactions. However, considering the recent
efforts undertaken to develop coupled ab initio PESs25 to study
spin-orbit and nonadiabatic effects in the Cl + H2 reac-
tion,21,35,36 it is not unreasonable to expect that multisurface
scattering calculations for the H + HCl/DCl f H2/HD + Cl
abstraction reactions will soon be within reach.
V. Summary
In the present work, a moderated hot H atom pulsed laser
“pump-and-probe” approach, based on a combination of single
collision reaction cross-section, H atom moderation, and non-
equilibrium D atom formation rate measurements,27 was applied
to determine the reaction threshold and a global representation
of the rotationally averaged excitation function σR(Ec.m.) for the

Dynamics of Gas-Phase H Exchange Reaction
J. Phys. Chem. A, Vol. 110, No. 9, 2006 3279
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H + DCl f HCl + D hydrogen atom exchange reaction. In
contrast to the results of previous reaction cross-section
measurements,16 the excitation function obtained in the present
study exhibits an energy dependence in accordance with theory.
Detailed comparison with results of dynamics calculations
performed on three different PESs showed that a single-surface
QCT approach11,12 using the high-quality BW2 ab initio ground-
state PES of Bian and Werner5 can accurately reproduce the
present experimental results, indicating that the exchange
reaction occurs adiabatically on the ground-state PES. The latter
finding contrasts with that of our previous dynamics studies of
the H + HCl/DCl f H2/HD + Cl abstraction reactions,12,17
which demonstrated that for these reactions nonadiabatic (Born-
Oppenheimer forbidden) reactive pathways, leading to the
formation of spin-orbit excited Cl*(2P1/2) products, play a
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Acknowledgment. This work was supported by the Deutsche
Forschungsgemeinschaft (DFG). A.L. was supported by the
Landesgraduierten-Fo¨rderung Baden-Wu¨rttemberg. R.K.V. thanks
DLR Bonn for a fellowship under the Indo-German bilateral
agreement. J.P.M. gratefully acknowledges the financial support
received by the Humboldt foundation through a Humboldt
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