Rate coefficients for photoinitiated NO2 unimolecular decomposition: Energy dependence in the threshold regime

Article abstract of DOI:10.1016/S0009-2614(02)00565-1

Rate coefficients k(E) for photoinitiated NO₂ unimolecular decomposition have been obtained by recording the product NO laser-induced fluorescence signal intensity versus the delay between the pump and probe pulses. A 10 ps pump-probe cross-correlation temporal width provides a useful compromise between time and frequency resolution (3 cm^-1). k(E) increases rapidly: from ～2 × 10¹⁰ to ≥ 1.3 × 10¹¹ s^-1 within 25 cm^-1 of reaction threshold. In this regime, long-range interfragment interactions play an important role. A high level of theory will be needed to reconcile these results.

Full text of DOI:10.1016/S0009-2614(02)00565-1

24 May 2002
Chemical Physics Letters 358 (2002) 71–76
www.elsevier.com/locate/cplett
Rate coefficients for photoinitiated NO2
unimolecular decomposition: energy dependence in
the threshold regime
1
D. Stolyarov, E. Polyakova, I. Bezel , C. Wittig
*
Department of Chemistry, University of Southern California, Los Angeles, CA 90089-1062, USA
Received 10 December 2001; in final form 13 March 2002
Abstract
Rate coefficients kðEÞ for photoinitiated NO2 unimolecular decomposition have been obtained by recording the
product NO laser-induced fluorescence signal intensity versus the delay between the pump and probe pulses. A 10 ps
pump-probe cross-correlation temporal width provides a useful compromise between time and frequency resolution
ð3 cmÀ1Þ. kðEÞ increases rapidly: from ꢀ2 Â 1010 to P1:3 Â 1011 sÀ1 within 25 cmÀ1 of reaction threshold. In this
regime, long-range interfragment interactions play an important role. A high level of theory will be needed to reconcile
these results. Ó 2002 Published by Elsevier Science B.V.
1. Introduction
are barely in excess of a given channel threshold,
the corresponding de Broglie wavelength for in-
terfragment translational motion exceeds any of
the linear dimensions of the molecule’s equilibrium
geometry. Consequently, the transition state (TS)
region for this channel is comparably large, un-
derscoring the need for a fully quantum mechani-
cal treatment of the dynamics.
In consideration of the above, it is inevitable
that properties of the reacting system are sensitive
to the long-range interfragment potential. More-
over, the convergence of potential energy surfaces
(PESs) correlating to the same products at large
values of the interfragment separation (r) needs to
be taken into account, in contrast to the situation
at higher energies and correspondingly smaller r
values. For example, PESs that are repulsive at
short range can be attractive at large r values [3],
The unimolecular decomposition of small
polyatomic molecules via barrierless path ways
continues to present intellectual challenges, with
NO2 being a benchmarksystem for such studies.
The situation is particularly intriguing at energies
(E) that lie just above reaction threshold ðD0 ¼
25128:57 Æ 0:05 cmÀ1 [1,2]), where
a
modest
number of independent reactive channels are en-
ergetically accessible. For example, at energies that
* Corresponding author. Fax: +1-213-746-4945.
E-mail addresses: ilya@xenon.cchem.berkeley.edu (I. Bezel),
wittig@usc.edu (C. Wittig).
1
Present address: Miller Institute for Basic Research in
Science, 2536 Channing Way, Berkeley, CA 94720, USA.
0009-2614/02/$ - see front matter Ó 2002 Published by Elsevier Science B.V.
PII: S0009-2614(02)00565-1

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D. Stolyarov et al. / Chemical Physics Letters 358 (2002) 71–76
thereby contributing to a marked increase in the
molecular density of states (q) in the threshold
regime [4–6]. This singular behavior of q affects
profoundly the reaction rate coefficients.
range part of the potential is eliminated from the
molecular space, thus causing q to decrease [7].
In this Letter, kðEÞ values are presented for the
threshold region: 0 6 E À D0 6 27 cmÀ1. Relative
to our earlier measurements [7], expansion cooling
has been improved markedly (i.e., ꢀ1 K versus ꢀ5
K), thus eliminating uncertainties that arise be-
cause of the occupation of low-lying parent rota-
tional levels. In addition, the temporal width has
been shortened from 25 to 10 ps, thereby im-
proving the accuracy with which the larger rates
can be determined, albeit with a slight loss of
In a previous publication [7], experimental re-
sults were presented in which ‘nearly-microca-
nonical’ (i.e., ꢀ2 cmÀ1 resolution) rate coefficients
kðEÞ for the unimolecular decomposition of ex-
pansion-cooled, photoexcited NO2 molecules were
measured at energies just above D0. It was shown
that kðEÞ increases rapidly, i.e., from ꢀ2 Â 1010 to
P1011 sÀ1 over a range of approximately 17 cmÀ1
.
The smaller kðEÞ values are consistent with spec-
troscopic measurements that have been carried out
just above D0, where some, albeit minimal, spectral
resolution is possible [4,8]. The larger kðEÞ values
are consistent with ultrafast time-domain mea-
surements, in which large laser linewidths (typi-
cally ꢀ30 cmÀ1 FWHM) precluded the possibility
of examining energies that lie just above D0 [9–11].
The NO2 system has provided the only experi-
mental verification to date of the rapid increase of
kðEÞ above its reaction threshold that is antici-
pated for barrierless reactions on the basis of long-
range interactions. In our earlier paper [7], time
and energy resolution were limited by the 25 ps
pump-probe cross-correlation temporal width
(hereafter referred to as the temporal width) and
the pump laser linewidth of ꢀ2 cmÀ1. This en-
spectral resolution (i.e., ꢀ2 cmÀ1 versus 3 cmÀ1
,
respectively). This has also enabled a larger energy
range to be examined. A dramatic increase of kðEÞ
is observed near 25 152 cmÀ1, which is 23 cmÀ1
above D0. These results provide a challenge to
theoretical models, which to date have been able to
rationalize results obtained at higher E (and
therefore smaller r values) by using conventional
statistical theories [12], but have yet to model
quantitatively the threshold regime.
2. Experimental
Much of the experimental arrangement has
been reported previously [7,11]. Referring to Fig.
1a, the ꢀ400 nm pump and 226 nm probe pulses
are obtained by up-converting the outputs of two
distributed feedbackdye lasers (DFDLs). A ꢀ30
ps Nd:YAG laser (EXPLA PL2143C) served as
the pump source for the DFDLs and amplifiers
and provided 1064 and 355 nm pulses for fre-
quency mixing. The cross-correlation of the pump
and probe pulses was measured simultaneously
with the signal by generating a difference fre-
quency (near 524 nm) in a BBO crystal. These
cross-correlation scans were used in the fitting
routine, which has been described elsewhere [11].
The changes to the laser system are summarized
here. First, the optical scheme of the Nd:YAG
laser was altered in order to shorten its pulses. As a
result, the pump-probe cross-correlation temporal
width decreased from 25 to 10 ps. Because of a
concomitant loss of energy, side-pumped dye cells
were introduced into the pump and probe
branches. The 5 mm BBO crystal used for the
abled the smallest kðEÞ values (i.e., ꢀ2 Â 1010 sÀ1
Þ
to be measured with acceptable accuracy. How-
ever, because of the 25 ps temporal width, these
measurements provided only rough estimates for
kðEÞ values that are comparable to the inverse of
the temporal width. Consequently, a lower bound
was recommended for kðEÞ values P1011 sÀ1
.
The manner in which the molecular density of
states enters transition state theory (TST) models
(e.g., RRKM theory) requires that regions are
identified as the molecular, TS, and product spaces
[12]. The location of the TS region along the re-
action coordinate depends on E, and this depen-
dence can be strong for barrierless reactions. In
this case, the reaction rate coefficient per open
channel excluding tunneling ð1=hq) can be said to
increase with E from a TST perspective. Namely,
as the TS region moves to smaller r, the portion of
the phase space volume that is due to the long-

D. Stolyarov et al. / Chemical Physics Letters 358 (2002) 71–76
73
Fig. 2. Rotational temperatures are determined by using LIF of
the NO2 absorption feature near 522 nm. The upper trace was
recorded under conditions similar to those used previously [7].
The lower trace is representative of the conditions used in the
workreported herein.
fication in the dye cell) was measured because the
wavemeter is more accurate at longer wavelengths.
The pump pulse spectral width was found to be
approximately 3 cmÀ1
.
The pump-probe scenario is presented in Fig.
1b. In our previous measurements, expansion-
cooled samples (0.6% NO2 in He at 3 bar) had
rotational temperatures (Trot) of ꢀ5 K [7]. Thus,
several low-lying rotational levels were occupied.
Rotational temperatures of ꢀ1 K have been
achieved in the workreported here by using 0.02%
NO2 in Ne at 7 bar. Laser-induced fluorescence
(LIF) near 522 nm was used to obtain rotational
temperatures (Fig. 2); a spectrum was recorded
prior to starting rate coefficient measurements at
each new pump wavelength, and the expansion
conditions were held constant throughout the en-
suing experiment. NO2 samples (Matheson,
99.5%) were purified prior to each set of experi-
ments by bubbling O2 through cooled liquid NO2
samples.
Fig. 1. (a) Schematic diagram of the experimental arrangement.
Acronyms are defined as follows: DFDL – distributed feedback
dye laser; DYE – dye amplifier; OPA – optical parametric
amplifier; R – sum frequency generation; PD – photodiode;
DFG – difference frequency generation; PMT – photomultiplier
tube. (b) Photoinitiated NO2 unimolecular decomposition is
monitored by detecting the NO product via A2Rþ X2P1=2
LIF as the pump-probe delay is varied. The excited 2B2 and
ground 2A1 electronic states of NO2 are strongly mixed, re-
sulting in vibronic manifolds having A1 and B2 symmetries,
which only interact via rotation.
cross-correlation measurements was replaced with
a 0.5 mm one in order to improve the temporal
resolution of the cross-correlator. Frequency drift
of the DFDLs [7] was minimized by careful ad-
justment of an active temperature stabilization
system. Frequency measurements of the pump
pulse were carried out by using a wavemeter
(Burleigh WA-4500) calibrated by using its inter-
nal He–Ne laser. The DFDL output (after ampli-
3. Results
Fig. 3 shows typical data (open circles) of LIF
signal intensity versus pump-probe delay, sdelay, for

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D. Stolyarov et al. / Chemical Physics Letters 358 (2002) 71–76
molecular response, whose convolution with the
cross-correlation yields the observed signal, is as-
sumed to be proportional to 1 À expfÀt=sriseg. The
srise values are obtained by using the fitting pro-
cedure that has been described previously [11],
which yields the solid-line fits to the data shownÀin1
Fig. 3. The kðEÞ values are taken to be the srise
values. The rapid increase of kðEÞ with E
throughout this modest energy range is striking.
Fig. 4 shows kðEÞ for E values that range from
the reaction threshold to 25 155 cmÀ1. A steady
increase is observed, albeit with point-to-point
fluctuations that increase with E. The smallest srise
values extracted from the fits are smaller than the
ꢀ10 ps cross-correlation widths, and therefore are
Fig. 3. Typical data showing LIF signal intensity (open circles)
versus pump-probe delay. The srise values were obtained by
fitting the data to a single exponential rise [11]. The corre-
sponding cross-correlations are shown as thin solid lines. Note
the pronounced variation of the srise values with E.
Fig. 4. (a) Rate coefficient versus E for the threshold regime.
(b) The result of three-point smoothing of the data in (a).
Vertical dashed lines indicate D0. At the largest E values, the
srise values are too small to be reliable. A lower bound of
1:3 Â 1011 is assigned to the corresponding rates; see text for
details.
four different values of the ‘center energies’ of the
pump-laser photons. The pump-probe cross-cor-
relations are shown as the thin solid traces. The

D. Stolyarov et al. / Chemical Physics Letters 358 (2002) 71–76
75
of insufficient accuracy. Thus, referring to Fig. 4,
the rate measurements at the largest E values are
assumed to yield a lower bound of 1:3 Â 1011,
which is obtained by averaging the srise values and
then taking the inverse. This is indicated by the
boxed region and the thickarrow, which denotes
k P 1:3 Â 1011. Likewise, large point-to-point
fluctuations between 25 145 and 25 150 cmÀ1 are
attributed mainly to the inability to uniquely de-
convolute the data. In addition, if the density of
molecular states decreases, as discussed below,
fluctuations may also occur because a modest
number of resonances are excited by the 3 cmÀ1
pump pulse. For example, if the extrapolated
vibronic density of states of 0.4 cmÀ1 is used [5,13],
the 3 cmÀ1 pump beam excites only a few reso-
nances, in which case fluctuations are inevitable.
The quality of the experimental data does not
support a multi-exponential fit. In Fig. 4b, the data
have been subjected to a three-point smoothing
routine. The results shown in Fig. 4 are in agreement
with those reported previously [7], with account
taken of the different rotational temperatures.
which is an order of magnitude larger than the
smallest rates reported here. A reconciliation of
the small kðEÞ values reported here for energies of
several cmÀ1 above D0 and the 1:6 Â 1011 sÀ1 value
reported earlier, requires that a dramatic increase
of kðEÞ occurs with increasing E. Indeed, this is
observed.
In the statistical theory of unimolecular de-
composition, the rate for each independent open
channel is given by 1=hq when tunneling is unim-
portant, as is the case for barrierless reactions,
where q is the density of strongly coupled molecular
states that participate in the reaction [12]. When
using this expression, it has generally been assumed
that q remains approximately constant over mod-
est energy intervals, such as the tens of cmÀ1 en-
countered in the workreported herein. For
barrierless reactions, however, the molecular and
product regions are separated by a TS region
whose location along the reaction coordinate varies
strongly with E in the threshold region of each
open channel. Thus, q can be a function of the
location of the TS, and consequently q can have a
significant energy dependence near threshold.
In this regime, the use of conventional TST to
describe variations of the rate must be questioned.
Indeed, even the definition of the average rate in
such systems is subjective, because it depends on
the energy interval over which the rates are aver-
aged. In the context of NO2 decomposition [7], it
has been argued that the couplings that occur at
large interfragment separation should be ‘counted’
in the molecular space for E values that are barely
in excess of D0 but in the product space for higher
E values. Thus, the corresponding density of mo-
lecular states can change with E, even if the
number of open channels does not. Such com-
plexity of the coupling hierarchy and the rapid
energy variation of the definition of the molecular
phase space lies beyond the use of statistical the-
ories or classical approaches to calculate reaction
rates. Though qualitative insight can be gained,
there is limited value in manipulating these models
in order to fit data. Quantum mechanical calcula-
tions that include the participation of multiple
PESs are likely to yield results that provide the
best insights into how these threshold reactions
occur.
4. Discussion
The data presented in Fig. 4 show that for ex-
pansion-cooled, photoexcited NO2, kðEÞ increases
by an order of magnitude over a modest energy
interval of ꢀ20 cmÀ1 above D0. The small k values
obtained when E is slightly in excess of D0 (i.e.,
ꢀ2 Â 1010 sÀ1Þ can be rationalized on the basis of
long-range interactions that play a role in the
threshold regime, as discussed previously [7].
These interactions account for the rate coefficients
being an order of magnitude smaller than those
calculated on the basis of an extrapolation of the
density of states [13,14].
The laser linewidth of 3 cmÀ1 used in the work
reported here averages over a number of reso-
nances, thereby lessening the fluctuations of the
observed rates that arise as a consequence of the
quantum-chaotic nature of the intramolecular
dynamics. Earlier studies that have used ultrafast
pulses whose linewidths are ꢀ30 cmÀ1 have yiel-
ded energy-averaged rate coefficients of approxi-
mately 1:6 Â 1011 sÀ1 in the threshold region [9],

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D. Stolyarov et al. / Chemical Physics Letters 358 (2002) 71–76
5. Summary
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