Specific rate constants k(E,J) for the dissociation of NO2. I. Time-resolved study of rotational dependencies

Article abstract of DOI:10.1063/1.1398305

The effect of rotational excitation was investigated on the specific rate constant of the unimolecular decomposition of NO₂. NO₂ molecules with rotational and vibrational energy distributions were optically excited near and above the

Full text of DOI:10.1063/1.1398305

Specific rate constants k(E,J) for the dissociation of NO 2 . I. Time-resolved study of
rotational dependencies
B. Abel, B. Kirmse, J. Troe, and D. Schwarzer
Citation: The Journal of Chemical Physics 115, 6522 (2001); doi: 10.1063/1.1398305
View online: http://dx.doi.org/10.1063/1.1398305
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 115, NUMBER 14
8 OCTOBER 2001
Specific rate constants k„E,J… for the dissociation of NO2.
I. Time-resolved study of rotational dependencies
B. Abel,a) B. Kirmse, and J. Troe
¨
¨
¨
¨
Institut fur Physikalische Chemie, Universitat Gottingen, Tammannstrasse 6, D-37077 Gottingen, Germany
D. Schwarzer
¨
¨
Max-Planck-Institut fur biophysikalische Chemie, Am Fassberg 11, D-37077 Gottingen, Germany
͑Received 22 January 2001; accepted 9 July 2001͒
The effect of rotational excitation on the specific rate constants k(E,J) of the unimolecular
decomposion of NO2 has been investigated. Time-resolved pump- and probe experiments with
sub-ps time resolution are reported in which NO2 molecules with well-defined rotational and
vibrational energy distributions were optically excited near and above the dissociation threshold.
The subsequent unimolecular decay of the reacting NO2 molecules was probed by time-resolved
laser-induced fluorescence of the disappearing NO2 via excitation to Rydberg states. At constant
photolysis wavelength, increasing rotational energy ͑up to 310 cmϪ1͒ was found to leave the overall
decay rate nearly unaffected. This observation can be rationalized by assuming a compensation of
the angular momentum and energy dependences of the specific rate constants when J and E are
changed at the same time. Keeping the total energy E nearly constant and changing J independently,
the effect of rotation on the decay rate can be separated and observed more clearly. From the
experimental data we conclude that, for sufficiently high J and constant total energy, molecules with
larger J dissociate more slowly than molecules with small J, which is in agreement with predictions
from statistical unimolecular rate theory. © 2001 American Institute of Physics.
͓DOI: 10.1063/1.1398305͔
I. INTRODUCTION
probe photofragment spectroscopy allowed for a time-
resolved investigation of the dissociation dynamics of
NO2.19–23 At energies high above the dissociation threshold,
the lifetime of excited NO2 is faster than the rotational pe-
riod, such that information about excited-state dynamics
could also be obtained from measurements of product angu-
lar distributions and of alignments of the rotational angular
momentum with respect to the fragment recoil velocity.24
The large number of experimental observations makes
NO2 an attractive system for examining theoretical models.
Potential energy surfaces ͑PES͒ have been calculated on
various levels of accuracy.25–30 In addition to statistical cal-
culations on parametrized potentials,6,9 and ab initio
PES’s,27,31–33 also full 3-D quantum mechanical calculations
of resonance spectra were reported for Jϭ0.33 The conclu-
sion from the earliest work,6,9 that near-statistical behavior
can be assumed for NO2 on average, was confirmed in the
recent experimental and theoretical studies. However, on a
more state-resolved level, a variety of complications arise.
Experimental, as well as theoretical work, provides evidence
for more state-specific properties of the dissociation rate be-
yond the E- and J-dependence accounted for by statistical
theories. On a microscopic level, the dissociation appears to
be inherently related to specific resonance states whose
widths show fluctuations around average values which, how-
ever, are related to the specific rate constants from statistical
theories ͑for more details see Refs. 31–34͒.
The unimolecular dissociation/recombination reaction
NO2⇔OϩNO has played an important role in the develop-
ment of unimolecular rate theory. Early studies of the pres-
sure dependence of the thermal unimolecular dissociation/
recombination reaction and of the wavelength dependence of
Stern–Volmer plots for photolysis quenching led to first es-
timates of the specific rate constants k(E) of dissociation.1–4
Although being indirect and only derived by calibration
against collision frequencies, the specific rate constants ap-
peared to follow the predictions from statistical unimolecular
rate theory.5,6 At the same time, first photofragment spectra
of NO2 photolysis were obtained7,8 which, however, were
more difficult to reconcile with statistical unimolecular rate
theory.5,6,9
It is not surprising that NO2 dissociation studies experi-
enced a renaissance when direct state- and time-resolving
experimental techniques became available. The question
arose whether the earlier conclusions about statistical behav-
ior of the unimolecular dissociation would still hold on a
more detailed level. A number of groups determined kinetic
energy distributions of the fragments,10 product state
distributions,11,12 photofragment excitation spectra,13,14 zero
kinetic energy photo-fragment spectra,15 transient grating
spectra,16,17 and double resonance spectra of excited NO2
close to the dissociation threshold.18 Picosecond pump-and-
Besides the general question of near-statistical or non-
statistical behavior, the influence of rotation on the dissocia-
tion rate is of interest.35–37 One asks again whether the rota-
a͒
Author to whom correspondence should be addressed. Electronic mail:
babel@gwdg.de
0021-9606/2001/115(14)/6522/9/$18.00
6522
© 2001 American Institute of Physics
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6523
J. Chem. Phys., Vol. 115, No. 14, 8 October 2001
k(E,J) for the dissociation of NO2. I
tional dependence of the specific rate constants follows
statistical predictions or is of different character.38,39 Much
work has been done on the quantum yield of photodissocia-
tion at wavelengths larger than the photodissociation thresh-
old. It was shown that rotational energy of the molecule is
available for the dissociation process.2–4,14,40,41 These find-
ings, however, do not provide quantitative information about
the rates of rotationally excited molecules in comparison to
nonrotating molecules.
At present, a large body of data is available for the pho-
todissociation of jet-cooled ͑almost͒ nonrotating NO2 mol-
ecules, while much less is known about the dependence of
the dissociation rates on rotation. There are two alternatives
for studying the effects of rotation in the time domain: Time-
resolved double-resonance experiments with state-resolution
or time-resolved experiments with well-characterized rovi-
brational ensembles distributions. Time-resolved double-
resonance ps pump-and-probe spectroscopy was recently ap-
plied by Wittig and co-workers.22,23 A series of rotationally
resolved decomposition experiments with time-resolved de-
tection of the forming NO was made, in which J was varied,
while the quantum number K was kept close to zero. Infrared
pre-excitation of NO2 was achieved by employing a high
resolution optical parametric oscillator for pre-excitation
prior to ps-excitation and subsequent decomposition of the
molecules. With this technique the rotational quantum num-
ber of dissociating molecules was well-defined without,
however, being able to have full energy resolution of the
excited molecules. In addition, the range of accessible J- and
K-values was limited for experimental reasons. It was found
that the dependence of the dissociation rates on J is small in
the investigated range of J- and K-values, which was attrib-
uted to full or partial conservation of the projection of J onto
the molecular axis, i.e., to K-conservation.
In the present article we describe an alternative experi-
mental approach in which we study rotational effects by
monitoring the decay of well-defined broader rotational dis-
tributions of NO2 in time-resolved subpicosecond experi-
ments. The rotational temperatures in the experiments of this
work were characterized spectroscopically. Although com-
plete J-resolution was sacrificed, a broad range of J- and
K-values could be accessed such that larger effects of mo-
lecular rotation on the lifetimes could be detected. The ex-
tension of the range beyond that accessible in Ref. 23 ap-
peared important because only small effects were detected
over the range of J-values between 1 and 15 at Kϭ0.23 In
addition, it appeared of interest to measure the decay of the
parent NO2 molecules instead of the formation of the product
NO. In this way multi-exponential decays of NO2 could be
identified over a broad range of rotational energies, total en-
ergies, and excitation energies which was not possible in
Refs. 22 and 23. The present work, therefore, complements
the J-resolved experiments from Ref. 23.
FIG. 1. Pump-and-probe level scheme of the present experiments. The
excited-state dynamics can be probed via laser-induced fluorescence and ion
detection.
we compare these results with more detailed quantum-
statistical adiabatic channel calculations.32
II. EXPERIMENTAL TECHNIQUE
A. Pump-and-probe level scheme
The level scheme of our pump-and-probe experiments is
illustrated in Fig. 1. The pump pulse excites either jet-cooled
molecules or molecules from a thermal ensemble in a static
cell at 300 K, to states slightly below, slightly above, or far
above the dissociation threshold. With this one-photon exci-
tation, mixed states are accessible which are a composition
of two zeroth order excited doublet states of 2A1 , and
2B2 electronic symmetry, which result from the well known
conical intersection of the corresponding electronic
surfaces.18,42–47 After the molecules have been excited above
their dissociation threshold, they dissociate and form the
products NO(2⌸⍀) and O(3Pj).
In contrast to the detection of the formation of NO,19–23
we detect the parent molecule by probing highly excited NO2
such as explained by Fig. 1. We use a near UV-laser pulse at
310 nm which further excites the molecules from the initially
ϩ
ϩ
2
2
reached energy to the ⌸g and ⌺u Rydberg states near to
54 000–56 000 cmϪ1. We finally detect laser-induced fluo-
rescence from these Rydberg states at wavelengths below
320 nm. The properties of these emitting states have been
investigated in Refs. 48 and 49. Although only ionization
was reported there, we also detected fluorescence from these
states in the UV spectral range. The observed fluorescence
allowed us to monitor the excited-state population of NO2
during the experiment. In one experiment reported here ͑see
Sec. III, 310 nm excitation͒ laser-induced ionization of ex-
cited NO2 was detected in a small quadrupole mass spec-
The present article ͑Part I͒ will be followed by an inves-
tigation of rotational influences on linewidths in the NO2
spectrum near to the photolysis threshold ͑Part II͒ which
again provides experimental information on k(E,J).34 Part
III of this series describes a detailed statistical theory for
k(E,J) employing classical trajectories,31 whereas in Part IV,
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6524
J. Chem. Phys., Vol. 115, No. 14, 8 October 2001
Abel et al.
wavelengths. One has to ask whether the same states are
probed as reached by the pump pulse. It is known that laser
pulses can coherently excite zeroth order bright states which
are not eigenstates but time-dependent linear combinations
of eigenstates of the molecule. In NO2 the situation is par-
2
2
ticularly complex because mixing of the B2 and A1Ϫ elec-
tronic states43–46 precedes intramolecular vibrational energy
redistribution ͑IVR͒. However, it is also known that the time
2
of mixing of the B2-state with the highly vibrationally ex-
cited 2A1 ground state in NO2 is well below 100 fs such that
the time scale for state mixing and IVR in our experiments
can be expected to always be below the cross-correlation
time of the two laser pulses and, thus, the time resolution of
the laser system. During the excitation pulse, therefore, cou-
pling of the zeroth order electronic states and IVR can be
considered to be complete such that quasieigenstates of the
molecule are populated and subsequently probed. The depen-
dence of the signals on the laser power has been controlled in
all experiments in order to avoid multiphoton processes. In
all cases the measured signals depended linearly on the en-
ergy of the pump and of the probe laser pulses. The time
resolution of the system was found to depend strongly on the
excitation wavelength. It varied between 180 and 650 fs
cross-correlation times. Most of our measurements were per-
formed with a time resolution of about 600 fs, which was
found to be sufficient for measurements at excitation ener-
gies up to 1000 cmϪ1 above the dissociation threshold where
NO2 lifetimes are longer than 1 ps.
B. Experimental setup
The used experimental setup is presented schematically
in Fig. 3. The required light pulses were generated by a laser
system employing an argon–ion laser ͑Lexel 3800-8͒-
pumped colliding-pulse mode-locked dye laser system. Its
output pulses at a wavelength of 620 nm were amplified at
20 Hz in a three stage dye amplifier which was pumped by a
frequency-doubled injection-seeded Nd:YAG laser ͑532 nm,
60 mJ, Continuum 8020͒. The details of this amplifier have
been described in Ref. 50. After recompression, the pulse
width was less than 100 fs at energies of about 100–200 ␮J,
pulse intensity fluctuations were about 5%. The pulses were
split into two parts of equal energy. One beam was focused
into a 0.3 mm type I KDP crystal with a lens of 500 mm
focal length generating frequency-doubled laser pulses at
the probe wavelength 310 nm. Typical pulse energies were
15 ␮J. The other beam was focused into a 1 cm water cell
generating a white light continuum. By means of interference
filters ͑bandwidth Ϸ5 nm͒ the desired pump wavelength at
370–420 nm was selected and subsequently amplified in a
three-stage dye amplifier which was transversely pumped by
the third harmonics of the Nd:YAG laser ͑355 nm, 50 mJ͒;
pulse energies of 30–50 ␮J with fluctuations of 15% were
generated. During the experiment the cross-correlation and
the zero delay could be measured via difference frequency
generation in a thin BBO crystal ͓Fig. 2͑a͔͒; the spectra of
the pump and probe pulses were recorded routinely with a
spectrograph equipped with a CCD array detector. The mea-
FIG. 2. Characterization of the pump-and-probe pulses. a͒ ͑Fitted͒ Cross-
correlation which shows the time resolution of the system. b͒ Fitted enve-
lope of the spectrum of the excitation pulse. c͒ Laser-induced fluorescence
of NO2 as a function of the delay between pump-and-probe laser pulses
͑pump pulses at 420 nm prepare molecules below the dissociation threshold;
probe pulses at 310 nm induce the fluorescence͒. This trace represents the
‘‘experimental’’ integral of the experimental cross-correlation in Fig. 2͑a͒.
trometer, attached to the vacuum chamber. Such experiments
will be described elsewhere. In the given scheme, molecules
also can be detected which do not dissociate; if the wave-
length of the pump laser is tuned to values, where molecules
are excited to energies below the dissociation threshold, a
signal is recorded which does not decay. This corresponds to
the situation and experimental conditions illustrated in Fig.
2: The cross-correlation of the pump and probe pulses is
displayed in Fig. 2͑a͒ whereas the spectral width of the ex-
citation pulse is shown in Fig. 2͑b͒. An experiment using a
420 nm-pump and 310 nm-probe pulse is shown in Fig. 2͑c͒.
The Franck–Condon factors for the pumped and probed
states have been found to be similar over a broad range of
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6525
J. Chem. Phys., Vol. 115, No. 14, 8 October 2001
k(E,J) for the dissociation of NO2. I
FIG. 3. Schematic experimental set up.
sured spectral width for the employed pulses typically was
210 cmϪ1 ͑FWHM͒ which is slightly larger than the Fourier
limit for 600 fs laser pulses.
time fluctuations of these resonances can give rise to nonex-
ponential time profiles of the detected signals. These can
only be analyzed by convoluting theoretically calculated life-
time distributions with the experimental pump- and probe-
properties. Agreement between measured and simulated sig-
nals then is taken as an indication for the correctness of the
analysis. We have succeeded to provide this internally con-
sistent analysis for jet-cooled NO2 near 2 K in Ref. 33. In the
following, we use these low temperature experiments as a
reference for comparison with our present experiments at
higher rotational temperatures and with the low temperature
experiments from Refs. 20 and 22.
After passing a computer-controlled delay stage, the
pump pulses were focused by a quartz lens of 350 mm focal
length into a vacuum chamber. The probe pulses were inde-
pendently focused with a 200 mm quartz lens. Finally, the
pump and probe pulses were combined with a dichroic mir-
ror such that they overlapped in the central part of the ther-
mal reaction cell on the vacuum chamber containing the jet.
The vacuum chamber was equipped with a pulsed nozzle of
400 ␮m diameter ͑General Valve, IOTA I͒ and a LIF f1.2
optics collecting the fluorescence light with
a
Besides the nonexponentialities arising from lifetime
fluctuations, broader rotational and energy distributions may
also add contributions to nonexponential time-profiles of the
observed signals, because the specific rate constants k(E,J)
markedly depend on the energy E and the angular momen-
tum ͑quantum number J͒. The variations of the time-resolved
traces as a function of average angular momentum is the
topic of the present article. It would be desirable to measure
and to resolve k(E,J) directly. Due to the bandwidth of our
ultrashort laser pulses and the broad excited-state distribu-
tions, in this type of experiment we obtain signals that rep-
resent complicated convolutions of individual resonance de-
cays ͑in the quantum mechanical picture͒ or rate constants
k(E,J) ͑in the language of statistical theories͒. However, a
deconvolution is, in any case, not feasible. Instead, theoreti-
cal k(E,J) have to be generated, convoluted with the life-
time distributions as well as with the rotational distributions
and the experimental resolution, before the simulated signal
can finally be compared with experimental signal. The agree-
ment between experiment and simulation then provides evi-
dence for the correctness of the employed ‘‘theoretical’’
k(E,J). Note, even a correctly averaged rate constant has to
be derived this way ͑see Sec. III C͒. While lifetime fluctua-
tions were theoretically derived from quantum mechanical
calculations for Jϭ0 in Ref. 33, similar quantum mechanical
calculations are not yet available for larger J. However, the
monochromator/solar blind photomultiplier tube combina-
tion ͑Hamamatsu, R166͒. Mixtures of 1–3% NO2 in argon
with stagnation pressures between 1 and 2 bar and back-
ground pressures around 10Ϫ4 mbar were used in the free jet
expansion experiments. The expansion conditions could be
varied to produce NO2 molecules with rotational tempera-
tures between 2 and 70 K such as determined by additional
LIF experiments employing high resolution lasers. Alterna-
tively, a small vacuum chamber was filled with about 1 mbar
of NO2 at room temperature. Whereas at 2 K only the two
lowest 2 rotational levels of the NO2 vibrational ground state
are noticeably populated, at 300 K a broad distribution with
J Ϸ20 is present. The population of the first excited vibra-
͗ ͘
tional level at room temperature is only small. Fluorescence
signals from the photomultiplier were integrated, digitized
͑Data-Translation, DT2821-G-16SE͒, and processed with a
personal computer. Pump- and probe-laser energies were al-
ways recorded.
III. RESULTS AND DISCUSSION
In time-resolved experiments employing ultra-short laser
pulses, NO2 dissociation can be followed directly in the time
domain. A principal drawback is, however, that short light
pulses have spectral widths which cover large numbers of
decaying resonances ͑see Sec. III A and Ref. 33͒. The life-
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6526
J. Chem. Phys., Vol. 115, No. 14, 8 October 2001
Abel et al.
calculations for Jϭ0 on average were shown to coincide
reasonably well with statistical theory. Therefore, statistical
theory is used to calculate the dependence of k(E,J) on E
and J and to predict rotational effects. The comparison with
the results from Sec. III B and III C then controls the pre-
dictions of statistical theory.
A. Reference experiments near 2 K
In Ref. 33 we have compared photodissociation experi-
ments of jet-cooled NO2 molecules at about 2 K with quan-
tum mechanical calculations for Jϭ0 which were based on a
global ab initio potential energy surface. In the present ar-
ticle we use these data as a reference for comparison with
time-resolved experiments in which broader rotational distri-
butions have been investigated. Before looking at our experi-
ments with broader J-distributions, we note that the experi-
mental data at about 2 K not only match the quantum
mechanical calculations from Ref. 33, but are also consistent
with data from Refs. 20 and 22. In order to make this point
clearer, we take the distribution of resonances from Ref. 33
and predict ‘‘experimental’’ population-time profiles S(t) via
the relation
2
S t͒ϭ
͑
͉
An
͉
•exp Ϫ⌫ t/ប͒,
͑1͒
͑
͚
n
n
with
2
2
2ϭ
͉
an
͉
exp Ϫ␣ EϪE ͒ ͒,
͑2͒
¯
͉
An
͉
͑
͑
n
¯
which accounts for the spectral widths of the laser pulse ͑E is
the center wavelength, ␣ is related to the bandwidth of the
laser pulse, ⌫n is the width of the resonance n, and an is
related to the intensity of the transitions which was assumed
to be equal for all states͒ and the vibrational Franck–Condon
͑FC͒ factors. Since we very likely approach saturation in the
excitation step the assumption of equal FC-factors appears to
be justified. In addition, we have studied the impact of this
approximation and found that ͑random͒ variations in the
An-coefficients with the correct average value did not signifi-
cantly degrade the fit as long as the variations were not too
large. Finally, the theoretical decay curves have been convo-
luted with the time resolution of the experimental system
which is characterized by the normalized cross-correlation
function of the two laser pulses
FIG. 4. a͒ LIF signal of NO2 after excitation at 398 nm ͑TϷ2 K, open
circlesϭexperimental points; dashed line: Simulation with convolution of
lifetime distribution and experimental resolution, see text͒. b͒ As a͒ but with
excitation at 396 nm.
Ref. 20͔. In these experiments the formation of NO after near
UV excitation ͑380–400 nm͒ has been monitored with pico-
second time resolution by Wittig et al. For these experimen-
tal conditions, we used Eqs. ͑1–3͒, added white noise to the
simulation, which is proportional to the signal amplitude,
and simulated NO-formation for these experiments. Figure 5
gives the results. The upper panel corresponds to an average
excess energy of about 18 cmϪ1 ͑rotational quantum number
NЈϭ1͒, a laser pulse bandwidth of ⌬␯ϭ30 cmϪ1, and a laser
pulse length of 1.6 ps ͑FWHM͒. The bandwidth of the laser
pulse and the distribution of resonances are shown in the
ϱ
2
˜ ˜
S t͒/S t͒
ϭ
max
S ␶͒exp Ϫ␦ tϪ␶͒ d␶.
͑3͒
͑
͑
͑
͓
͑
͔
͵
insert of Fig. 5͑a͒. The full line ͑
͒ in Fig. 5 is a single
0
exponential fit to the simulated data points ͑᭺͒. The fitted
single-exponential rise time of ␶ϭ5 ps is in excellent agree-
ment with the results from the fit of the experimental data
given in Ref. 22. A simulation ͑᭺͒ and a single exponential
The Gaussian in Eq. ͑3͒ is fitted to the cross-correlation func-
tion of the particular experiment. With this procedure time
profiles are generated without adjustable parameters. A com-
parison of a theoretical prediction and our present experi-
mental results for two excitation wavelengths 398 and 396
nm is shown in Fig. 4. The agreement between experiment
and theory is very good. With the same procedure ‘‘experi-
mental’’ results with quite different time resolutions and laser
parameters for NO2 decay as well as for NO-formation ͓re-
placing exp(Ϫ⌫n t/ប) by 1Ϫexp(Ϫ⌫nt/ប) in Eq. 1͔ can be
predicted. We demonstrate the latter for two experiments
from Refs. 20 and 22 ͓Fig. 2͑b͒ of Ref. 22 and Fig. 4͑c͒ of
fit ͑
͒ for a higher excitation energy is given in Fig. 5͑b͒
͓to be compared with Fig. 4͑c͒ of Ref. 20͔ corresponding to
an excitation wavelength of 396.54 nm, a laser pulse band-
width of ⌬␭ϭ0.5 nm, and a pulse length of 1.4 ps. Our fitted
single-exponential rise time of 3.5 ps to the modeled ͑pre-
dicted͒ NO-signal ͑᭺͒ again is in excellent agreement with
the fit to the experimental data in Ref. 20. This procedure
shows that the experiments from Wittig’s and our laborato-
ries are consistent and agree quantitatively with the quantum
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6527
J. Chem. Phys., Vol. 115, No. 14, 8 October 2001
k(E,J) for the dissociation of NO2. I
FIG. 6. Rotational distributions of NO at 65 K ( E ϭ68 cmϪ1) and at 300
͗
͘
2
K ( E ϭ313 cmϪ1), respectively, which have been normalized to their
͗
͘
maximum amplitude for clarity ͑not to const. area͒. Also shown is the spec-
tral band width of the laser pulse used in the present experiments. See the
text for more details.
lengths, when practically all molecules dissociate ͓signal of
Fig. 7͑c͔͒, the time dependence does not show a major influ-
ence of rotational energy. This agrees with the observations
from Wittig’s group.20,22,23
FIG. 5. Simulation ͑᭺͒ of NO formation in NO2 photolysis for the experi-
mental conditions given in Ref. 20, 22 and single exponential fit ͑
͒ to
the simulation. Upper trace: 18 cmϪ1 in excess of the dissociation energy
E0 ; lower trace: 87 cmϪ1 in excess of E0 . Inserts: Calculated fluctuating
rate constants ͑full circles͒ from Ref. 33 and spectral distributions of the
excitation pulses.20,22 For details of the simulation, see text.
mechanical calculations from Ref. 33. However, the nonex-
ponential character of the time profiles, which is due to the
marked lifetime fluctuations shown in the inserts of Fig. 5, is
obviously detected more easily in our NO2 profiles than this
is possible in Wittig’s NO signals.
B. Experiments at 65 and 300 K with constant
excitation wavelengths
In this section, experiments at constant excitation wave-
length are reported for rotational distributions corresponding
to 65 and 300 K and compared with those for 2 K. The
rotational temperature in the jet experiments was determined
spectroscopically via standard LIF of jet-cooled NO2 in the
spectral range near to 585 nm such as elaborated in Ref. 51
Rotational energy distributions are compared with the spec-
tral distribution of the excitation laser in Fig. 6. The shown
rotational distributions and the excitation laser bandwidth
͑causing a significant energy distribution of the reacting mol-
ecules͒ have to be further convoluted with k(E,J) from Ref.
31 when a comparison with experiments is made. Figure 7
shows experimental signals at three different excitation
wavelengths and three temperatures, namely 2 K, 65 K with
E Ϸ68 cmϪ1(JmaxϷ6, J Ϸ9) and 300
K
with E
͗ ͘
͗ ͘
͗ ͘
ϭ313 cmϪ1(JmaxϷ15, J ϭ20). Figure 7 indicates that the
FIG. 7. LIF signals from NO2 for various excitation conditions. a͒ Excita-
tion at 398 nm; NO2 temperatures: 2 K ͑filled circles͒, 65 K ͑open dia-
monds͒, and 300 K ͑open circles͒. b͒ Excitation at 396 nm; NO2 tempera-
tures: 2 K ͑filled circles͒, 65 K ͑open diamonds͒, and 300 K ͑open circles͒.
c͒ Excitation at 383 nm; NO2 temperatures: 2 K ͑filled circles͒, 65 K ͑open
diamonds͒, and 300 K ͑open circles͒.
͗ ͘
time profile does not change significantly when the total en-
ergy is increased by increasing rotational energy. However,
near to threshold the fraction of nondissociating molecules
decreases with increasing rotational energy. At shorter wave-
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6528
J. Chem. Phys., Vol. 115, No. 14, 8 October 2001
Abel et al.
FIG. 8. LIF signals from NO2 after various excitations. a͒ Excitation at 398
nm and Tϭ300 K ͑open circles͒; excitation at 396 nm and Tϭ2 K ͑filled
circles͒; excitation at 396 nm and Tϭ300 K ͑open diamonds͒ with average
energies of 25 438, 25 253, and 25 565 cmϪ1, respectively. b͒ Energy distri-
butions corresponding to the three experiments form a͒. Note, for clarity the
distributions have been normalized to their maximum amplitude and not to
constant area. See the text for further details.
FIG. 9. Specific rate constants k(E,J) for NO2 dissociation. ᭺: J Ϸ0;
͗ ͘
᭿: J Ϸ10; ᮀ: J Ϸ20; ᭢: High energy decomposition k(E) for rotation-
͗ ͘ ͗ ͘
ally cold NO2(TϷ2 K) for excitation at 310 nm ͑this work͒. ¯ϫ¯: Rate
coefficients for jet-cooled NO2 from Ref. 20 ᭝: Rotationally resolved rate
constants with Eϭ10 cmϪ1ϩBN͑Nϩ1͒ from Ref. 23. ࡗ: Rotationally re-
solved rate constants with Eϭ75 cmϪ1ϩBN͑Nϩ1͒ from Ref. 23. E repre-
sents the sum of the vibrational and rotational energy of the reacting NO2
molecules, averaged over the experimental distribution of excited states.
Numbers in the plot are experimentally resolved J-values for data from Ref.
23: a͒ Larger excitation energies. b͒ Smaller excitation energies.
C. Experiments with variable excitation wavelengths
and rotational temperatures
Statistical unimolecular rate theory predicts that, near
threshold, the specific rate constants k(E,J) at constant total
energy E decrease with increasing J.6 By varying excitation
wavelength and rotational temperature independently, in
principle, this effect could be tested exactly. For experimen-
tal reasons, we did not succeed completely to realize this
test, but the set of experiments in Fig. 8 is able to show the
effects of rotational excitation for sufficiently high J. In Fig.
8 we compare experiments at 398 nm with an average rota-
tional energy of 312 cmϪ1, at 396 nm without rotational
energy, and at 396 nm with 312 cmϪ1 of rotational energy,
i.e., with average total energies of 25 438, 25 253, and 25 565
cmϪ1, respectively. Although the energy Eϭ25 438 cmϪ1 of
the 398 nm/300K experiment is larger than the energy E
ϭ25 253 cmϪ1 of the 396 nm/2K experiment, the decay is
markedly slower. This effect is ͑qualitatively͒ in line with
statistical predictions, see below. One should note that the
fraction of nondissociative molecules accidentally is the
same for the 396 nm/2K and 398 nm/300K experiments, be-
cause the broad spectral width of the 396 nm pulse also
covers wavelengths larger than the threshold wavelengths
near 398 nm.
single averaged number k(E,J) is derived which can be
͗
͘
compared with the statistical results on an ab initio potential
energy surface without employing any adjustable
parameter.31 This appears to be the only way to obtain cor-
rectly averaged rate constants from multiexponential decays.
Figure 9͑a͒ shows the results of this procedure, i.e., k(E,J)
͗
͘
as a function of E–E0 . In Fig. 9͑a͒ we have plotted our
average rate constants for J Ϸ0, J Ϸ10, and J Ϸ20 and
͗ ͘
͗ ͘
͗ ͘
a k (E) for rotationally cold NO2(Tϳ2 K, this work͒ for
excitation at 310 nm. The data for J Ϸ0 agree quite well, in
͗ ͘
general, with the data of Wittig and co-workers. Their pub-
lished data, also shown in Fig. 9͑a͒ may suggest a rapid
increase of k (E) at higher energies. Our measured rate of
2–3ϫ1012 sϪ1 at about 7800 cmϪ1 excess energy shows,
however, that the rate constant gradually approaches a ‘‘satu-
ration limit’’ for high excess energies E. If we compare the
results for J Ϸ0 with those for J ӷ0 from our study, we
͗ ͘ ͗ ͘
As emphasized above, the experimental results cannot be
deconvoluted to derive k(E,J) directly. Instead, on the basis
of a given k(E,J) ͑here taken from Ref. 31͒, the convoluted
experimental signal is repeatedly simulated with different
global amplitudes of the parametrized k(E,J) curves and
compared with the experimental data. The nonreactive part
of the time-resolved traces ͑offset͒ can be accounted for by
assigning infinite lifetimes to the states below E0(J). Then a
conclude that rotating molecules with the same total internal
energy ͗E͘ decompose more slowly than nonrotating mol-
ecules. For the range of average ͗J͘- values covered in this
work ( J Ϸ0, J Ϸ10, J Ϸ20), this effect appears to be
͗ ͘ ͗ ͘ ͗ ͘
most pronounced for the highest average ͗J͘-values ( J
͗ ͘
Ϸ20) at low excess energies where the ratio of k(E,J
͗
Ϸ0) over k(E,JϾ0) is larger than two. It is impressive,
͘
͗
͘
that for our relatively broad excited-state distributions, this
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6529
J. Chem. Phys., Vol. 115, No. 14, 8 October 2001
k(E,J) for the dissociation of NO2. I
effect is not averaged out. However, we do not see large
disappearing molecules instead of the forming products, non-
exponential time profiles become manifest. In the presence
of lifetime fluctuations, broad spectral distributions from the
excitation light, and of broad thermal rotational distributions,
the deconvolution of the experimental profiles is a problem.
A simulation starting from a plausible set of k(E,J) calcula-
tions with subsequent convolutions and comparison with the
experiments then provides the logical approach.
By studying broader distributions, we obtained a series
of results which are consistent with the J-resolved results
from Wittig and co-workers.20,22,23 We could demonstrate
that, at a given total energy E, the measured k(E,J) decrease
with increasing J. This is in line with predictions form sta-
tistical unimolecular rate theory. A more quantitative theoret-
ical analysis of the J-dependence is given in Part III of this
series.31 This analysis also demonstrates that the apparent
lack of a rotational influence on k(E,J) observed in Refs. 22
and 23 can be, at least in part, due to the compensation of
two effects, i.e., the increase of k(E,J) for a given J with
increasing total E and the decrease of k(E,J) for a given
total E with increasing J. As shown in Part III, the statistical
theory in this way explains the results from Refs. 22 and 23
for JϾ10 ͑see data in Fig. 9͒. However, it does not account
for results at smaller J near to threshold ͑see the discussion
in Ref. 31͒.
differences ͓between k(E,JϷ0) and k(E,JϾ0) ͔ at
͗
͘
͗
͘
larger excess energies anymore. Also, there appears to be no
large difference between the average rate constants for J
͗ ͘
Ϸ10 as opposed to J Ϸ0 at all energies ͑at constant total
͗ ͘
internal energy ͗E͒͘.
The representation of Fig. 9 also contains J-resolved re-
sults from Refs. 20 and 23. In the following, we will show
that these data, when plotted in the way of Fig. 9, follow the
same trends as found in the present work. In addition to the
data from this work, Fig. 9͑b͒ contains rotationally resolved
data from Ref. 23, from two vibrational progressions for
which the excess energy is E ϪD ϭ10 cmϪ1ϩErot(101)
͗ ͘
0
and E ϪD ϭ75 cmϪ1ϩErot(101) ͓D0 denotes the disso-
͗ ͘
0
ciation energy for Jϭ0 and Erot(101) the rotational energy
of the intermediate 101 combination vibration͔ and data for
Jϳ0. Looking at the values of the J-resolved data alone, one
may be tempted to conclude that there is no effect on the
specific rate constant when changing J. However, when com-
paring rate constants for JϾ0 and for Jϳ0 in Fig. 9͑b͒ a
pronounced deviation of the two sets of data with increasing
J is obvious and clearly visible. Under isoenergetic condi-
tions, i.e., for constant Etot here, the rates for Jϳ0 and J
Ͼ0 appear to deviate for larger rotational excitation. Appar-
ently, the rates for rotating molecules remain below the rates
for nonrotating molecules with Jϳ0. This is clearly observ-
able for Nϭ11–15 in Fig. 9͑b͒. It is interesting to note that
ACKNOWLEDGMENTS
the ratio of the rates for Jϳ0 and Nϭ15 ͑e.g., in the E
͗ ͘
ϪD0ϭ75 cmϪ1ϩErot(101) progression͒ is about a factor of
The authors enjoyed stimulating discussions of this
work with R. Schinke, S. Grebenshchikov, V. Ushakov,
A. Maergoiz, and C. Wittig. Financial support from the
Deutsche Forschungsgemeinschaft ͑SFB 357 ‘‘Molekulare
Mechanismen Unimolekularer Prozesse’’͒ is gratefully ac-
knowledged. The authors also thank G. Thurau for valuable
assistance with the experimental set up.
two. Our experiments with J ϭ20 and Jmaxϭ16 actually
͗ ͘
seem to complement these data and appear to be consistent
with them. In contrast to the conclusions of Ref. 23, we
conclude that for higher J the experimental findings may be
consistent with predictions from statistical theory. However,
at the same time Fig. 9͑b͒ also shows, that for constant total
energy E, the rates for lower angular momentum N are very
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͗ ͘
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