Unimolecular decomposition of NO3: The NO+O2 threshold regime

Article abstract of DOI:10.1063/1.472527

The unimolecular decomposition of expansion-cooled NO₃ has been investigated in the threshold regime of the NO+O₂ channel. Photoexcitation in the region 16 780-17 090 cm^-1 (596-585 nm) prepares ensembles of molecular eigenstates, each of which is a mixture of the B ²E′ bright state and lower electronic states. The X ²A′₂ ground state is believed to be the probable terminus of ²E′ radiationless decay, though participation of A ²E″ is also possible. For these photon energies, unimolecular decomposition occurs exclusively via the NO+O₂ channel, and NO yield spectra and state distributions have been obtained. The yield spectra are independent of the rotational state monitored, as expected for a large reverse barrier. The state distributions are insensitive to the photolysis photon energy and can be rationalized in terms of dynamical bias. The NO yield goes to zero rapidly above the O+NO₂ threshold (17 090±20 cm^-1). Because of tunneling, the NO+O₂ channel does not have a precise threshold; the value 16 780 cm^-1 is the smallest photon energy that yielded signals under the present conditions. Very small decomposition rates were obtained via time-domain measurements in which reactive quenching of long-lived NO₃ fluorescence was observed. The rates varied from 1×10⁴ at 16780 cm^-1 to 6×10⁷ s^-1 at 16 880 cm^-1, and their collision free nature was confirmed experimentally. These data were fitted by using a one-dimensional tunneling model for motion along the reaction coordinate combined with the threshold Rice-Ramsperger-Kassel-Marcus (RRKM) rate. The top of the NO+O₂ barrier is estimated to lie at 16 900 ± 15 cm^-1. Translational energy measurements of specific NO (X ²∏Ω,v,J) levels showed that O₂ is highly excited, with a population inversion extending to energies above the a ¹Δ_g threshold, in agreement with previous work. It is possible that the main O₂ product is X ³∑_g^-, though some participation of a ¹Δ_g cannot be ruled out. Within the experimental uncertainty, b ¹∑_g⁺ is not produced.

Full text of DOI:10.1063/1.472527

Unimolecular decomposition of NO3: The NO+O2 threshold regime
K. Mikhaylichenko, C. Riehn, L. Valachovic, A. Sanov, and C. Wittig
Citation: The Journal of Chemical Physics 105, 6807 (1996); doi: 10.1063/1.472527
View online: http://dx.doi.org/10.1063/1.472527
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Unimolecular decomposition of NO3: The NO؉O2 threshold regime
K. Mikhaylichenko, C. Riehn,a) L. Valachovic, A. Sanov, and C. Wittig
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
͑Received 13 June 1996; accepted 16 July 1996͒
The unimolecular decomposition of expansion-cooled NO3 has been investigated in the threshold
regime of the NOϩO2 channel. Photoexcitation in the region 16 780–17 090 cmϪ1 ͑596–585 nm͒
2
prepares ensembles of molecular eigenstates, each of which is a mixture of the B EЈ bright state
2
and lower electronic states. The X AЈ2 ground state is believed to be the probable terminus of
2
2E radiationless decay, though participation of A E is also possible. For these photon energies,
Ј
Љ
unimolecular decomposition occurs exclusively via the NOϩO2 channel, and NO yield spectra and
state distributions have been obtained. The yield spectra are independent of the rotational state
monitored, as expected for a large reverse barrier. The state distributions are insensitive to the
photolysis photon energy and can be rationalized in terms of dynamical bias. The NO yield goes to
zero rapidly above the OϩNO2 threshold ͑17 090Ϯ20 cmϪ1͒. Because of tunneling, the NOϩO2
channel does not have a precise threshold; the value 16 780 cmϪ1 is the smallest photon energy that
yielded signals under the present conditions. Very small decomposition rates were obtained via
time-domain measurements in which reactive quenching of long-lived NO3 fluorescence was
observed. The rates varied from 1ϫ104 at 16 780 cmϪ1 to 6ϫ107 sϪ1 at 16 880 cmϪ1, and their
collision free nature was confirmed experimentally. These data were fitted by using a
one-dimensional tunneling model for motion along the reaction coordinate combined with the
threshold Rice–Ramsperger–Kassel–Marcus ͑RRKM͒ rate. The top of the NOϩO2 barrier is
estimated to lie at 16 900Ϯ15 cmϪ1. Translational energy measurements of specific NO
2
(X ⌸ , ,J) levels showed that O is highly excited, with a population inversion extending to
v
⍀
2
1
energies above the a ⌬g threshold, in agreement with previous work. It is possible that the main
O2 product is X
experimental uncertainty, b ͚ is not produced. © 1996 American Institute of Physics.
Ϫ
g
3
1
͚
, though some participation of a ⌬g cannot be ruled out. Within the
ϩ
1
g
͓S0021-9606͑96͒00240-1͔
catalytic destruction of ozone.3 Appreciation of the atmo-
I. INTRODUCTION
spheric significance of NO3 has resulted in numerous spec-
troscopic and kinetics studies;4 however, its absorption spec-
trum, electronic states, intramolecular dynamics, and
photochemistry are not well understood. The main reason
that NO3 has not been more thoroughly investigated experi-
mentally is the difficulty of preparing sufficiently clean, yet
intense, beams of cold NO3 for studies in collision-free en-
vironments.
Polyatomic molecules and radicals that exhibit a break-
down of the Born–Oppenheimer approximation and have al-
ternative pathways for unimolecular decay are of great inter-
est in physical chemistry. Detailed studies of such species
improve our understanding of how nonadiabatic interactions
between zeroth-order electronic potential energy surfaces
͑PESs͒ affect the reaction pathways of an excited molecule
as it evolves to products. Ultimate goals range from a deeper
understanding of the relevant physical and chemical pro-
cesses to the control of chemical reactivity. In consideration
of the above, the nitrate radical ͑NO3͒ provides an excellent
model system for examining those aspects of its molecular
physics that are involved in chemical change via unimolecu-
lar reactions.
Since the discovery of the night-time presence of NO3 in
both the stratosphere1 and troposphere,2 NO3 has been rec-
ognized as an important participant in a growing list of at-
mospherically relevant chemical transformations ͑e.g., con-
version of NOx to HNO3; hydrocarbon and halocarbon
oxidation͒. Furthermore, the photolysis of NO3 at visible
wavelengths is known to yield NO, which contributes to the
The only low-lying, optically accessible state of NO3 is
2
B E . Its absorption features lie at convenient photon ener-
Ј
2
2
gies, and the E ← A
Ј system has a large absorption cross
Ј
2
section ͑␴662 nmϭ2.2ϫ10Ϫ17 cm2͒.5,6 Fluorescence following
excitation in the region of 604–678 nm is characterized by
diffuse bands7,8 and by the Douglas effect.9 Namely, the
fluorescence lifetimes are much longer than the radiative life-
2
time of the zeroth-order E state ͑i.e., several hundred mi-
Ј
croseconds versus ϳ1 ␮s, respectively͒.10
2
The three low-lying doublets ͑i.e., the X AЈ2 ground
Ϫ1
Ϫ1
2
2
state, A E at 7005 cm , and B E at 15 110 cm ͒ are
Љ
Ј
subject to strong nonadiabatic ͑vibronic͒ interactions that
mix the zeroth-order electronic states.11 Consequently, E
2
Ј
undergoes internal conversion to a quasicontinuum of near-
isoenergetic dark levels, resulting in a dense manifold of
molecular eigenstates having mixed 2E /2AЈ electronic char-
Ј
a͒
2
2
¨
¨
Permanent address: Universitat Frankfurt a. M., Institut fur Physikalische
und Theoretische Chemie, Marie-Curie-Str. 11, D-60439 Frankfurt a. M.,
Germany.
acter, with possible contributions from E . As a result, al-
Љ
though the wave functions of the optically excited radical
J. Chem. Phys. 105 (16), 22 October 1996
0021-9606/96/105(16)/6807/11/$10.00
© 1996 American Institute of Physics
6807
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6808
Mikhaylichenko et al.: Unimolecular decomposition of NO3
2
retain some E electronic character, they are dominated by
Ј
the lower electronic manifolds on time scales exceeding the
inverse of the mean level spacing, i.e., after any optically
prepared coherences have dephased. Note that there is no
reason to assume that all members of the full ensemble of
molecular eigenstates acquire the same degree of bright char-
acter via vibronic interaction, since the most pronounced ef-
fect will be to couple levels within the 2E bright-state mani-
Ј
fold to dark levels of the same vibronic symmetry. Following
the example of NO2,12 weaker interactions ͑second-order
spin–orbit and orbit–rotation͒13 would be responsible for the
couplings between levels having different vibronic symme-
tries.
The nature of the nonadiabatic interactions in NO3 has
been the subject of a number of experimental14–17 and
theoretical18 investigations. Briefly, these interactions can be
described as: ͑i͒ Jahn–Teller ͑JT͒ intrastate couplings within
FIG. 1. Energy level diagram showing low-lying NO3 doublets and ener-
getically accessible O2 electronic states.
2
2
the doubly degenerate E and E electronic states due to
Ј
Љ
doubly degenerate vibrations of e symmetry ͑␯ and/or ␯ ͒;
Ј
and its presence permits tunneling. In most chemical sys-
tems, tunneling of species other than electrons is significant
only for hydrogen.24 An example relevant to the present dis-
cussion is HFCO, where the HFϩCO channel has been ob-
served as much as 2000 cmϪ1 below the barrier.25 Though
tunneling probabilities are quite small when larger masses
are involved, tunneling will nonetheless dominate as long as
competitive decay paths such as spontaneous emission and
collisional deactivation are relatively slow. In this regard,
due to the very small radiative rates of its individual eigen-
states, NO3 is an ideal candidate to observe heavy-particle
tunneling under collision-free conditions.
3
4
͑ii͒ linear interstate pseudo-Jahn–Teller ͑PJT͒ interactions
between 2E and 2AЈ , due to the ␯ and/or ␯ vibrations; ͑iii͒
Ј
3
4
2
bilinear PJT couplings in 2E /2E and 2E /2AЈ electronic
Ј
Љ
Љ
2
subsets that symmetrywise require excitation of odd quanta
of ␯ in addition to ␯ and/or ␯4. Since a separate treatment
2
3
of all vibronic coupling mechanisms does not describe a
given electronic state correctly, NO3 presents a complicated
multimode vibronic coupling problem.11,18,19
2
At energies near the E origin, were the nuclear motion
Ј
to transpire exclusively on the ground PES, it would prob-
ably be chaotic.20 Since NO3 has six vibrational degrees of
freedom and a vibrational density of states of ϳ100 per
The narrow NOϩO2 reaction window has been observed
recently by using the molecular beams technique to obtain
photofragment translational energy distributions.26 Since re-
action ͑1͒ can contribute to the catalytic destruction of
ozone,3 it is important to determine the photon energy range
over which it takes place. From the wavelength dependence
of the NO time-of-flight ͑TOF͒ signal, the reaction ͑1͒ barrier
was placed at 16 555Ϯ280 cmϪ1 and the reaction ͑2͒ thresh-
old was found to be 17 040Ϯ90 cmϪ1. A NO3 rotational
temperature of ϳ70 K precluded a more precise threshold
cmϪ1 21
even small coupling matrix elements result in effi-
,
cient mixing of zeroth-order vibrational levels and are ex-
pected to lead to complete intramolecular vibrational redis-
tribution ͑IVR͒. Any description of vibronic coupling
mechanisms in terms of promoting-mode selection rules can
be relevant only at short times, since at longer times the
vibrational quantum numbers are destroyed by IVR. Such a
hierarchy was suggested as a possible explanation for the
structure of the NO3 laser-induced fluorescence ͑LIF͒ spec-
14
2
2
Ϫ
3
trum near the E ← AЈ origin. Specifically, the width of
Ј
determination. A substantial yield of O2 (X ͚g )was ob-
2
2
the LIF spectrum indicates that the zeroth-order E state
Ј
survives for only ϳ100 fs, and if this relaxation occurs via
levels with promoting-mode character, these levels will de-
cay via IVR into the quasicontinuum of vibrational levels.
Dissociation proceeds via two pathways, with reaction
͑1͒ dominating only below the reaction ͑2͒ threshold ͑Fig. 1͒
NO3→NOϩO2 , ⌬HϷ1000 cmϪ1
,
͑1͒
͑2͒
→OϩNO2 , ⌬HϷ17 000 cmϪ1
.
Geometric properties of the reactant and products are shown
in Fig. 2.17,22,23 Whereas reaction ͑2͒ occurs via simple bond
fission, reaction ͑1͒ involves a three-center mechanism and a
tight transition state, i.e., the ground PES correlates to
NOϩO2 via a barrier along the reaction coordinate. This bar-
rier presumably arises from an avoided crossing of the
ground PES with a repulsive PES correlating to NOϩO2,
FIG. 2. Schematic diagram showing geometrical properties of NO3 and
reaction products. Molecular parameters are from Ref. 17 ͑NO3͒, Ref. 22
͑NO2͒, and Ref. 23 ͑NO and O2͒.
J. Chem. Phys., Vol. 105, No. 16, 22 October 1996
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Mikhaylichenko et al.: Unimolecular decomposition of NO3
6809
served for photolysis below 16 835 cmϪ1. However, at
17 005 cmϪ1 the O2 internal energy distribution was seen to
peak at ϳ13 400 cmϪ1, suggesting the possible participation
of the a ⌬g state, which lies 7918 cmϪ1 above the
1
Ϫ
3
X
͚g ground state. Unfortunately, the measurements do not
Ϫ
3
distinguish between high vibrational levels of ͚ and low
vibrational levels of ⌬g .
g
1
As the photon energy is increased above the OϩNO2
threshold, k2 quickly exceeds k1 . The 2E surface is be-
Ј
lieved to correlate to ground state OϩNO2 via a path without
an exit barrier, and it has been suggested that reaction ͑2͒
might proceed directly via the 2E surface following
Ј
photoexcitation.10 On the other hand, internal conversion to
highly excited vibrational levels of the ground PES can be
followed by competition between reactions ͑1͒ and ͑2͒. Even
on the ground PES, k2 will eventually dominate with increas-
ing energy due to the qualitatively different transition states.
Accordingly, the NO yield spectrum just above the reaction
͑2͒ threshold will reflect transition state properties as well as
the different couplings.
This paper reports an experimental study of NO3 unimo-
lecular decay. Photoexcitation in the region 16 530–17 240
cmϪ1 ͑605–580 nm͒ has been used to record LIF spectra of
expansion-cooled NO3 and to initiate its unimolecular de-
composition. Reaction mechanisms have been investigated
by recording NO yield spectra and state distributions. In ad-
dition, collision-free decomposition rates were recorded both
by monitoring the NO yield as the pump–probe delay was
varied, as well as by monitoring the quenching of the long-
lived NO3 fluorescence. Rates as low as 1ϫ104 sϪ1 are re-
ported and a tunneling mechanism is implicated. Finally,
state-selective center-of-mass ͑c.m.͒ translational energy
FIG. 3. Schematic diagram of the pulsed pyrolysis nozzle.
Because rotational components of the NO3
2
2E ← A spectrum are unassigned, Trot was estimated by as-
Ј
Ј
suming that cooling is the same as for the coexpanded NO2.
Relative intensities of NO2 transitions near 16 709 cmϪ1
R(0)/R(2) and P(2)/P(4)]28 were used, and it was found
͓
that Ar carrier cools more efficiently than He carrier ͑6Ϯ1 vs
25Ϯ1 K͒.
The LIF apparatus has been described previously.29
Briefly, a Nd:YAG-pumped dye laser was used to excite
2
2
NO via the E ← AЈ system, and the doubled output of an
Ј
3
2
excimer-pumped dye laser was used for LIF detection of NO
2
ϩ
2
via the A ͚ ←X ⌸system. The excitation and probe
beams were counterpropagated with beam diameters of 2.5
and 1 mm, respectively, in the interaction region. Typical
energies were 5–10 mJ for the excitation laser and ϳ100 ␮J
for the probe laser.
measurements have been used to estimate O2 internal energy
Since NO2 has LIF features in the same spectral region
as NO3, a portion of the LIF signal near the opening of the
NOϩO2 channel is due to the NO2 that is present in the
expansion. For the NO yield measurements, NO2 fluores-
cence was eliminated by using an interference filter. Signal
due to NO background in the expansion was an order of
magnitude smaller than the NO signal arising from NO3 pho-
todissociation when probing low NO rotational states (J
Ͻ 3.5). For higher NO rotational levels, signals from the NO
background were negligible.
2
distributions for specific NO (X ⌸ , ,J) levels. The dis-
v
⍀
tributions peak ϳ10 000 cmϪ1, with at least one-third of the
Ϫ
3
1
population formed in X
͚
below the a ⌬g threshold. This
g
portion displays a population inversion which is most likely
vibrational. Though a significant portion of the population
1
1
lies above the a ⌬g threshold, the role of a ⌬g versus
Ϫ
Ϫ
3
3
X
͚
is unclear; it is possible that X
͚
dominates.
g
g
II. EXPERIMENTAL ARRANGEMENT
In pump–probe experiments, fluorescence was collected
perpendicular to the laser/molecular-beam plane with a pho-
tomultiplier tube ͑PMT͒ which monitored a 3 mm region
along the central portion of the expansion. NO yield spectra
were recorded for photon energies in the range of 16 780–
17 090 cmϪ1 and at various delays between the excitation
and probe pulses. NO product state distributions were re-
corded at a pump–probe delay of 350 ns. The probe energy
was sufficient to ensure complete saturation for all rotational
branches.
Reaction rates were measured by monitoring their
quenching of NO3 fluorescence in real time. The PMT was
placed on the expansion axis 30 cm from the interaction
region and fluorescence was collected by the photocathode
without the use of imaging optics. Scattered laser light was
blocked by a filter and NO3 emission was monitored at
An intense beam of cold NO3 was developed, based on
the pulsed pyrolysis of N2O5 using a Chen-type nozzle.27 Ar
was bubbled through N2O5 cooled to Ϫ15 °C ͑N2O5 vapor
pressure ϳ20 Torr; total pressure ϳ1.1 atm͒. The resulting
2% N2O5/Ar mixture was expanded through a piezoelectri-
cally activated valve ͑0.5 mm orifice diam͒ into a resistively
heated SiC tube ͑25 mmϫ2.2 mm O.D.ϫ1.2 mm I.D.͒ and
then into a low pressure chamber ͑Fig. 3͒. Under typical
nozzle operating conditions ͑10 Hz, 500 ␮s pulse duration͒
the chamber pressure was Ͻ10Ϫ4 Torr, with a base pressure
of ϳ10Ϫ6 Torr. NO3 production was optimized by adjusting
2
the nozzle temperature while monitoring 2E ← AЈ LIF near
Ј
2
662 nm. The present design allowed us to achieve high NO3
concentrations in the expansion ͑despite the concomitant
production of NO2͒ and good rotational cooling.
J. Chem. Phys., Vol. 105, No. 16, 22 October 1996
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6810
Mikhaylichenko et al.: Unimolecular decomposition of NO3
2
FIG. 4. Schematic diagram of arrangement for correlated NO͑
⌸ , ,J)
v
⍀
ϩO2 distribution measurements. On the right-hand side are examples of the
distributions of NO correlated with different O2 electronic states ͑ ϭ0,
v
Ϫ
g
3
1
Jϭ0͒ assuming a
X
͚
/ a
͔ ͓
⌬
ratio of 2.
͔
g
͓
wavelengths where NO2 emission is insignificant. This ar-
rangement facilitated monitoring long-lived excited states.
The signals reflect both the decay of the excited state and the
experimental response function, the latter limiting the esti-
mation of unimolecular decay rates to ϳ1ϫ104 sϪ1
.
The arrangement for measuring correlated NO
2
(X ⌸ , ,J)ϩO translational energy distributions is
v
⍀
2
shown in Fig. 4; it is the same as that used to study NO2
unimolecular decomposition.30 NO3 is excited in the photoly-
sis region and dissociation takes place as the NO3 c.m. trav-
els with the molecular beam. After a delay, the products
reach the detection region, which is separated spatially from
FIG. 5. ͑a͒ NO͑ ϭ0͒ rotational populations for photolysis at 16 990 cmϪ1
the lines through the data serve to guide the eye. ͑b͒ Boltzmann plots for the
data in Fig. 5͑a͒; the lines represent linear fits to the data. All slopes corre-
spond to 1400Ϯ300 K.
;
v
2
the photolysis region. The NO (X ⌸ , ,J)fragments that
v
⍀
correlate with different O2 internal energies reach the probe
region spatially separated as per their recoil velocities. By
scanning the position of the probe beam in the z direction
2
͑Fig. 4͒, spatial profiles of selected NO(X ⌸ , ,J) prod-
v
⍀
creases quadratically with radius, which is proportional to
recoil velocity.
ucts were obtained at a pump–probe delay of 2.55 ␮S. To
improve resolution, the photolysis and probe beams were
focused to diameters of ϳ0.2 mm in their respective interac-
tion regions. NO was detected by 1ϩ1 REMPI, which pro-
vides the highest sensitivity possible.30 Data analyses take
into account: ͑i͒ the fact that each NO recoil profile is a sum
of contributions from NO fragments correlated with different
O2 states; and ͑ii͒ spatial broadening effects due to the finite
III. RESULTS
Photolysis at 16 990 cmϪ1 yielded the NO
2
(X ⌸1/2,3/2
,
ϭ 0) rotational distributions shown in Fig.
v
5͑a͒. Vibrational excitation ͑not shown͒ is modest, with
2
р10% of the NO formed in ϭ 1. The ⌸1/2 lower spin–
v
2
sizes of the photolysis and probe beams, the velocity com-
orbit state is slightly more populated than the ⌸3/2 upper
vz
ponents of parent NO3 in the molecular beam, the NO3 rota-
spin–orbit state, and the AЈ⌳-doublet components are
slightly more populated than the AЉ components. The rota-
tional distributions shown in Fig. 5͑a͒ can be characterized
by using the Boltzmann plots shown in Fig. 5͑b͒. The slopes
correspond to 1400Ϯ300 K. These slopes should be consid-
ered figures of merit rather than temperatures, since they
apply to a limited range of rotational levels. NO populations
at other photon energies in the range of 16 840–17 000 cmϪ1
tional temperature, and long dissociation times.30,31
Spatial anisotropy is not expected because of the small
NO3 dissociation rates. The NO signal is observed at all val-
ues of ͉z͉ smaller than the appearance threshold defined by
the recoil velocity and the pump–probe delay. However, due
to the geometrical arrangement, spatial profiles for a given
͉z͉have maximum intensity at their furthest displacements
from the molecular beam axis, i.e., where the probe beam
illuminates the recoil sphere at a grazing angle. This is illus-
trated by the profiles on the right-hand side of Fig. 4. It is
also noted that this arrangement is more sensitive to the
slower recoiling products since the two-dimensional number-
density of products on the surface of the recoil sphere de-
were examined and no significant differences were noted.
2
Figure 6 shows the NO(X ⌸1/2
, ϭ 0, J ϭ 13.5) yield
v
spectrum and the NO3 LIF spectrum recorded just below the
NOϩO2 barrier. Since some of the features in the latter are
due to NO2 contamination, a NO2 LIF spectrum is also
shown. Both the NO3 LIF and the NO yield spectra are in
J. Chem. Phys., Vol. 105, No. 16, 22 October 1996
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Mikhaylichenko et al.: Unimolecular decomposition of NO3
6811
2
FIG. 6. LIF signals relevant to reaction ͑1͒: NO(X
⌸
,
ϭ 0, J ϭ 13.5)
v
1/2
yield spectrum ͑monitoring R11)at a pump–probe delay of 1 ␮s; NO3 LIF
spectrum just below the NOϩO2 barrier ͑including contaminant NO2 lines͒;
NO2 LIF spectrum for Trotϭ6 K. Also shown ͑open circles͒ is the NO3 230
K absorption spectrum ͑Ref. 6͒.
accord with the 230 K NO3 absorption profile.6 The NO
yield spectrum is independent of the rotational state moni-
tored, as expected for a large reverse barrier, and the narrow
NOϩO2 reaction window is seen to extend from 16 820Ϯ40
to 17 090Ϯ20 cmϪ1. As in previous studies,24 the largest NO
signals were recorded near 16 980 cmϪ1, which corresponds
to a peak in the NO3 absorption.
2
FIG. 7. NO(X
⌸
,
ϭ 0, J ϭ 13.5)yield spectra at the indicated pump–
v
1/2
probe delay times for NO3 rotational temperatures of 6 and 25 K. Apparent
thresholds for Trotϭ6 and 25 K and 30 ns delay are shown as a vertical
dotted line. Arrows indicate the photon energies at which correlated NO
Below 16 890 cmϪ1, NO buildup is not prompt on the
time scale of the nanosecond-resolution pump–probe mea-
surements. In addition, NO3 fluorescence is also present in
this wavelength region. The existence of a slow process as-
sociated with reaction ͑1͒ is illustrated by the time depen-
dence of the NO yield spectra for rotational temperatures of
6 and 25 K, as shown in Fig. 7. For a pump–probe delay of
(2⌸⍀ , ,J)ϩO distributions were obtained.
v
2
response function, the deconvolution of the unimolecular de-
cay rates from the measured traces was done assuming biex-
ponential behavior. Moreover, the fit was sensitive to param-
eters such as the baseline and zero of time used in the fitting
procedure. As a result, the estimated uncertainty for each of
the k1 values is Ϯ50%.
30 ns, there is an apparent threshold at 16 878Ϯ10 cmϪ1
.
However, upon increasing the pump–probe delay, this
threshold is shifted to lower energies. For example, for de-
lays as long as ϳ1 ␮s, the threshold drops to 16 815 cmϪ1
.
Figure 9 displays k1 versus photon energy. The rates
extracted from the fast components of the decay curves are
indicated by open circles and squares. The open circles rep-
resent Trotϭ6 K. These rates increase from 1ϫ104 sϪ1 at
16 780 cmϪ1 to 6ϫ107 sϪ1 at 16 880 cmϪ1. The squares
represent Trotϭ20 K ͑350 Torr nozzle backing pressure, 5 Hz
operation͒. Under these conditions the chamber pressure is
Ͻ10Ϫ5 Torr, which is an order of magnitude lower than un-
der the Trotϭ6 K conditions, thus minimizing beam–gas col-
lisions. The higher value of Trot appears to shift the data to
slightly lower photon energies without changing the overall
trend. In fact, the shift is comparable to the change in the
average parent rotational energies in going from 6 to 20 K.
The fact that lowering the backing pressure does not affect
the slow reaction is consistent with the collision-free nature
of this process.
For delays longer than ϳ1 ␮s, the excited molecules are
transported out of the probe region as per the molecular
beam velocity. Also, because of the large translational en-
ergy release in the exit channel, NO recoil out of the probe
region is significant. Thus, monitoring NO buildup times
provides an upper limit to the decomposition rates.
The slow unimolecular decay rates described above were
also observed via their reactive quenching of the long-lived
NO3 emission. Time resolved emission profiles were ob-
tained at several photon energies, as shown in Fig. 8. Fluo-
rescence quenching was evident above 16 780 cmϪ1 and uni-
molecular decay rates larger than 1ϫ104 sϪ1 could easily be
discerned ͓Fig. 8͑c͔͒. As the photon energy was increased,
reactive quenching of the fluorescence increased rapidly
͓Figs. 8͑a͒ and 8͑b͔͒. At still larger photon energies, mea-
surement of excited state lifetimes was limited by the 30 ns
experimental resolution. Since the decay curves contain con-
tributions from both the NO3 fluorescence and the apparatus
Spatial distributions of specific NO quantum states were
obtained for the photon energies indicated by arrows in Fig.
7. A representative profile obtained at 16 992 cmϪ1 is shown
J. Chem. Phys., Vol. 105, No. 16, 22 October 1996
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6812
Mikhaylichenko et al.: Unimolecular decomposition of NO3
2
FIG. 10. NO(X
⌸
,
ϭ 0, J ϭ 17.5) spatial profiles obtained at 16 992
v
3/2
cmϪ1 by monitoring the A ͚←X 2⌸P22 transition. The bottom axis gives
the distance between the centers of the probe and photolysis beams along
the z axis; the top axis lists O2 internal energies.
2
experimental broadening. Note that the signal associated
Ϫ
g
3
with O2 (X
͚
,
ϭ 0)is small. For shorter recoil distances,
v
the signal increases gradually, peaking in the vicinity of the
appearance threshold for O2 internal energies of ϳ10 000
cmϪ1. Although this internal energy is sufficient to access the
1
a ⌬g state, no abrupt signal increase is observed near the
1
a ⌬g threshold. In addition, the integrated intensity of the
signal arising from NO with enough translational energy to
1
preclude a ⌬g formation accounts for a significant fraction
FIG. 8. Time resolved NO3 emission at the given excitation energies. The
lines represent biexponential fits to the data. Also shown are the NO3 uni-
molecular decay rates extracted from the fast component of the fluorescence
decay curves.
of the total ͑at least one-third͒. Thus, the data indicate that
Ϫ
3
O2(X ͚g ) is formed with a population inversion. Similar
results were obtained at 16 863 and 16 892 cmϪ1, and when
monitoring different NO rotational and spin–orbit states.
At 16 841 cmϪ1, the NO(X ⌸3/2
, ϭ 0, J ϭ 17.5) spa-
v
2
in Fig. 10. The bottom axis indicates the displacement of the
monitored NO along the z axis at a pump–probe delay of
2.55 ␮s. The top axes indicate the appearance thresholds for
O2 electronic and vibrational levels without accounting for
tial profile corresponds to a larger relative population of the
Ϫ
5
3
lower O2(X ͚g )levels. However, k1 is so small ͑ϳ2ϫ10
sϪ1͒ that NO buildup is comparable to the maximum pump–
probe delay of 3 ␮s allowed by the dimensions of the appa-
ratus and the product recoil, thus complicating analyses. This
preliminary result will be the subject of future work.
IV. DISCUSSION
A. The roles of the X 2AЈ2 , A 2E , and B 2E states
Љ
Ј
Nelson et al. used the integrated absorption coefficient
2
of the 2E ← AЈ origin to estimate the spontaneous emission
Ј
2
lifetime of the zeroth-order 2E state, obtaining a value of ϳ1
Ј
␮s.10 We confirmed this by using a well-established
procedure.32,33 They also reported long fluorescence lifetimes
2
͑␶ ϳ340 ␮s͒ at the E origin ͑with some evidence for non-
Ј
fl
exponential decay at shorter times͒, indicating an oscillator
strength dilution factor of ϳ340 for the observed levels,
which span a region of ϳ50 cmϪ1 around the origin. Thus, in
this energy range, ϳ7 vibronic levels per cmϪ1 ͑i.e.,
2
340Ϭ50͒ are mixed with the E bright state, which is con-
Ј
2
FIG. 9. NO3 decomposition rate vs photon energy. Open circles and squares
represent data obtained by monitoring time resolved NO3 emission for
siderably less than the estimated density of AЈ2 vibrational
levels ͑ϳ100/cmϪ1͒.34
T
rotϭ6 and ϳ20 K, respectively. Filled circles represent data obtained by
On the basis of a dilution factor of ϳ340, it follows that
using the picosecond-resolution pump–probe technique averaged over the
2
2
60 cmϪ1 linewidth of the ultrafast laser ͑Ref. 44͒.
the E ← AЈ oscillator strength is not distributed statisti-
Ј
2
J. Chem. Phys., Vol. 105, No. 16, 22 October 1996
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Mikhaylichenko et al.: Unimolecular decomposition of NO3
6813
cally among all nearby levels, in which case the dilution
factor would be much larger. Such modest dilution can be
rationalized if the matrix elements connecting levels of dif-
ferent vibronic symmetries are smaller than typical energy
separations between the levels. However, by analogy with
NO2, where second-order spin–orbit and orbit–rotation ma-
trix elements have been found to be several tenths of a wave
number,13 at least some coupling between levels of different
vibronic symmetries is expected, though oscillator strength
may be distributed inhomogeneously among the different vi-
bronic species.
lecular eigenstates have little 2E character. Instead, they are
Ј
dominated by the lower electronic manifolds, tentatively as-
2
sumed to be A2Ј
͉
␺ ϭ
2E ,
͉␺ ͉
2E ,
v v
Ј
͘
n i n
Ј
͘
͗
͘
͚
i
n
ϩ
2AЈ ,
͉
␺
͉
2AЈ ,
,
vm
͘
͑3͒
vm
͗
͘
͚
i
2
2
m
where
͉
␺
is a molecular eigenstate, the sums over
and
vn
͘
i
Since it has not been possible to fully quantify the extent
of dilution or to establish radiationless decay mechanisms,
include all vibrational levels ͑rotational quantum num-
vm
bers are suppressed͒, and mӷn because of the different vi-
the relative 2E and 2A2Ј contributions remain un-
brational level densities for the 2E and 2AЈ manifolds. Note
Љ
Ј
2
known. However, 2E /2AЈ coupling has been confirmed both
Ј
that the term ‘‘molecular eigenstate’’ is used even when
these levels are coupled weakly to a continuum.
2
experimentally14–17 and theoretically,18 and 2E /2E cou-
Ј
Љ
pling is believed to be a higher-order process.18,19 Also,
For the tunneling regime examined in the present experi-
ments, all of the measured k1 values are Ͻ108 sϪ1, which
corresponds to Lorentzian widths Ͻ0.0005 cmϪ1. Because of
the narrowness of these widths, the energy level structure can
be treated as a quasicontinuum of isolated ͑nonoverlapping͒
resonances. The high degree of spectral overlap observed
experimentally is due to several factors: congestion caused
by the many different rotational levels excited when using 6
K samples, the Doppler effect in unskimmed expansions, and
the laser linewidth. However, these factors do not lead to
quantum interferences, so the approximation of isolated reso-
nances is still valid insofar as the statistical properties of the
decay widths is concerned.
Though the decay widths of individual resonances fluc-
tuate about a mean value,39 the present conditions ensure that
a large number of resonances are excited by the laser pulse.
Thus, fluctuations between measured k1 values were neither
anticipated nor observed. Moreover, coherences imparted by
the photoexcitation step dissipate quickly on the time scale
of the rate measurements. Thus, we believe that the excited
ensemble of levels can be modeled as decaying incoherently
with a distribution of rates. It is the relaxation of this opti-
cally prepared ensemble that we record as k1 . The unimo-
lecular decomposition was taken to be single exponential
because, within the present experimental uncertainty, it fits.
However, there is no theoretical basis for this, and higher
quality data may reveal deviations from single-exponential
decay.
2
2AЈ is preferred over E on statistical grounds, i.e., at the
Љ
2
present energies, the vibrational level density within the
2
2AЈ manifold is significantly larger than that within the E
Љ
2
2
manifold. Thus, we assume that AЈ2 is the main terminus of
radiationless decay, though participation of E cannot be
2
Љ
ruled out. The conclusions presented below would not be
2
altered seriously by including E .
Љ
B. Intramolecular dynamics
At the energies and vibrational state densities of interest
in the present study, it is highly probable that the nuclear
dynamics would be chaotic even if they were to transpire
2
solely on the AЈ2 zeroth-order PES, i.e., ignoring vibronic
interactions. This assumption is based on the exhaustive
body of experimental and theoretical data that has accrued in
the area of intramolecular vibrational dynamics.20 However,
vibronic interactions are known to efficiently promote cha-
otic dynamics within the vibronic manifolds.11,35,36 Therefore
we assume that the system displays full vibronic chaos for
the energies and time scales of interest in the present study,
as was found to be the case for NO2.12,37 Since couplings
between different vibronic species are weaker than the cou-
plings within each vibronic manifold, the system can be vi-
bronically chaotic ͑i.e., within each manifold͒ without being
rovibronically chaotic ͑i.e., between manifolds͒. However,
again by invoking analogy with NO2, where it has been re-
ported that rovibronic chaos exists just below D0 as a con-
sequence of second-order spin–orbit and orbit–rotation
interactions,13 there exists the possibility that NO3 is rovi-
bronically chaotic.
Photoexcitation does not access the full manifold of mo-
lecular eigenstates equivalently. In the absence of saturation,
it excites levels in proportion to the squares of their electric
dipole matrix elements, and is thus biased. Nonetheless, it is
expected that measured k1(E) values differ little from k1(E)
values averaged over all molecular eigenstates within the
same energy window. The reason is that the reaction rates
C. Optical excitation
The vibronic interactions that mix the zeroth-order elec-
tronic states provide a means of optically preparing vibra-
tionally excited states that decay via one or more unimolecu-
lar decomposition mechanisms. For example, reaction ͑1͒
results from weak couplings between the optically prepared
molecular eigenstates38 and the NOϩO2 continuum. From
are not characteristic of the 2E surface, which carries the
Ј
oscillator strength but is unreactive toward NOϩO2.10 Since
the 2E surface contributes little to the makeup of individual
Ј
eigenstates, as seen by its small weighting coefficient in the
expansion of the wave function, the distribution of decay
rates is expected to be almost independent of the bright-state
contribution to the molecular eigenstate.
the 50 cmϪ1 width of the E ← AЈ origin LIF feature and
2
2
Ј
2
the dilution of the oscillator strength, it follows that the mo-
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6814
Mikhaylichenko et al.: Unimolecular decomposition of NO3
D. Reaction rates
mass, parameters which are not known. However, we note
that a value of ␻bϭ300 cmϪ1 ͑corresponding to a ϳ1 Å
width 100 cmϪ1 below the top of the barrier and an 8 amu
effective mass͒ yields rates that are consistent with the data
shown in Fig. 9.
It follows from the above arguments that reaction ͑1͒ can
be described as proceeding via the ground PES and that sta-
tistical rate models can be applied which: ͑i͒ are semiclassi-
cal in nature ͓e.g., RRKM, phase space theory ͑PST͒, statis-
tical adiabatic channel model ͑SACM͔͒ when the resonances
are averaged over;40–42 and ͑ii͒ exhibit distributions of decay
rates, level spacings, absorption strengths, etc., when the
resonances are resolved.39,43 This picture can be comprised
when reactions ͑1͒ and ͑2͒ compete, specifically, when the
latter occurs so rapidly that decay to and within the lower
electronic manifolds is incomplete on the time scale of that
reaction.
As indicated in Fig. 9, there is no precise reaction ͑1͒
threshold—nor, because of the inevitable participation of
tunneling, can there be one. The marked variation of k1 with
photon energy shown in Fig. 9 has been verified by repeated
measurements and by using two complementary experimen-
tal techniques. Namely, rates obtained by monitoring reac-
tive quenching of the NO3 fluorescence are consistent with
rates obtained by recording NO buildup times, though the
latter are limited to values у106 sϪ1. Also, the collision-free
nature of this slow unimolecular process was confirmed ex-
perimentally.
As mentioned above, the NO yield spectrum near the
reaction ͑2͒ threshold reflects the k1/k2 ratio. Whereas reac-
2
2
2
tion ͑1͒ proceeds via the AЈ ground state, the AЈ and E
Ј
2
2
surfaces can both contribute to reaction ͑2͒. It is also possible
2
that E participates. It is a daunting task to establish the
Љ
respective roles of the different PESs involved in reaction
͑2͒.
An important point can be made concerning the possible
role of 2E ; namely, were a unimolecular reaction to proceed
Ј
exclusively on the zeroth-order 2E surface, its threshold rate
Ј
would be ͑h␳)Ϫ1ϳ1012 sϪ1, as estimated by using the ␳
value of 0.03/cmϪ1 obtained by direct count.47 This is too
slow to overcome internal conversion, which occurs with a
rate of ϳ1013 sϪ1, as estimated from the width of the E
2
Ј
original LIF feature. Moreover, for reaction rates Ͼ1012 sϪ1
,
the transition state will tighten with increasing energy, pre-
venting the rate from rising as rapidly with energy as pre-
dicted by a very loose transition state. Thus, it seems un-
likely that unimolecular reaction exclusively via the
2E surface can dominate in the k threshold region.
Ј
2
NO3 decay rates above the reaction ͑1͒ barrier have been
reported by Davis et al.,44 who used the picosecond-
resolution pump–probe technique to record NO buildup
times. They found that in the ϳ200 cmϪ1 window between
the top of the barrier and the OϩNO2 threshold, k1 varied
from 1 to 5ϫ109 sϪ1, with each measurement averaging rates
over the broad ͑60 cmϪ1͒ linewidth of the photolysis laser.
These data were fitted by using RRKM theory with a lowest
Another extreme case is when reactions ͑1͒ and ͑2͒ both
proceed via the ground state surface. This would occur in the
event that internal conversion went to completion prior to
reaction. In the rate equation limit, the NO yield above the
reaction ͑2͒ threshold is then determined by the k1/k2 ratio,
with each of the rates given by
transition state frequency of 70 cmϪ1
.
N‡ EϪE ͒
͑
0
kϭ
,
͑5͒
Figure 9 shows that below the barrier, k1 varies much
more rapidly than it does above the barrier, changing by
three orders of magnitude in ϳ100 cmϪ1. Since small tun-
neling probabilities display near-exponential dependencies
on the area beneath the top of the barrier, such rapid varia-
tion is expected. Moreover, tunneling can account for the
very different slopes that characterize the regimes above and
below ϳ109 sϪ1 ͑Fig. 9͒.26
The simplest way to incorporate tunneling into the sta-
tistical model is via motion along a one-dimensional reaction
coordinate that is separable at the transition state from the
orthogonal degrees of freedom. The tunneling probability
can then be calculated by using the WKB approximation,45,46
with the potential along the reaction coordinate taken as an
inverted parabola. The resulting expression is46
h␳ E͒
͑
where N‡(E Ϫ E0) is the number of open channels at the
transition state and ␳(E) is the parent density of states. For a
common intermediate, ␳(E) is the same for both decompo-
sition paths, and therefore k1/k2 is the ratio of the numbers of
open channels at the transition states for reactions ͑1͒ and
͑2͒, respectively. Since the reaction ͑1͒ transition state is
tight, its levels can be described as vibrational. Though the
frequencies are uncertain, values of 70 and 140 cmϪ1 for the
two lowest transition state frequencies yielded k1(E) values
in agreement with the experimental results.44 This predicts
an increase in k1 by a factor of several within a 100 cmϪ1
energy interval near the OϩNO2 threshold. On the other
hand, since the reaction ͑2͒ transition state is loose, k2 will
increase rapidly with energy relative to k1 , leading to the
rapid dominance of reaction ͑2͒.
At this point, we have not been able to draw firm con-
clusions concerning the roles of the zeroth-order PESs inso-
far as reaction ͑2͒ is concerned. An obvious extension of the
present work is double-resonance experiments in which the
reaction ͑2͒ threshold regime is examined with good energy
resolution and dissociation via the ground PES is decoupled
from the radiationless decay step.
exp Ϫ2␲E /␻ ͒
͑
Ј
b
P E ͒ϭ
,
͑4͒
͑
Ј
1ϩexp Ϫ2␲E /␻ ͒
͑
Ј
b
where ␻ is the magnitude of the imaginary frequency of the
b
barrier and EЈ is the energy in the reaction coordinate below
the zero point of the transition state ͑i.e., EЈϾ0͒. To obtain
␻b , it is necessary to have the barrier width and the effective
J. Chem. Phys., Vol. 105, No. 16, 22 October 1996
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Mikhaylichenko et al.: Unimolecular decomposition of NO3
6815
versus reaction via the NO3† intermediate. Since OϩNO2 col-
E. NO product state distributions and yield spectra
lisions can form NO†3 efficiently, there is the possibility that
The NO product state distributions can be rationalized
by invoking dynamical bias, namely, since the NOϩO2 re-
verse barrier is large, product excitations are strongly influ-
enced by the transition state region and the exit channel. As
anticipated for a large reverse barrier, the NO excitations are
insensitive to the photolysis photon energy in the small en-
ergy range between the top of barrier and the reaction ͑2͒
Ϫ
g
3
the observed X
͚
vibrational levels derive, at least in part,
from NO3 unimolecular decomposition.
The data shown in Fig. 10 indicate a monotonically de-
creasing population for O2 internal energies above ϳ10 500
Ϫ
g
cmϪ1. This corresponds to X ͚ vibrations from ϭ6 or 7
3
v
to ϭ11, though, as stated above, neither our measurements
v
nor those of Davis et al.24 resolve the separate contributions
threshold. The absence of a significant NO ( у 1) popula-
v
Ϫ
g
3
1
from X
͚
and a ⌬g . The data of Davis et al. are of
tion can be understood as vibrational adiabaticity from the
transition state to products. Specifically, vibrational quantum
numbers in degrees of freedom orthogonal to the reaction
coordinate are conserved past the transition state and appear
superior resolution, showing some vibrational structure,
whereas the present results are product state selective. How-
ever, the two data sets are consistent and the correspondence
between the translational energy distributions and the
in the fragments. The predominance of NO ͑ ϭ0͒ suggests
v
Ϫ
g
3
X
͚
LIF measurements is striking. We interpret this as
that the N–O bond lengths do not differ significantly be-
tween the transition state region and free NO. It is also con-
sistent with the stiffness of the N–O stretch coordinate in the
exit channel.
Ϫ
3
supporting a major, if not dominant, role for the X
͚
state.
g
If the O2 internal excitation resides predominantly in
3
X
͚
Ϫ , there is probably a significant vibrational population
g
inversion, since it is unlikely that rotations would be excited
to such a large extent. This can be rationalized by a reaction
͑1͒ transition state having a long O–O bond relative to free
O2. However, though we would have no difficulty accepting
The present work provides characterization of the
threshold regions of reactions ͑1͒ and ͑2͒. Much of this in-
formation is obtained from NO yield spectra ͑Fig. 8͒, whose
spectral density is nearly continuous, albeit with a lumpiness
that resembles the NO3 LIF spectra but with poorer
resolution.14 The NO yield spectrum on the low energy side
reflects the threshold region of reaction ͑1͒, which proceeds
through the barrier at the lowest energies. On the high en-
ergy side, the yield spectrum reflects competition between
reactions ͑1͒ and ͑2͒.
Ϫ
g
3
a X
͚
vibrational distribution peaked near ϭ6 or 7 based
v
on this mechanism, there currently exists no basis for inde-
pendent support, for example, through theoretical calcula-
tions.
V. CONCLUSIONS
F. Internal excitations
This paper reports and discusses measurements of NO3
unimolecular reactions under collision-free conditions. A
number of complementary data are presented: NO product
yield spectra; NO3 LIF spectra; NO rotational and fine-
structure state distributions; rates of NO3 decomposition; and
The data shown in Fig. 10 provide qualitative informa-
tion concerning O2 internal excitations despite the low reso-
lution. First, the amount of signal associated with O2 internal
1
energies lying below the a ⌬g threshold is significant. This
Ϫ
2
can only derive from X ͚g rovibrational excitation. Recall
that correcting the raw data shown in Fig. 10 for the R2
factor ͑where R is the radius of the recoil sphere͒ only en-
O2 internal energies correlated with
a
specific NO
2
(X ⌸ , ,J) state. The NO intramolecular dynamics are
v
⍀
3
strongly influenced by nonadiabatic interactions in the
Ϫ
g
hances the large-z contribution.30,31 Thus, X
͚
is defi-
3
14
2
2
2
B E /A E /X AЈ electronic subset. Nuclear motions at
Ј
Љ
2
nitely produced as a counterfragment of the monitored NO
level. The monotonic increase of the signal up to the a ⌬g
these energies are believed to be chaotic, resulting in decom-
position rates that can be calculated by using statistical theo-
ries.
1
threshold indicates a considerable population inversion
Ϫ
g
3
within the X
͚
ground electronic state.
The NOϩO2 channel involves molecular eigenstates
Ϫ
3
1
having modest 2E character, and dominant character of
In the region where X
͚
and a ⌬g are both energeti-
Ј
g
cally accessible, their separate contributions cannot be re-
solved. However, the decrease in signal in the spatial region
lower electronic manifolds. The most probable terminus of
2
radiationless decay is believed to be AЈ2, but we leave open
ϩ
1
2
close to the center of the recoil sphere ͑i.e., where b
͚
the possibility of E participation.
Љ
g
would appear͒ is clear. Combined with the fact that the ex-
A narrow window exists for the NOϩO2 channel. Very
slow rates were observed after excitation with photons that
promote the system to energies that lie below the reaction ͑1͒
barrier. Specifically, rates for collision-free photoinitiated
unimolecular decomposition ranged from 1ϫ104 sϪ1 at
16 780 cmϪ1 to 6ϫ107 sϪ1 at 16 880 cmϪ1. Tunneling is
believed to be responsible for this behavior. A simple exten-
sion of RRKM theory confirms that tunneling could indeed
result in unimolecular decay rates that vary rapidly enough
with energy to be consistent with the experimentally mea-
sured rates.
perimental method is most sensitive to slow fragments, this
ϩ
g
1
observation rules out significant population of the b
͚
state.
Smith et al.48 have shown that the OϩNO2→O2ϩNO
Ϫ
3
bimolecular reaction ͑300 K͒ yields O2 (X ͚g ) in high vi-
brational levels. They report a monotonic decrease in popu-
lation from ϭ6 to ϭ11, i.e., for O internal energies
v
v
2
above 9800 cmϪ1. Lower vibrational levels could not be de-
tected by using the LIF method they employed, and it was
not possible to isolate the respective roles of direct reaction
J. Chem. Phys., Vol. 105, No. 16, 22 October 1996
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6816
Mikhaylichenko et al.: Unimolecular decomposition of NO3
13
´
NO rotational excitation is modest and the distributions
are insensitive to the excitation photon energy. Vibrational
A. Delon, P. Dupre, and R. Jost, J. Chem. Phys. 99, 9482 ͑1993͒.
14 L. Valachovic, C. Riehn, K. Mikhaylichenko, and C. Wittig, Chem. Phys.
Lett. ͑in press͒.
excitation is also modest: ϭ 1 / ϭ 0 ϳ 0.1. There is a
͓v
͔ ͓v
͔
15 A. Weaver, D. W. Arnold, S. E. Bradforth, and D. M. Neumark, J. Chem.
Phys. 94, 1740 ͑1991͒.
Ϫ
g
3
high degree of O2 internal excitation, with the X
͚
ground
state produced throughout the entire photolysis region, in
agreement with results from previous measurements of c.m.
translational energy distributions.24 A significant fraction ͑at
least one-third͒ of the O2 is formed with internal energies
16 E. Hirota, K. Kawaguchi, T. Ishiwata, and I. Tanaka, J. Chem. Phys. 95,
771 ͑1991͒; T. Ishiwata, I. Tanaka, K. Kawaguchi, and E. Hirota, ibid. 82,
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17 K. Kawaguchi, E. Hirota, T. Ishiwata, and I. Tanaka, J. Chem. Phys. 93,
951 ͑1990͒.
1
18
¨
below the a ⌬g threshold, and it is assumed that excitation
M. Mayer, L. S. Cederbaum, and H. Koppel, J. Chem. Phys. 100, 899
Ϫ
3
͑1994͒.
within X ͚g is predominantly vibrational as opposed to ro-
19
¨
E. Haller, H. Koppel, and L. S. Cederbaum, J. Chem. Phys. 78, 1359
Ϫ
g
3
tational. The distribution within X
͚
indicates a popula-
͑1983͒.
20 See, for example, D. W. Noid, M. L. Koszykowski, and R. A. Marcus,
Annu. Rev. Phys. Chem. 32, 267 ͑1981͒; E. B. Stechel and E. J. Heller,
ibid. 35, 563 ͑1984͒; V. E. Bondybey, ibid. 35, 591 ͑1984͒.
tion inversion which can be rationalized as due to the geom-
etry of the 3-center transition state.
1
If O2(a ⌬g) is not produced, the most populous
21 The density of vibrational states in the ground PES near the 2E origin
Ј
Ϫ
3
X
͚
vibrational levels are ϳ ϭ6 or 7 for the photolysis
v
g
was obtained by direct harmonic count using the ground state vibrational
frequencies from Ref. 8.
region 16 860–17 080 cmϪ1. It is important to keep in mind
that the measurements do not distinguish between low-lying
22 G. Herzberg, Molecular Spectra and Molecular Structure. III. Electronic
Spectra and Electronic Structure of Polyatomic Molecules ͑Krieger, Mala-
bar, 1991͒.
1
vibrational levels within a ⌬gand high vibrational levels of
3
X
X
͚
͚
Ϫ . Nonetheless, there is a good possibility that
23 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Struc-
ture. IV. Constants of Diatomic Molecules ͑Van Nostrand Reinhold, New
York, 1979͒.
g
Ϫ
3
is the dominant O2 species. For example, Smith
g
et al.48 report that O2 from the OϩNO2→NOϩO2 reaction is
24 W. H. Miller, Chem. Rev. 87, 19 ͑1987͒.
formed in vibrational levels whose populations decrease
25 Y. S. Choi and C. B. Moore, J. Chem. Phys. 97, 1010 ͑1992͒.
26 H. F. Davis, B. Kim, H. S. Johnson, and Y. T. Lee, J. Phys. Chem. 97,
2172 ͑1993͒.
monotonically from ϭ6 to ϭ11. The O internal energy
v
v
2
distribution ͑see Fig. 10͒ also decreases monotonically over
Ϫ
27 D. W. Kohn, H. Clauberg, and P. Chen, Rev. Sci. Instrum. 63, 4003
͑1992͒.
3
this range, further supporting O2(X ͚g ) as a major ͑if not
dominant͒ O2 species.
28 R. E. Smalley, L. Wharton, and D. H. Levy, J. Chem. Phys. 63, 4977
Above the OϩNO2 threshold, reaction ͑2͒ dominates.
͑1975͒.
Though 2E is believed to correlate without a barrier to
29
Ј
¨
E. Bohmer, S. K. Shin, Y. Chen, and C. Wittig, J. Chem. Phys. 97, 2536
͑1992͒.
ground state products, unimolecular reaction exclusively on
30 A. Sanov, C. R. Bieler, and H. Reisler, J. Phys. Chem. 99, 13637 ͑1995͒.
31 H. Ni, J. M. Serafin, and J. J. Valentini, J. Chem. Phys. 104, 2259 ͑1996͒.
32 R. C. Hilborn, Am. J. Phys. 50, 982 ͑1982͒.
2E is not fast enough to bypass internal conversion. Specifi-
Ј
cally, the estimated k2 value is an order of magnitude smaller
than the radiationless decay rate of 1013 sϪ1 inferred from the
33 H. Okabe, Photochemistry of Small Molecules ͑Wiley-Interscience, New
York, 1978͒.
2
LIF spectrum of the 2E ← AЈ origin. Therefore, several sur-
Ј
2
34 A number of vibronic level densities have potential relevance for the
faces may contribute. It is a daunting task to establish the
2
2E ← AЈ origin region. First, consider all levels of E vibronic symmetry
Ј
Ј
2
respective roles of the different PESs involved in reaction
͑2͒.
having one quantum of ␯ or ␯ excitation. In this case, ␳ϳ5/cmϪ1. Ac-
3
4
cording to PJT selection rules, these should have the largest coupling
matrix elements with the 2E bright state. Alternatively, counting all lev-
Ј
els having E vibronic symmetry yields ␳ϳ20/cmϪ1, which can be com-
Ј
ACKNOWLEDGMENTS
pared to ␳ϳ100/cmϪ1 for all levels within the 2A2Ј electronic state irre-
We thank D. Arnold, P. Ionov, I. Bezel, H. Reisler, I. W.
M. Smith, and F. Davis for valuable input.
spective of vibronic symmetry. The similarity between the density of PJT-
promoting-mode levels and the density of mixed levels estimated from the
oscillator strength dilution factor is noteworthy. However, this may be
fortuitous. For example, since measurements of ␶fl values in excess of 100
␮s are difficult, it is possible that the zero-pressure lifetimes extend even
to the millisecond regime.
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39
´
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47 The following 2E vibrational frequencies were used in calculating densi-
ties of states for the 1900–2100 cmϪ1 interval above the 2E origin:
␯1ϭ773 cmϪ1, ␯2ϭ944 cmϪ1, ␯3ϭ1446 cmϪ1 ͑Ref. 8͒, and ␯4ϭ380 cmϪ1
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Ј
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45 L. D. Landau and E. M. Lifshitz, Quantum Mechanics ͑Pergamon,
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137.222.114.240 On: Wed, 26 Nov 2014 11:38:45