Energy partitioning in two kinds of NO molecules generated from the reaction of O(1D) with N2O: Vibrational state distributions of "new" and "old" NO's

Article abstract of DOI:10.1063/1.479363

The reaction of O(¹D) with N₂O produces two kinds of NO molecules, the "old" one which originally exists in N₂O and the "new" one which includes the attacking O atom. Using the isotopically labeled reagent, we determined the vibrational state distributions of these NO's (X²∏; v = 0-17) separately. To obtain the distributions, two types of experiments were performed with the laser-induced fluorescence (LIF) technique via the NO A→X and B→X transitions. First, the relative populations of NO molecules (the sum of the two kinds of NO's) in v = 0-11 levels were measured with unlabeled reagents. Then, isotopically labeled reaction, ₁₈O(¹D) + N₂¹⁶O→N¹⁸O+N¹⁶O, was utilized to determine the relative ratio between the two kinds of NO's in the vibrational levels of v = 0-5 and 12-15. Combining the above results with previously determined vibrational state distribution of NO in high vibrational levels (v=11-17) [J. Chem. Soc., Faraday Trans. 94, 1575 (1998)], we were able to obtain a complete set of vibrational state distributions. It was found that the old NO dominantly populated in v = 0 and 1 whereas the new NO extended its population toward higher vibrational levels (v = 4-15). However, in high vibrational levels, the old NO still have a considerable population due to the rapid energy transfer to the old NO. The observed efficient energy transfer to the old NO is attributed to the absence of light atoms in the present reacting system. Compared with the system including hydrogen atoms, the state density and the momentum coupling among the vibrational modes are much larger and accelerate the energy redistribution in spite of the short lifetime.

Full text of DOI:10.1063/1.479363

Energy partitioning in two kinds of NO molecules generated from the reaction of O ( 1
D) with N 2 O : Vibrational state distributions of “new” and “old” NO’s
Hiroshi Akagi, Yo Fujimura, and Okitsugu Kajimoto
Citation: The Journal of Chemical Physics 111, 115 (1999); doi: 10.1063/1.479363
View online: http://dx.doi.org/10.1063/1.479363
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 111, NUMBER 1
1 JULY 1999
Energy partitioning in two kinds of NO molecules generated
1
from the reaction of O„ D… with N2O: Vibrational state distributions
of ‘‘new’’ and ‘‘old’’ NO’s
Hiroshi Akagi, Yo Fujimura, and Okitsugu Kajimotoa)
Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho,
Sakyo-ku, Kyoto 606-8502, Japan
͑Received 8 December 1998; accepted 8 April 1999͒
The reaction of O(1D) with N2O produces two kinds of NO molecules, the ‘‘old’’ one which
originally exists in N2O and the ‘‘new’’ one which includes the attacking O atom. Using the
isotopically labeled reagent, we determined the vibrational state distributions of these NO’s ͑X 2⌸;
ϭ0–17͒ separately. To obtain the distributions, two types of experiments were performed with
v
the laser-induced fluorescence ͑LIF͒ technique via the NO A←X and B←X transitions. First, the
relative populations of NO molecules ͑the sum of the two kinds of NO’s͒ in ϭ0–11 levels
v
were measured with unlabeled reagents. Then, isotopically labeled reaction, 18O(1D)
ϩN216O→N18OϩN16O, was utilized to determine the relative ratio between the two kinds of NO’s
in the vibrational levels of ϭ0–5 and 12–15. Combining the above results with previously
v
determined vibrational state distribution of NO in high vibrational levels ( ϭ11–17) ͓J. Chem.
v
Soc., Faraday Trans. 94, 1575 ͑1998͔͒, we were able to obtain a complete set of vibrational state
distributions. It was found that the old NO dominantly populated in ϭ0 and 1 whereas the new NO
v
extended its population toward higher vibrational levels ( ϭ4–15). However, in high vibrational
v
levels, the old NO still have a considerable population due to the rapid energy transfer to the old
NO. The observed efficient energy transfer to the old NO is attributed to the absence of light atoms
in the present reacting system. Compared with the system including hydrogen atoms, the state
density and the momentum coupling among the vibrational modes are much larger and accelerate
the energy redistribution in spite of the short lifetime. © 1999 American Institute of Physics.
͓S0021-9606͑99͒02225-4͔
I. INTRODUCTION
that is, a ‘‘new’’ NO which contains a reactant O atom and
an ‘‘old’’ NO which originally exists in the reactant N2O.
Isotopically labeled studies of this reaction have been carried
out by two groups. Using 15N14NO, Simons and co-workers
have observed the overlapped signal of 15NO and 14NO in
Nascent internal state distribution of reaction products
contains rich information of reaction dynamics on a
potential-energy surface ͑PES͒ and hence detailed data of the
product state distribution have been accumulated for a vari-
ety of reactions.1 However, there are few cases where the
internal state distribution of all the reaction products were
reported. One such example is the reaction 16O(1D)
the lower vibrational levels ϭ0–2 and they reported that
v
the contributions from the 15NO and 14NO signals in the
v
ϭ1 and 2 levels were comparable.3 Their observation indi-
cates that the vibrational energy is distributed equally be-
tween the two NO’s. On the other hand, Honma et al. per-
formed an aligned O(1D)ϩ15N14NO reaction using a
15N14NO dimer formed in a supersonic jet and compared the
2
16
ϩH218O→ OHϩ18OH. The authors found a completely
different state distribution between 16OH and 18OH. This ob-
servation clearly indicated that the energy mixing was far
from complete even in the reaction having a deep potential
well on the PES. Thus, the determination of the state distri-
butions in all reaction products is extremely important to
deepen the understanding of reaction dynamics on the
potential-energy surface.
relative populations of the two kinds of NO’s at ϭ0 and 3.4
v
v
They found that the old 14NO was dominant in ϭ0 while
the new 15NO was more populated in ϭ3. Based on their
v
experimental results, they have proposed an interpretation
that the excess energy is mainly poured into the new 15NO
while the old 14NO stays in its low vibrational level.
In the present study, we have determined the vibrational
state distribution of all the products of the reaction,
The reaction ͑a͒ occurs almost at every collision with the
rate constant of 7.2ϫ10Ϫ11 cm3 moleculeϪ1 sϪ1,5 and has a
large exothermicity ⌬H0(0)ϭϪ342.6 kJ molϪ1,6 which can
1
O D͒ϩN O→2NO X 2⌸͒.
͑a͒
͑
͑
2
This reaction is one of the fundamental reactions in strato-
spheric chemistry and also a prototype reaction of O(1D)
atoms. The reaction produces two kinds of NO molecules,
excite the product NO up to ϭ16. In contrast to the large
v
exothermicity, the bond dissociation energy of (NO)2 , a
possible intermediate of this reaction, is very small (D0
Ϸ700 cmϪ1).7 Therefore, the well of PES, if any, must be
extremely shallow. According to the ab initio MO calcula-
a͒
Author to whom correspondence should be addressed.
0021-9606/99/111(1)/115/8/$15.00
115
© 1999 American Institute of Physics
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116
J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
Akagi, Fujimura, and Kajimoto
the 16O(1D) and 18O(1D) atoms, together with the heat of
reaction, provide the total available energies of 364.2 and
363.5 kJ molϪ1, respectively,11 and can excite N16O and
tions, this reaction has a significantly attractive PES, on
which the heat of reaction is mainly released during the ap-
proach of the O atom toward N2O.8 Under such a situation,
the trajectories running on the PES quickly pass through the
interactive region, where the four atoms can interact with
each other, and the lifetime of a collision complex must be
quite short. Consequently, incomplete vibrational energy re-
distribution within the collision complex is expected. These
considerations suggest that most of the available energy is
given to the newly formed NO, with a possibility of inverted
vibrational state distribution. On the other hand, the old NO
acts as a spectator and remains vibrationally cold. As a re-
sult, the vibrational state distribution of NO in the unlabeled
reaction could be bimodal, corresponding to the distribution
of each NO molecules. In order to check the above expecta-
tion and obtain more detailed information of the reaction
dynamics, we have determined the complete vibrational en-
ergy distributions of the two NO molecules.
N18O up to ϭ18 and 19, respectively. N O and O ͑or 18O3͒
v
2
3
gases were introduced into a reaction cell, a glass bulb of 24
cm diam, up to 1 Torr. Partial pressures of N2O and O3 were
900 and 100 mTorr, respectively. O3 and 18O3 were synthe-
sized by the silent discharge technique12 from O2 ͑Teisan
99.995%͒ and 18O2 ͑Matheson 99.2 at %͒, respectively. Be-
cause 18O2 gas is costly and easily consumed in the flow
system, all experiments were carried out under static condi-
tions. N2O ͑Showa-Denko 99.999%͒ was used without fur-
ther purification.
The O(1D)ϩN2O reaction was initiated by O3 photoly-
sis at 266 nm, with a frequency-quadrupled Nd:YAG laser
͑Quanta Ray DCR-11͒. The reaction product NO was de-
tected with a LIF technique by using the NO A 2⌺ϩ(
v
v
ϭ0–2)←X 2⌸( ϭ0–11) and B 2⌸( ϭ0–2)←X 2⌸(
v
v
According to the previous studies on the unlabeled reac-
tion, the vibrational state distribution in lower vibrational
ϭ12–15) transitions. For the LIF detection, three types of
light sources were used. For the wavelength shorter than 290
nm, a frequency doubled output ͑Inrad Autotracker-III AT-
III͒ of a dye laser ͑LAS LDL20505͒ pumped by the third
harmonics of a Nd:YAG laser ͑Quanta Ray GCR-4͒ was
used. The dye laser was pumped by the second harmonics of
the Nd:YAG laser for the light 290Ͻ␭Ͻ370 nm. The light of
the third region ␭Ͼ370 nm was obtained by pumping a dye
laser ͑Lambda Physik LPD 100͒ with a XeCl excimer laser
͑Lambda Physik LPX 3000͒. The intensity of the probe laser
light was attenuated in order to avoid saturation in absorp-
tion. The delay time between the photolysis and the probe
laser lights was 5 ␮s. All systems were operated with a rep-
etition rate of 10 Hz.
levels ( ϭ0–4) looks statistical.3 In our previous work de-
v
tecting the highly vibrationally excited NO( ϭ11–17), the
v
vibrational population gradually declines as the vibrational
quantum number increases without any indication of inverted
population, and it is even slightly colder than the statistical
distribution.9 Brouard et al. have determined the rotational
and translational state distributions in detail,10 and concluded
that there are two types of reaction dynamics. A direct strip-
ping reaction yields NO( ϭ0) and NO( ϭ16–18) whereas
v
v
an indirect process, in which the collision complex survives
for a sufficient time to allow extensive rovibrational energy
redistribution, leads to the formation of rotationally excited
NO products in ϭ1–15.
v
To determined the relative vibrational distribution
The present work aims at determining the complete set
of the vibrational state distributions of product NO’s gener-
ated from the isotopically labeled reaction,
among ϭ0, 1, 3, 6, 9, and 11 vibrational levels, we com-
v
pared the relative intensity of the two transitions originating
from different ground vibrational levels. When a single dye
covers the wavelength range of the two transitions from dif-
ferent vibrational levels, it is easy to estimate the relative
population for these two vibrational levels. This was not the
1
18O D͒ϩN 16O→N18OϩN16O.
͑aЈ͒
͑
2
For this purpose, we carried out two types of experiments
utilizing the LIF technique. First, we measured the vibra-
tional state distribution of total NO produced from the unla-
beled 16O(1D)ϩN216O reaction. Then, using isotopically la-
beled reaction, we determined the relative populations
between the old N16O and the new N18O in each vibrational
level. These two types of experiments bring the ‘‘complete’’
vibrational state distributions. Although the experimental and
analytical procedures are almost the same as our previous
work,9 the LIF detection with the A←X transition was uti-
lized in this experiment in addition to the previously used
B←X transition. The quenching rate coefficient of NO(A)
by N2O, O3, and O2 were also determined in this study in
order to deduce reliable vibrational populations.
case for measuring the relative populations between ϭ1
v
and 3, and between ϭ9 and 11. For these vibrational lev-
v
els, we have to change dye solutions for a set of experiments,
which often deflect the laser path away, and consequently,
the laser power monitored at the cell entrance might not co-
incide with the power at the center of the reaction cell. To
avoid this discrepancy, we monitored the laser power at the
cell exit using a joulemeter ͑Gentec ED-100A͒ with a wide
surface. The detailed procedures for calculating the real
population from the observed intensity were described in de-
tail in the previous paper.9
III. ANALYSIS
II. EXPERIMENT
In the previous study, we have carefully assessed several
factors which prevent us from accurate determination of the
vibrational population, and carried out the necessary
corrections.9 Since the corrections are almost the same for
the present study, only a brief description will be given in the
following sections with a due stress on the new corrections.
Since the experimental procedure used in the present ex-
periments is similar to the previous one,9 the experimental
apparatus and procedure are described briefly. O(1D) and
18O(1D) atoms were generated by the O3 and 18O3 photodis-
sociations at 266 nm, respectively. The kinetic energies of
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
Energy partition reaction of O(1D) with N2O
117
2
ϩ
TABLE I. Rate constants for the quenching of NO(A
⌺
;
ϭ0–2) by O ,
v
A. Corrections for the decrease of O3 concentration
3
N2O, and O2.a
Because the present experiments are performed in a bulb
under static conditions, the composition of the reaction gas
mixture gradually varies as the photolysis proceeds. In par-
ticular the decrease of O3 concentration requires the follow-
ing corrections:
2
kq of NO(A
⌺
ϩ)/10Ϫ12 cm3 moleculeϪ1 sϪ1
Quencher
O3
0
1
2
573Ϯ57
͓Ϫ͔
450Ϯ45
͓Ϫ͔
781Ϯ78
͓Ϫ͔
͑1͒ Decrease in the amount of O(1D) atoms generated from
O3 photodissociation.
471Ϯ47
͓506Ϯ33͔
499Ϯ50
͓Ϫ͔
160Ϯ16
͓140Ϯ13͔
466Ϯ47
͓Ϫ͔
149Ϯ15
͓Ϫ͔
N2O
O2
c
151Ϯ15
͑2͒ Increase in the fraction of O(1D) reacting with N2O.
͑3͒ Decrease in the absorption of fluorescence from
NO(A,B) by O3.
c
d
͓162Ϯ5͔
Radiative rateb
/105 sϪ1
49.5Ϯ3.7
52.1Ϯ4.1
54.9Ϯ3.2
͑4͒ Decrease in the rate of NO(A,B) quenching by compo-
nent gases.
͑5͒ Decrease in the absorption of probe laser light by O3.
aThe experimental uncertainty corresponds to 1␴ in the least-squares fit.
bReference 14.
cReference 16.
dReference 18.
Since the A←X transition is utilized for the LIF detection in
the present experiments, the third and fourth effects are more
serious than in the previous study. Furthermore, when NO
molecules in the lower vibrational levels ( ϭ0–6) are
v
the information of other rate constants was not available, we
have determined the quenching rate constants of NO(A) in
vϭ0–2 by measuring the lifetimes at five different gas com-
monitored with the A←X transitions, the wavelengths of the
probe laser light overlaps with the Hartley band of O3 ͑200–
320 nm͒, whose absorption coefficients are quite large.5,12,13
We should, then, estimate the probe laser intensity at the
center of reaction cell to correct for the signal intensities. For
the three corrections, 3–5, the detailed procedures are de-
scribed below.
positions. Using the obtained lifetimes of NO(A; ϭ0–2),
v
we have evaluated the absolute rate constants based on the
most recently reported quenching constants of NO(A;
v
ϭ0) by N2O and O2.16 We have assumed that the relative
rate constants between N2O and O2 are not dependent on the
vibrational level. The results obtained for each vibrational
level of NO(A) are listed in Table I, together with the radia-
tive rates used in this analysis.14 The quenching rate con-
stants are compared with the available data, showing a good
agreement. These values were used to estimate the loss of the
NO(A) fluorescence by the quenching processes.
1. Absorption of the NO„A… fluorescence by O3
Because of the large absorption cross-section of O3 at
Hartley band, ca. 8%–26% of the fluorescence from the
NO(A) in ϭ0–2 is absorbed by 100 mTorr O during the
v
3
passage from the center to the detection window of the reac-
tion cell. To obtain the reliable relative populations among
different vibrational levels of NO(A), experimental data
must be corrected for this O3 absorption. The procedure used
previously for NO(B) was adopted for this correction except
3. Absorption of the probe laser light by O3
Ozone gases significantly absorbs the probe laser light
for using the transition wavelength ␭
and the transition
v
v
Ј Љ
probability Rv of NO(A).14 To apply Eq. ͑IX͒ in Ref. 9 to
used for the detection of NO’s in ϭ0–6 levels; the wave-
v
v
Ј Љ
lengths of probe laser are in the O3 Hartley band. In a typical
case, the probe laser intensity at 256 nm is reduced to the
two-thirds of the incident light by the time it reaches the
center of the cell.5 Using the Lambert–Beer’s law, we can
estimate the probe laser intensity at the center of reaction cell
as
the correction, we measured the O3 absorbance at 266 nm
from the intensities of photolysis laser light before and after
passing through the reaction cell.
2. Rates of NO„A… quenching by buffer gases
In the previous work using NO B←X transition for the
probe
in
IpceronbteerϭI
exp Ϫk ␭
;O ͒ O l /2
͑1͒
LIF detection,9 we have measured the fluorescence decay
͓
͑
͓
͔
͔
v
v
Ј Ј
3
3
cell
rates of NO(B) in ϭ0–3, and determined the quenching
v
k ␭
;O3͒
v
Iin
͑
v
probe
in
Ј Љ
2k 266 nm;O ͒
rate constants of NO(B) by O3, N2O, O2, and N2 in order to
correct the LIF intensity for the loss of NO(B). Since A state
fluorescence was used for the LIF detection in the present
experiments, we should correct for the quenching of NO(A)
by the component gases in the reaction cell. The quenching
processes by O3, N2O, and O2 could be significant, since
these gases are abundant in the cell. The quenching rate con-
ϭI
exp Ϫ
ln
͑2͒
ͫ
ͩ ͪ
ͬ
Iout
͑
3
k͑␭
;O ͒/2k͑266 nm;O ͒
3 3
v
v
Ј Љ
Iout
probe
in
ϭI
,
͑3͒
ͩ ͪ
Iin
probe
in
where I
is the intensity of probe laser light at the cell
entrance, k(␭
wavelength ␭
;O3) is the O3 absorption coefficient at a
, ͓O3͔ is the O3 concentration, and lcell is
v
v
Ј Љ
v
Ј Љ
stants of NO(A) in ϭ0 by N O ͑Refs. 15 and 16͒ and O
v
2
2
v
͑Refs. 15–18͒ and in ϭ1 by O ͑Ref. 18͒ have already been
the path length of the photolysis laser light in the reaction
cell, respectively. In the derivation Eq. ͑2͒ from Eq. ͑1͒, we
substitute Eq. ͑I͒ of Ref. 9 into ͓O3͔. Equation ͑3͒, together
with experimentally obtained value of Iout /Iin , was used for
the correction of the signal intensities.
v
2
reported, and all of these processes are found to be com-
pleted in almost a single collision efficiency. This large
quenching efficiency must seriously affect the evaluation of
the vibrational population by the LIF measurements. Since
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118
J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
Akagi, Fujimura, and Kajimoto
B. Possibility of vibrational relaxation and vibrational
energy transfer between two NO’s
Since the present experiment were carried out under me-
dium pressure and long delay conditions, we should consider
vibrational quenching of product NO. In our previous paper,
we mentioned that the vibrational quenching had no signifi-
cant effect for high vibrational levels ( ϭ11–17).9 In the
v
lower vibrational states, the vibrational quenching rate con-
stants for NO ( ϭ1–11) colliding with N O ͑Ref. 19͒ and
v
2
those for NO ( ϭ1–7) colliding with O ͑Ref. 20͒ have
v
2
already been known. According to the available information,
the fraction of vibrationally quenched NO is calculated to be
less than 2% at 5 ␮s after the photolysis. However, the
quenching rate constant by O3 which is the highly abundant
component in the gas mixture, has not yet been reported to
our best knowledge. Thus, we made a comparison between
signal intensities under the conditions of different O3 partial
FIG. 1. Vibrational state distribution of NO(X 2⌸) generated from the
O(1D)ϩN2O reaction. The large and small square symbols mean the
present results and those calculated from the data in Ref. 9, respectively.
The solid line shows the distribution predicted from the phase space theory.
The given experimental uncertainty corresponds to 1␴ in the least-squares
fit.
pressures. We did not find any changes in ϭ1–11, and
v
therefore neglected the vibrational quenching of NO by the
component gases including O3.
In addition to the vibrational quenching, vibrational en-
ergy transfer between N16O and N18O should be considered
since this effect is expected to equalize the populations of the
two NO’s in each vibrational level by scrambling the nascent
populations. However, this had little influence, because the
partial pressures of N16O and N18O in the reaction cell were
negligibly small and they were quickly consumed by the
efficient reaction
Once we know the accurate rotational temperature for
each vibrational level under the rotationally relaxed condi-
tion, the measurement of only one rovibrational peak of a
given vibrational level is enough to estimate the total popu-
lation of the vibrational level ͑i.e., the sum of all rotational
levels͒. For the actual experiments, the intensities of more
than three rovibrational peaks were selected in each band and
their intensities were measured. To determine the population
ratio between two different vibrational levels, the intensities
of the selected peaks in the two corresponding bands were
measured within a single scan. This measurements were per-
formed three times for each pair of vibrational levels. A sta-
tistical analysis for the results of these measurements was
made to evaluate the population ratio.
NOϩO3→NO2ϩO2
k
298ϭ1.8ϫ10Ϫ14 cm3 moleculeϪ1 sϪ1͒5,
͑b͒
͑
and all NO molecules disappeared before the next shot of the
photolysis laser. To ascertain that the vibrational energy
transfer does not produce any serious effect on the popula-
tion ratio between two NO’s, we performed an additional
experiments with shorter ͑3 ␮s͒ and longer ͑7 ␮s͒ delay
IV. RESULTS
times for ϭ4, 14, and 15 levels. The relative populations
v
A. Vibrational state distribution of total NO products
1
generated from 16O„ D…؉N216O
evaluated from these three sets of data did not showed any
difference within the experimental error, which confirmed
the negligible influence by the energy transfer.
To extend the previously obtained vibrational state dis-
tribution of highly excited NO ( ϭ11–17) ͑Ref. 9͒ to the
v
lower vibrational levels ( ϭ0–11), we determined the rela-
v
C. Determination of vibrational state distribution or
relative populations between NO’s
tive vibrational distribution among ϭ0, 1, 3, 6, 9, and 11
v
vibrational levels and estimated the vibrational populations
of in-between levels by interpolation.
In order to determine the vibrational state distribution or
the population ratio between N16O and N18O, we need to
obtain the rotational state distribution in each vibrational
level with high accuracy. Since the extremely high rotational
excitation of the NO molecules produced from this reaction
prevents us from the accurate determination of rotational dis-
tribution, we performed the experiments under medium pres-
sure ͑1 Torr͒ and long delay time ͑5 ␮s͒ conditions. Under
such conditions, product NO molecules can collide with
other buffer gases about 100 times before the detection.
Thus, rotationally excited NO molecules are fully relaxed to
the thermal distribution, whereas the vibrational population
remains the same as nascent. The experiments showed that
the rotational distribution can well be described by a single
Boltzmann temperature around 300 K.
The vibrational state distribution thus obtained is shown
in Fig. 1, together with the previous results for ϭ11–17.
v
As a whole, the vibrational population declines as the vibra-
tional quantum number increases. In Fig. 1, we also plotted
the distribution predicted from phase space theory ͑PST͒.21
The experimental populations between ϭ0 and 9 agree
v
closely with the PST distribution, whereas the population
above ϭ9 rapidly decreases with increasing vibrational
v
quantum number and the distribution is apparently colder
than the statistical one. From this distribution, we could es-
timate the average vibrational energy E
by assuming that
͘
vib
͗
the vibrational population changes smoothly. The obtained
value, 5500 cmϪ1, is comparable to that predicted from the
PST distribution, 6400 cmϪ1. The discrepancy in the high
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
Energy partition reaction of O(1D) with N2O
119
28 077 cmϪ1, whereas that of N18O is 27 449 cmϪ1. The
energy difference ͑628 cmϪ1͒ is, however, smaller than a
half of the vibrational quantum at ϭ16 of N18O ͑1400
v
cmϪ1͒. Thus, the difference in the vibrational-energy levels
between the isotopically different NO’s has very little influ-
ence.
The obtained population ratios between N18O and N16O,
N(N18O; )/N(N16O; ), are listed in Table II, together with
v
v
the vibrational state distribution of NO produced from the
unlabeled reaction. The listed data clearly shows that old
N16O exceeds the new N18O in the lower vibrational levels
͑ ϭ0 and 1͒, whereas the new N18O becomes the major
v
component above ϭ4. The average vibrational energies of
v
FIG. 2. Rotationally relaxed LIF spectrum of N16O( ϭ12) and N18O(
v
v
new and old NO’s are calculated to Ϸ7000 and 4000 cmϪ1
,
ϭ13) produced from the 18O(1D)ϩN216O reaction. The transitions corre-
spond to N16O B←X(0←12) and N18O B←X(1←13). Spectrum was
taken with 5 ␮s delay time and 1 Torr total pressure. Since the transition
probability of the B←X(1←13) is approximately 2.4 times larger than that
respectively. These results coincide with the expectation that
the newly formed NO is vibrationally excited and the NO
already existing in N2O is vibrationally cold.
It is noteworthy, however, that the amount of energy
gained by the old NO is more than what we expected from a
simple consideration. Actually, the old NO has a consider-
of the B←X(0←12), the population of the old NO in ϭ12 level is almost
v
the same as that of the new NO in ϭ13 level.
v
vibrational levels ( ϭ9–17) has little influence on the av-
erage vibrational energies, because of the minor populations
in these levels.
v
able population even in ϭ12–15, which amounts to be
v
1/3–1/5 population of the new NO. This fact is also apparent
from Fig. 2. Since the transition probability of the B←X(1
←13) for N18O is approximately 2.4 times larger than that of
the B←X(0←12) used for N16O,24 this spectrum implies
Simons and coworkers have reported that the vibrational
distribution in ϭ0–4 is described by a Boltzmann-type
v
function with a vibrational temperature TvibϷ6000K.3 How-
that the population of the old NO in ϭ12 level is almost the
v
ever, the distribution in ϭ0–17 determined by our experi-
v
same as that of the new NO in ϭ13.
v
ments could not be described by a single Boltzmann distri-
bution. If we fit the distributions in ϭ0–9 and 9–17 ranges
v
V. DISCUSSION
separately with different single exponential functions, the
temperatures are Ϸ 12 000 and 2 000 K, respectively. The
discrepancy in the vibrational temperature between the two
groups may arise from vibrational relaxation, since Simons’
group performed the experiments under higher pressures ͑40
Torr͒. Recently, Wang et al. have determined the vibrational
The vibrational energy distributions of the new and old
NO’s obtained for the O(1D)ϩN2O→2NO reaction in the
present experiment indicate that the new NO is vibrationally
more excited than the old NO. The old NO shows its maxi-
mum at ϭ0 whereas the population in the new NO has a
v
state distribution in ϭ1–11 and reported that the distribu-
v
broad maximum between ϭ1–6. The average vibrational
v
tion is characterized by a single Boltzmann temperature
energy of the old NO is 4000 cmϪ1, which is much smaller
than that of the new NO, 7000 cmϪ1. This trend is under-
standable because at the initial stage of forming the new NO
T
vibϷ9000 K.22 This figure is in satisfactory agreement with
our result for the lower vibrational levels.
*
all the exothermic energy may be located at the O –N–N
B. Relative populations between N18O and N16O
part of the collision complex. The localized exothermic en-
ergy is gradually transferred into the old NO as the reaction
proceeds. This energy mixing process, however, competes
with the fission of the N–N bond to form the two NO’s. The
old NO, therefore, has less chance of accepting the vibra-
tional energy when the lifetime of the collision complex is
short.
However, if having observed all the vibrational levels
indicated in Fig. 3, one may have another impression that the
vibrational energy distributions in the two NO’s are rather
similar except for the lower levels. In the higher vibrational
1
generated from 18O„ D…؉N216O
Using 18O3, we have determined the relative populations
between the new N18O and the old N16O in both the lower
( ϭ0–5) and higher ( ϭ12–15) levels. The LIF spectrum
v
v
containing the N18O B←X(1←13) and N16O B←X(0
←12) transitions is shown in Fig. 2. Each spectrum was
obtained in the rotationally relaxed conditions. For the as-
signment of N18O peaks, we utilized the rotational constants
which were obtained from the rotational constants23 of N16O
16
18
multiplied by the isotope factor, ␳ϭͱ␮(N O)/␮(N O)
ϭ0.973 66, where ␮(N16O) and ␮(N18O) are the reduced
masses of N16O and N18O, respectively. These rotational
constants of N18O well reproduced the obtained spectra. It
should be noted for the isotopically labeled reaction that the
vibrational-energy levels of N18O is slightly different from
those of N16O, since the vibrational and rotational quanta are
different due to the different reduced masses. For example,
levels of ϭ12–15, the old NO is produced as many as
v
one-fourth of the new NO. In contrast to the extreme case
where all the vibrational excitation is limited to the new NO
and the old NO act as a mere spectator, the obtained result
indicates that the partitioning of the available energy be-
tween the two NO’s occurs to a considerable extent. This
fact implies that the energy mixing actually occurs between
the collisional encounter and the departure of the two NO
the vibrational energy of N16O molecule in ϭ17 level is
v
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120
J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
Akagi, Fujimura, and Kajimoto
TABLE II. Vibrational state distributions of N 18O, N 16O, and the sum of NO’s produced from the O(1D)
ϩN2O reactions.a,b
P(N 18OϩN 16O,
)
v
N(N 18O; )/N(N 16O;
)
P(N 18O, )/2c
P(N 16O; )/2c
v
v
v
v
v
0
1
2
3
4
5
6
7
0.23
0.17Ϯ0.01
͑0.11͒
0.090Ϯ0.019
͑0.084͒
͑0.082͒
0.30Ϯ0.03
0.62Ϯ0.13
1.0Ϯ0.1
1.0Ϯ0.1
1.6Ϯ0.1
1.8Ϯ0.1
͑2.2͒
0.053
0.065
0.057
0.046
0.052
0.052
0.054
0.047
0.17
0.11
0.057
0.044
0.032
0.030
0.024
0.017
0.078Ϯ0.018
͑0.064͒
͑2.9͒
8
͑0.046͒
͑3.4͒
0.035
0.010
9
0.027Ϯ0.006
͑0.012͒
͑4.3͒
͑4.5͒
͑3.6͒
2.9Ϯ0.2
4.3Ϯ0.3
͓5.2Ϯ0.6͔
3.0Ϯ0.3
͑4.0͒
0.022
0.010
0.0051
0.0022
0.00077
0.00018
0.000036
0.0000067
0.0000026
0.00000069
0.00000026
¯
10
11
12
13
14
15
16
17
18
0.0035Ϯ0.0011
0.0028
0.00053
0.00015
0.000035
0.0000077
0.0000028
0.0000010
¯
0.00071Ϯ0.00023e
0.00019Ϯ0.00006e
0.000042Ϯ0.000013e
0.000010Ϯ0.000004e
0.0000035Ϯ0.0000013e
0.0000013Ϯ0.0000006e
р0.0000009e
d
͑4.0͒
¯
aThose values given in parentheses are interpolated data.
bThe experimental uncertainty corresponds to 1␴ in the least-squares fit.
cThese data are calculated from the data included the interpolated values.
dThis value may be overestimated, because the Franck–Condon factor of the B–X(1–14) for N 16O is almost
10 times larger than that of the B–X(0–14) used for N 18O ͑Ref. 24͒.
eThose values are calculated from the results in Ref. 9.
molecules and the observed vibrational distribution shows an
intermediate features between the complete spectator and the
fully statistical cases.
within a stable molecule. The rate of IVR for large molecules
in the statistical limit is considered to be proportional to the
v2
square of the effective coupling
and the state density ␳
The degree of energy randomization essentially depends
on the three factors, the coupling among vibrational modes,
the state density at a given energy, and the time for the
mixing ͑the duration of the collisional interaction in the
present case͒. That is, the large coupling, high state density,
and the long lifetime of the collision complex enhance the
energy randomization. Quantitatively, we can use an analogy
between the energy mixing within a collision complex and
the intramolecular vibrational-energy redistribution ͑IVR͒
as,25
2
2␲
␳
v
kϭ
.
͑4͒
ប
Since the collision complex has a certain lifetime, we have to
take the mixing time into account. When the lifetime of the
collision complex is extremely short, the energy mixing can
not be achieved even though the IVR rate is quite large.
Concerning the present reaction, O(1D)ϩN2O→2NO,
the lifetime of the collision complex is expected to be short,
since the potential well for the O–N–N–O intermediate is
extremely shallow comparing with the exothermicity of the
reaction. The vector correlation data for this reaction ob-
tained in our laboratory26 suggest that the lifetime is not
more than one rotational period. Therefore, the observed
mixing of the vibrational energy between the two NO in the
present experiments indicates the rapidness of the IVR rate
within the collision complex. The reasons for the rapid IVR
are discussed in the following sections based on the two
main features of the present reaction, that is, the production
of the same NO species and the participation of the heavy
atoms as compared with the reaction like O(1D)
ϩH2O→2OH.
A. Production of two NO molecules
FIG. 3. A complete set of vibrational state distributions of NO( ϭ0–17)
v
produced from the reaction of O(1D) with N2O. The closed and open tri-
angles depict the populations calculated from the measured and interpolated
ratios N(N18O)/N(N16O), respectively. The sum distribution is shown by
the solid line. The small open circles indicate the population of NO obtained
from the unlabeled reaction.
The production of two identical NO species is a unique
feature of the present reaction and must give a noticeable
influence on the energy mixing. Among the three factors
stated above, the state density is strongly affected by the
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J. Chem. Phys., Vol. 111, No. 1, 1 July 1999
Energy partition reaction of O(1D) with N2O
121
vibrational frequencies of the available vibrational modes.
When the identical moieties participate in the IVR process,
the presence of completely identical vibrational energy levels
considerably enhances the state density at certain energy re-
gions. For example, a bunch of energy levels including the
ϩN2O reaction, making the two vibrational distributions
more alike than in the HOOH case.
The state density must be also large for the collision
complex containing only heavy atoms. When the molecular
size is the same, the vibrational frequencies are smaller for
the molecules consisting of heavy atoms than those with
light atoms. In the present case, very low vibrational fre-
NO stretching vibrations (
ϩ old NOϭ17) appears
vnew NO v
near the threshold energy and accelerates the energy transfer
between the two NO molecules. In terms of the perturbation
theory, the process including two nearly identical energy
states is estimated to be quite large because the denominator
of the perturbation equation is the energy difference of the
relevant states and becomes nearly zero. This is called the
resonance effect and corresponds to the enhancement of the
state density in the expression like the Fermi’s Golden Rule.
The above situation is almost the same for the isotopi-
cally labeled reaction, 18O(1D)ϩN216O→N18OϩN16O. Al-
though the vibrational frequencies are not strictly the same
due to the difference in the mass of oxygen, the two vibra-
tional frequencies of NO’s are very similar. The rapid IVR
expected in the present experiment can be partly attributed to
the resonance effect.
quencies are reported for
a
possible intermediate,
͑NO͒2:␯ ͑symmetric ONN bending͒ϭ239.4 cmϪ1, ␯ ͑N–N
2
3
stretching͒ϭ134.5 cmϪ1
,
␯ ͑torsion͒ϭ117 cmϪ1
,
and
4
28
␯ ͑antisymmetricbending͒ϭ429.1 cmϪ1
.
Thus, there is no
6
doubt that the state density in the highly excited level of the
collision complex is extremely high in the O(1D)ϩN2O re-
action as compared with in the O(1D)ϩH2O reaction.
As mentioned above, the heavy mass effect contributes
to the acceleration of IVR in two ways, one through the
momentum coupling and the other through the state density.
Then, we want to compare the significance of such mass
effect with the resonance effect described in the preceding
section. Although the resonance effect can contribute both
the reactions O(1D)ϩN2O and O(1D)ϩH2O, the observed
vibrational distributions indicate that the energy partitioning
between the two identical products is more enhanced in the
case of O(1D)ϩN2O. This fact implies that the mass effect
plays the major role comparing with the resonance effect. To
further elucidate the relative importance between the mass
and the resonance effects, we have performed the experiment
for the S(1D)ϩN2O→NSϩNO reaction, which lacks the
symmetry and hence the resonance effect. The results con-
firm the primary importance of the mass effect in the energy
randomization within the collision complex.29
B. Absence of light atoms in the reaction intermediate
An analogous reaction, O(1D)ϩH2O→2OH, produces
two OH radicals which possess completely different vibra-
tional energy distribution; the new OH is highly excited
whereas the old one is quite cold just like a spectator.2 In
view of the resonance effect mentioned above, the two iden-
tical OH moieties must enhance the IVR and could give a
vibrational distribution similar to the NO molecules in
O(1D)ϩN2O→2NO. Then, we have to seek the reason for
the observed difference between the vibrational energy dis-
tributions of these two reactions. The essential difference
between these two reactions lies in the weight of atoms con-
stituting the reaction system; the O(1D)ϩH2O reaction con-
tains light hydrogen atoms whereas only the heavy atoms
form the reaction system, O(1D)ϩN2O. Such difference in
their character certainly affects the size of coupling and the
state density.
ACKNOWLEDGMENTS
The authors are indebted to Dr. J. Luque for his detailed
information of updated spectroscopic data. This work was
supported in part by Grant-in-Aid for Scientific Research on
Priority Areas No. 07240102 from the Ministry of Educa-
tion, Science, and Culture in Japan.
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