Scalar and vector properties of the NO(v′ = 0) produced from the reaction O(1D) + N2O→NO+NO

Article abstract of DOI:10.1063/1.479340

We have measured the product state-selected differential cross-section (DCS), and the rotational angular momentum polarization, together with the energy distributions for the reaction O(¹D) + N₂O→NO+NO by utilizing Doppler-resolved polarization spectroscopy. The reaction dynamics of the vibrational channel forming the product NO(v′ = 0) is discussed based on both the scalar and vector properties. The product rotational and center-of-mass translational energy distributions are described as Boltzmann distributions with T_rot≈10 000 K and T_tr=13 000 K, respectively. These energy distributions are close to statistical predictions. The product DCS has substantial intensities over the whole angular range with a slight preference for backward scattering. The product rotational angular momentum vector j′ does not have a noticeable angular correlation with either k or k′ (the relative velocity vectors of the reactant and product, respectively). This nearly isotropic angular distribution of j′ indicates that both in-plane and out-of-plane motions of the collisional ONNO complex contribute to the product rotation to almost the same degree. Considering that this reaction has no potential well deep enough for the formation of a long-lived complex, these nearly statistical scalar and isotropic vector properties suggest that the energy redistribution among the internal modes of the collisional ONNO complex efficiently takes place. It implies that there are strong couplings among the internal modes.

Full text of DOI:10.1063/1.479340

Scalar and vector properties of the NO (v ′ =0) produced from the reaction O ( 1 D)+ N 2
O→NO+NO
Hiroshi Tsurumaki, Yo Fujimura, and Okitsugu Kajimoto
Citation: The Journal of Chemical Physics 111, 592 (1999); doi: 10.1063/1.479340
View online: http://dx.doi.org/10.1063/1.479340
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 111, NUMBER 2
8 JULY 1999
Scalar and vector properties of the NO„v ؍0… produced from the reaction
Ј
1
O„ D…؉N2O˜NO؉NO
Hiroshi Tsurumaki, Yo Fujimura, and Okitsugu Kajimoto
Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho,
Sakyo-ku, Kyoto 606-8502, Japan
͑Received 22 December 1998; accepted 14 April 1999͒
We have measured the product state-selected differential cross-section ͑DCS͒, and the rotational
angular momentum polarization, together with the energy distributions for the reaction O(1D)
ϩN2O→NOϩNO by utilizing Doppler-resolved polarization spectroscopy. The reaction dynamics
of the vibrational channel forming the product NO( ϭ0) is discussed based on both the scalar and
v
Ј
vector properties. The product rotational and center-of-mass translational energy distributions are
described as Boltzmann distributions with TrotϷ10 000 K and TtrϷ13 000 K, respectively. These
energy distributions are close to statistical predictions. The product DCS has substantial intensities
over the whole angular range with a slight preference for backward scattering. The product
rotational angular momentum vector j does not have a noticeable angular correlation with either k
Ј
or k ͑the relative velocity vectors of the reactant and product, respectively͒. This nearly isotropic
Ј
angular distribution of j indicates that both in-plane and out-of-plane motions of the collisional
Ј
ONNO complex contribute to the product rotation to almost the same degree. Considering that this
reaction has no potential well deep enough for the formation of a long-lived complex, these nearly
statistical scalar and isotropic vector properties suggest that the energy redistribution among the
internal modes of the collisional ONNO complex efficiently takes place. It implies that there are
strong couplings among the internal modes. © 1999 American Institute of Physics.
͓S0021-9606͑99͒00226-3͔
Akagi et al.11 recently observed the individual vibra-
tional distributions of the two NO products in the range of
vibrational levels ϭ0–18 under much lower pressure than
I. INTRODUCTION
The reaction of O(1D) with N2O yielding two NO prod-
uct molecules
v
Ј
in the previous study.3 The vibrational populations showed
that the energy partitioning between the two NO products
was more symmetric than that generally expected from a
direct pathway although it was more asymmetric than that
reported in Ref. 3. This result suggests that energy random-
ization occurs in spite of the fact that this reaction is not a
typical statistical complex reaction with a deep potential
well.
1
O D͒ϩN O→NOϩNO ⌬H0 0͒ϭϪ341 kJ/mol,
͑1͒
͑
͑
2
plays an important role in atmospheric chemistry and thus
has been of great interest. With many kinetic studies show-
ing large rate constants,1,2 the dynamics of this highly exo-
thermic reaction has been investigated by measuring the
product internal state distributions3–6 and recently by prob-
ing vector properties such as product recoil anisotropy and
rotational angular momentum polarization.7,8
Brouard et al. recently examined the stereodynamics
of the vibrational channel O(1D)ϩN O→NO( ϭ16,17)
v
Ј
2
Although the two NO products of this reaction are
chemically identical species, they are generated from dis-
tinctly different origins. One is the ‘‘new’’ NO formed in the
reaction and the other is the ‘‘old’’ NO present in the reac-
tant N2O molecule. An early study using isotopically labeled
reagents showed almost symmetric energy partitioning
among the two NO products in the low vibrational levels
ϭ0–2.3 From a traditional understanding, this result is
ϩNO( ϭ0) based on the product recoil anisotropy ob-
v
Ј
tained by utilizing Doppler-resolved polarization spectro-
scopy.8 The product NO( ϭ16,17) was translationally hot
v
Ј
and recoiled with the upper limit of the anisotropy parameter
in the laboratory ͑LAB͒ frame, corresponding to the forward
scattering in the center-of-mass ͑CM͒ frame, while the sister
fragment NO( ϭ0) had extremely low translational energy
v
Ј
v
Ј
close to thermal energy. Furthermore, they found hot rota-
tional distributions of NO( ϭ16,17) in contrast to a cold
expected to imply that this reaction proceeded via an inter-
v
Ј
mediate complex.
rotational distribution of NO( ϭ0) almost identical to a
v
Ј
As a possible intermediate species of this reaction, an ab
initio calculation suggested a cis-planar ONNO structure.9
The binding energy of the cis-planar NO dimer was experi-
mentally determined to be about 8.5 kJ/mol.10 Since this
binding energy is negligibly small compared with the avail-
able energy of about 400 kJ/mol, this reaction is not likely to
proceed via a long-lived complex.
thermal distribution. They consequently concluded that the
vibrational channel forming NO( ϭ16–18)ϩNO( ϭ0)
v
v
Ј
Ј
was dominated by a near-stripping mechanism where the old
NO behaves as a spectator during the reaction. They also
found relatively high rotational excitation of the NO(
vЈ
у1) products, remarkably different from that of the
0021-9606/99/111(2)/592/8/$15.00
592
© 1999 American Institute of Physics
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The reaction O(1D)ϩN2O→NOϩNO
593
J. Chem. Phys., Vol. 111, No. 2, 8 July 1999
NO( ϭ0).7 Thus, they suggested that the NO(1р
р15) products were formed via a short-lived complex in
contrast to a direct stripping process for the formation of
cimer laser ͑Lambda Physik COMPex 102͒. For the mea-
surement of Doppler profiles, the dye laser was equipped
with an intracavity etalon and the bandwidth of the UV light
used for probing the products was about 0.14 cmϪ1 in full
width at half maximum ͑FWHM͒.
v
v
Ј
Ј
NO( ϭ0,16–18). Such drastic change of the reaction dy-
v
Ј
namics, though not impossible, seems to be somewhat puz-
zling.
The fluorescence was collected by a synthetic silica lens
and focused by another silica lens on a photomultiplier tube
͑Hamamatsu R928͒ mounted perpendicular to both the pho-
tolysis and probe laser beam axes. A long-pass filter ͑Corn-
ing CS9-54͒ was placed in front of the photomultiplier tube
to eliminate the strong scattered light and emission arising
from the photolysis laser. The LIF signal was amplified by a
fast preamplifier ͑Comlinear CLC100͒ and gated by a boxcar
integrator ͑Stanford Research System SR250͒. The gated sig-
nal was digitized by an A/D convertor ͑Stanford Research
System SR245͒ and stored in a personal computer via a
GPIB interface. The photolysis-probe experiments were per-
formed at a repetition rate of 10 Hz. The timing of the laser
system was adjusted by a digital pulse/delay generator ͑Stan-
ford Research System DG535͒. Each laser power was moni-
tored by a photodiode ͑Hamamatsu 1336-5BQ͒ for normal-
izing the LIF signal to correct for the fluctuations of the
power.
The Doppler-resolved spectral line profiles were mea-
sured in several LIF excitation–detection geometries which
were characterized by the combination of the directions of
the polarization and propagation vectors of each laser. In-
complete horizontal polarization of the output of the probe
laser was converted to higher horizontal linear polarization
with a Glan laser prism ͑Meiritsu LAN-10-L͒. This horizon-
tally polarized light was sent to a half-wave plate ͑New Fo-
cus 5540͒ to obtain a vertically polarized light ͑degree of
polarization Ͼ0.99͒. Unpolarized ArF laser light was passed
through a pile of plates consisting of 12 quartz plates in
Brewster’s angle to obtain vertically polarized light ͑degree
of polarization Ͼ0.95͒. The polarization direction of the pho-
tolysis laser was alternately changed from vertical to hori-
zontal in a shot-by-shot manner with a photoelastic modula-
tor ͑Hinds PEM-90͒. The trigger pulses switching the two
appropriate timings for the vertical and horizontal polariza-
tion were generated with homemade electronic devices. This
shot-by-shot alternation of the polarization vector allows one
to observe the polarization-dependent spectral line profiles in
the two different LIF geometries in a single frequency scan.
Such shot-by-shot alternate observation gave the rotational
alignment A(02)ϭ0.00Ϯ0.02(1␴) for both of P1(34.5) and
Q1ϩQP21(34.5) which was used for the subsequent Doppler
profile analysis. In order to improve the signal-to-noise ratio,
50–100 laser shots were averaged at each step of a frequency
scan and the spectra obtained from 9–25 scans were summed
up.
As opposed to the rotational distribution of NO( ϭ0)
v
Ј
reported by Brouard et al.,7,8 our unpublished preliminary
works suggested that the rotational distribution of this level
was more excited than those of NO( у1) products re-
v
Ј
ported in Ref. 7. Furthermore, considering that the vibra-
tional populations of the NO products monotonously decline
with increasing vibrational quantum number,4,6,11 the forma-
tion of NO( ϭ16–18) is estimated to be a minor channel.
v
Ј
Thus, probing the channel forming the product NO( ϭ0)
v
Ј
is essential to clarify the dynamics dominant for this reaction
and reexamine the large gap between the reaction dynamics
for the formation of NO( ϭ0) and NO( у1).
v
v
Ј
Ј
For examining the reaction dynamics in more detail, the
measurement of vector properties as well as scalar properties
is important. Several groups7,8,12–29 have recently measured
vector properties for bimolecular reactions with fundamental
importance so far and provided a better understanding of the
reaction dynamics. We have measured the state-selected dif-
ferential cross-section and the rotational angular momentum
polarization of the product NO( ϭ0) by utilizing Doppler-
v
Ј
resolved polarization spectroscopy, as well as the rotational
and translational energy distributions. In the present study,
although the two NO products are not isotopically distin-
guished, the observed NO( ϭ0) products are mainly con-
v
Ј
sidered as the old NO since the population of the old NO in
ϭ0 was found to be about four times larger than that of
v
Ј
the new NO.11
The observed scalar properties of NO( ϭ0) shows that
v
Ј
the NO( ϭ0) is rotationally and translationally excited to
v
Ј
the same degree as predicted by statistical models. The vec-
tor properties suggest the efficient energy redistribution
among the internal modes of the short-lived collision com-
plex.
II. EXPERIMENT
Experiments were carried out in a stainless steel vacuum
chamber. Nitrous oxide ͑Showa Denko 99.999%͒ was used
without further purification. This sample gas was introduced
into the reaction chamber and the flow rate was controlled
with stainless steel needle valve. The sample gas in the re-
action chamber was continuously pumped by using a rotary
pump. The pressure of N2O was about 200 mTorr at 300 K.
The electronically excited oxygen atom O(1D) was pro-
duced from the photodissociation of N2O with 193 nm light
generated by an ArF excimer laser ͑Lambda Physik EMG 53
MSC͒. At a delay time of 100 ns after the photolysis laser
irradiation, a tunable UV light ͑223–227 nm͒ was introduced
For extracting vector correlations, we measured Doppler
profiles for the rotational branches of P1 and Q1ϩQP21 due
to the A and A ⌳-doublet states, respectively, with as-
Ј
Љ
into the reaction chamber to probe the nascent NO( ϭ0)
sumption that these two ⌳-doublet states have the same vec-
tor properties. The Doppler-resolved spectral line shapes did
not show any appreciable changes at a delay time ranging
from 50 to 100 ns at a pressure of 200 mTorr. Furthermore,
we checked that the probe laser power was weak enough to
v
Ј
with laser-induced fluorescence ͑LIF͒ via the NO
2
2
A ⌺ϩ –X ⌸(0,0) excitation. The tunable UV light was
generated by doubling the output of the dye laser ͑Lambda
Physik SCANmate 2E, Coumarin 2͒ pumped by a XeCl ex-
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594
J. Chem. Phys., Vol. 111, No. 2, 8 July 1999
Tsurumaki, Fujimura, and Kajimoto
2
2
avoid the saturation of the NO A ⌺ϩ –X ⌸(0,0) excita-
tion.
III. ANALYSIS
Only the outline of Doppler profile analysis is given here
since the details have been described elsewhere.30 In recent
years, Aoiz et al. have extended the Dixon’s formulation for
the Doppler analysis of the vector correlations in photodis-
sociation processes31 to those in photo-initiated bimolecular
reactions.32,33 They have developed a theoretical basis to ex-
tract the mutual angular correlations among the LAB veloc-
ity vectors of an atomic reagent ͑v͒ and product (v ), and the
Ј
product rotational angular momentum vector (j ) from the
Ј
polarized Doppler-resolved line profiles. In case of a linearly
polarized photolysis-probe experiment, the 1ϩ1 LIF Dop-
pler profile D(␯) as a function of the displaced frequency ␯
FIG. 1. LIF spectra of NO(2⌸1/2
,
ϭ0) measured at the two different
vЈ
from the line center frequency ␯ can be written by the Leg-
0
delay times and their difference in the reaction of O(1D) with N2O in the
endre polynomial expansion of Pn(x) up to the second-order
as
2
region of A
⌺
ϩ –X 2⌸(0,0) band. ͑a͒ The probe laser is fired at 100 ns
after the photolysis laser irradiation. ͑b͒ The probe laser is fired at 600 ns
before the photolysis laser irradiation. ͑c͒ The difference spectrum ͑a͒Ϫ͑b͒.
The spectrum corresponding to the nascent products shown in ͑c͒ is obtained
by subtracting the background contamination of thermalized NO shown in
͑b͒ from the raw spectrum shown in ͑a͒.
ϱ
1
␷
p
D ␯͒ϭ
͑
g
␷ ͒ϩg ␷ ͒P
2
d␷ .
͑2͒
͑
͑
Ј
2
Ј
Ј
͵
ͫ
ͩ ͪ
ͬ
0
2␷
␷
Ј
Ј
͑␯/␯ ͒c
␷ ϭ͉ ͉
0
p
Here, ␷pϭ
͉
(␯/␯0)c
͉
͑c; the speed of light͒ represents the
minimum product LAB speed giving the displaced frequency
␯ as the Doppler shift proportional to the projection of v
Ј
using the least-squares fitting method for the observed com-
posite Doppler profiles D0K(k1 ,k2 ;␯) with appropriate basis
functions.
onto the propagation direction of the probe laser. The coef-
ficients g (␷ ) and g (␷ ) in Eq. ͑2͒ are expressed by linear
Ј
Ј
0
2
combinations of bipolar moments averaged over all the pos-
For preparing the basis functions, we used the recoil
velocity distribution of O(1D) produced from the 193 nm
photodissociation of N2O which was reported by Felder
et al.35 In order to consider all the possible collisions, the
velocity distribution of O(1D) was convoluted with the ther-
mal motions of the precursor N2O and the reactant N2O as
well as the angle between the velocity vectors of the reac-
tants. The mean collision energy for the reaction of O(1D)
with N2O is 55 kJ/mol and the spread of the distribution is
about 40 kJ/mol ͑FWHM͒. Felder et al. gave a single anisot-
ropy parameter, ␤photoϭ0.48, without taking account of the
recoil speed dependence of ␤photo for their angle-resolved
time-of-flight measurement.35 On the other hand, Suzuki
et al. showed the recoil speed dependence of ␤photo for the
205 nm photodissociation with a two-dimensional imaging
method.36 Considering the latter results, we represented the
distribution for the 193 nm photodissociation by using two
components with different ␤photos (␤photoϭ0.0 for the broad
component and ␤photoϭ1.03 for the narrow component͒, so
as to reproduce the average ␤photoϭ0.48.35
sible velocities of the reagents, ␤K(k ,k ;␷ ). The bipolar
Ј
1
2
0
moments reflect the LAB frame vector correlations as a func-
tion of product LAB speed ␷ .
Ј
As shown by Docker,34 an appropriate linear combina-
tion of the Doppler profiles measured in several LIF
excitation–detection geometries for two different types of
rotational transitions ͑P or R vs Q͒ gives the composite Dop-
pler profile DK0 (k1 ,k2 ;␯) which depends on a single bipolar
moment ␤K(k ,k ;␷ ) in g or g . The composite Doppler
Ј
1
2
0
2
0
profile DK0 (k1 ,k2 ;␯) is expressed as33
ϱ
1
␷
p
K
0
DK0 k ,k ;␯͒ϭ
␤
k ,k ;␷ ͒P
͑
1
d␷ .
Ј
͑
Ј
͵
ͩ ͪ
1
2
2
k
1
2␷
͑␯/␯ ͒c
␷ ϭ͉ ͉
0
␷
Ј
Ј
p
͑3͒
The composite Doppler profiles D00(0,0;␯) and D02(2,0;␯)
are related to the LAB speed distribution ͑population͒ and
v–v correlation ͑anisotropy͒, respectively. The other three
Ј
composite Doppler profiles reflect the polarization of the
product rotational angular momentum vector, j in the three
Ј
correlations: D2(0,2;␯) for v–j , D0(2,2;␯) for v –j , and
Ј
Ј
Ј
0
0
D2(2,2;␯) for v–v –j correlations.
Ј
Ј
IV. RESULTS
0
To discuss the dynamics of collisional events, the LAB
A. Scalar properties
frame vector correlations described above need to be con-
verted to those in the CM frame, that is, the angular correla-
tions among the relative velocity vectors of the reactant ͑k͒
Figure 1͑a͒ shows the laser-induced fluorescence ͑LIF͒
spectrum of the NO( ϭ0) products in the reaction of
v
Ј
O(1D) with N2O which was measured at a time delay of 100
ns. The spectrum seems to consist of two components: strong
peaks above 225.5 nm and numerous weak peaks below
225.5 nm. We also measured in the same region under an-
other photolysis-probe delay time condition where the probe
and product (k ), and the product rotational angular momen-
Ј
tum vector (j ). Aoiz et al. have derived the relationship
Ј
between the LAB frame vector correlations represented by
DK0 (k1 ,k2 ;␯) and those in the CM frame.33 Based on their
formalism, we obtained the CM frame vector correlations by
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The reaction O(1D)ϩN2O→NOϩNO
595
J. Chem. Phys., Vol. 111, No. 2, 8 July 1999
FIG. 2. Rotational energy distribution of the product NO(2⌸1/2
,
ϭ0).
vЈ
Solid and dotted lines represent Boltzmann fit (TrotϷ10 000 K) and a prior
distribution, respectively. The highly excited rotational distribution arises
from the energy partitioning of the large available energy close to a statis-
tical prediction.
laser was fired at 600 ns before the photolysis laser irradia-
tion, and the spectrum is shown in Fig. 1͑b͒ on the same
scale as used in Fig. 1͑a͒. The rotational lines observed at
such reversed time delay definitely arise from the ‘‘residual’’
NO molecules present in the reaction chamber. Such ther-
malized NO products (TrotϷ300 K) always contribute espe-
cially to the spectrum of NO( ϭ0) as the background
v
Ј
FIG. 3. Observed composite Doppler profiles for the product
peaks. Comparison between Figs. 1͑a͒ and 1͑b͒ clearly
shows that the strong peaks above 225.5 nm in Fig. 1͑a͒ are
assigned to those arising from the residual NO molecules.
Therefore, the weak peaks below 225.5 nm are assigned to
those originating from the nascent NO products.
NO(2⌸1/2
,
ϭ0,j ϭ34.5). ͑a͒ D00(0,0;␯) ͑population͒ ͑᭺͒ and ͑b͒
vЈ
Ј
D2(2,0;␯)(vϪv ). Smooth solid lines in the two panels are best fits to these
Ј
0
profiles.
To separate the LIF signals of the nascent NO from
those contaminated by the residual NO, a shot-to-shot sub-
traction was performed to minimize the effect of the time
drift of the amount of the residual NO during the experiment.
The devices used for alternating the laser polarization ͑see
Sec. II͒ were utilized to the shot-by-shot alternation of the
delay time. The LIF spectrum of the nascent NO products
obtained by the shot-to-shot subtraction is shown in Fig.
1͑c͒. The rotational energy distribution of the nascent
described here, it could be possible that the thermalized re-
sidual NO contaminated the spectrum in the previous study.7
Figure 3 shows the observed composite Doppler profiles
D00(0,0;␯) and D02(2,0;␯) for the NO(2⌸1/2
,
ϭ0,j
v
Ј Ј
ϭ34.5), reflecting the LAB speed distribution and recoil an-
isotropy, respectively. The least-squares fitting to these pro-
files yields the product center-of-mass ͑CM͒ transitional en-
ergy distribution and differential cross-section ͑DCS͒. We
carefully checked that the LIF signal arising from the re-
sidual NO was negligibly small and did not have any influ-
ence on the Doppler profiles for the nascent NO in the ob-
NO( ϭ0) is derived from the line intensities of P and R
v
Ј
1
1
branches and is displayed in Fig. 2, plotted on a linear scale.
This rotational distribution can be described as a Boltzmann
distribution with TrotϷ10 000 K. As shown in Fig. 2, a com-
parison with a prior distribution shows that the rotational
distribution of the nascent NO( ϭ0) is close to the statis-
v
Ј
tical distribution. This implies that the rotational distribution
with TrotϷ10 000 K corresponds to a moderate rotational ex-
citation resulting from a partitioning of the large available
energy of this reaction.
The amount of the residual NO is estimated to be only
5% of the total NO molecules in ϭ0. However, as shown
v
Ј
in Fig. 1͑a͒, even such a small amount of the residual NO
yields the spectrum in which thermalized NO molecules are
emphasized because of the significant difference between the
spreads of the rotational distributions with TrotϷ300 K and
TrotϷ10 000 K.
FIG. 4. Center-of-mass translational energy distribution given to the
NO(2⌸1/2
,
ϭ0,j ϭ34.5) and its sister fragment ͑᭹͒. Solid and dotted
vЈ
Ј
The rotational distribution of NO( ϭ0) observed here
v
Ј
lines represent Boltzmann fit (TtrϷ13 000 K) and a prior distribution, re-
spectively. Error bars correspond to Ϯ1␴. The distribution is, though
slightly colder, roughly close to a statistical prediction.
is obviously different from that with TrotϷ320 K previously
reported by Brouard et al.7 However, from the observation
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596
J. Chem. Phys., Vol. 111, No. 2, 8 July 1999
Tsurumaki, Fujimura, and Kajimoto
FIG. 5. Total DCS for the NO(2⌸1/2
,
ϭ0,j ϭ34.5) averaged over the
vЈ
Ј
recoil energy. Error bars correspond to Ϯ1␴. The DCS shows substantial
intensities over the whole angular range with a slight preference for back-
ward scattering.
served rotational level, j ϭ34.5. Figure 4 shows the product
Ј
CM translational energy distribution. This distribution can be
described as a Boltzmann distribution with TtrϷ13 000 K.
The translational energy distribution is, though slightly
colder, roughly close to the statistical prediction as observed
for the rotational energy distribution. The wide spread of the
translational energy distribution suggests that the sister prod-
ucts of the observed NO( ϭ0) are populated over various
v
Ј
rovibrational states.
FIG. 6. Observed composite Doppler profiles for the product NO(2⌸1/2
ϭ0,j ϭ34.5). ͑a͒ D2(0,2;␯) (v–j correlation͒, ͑b͒ D0(2,2;␯) (v –j
Ј
,
Brouard et al. reported the nearly statistical excitation of
rotational and translational degrees of freedom for the NO
vЈ
Ј
Ј
Ј
0
0
correlation͒, and ͑c͒ D2(2,2;␯) (v–v –j correlation͒. The smooth solid
Ј
Ј
0
products in у1 ͑Ref. 7͒ as observed for NO( ϭ0) in
lines are the best fits to these profiles.
v
v
Ј
Ј
this work. Since the population of the old NO is about four
times larger than that of the new NO in the observed vibra-
tional level ϭ0,11 the energy distributions obtained here
v
Ј
gular correlations of j with k and k , respectively, are
Ј
Ј
are almost assigned to those of the old NO. Therefore, these
shown in Figs. 7͑b͒, and ͑c͒, where ␪ is the angle between
tr
results indicate that not all the old NO( ϭ0) are produced
v
Ј
j
and k . These nearly flat distributions imply that j is
Ј Ј
Ј
from a near-stripping mechanism8 where the old NO almost
behaves as a spectator.
almost isotropic with respect to both k and k .
Ј
V. DISCUSSION
B. Vector properties
A. Origin of the nearly isotropic DCS
The total DCS averaged over the recoil energy for the
product NO(2⌸1/2
,
ϭ0,j ϭ34.5) is shown in Fig. 5. The
A nearly isotropic product DCS is ordinarily attributed
to the lifetime of a collision complex comparable to or
longer than its rotational period. If the intermediate of the
reaction has a long lifetime, the observed nearly statistical
energy distributions of the products are easily understood.
However, since the O(1D)ϩN2O reaction is known to have
no deep potential well, the lifetime of the complex is not
expected to be long. The quasiclassical trajectory ͑QCT͒ cal-
culations on a London-Eyring-Polanyi-Sato surface accord-
ingly suggested that the lifetime of the collision complex was
at most 1 ps.37 We estimated the rotational period of the
possible intermediate of a cis-planar ONNO complex9 to be
about 1.8 ps by using the rotational constants of cis-NO
dimer38 and the average orbital angular momentum ͑Ϸ50ប͒
of the reactants. Thus, the lifetime of the collisional ONNO
complex is about half of its rotational period and cannot fully
explain the nearly isotropic DCS obtained here.
v
Ј
Ј
DCS shows substantial intensities over the whole angular
range with a slight preference for backward scattering. In the
analysis for extracting DCS, the variation in DCS with the
product recoil energy was allowed. The DCS obtained for
each recoil energy was not so much different.
Figure 6 shows the observed composite Doppler profiles
D20(0,2;␯), D02(2,2;␯), and D20(2,2;␯), reflecting the polar-
ization of rotational angular momentum vector j of the ob-
Ј
served NO. The least-squares fitting to these profiles yields
the distribution function P(␪r ,␾r) representing the angular
distribution of j with reference to the relative velocity vec-
Ј
tors of the reactant ͑k͒ and product (k ) as shown in Fig.
Ј
7͑a͒. Here, ␪ and ␾ are the angle between k and j , and the
Ј
r
r
dihedral angle between kk plane and kj plane. The nearly
Ј
Ј
flat P(␪r ,␾r) shows that there is not a noticeable spatial
correlation between j and the collision plane spanned by k
Ј
and k . In order to examine this weak spatial correlation
The spread of scattering angle distribution for the reac-
tion not involving a long-lived complex is usually related to
the spread of impact parameters. Since the total cross-section
Ј
between j and the collision plane in more detail, the distri-
Ј
bution functions P(cos ␪r) and P(cos ␪tr) representing the an-
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The reaction O(1D)ϩN2O→NOϩNO
597
J. Chem. Phys., Vol. 111, No. 2, 8 July 1999
FIG. 8. Angular distributions P(cos ␪ ) representing the k –j correlations
Ј
Ј
tr
for forward and backward components. The almost isotropic k –j correla-
Ј
Ј
tions imply the contribution of both in-plane and out-of-plane motions to the
product rotation irrespective of scattered hemispheres.
lation indicates that both the in-plane and out-of-plane mo-
tions of the N–N–O moiety contribute to the product rota-
tion to almost the same degree. Nearly equivalent
contribution of several modes to the product rotation most
probably suggests that the energy redistribution among the
internal modes of the collision complex is almost completed
prior to its fragmentation and leads to the nearly statistical
energy distributions even with the short lifetime of the com-
plex.
FIG. 7. ͑a͒ Angular distribution function P(␪r ,␾r) representing the polar-
As another origin of the nearly statistical distributions
for the reaction not involving a long-lived complex, the
spread of the impact parameters suggested from the DCS
should be discussed. Even if each reactive collision with a
specific range of impact parameters yields an unstatistical
distribution, the seemingly statistical distributions would
happen to be given by summing up the individual unstatisti-
cal distributions. For a direct reaction, it is known that there
is a relatively tight correlation between impact parameters
and scattering angles. The QCT calculation for this reaction
indicated that the collisions with small and large impact pa-
rameters preferentially yielded the backward and forward
scattering of the new NO, respectively.37 Thus, the possibil-
ity that the observed statistical distributions originate from
the spread of the impact parameters can be examined by the
extent of the difference between the angular momentum po-
larization of the forward and backward components. Figure 8
ization of the rotational angular momentum vector,
j
for the
Ј
NO(2⌸1/2
,
ϭ0,j ϭ34.5). ͑b͒ Angular distribution P(cos ␪ ) representing
vЈ
Ј
r
the k–j correlation. ͑c͒ Angular distribution P(cos ␪tr) representing the
Ј
k –j correlation. The nearly flat angular distribution of j with respect to
Ј
Ј
Ј
the collision plane shown in ͑a͒ arises from the isotropic angular distribution
of j with respect to both k and k shown in ͑b͒ and ͑c͒, respectively.
Ј
Ј
of this reaction was very large, the collisions with wide range
of impact parameters can contribute to the reaction. Such
wide spread of opacity function generally gives rise to the
scattering of the products over wide angular range as also
suggested in the QCT calculation for the reaction O(3P)
ϩCS→COϩS.29
Thus, we attribute the nearly isotropic DCS to both the
wide range of impact parameters and the lifetime of the col-
lision complex comparable to half of the rotational period.
shows the k –j correlations of the products scattered into
Ј
Ј
B. Implication of the isotropic rotational angular
momentum polarization
the forward and backward hemispheres. The correlations in
both hemispheres are isotropic to almost the same degree. As
mentioned in Sec. IV B, the product DCS was not found to
significantly depend on the recoil energy, or the internal en-
ergy of the sister fragment. In other words, this implies that
As described in Sec. IV A, we have found the nearly
statistical rotational and translational energy distributions. In
the recent study,6,11 the vibrational energy distribution of this
reaction was shown to be closer to the statistical prediction
than that expected from a direct process. To clarify the origin
of these nearly statistical energy distributions, examining the
rotational angular momentum polarization sensitive to reac-
tion dynamics is advantageous.
the energy distribution as well as the k –j correlation does
Ј
Ј
not have a significant dependence on scattering angles. These
results indicate that the nearly statistical energy distributions
observed here do not accidentally originate from a special
superposition of individual reaction dynamics initiated by the
collisions with specific impact parameters.
As shown in Fig. 7͑c͒, j is nearly isotropic with respect
Ј
to k for this reaction. If the in-plane ͑out-of-plane͒ motion
of the N–N–O moiety contributes primarily to the product
We can therefore conclude that the nearly statistical dis-
tributions observed for the O(1D)ϩN2O reaction are attrib-
uted to the occurrence of almost complete energy random-
ization within the lifetime of the collision complex.
Ј
rotation, j should be predominantly polarized perpendicular
Ј
͑parallel͒ to k . Therefore, the nearly isotropic k –j corre-
Ј
Ј
Ј
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598
J. Chem. Phys., Vol. 111, No. 2, 8 July 1999
Tsurumaki, Fujimura, and Kajimoto
C. Origin of efficient energy redistribution
VI. SUMMARY
As mentioned in Sec. V A, the QCT calculation37 sug-
gested that an interaction time of this reaction was at most 1
ps. Whether or not such an interaction time of picosecond
order is essential to yield the statistical energy partitioning
can be examined by comparing with other bimolecular reac-
We have measured scalar and vector properties of the
product NO( ϭ0) generated from the reaction O(1D)
v
Ј
ϩN2O→NOϩNO. The observed rotational and translational
energy distributions of the NO( ϭ0) are considerably hot
v
Ј
and described as Boltzmann distributions with Trot
Ϸ10 000 K and TtrϷ13 000 K, respectively. These results in-
tions. For the bimolecular reactions O(1D)ϩCH4
12,39,40
→OHϩCH3
and H(2S)ϩCO2→OHϩCO,18,41–45 the
dicate that the formation of all the old NO( ϭ0) is not
v
Ј
real time pump–probe experiments utilizing ultrafast lasers
showed that each reaction involved a complex with a lifetime
of picosecond order exceeding the rotational period: 3 ps for
the O(1D)ϩCH4 reaction40 and 0.5–5 ps for the H(2S)
ϩCO2 reaction.43–45 These results imply that these two reac-
tions are complex-mode reactions involving ‘‘long-lived’’
complexes. However, as opposed to a traditional expectation
for complex-mode reactions, the energy distributions of the
products deviated from the statistical predictions,39,41,42 and
the product rotational angular momentum was polarized for
both reactions.12,18 Therefore, a comparison of the three re-
actions involving intermediates with similar lifetimes of pi-
cosecond order suggests that the statistical energy distribu-
tions do not essentially depend on the absolute value of the
lifetime of the collision complex.
dominated by a stripping mechanism where the old NO be-
haves as a spectator during reaction. These energy distribu-
tions are close to the statistical predictions.
The DCS of the product NO( ϭ0,j ϭ34.5) has a
v
Ј
Ј
nearly isotropic distribution with a slight preference for
backward scattering. The product angular momentum vector
j
Ј
is almost isotropic with respect to both k and k ͑the
Ј
relative velocity vectors of the reagents and products, respec-
tively͒. This suggests that both the in-plane and out-of-plane
motions of the collisional ONNO complex contribute to the
product rotation to almost the same degree. Considering that
this reaction has no potential well deep enough for the for-
mation of a long-lived complex, the nearly statistical scalar
and isotropic vector properties suggest that the energy redis-
tribution efficiently takes place among the internal modes of
the short-lived ONNO complex. It suggests that there are
strong couplings among the internal modes of the complex.
Based on the above comparison, for the O(1D)ϩN2O
reaction the redistribution of the available energy among the
internal modes of the collision complex is expected to take
place more efficiently than for the other two reactions. The
efficient energy redistribution expected in this reaction sug-
gests that there should be strong couplings among the inter-
nal modes of the collisional ONNO complex.
For considering such energy flow, the difference be-
tween normal mode and local mode characters will give an
insight. For the molecules containing two equivalent bonds
with a common vibrational frequency, the energy deposited
in one bond flows into the other bond according to the
strength of the coupling between the two bonds.46 The mol-
ecules involving heavy atoms with light hydrogen atoms
such as H2O and H2S have local mode characters, where the
two equivalent modes are localized because of the relatively
weak interbond coupling and the strong anharmonicity.46 On
the other hand, the molecules with heavy terminal atoms
such as CO2 and SO2 have the large couplings and behave
with normal mode characters. Since the normal mode char-
acter will be applied to the ONNO system due to its mass
combination, the efficient energy redistribution in this sys-
tem can be reasonably expected to occur.
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