Exit channel dynamics in the ultraviolet photodissociation of the NO dimer: (NO)2 → NO(A2Σ+)+NO(X2∏)

Article abstract of DOI:10.1063/1.1606442

The UV photodissociation of the NO dimer was studied at the pair correlation level with emphasis on the dynamics of the NO(X)+NO(A) channel. Both vector and scalar properties were examined from 221 nm to 213 nm. Overall, significant results were obtained.

Full text of DOI:10.1063/1.1606442

Exit channel dynamics in the ultraviolet photodissociation of the NO dimer: ( NO ) 2 →
NO (A 2 Σ + )+ NO (X 2 Π)
A. B. Potter, V. Dribinski, A. V. Demyanenko, and H. Reisler
Citation: The Journal of Chemical Physics 119, 7197 (2003); doi: 10.1063/1.1606442
View online: http://dx.doi.org/10.1063/1.1606442
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 14
8 OCTOBER 2003
Exit channel dynamics in the ultraviolet photodissociation of the NO dimer:
2
¿
2
„
NO… \NO„A ⌺ …¿NO„X ⌸…
2
A. B. Potter, V. Dribinski, A. V. Demyanenko, and H. Reislerb)
Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482
a)
͑
Received 1 May 2003; accepted 15 July 2003͒
The correlated angular and product rotational state distributions obtained in the 221.67 nm
2
ϩ
2
photodissociation of (NO) yielding NO(A ⌺ )ϩNO(X ⌸) have been examined in the molecular
2
beam using the velocity map ion imaging technique. The translational energy and angular
2
ϩ
distributions of selected rotational states of NO(A ⌺ ) products in Nϭ0, 5, 6 for which the
2
Ϫ1
maximum energies available to the NO(X ⌸) products are 202.5, 142.5, and 118.5 cm
respectively, have been measured. The recoil anisotropy parameter of the photofragments, ␤eff , is
.2Ϯ0.1, less than that previously measured at 213 nm ͑1.36Ϯ0.05͒. The correlated product state
,
1
distributions near dissociation threshold agree with the predictions of phase space theory. These
experimental results, as well as those obtained previously at 213 nm, are compared to statistical
calculations, including v"J correlations. Application of the ␤-E correlation model to the 213 nm
T
results indicates that ͓NO(A,N),NO(X,J)͔ pairs with high NO(X,J) rotational levels are produced
preferentially via planar dissociation, in contrast to the statistical expectation of the v"J correlation,
which reveals no preference for planar dissociation. A mechanism involving vibrational
predissociation with restricted intramolecular vibrational energy redistribution can explain both the
observed scalar and vector properties. Specifically, the low frequency torsional ͑out-of-plane͒ mode
does not couple efficiently to the other modes, especially at higher excess energies when the
dissociation is rapid. On the other hand, the long-range attraction between NO(A) and NO(X),
which is revealed both in the photodissociation dynamics of the dimer and in the quenching of
NO(A) by NO(X), encourages long-range mode couplings and can explain the largely statistical
rotational state distributions observed near threshold. From images obtained near threshold, the
Ϫ1
bond energy of the NO dimer in the ground state is determined to be 710Ϯ10 cm , in good
agreement with previous results. © 2003 American Institute of Physics.
͓
DOI: 10.1063/1.1606442͔
I. INTRODUCTION
The electronic structure and UV photodissociation of
3
–7
(
NO) and its excited states have been studied before. Ab
2
The nitric oxide dimer (NO)2 is a weakly covalently
bound complex formed by the pairing of two electrons resid-
ing originally in singly occupied ␲* orbitals of the
initio calculations have shown the existence of a large num-
ber of electronic states that have no counterpart in the sepa-
rate monomers.8 States accessed in the near IR and in the
,9
2
2
NO(X ⌸) monomers. The ground state radical has a planar
UV correlate asymptotically with two NO(X ⌸) radicals
ϩ
Ϫ
cis-ONNO structure of C2v symmetry and its N–N bond
and with the ion pair NO ϩNO , respectively. Between
these two groups of states, lie manifolds of Rydberg and
valence states that correlate asymptotically with
1
length is 2.236 Å. Its dissociation energy, D ϭ710
0
Ϫ1
Ϯ10 cm , though low, reflects the covalent nature of the
2
2
ϩ
2
2
2
binding.
NO(A ⌺ )ϩNO(X ⌸) and NO(B ⌸)ϩNO(X ⌸), but
8
This somewhat unique character of the binding raises the
interesting question of which properties of the dimer reflect
the chemical nature of a cis-ONNO molecule, and which
processes exhibit behavior akin to a weakly bound complex;
e.g., a van der Waals cluster. Photodissociation dynamics is
particularly suitable for exploring chemical and physical
properties of molecules in electronically excited states to
learn about exit-channel dynamics, and the present study ex-
their energies are still unknown. These two channels have
been observed experimentally following photolysis at 193–
210 nm,3 though the mechanism and dynamics of their for-
mation are still not well understood.
,5
The focus of the present work is on the dynamics photo-
1
1
initiated by a B � A transition and terminating in the
2
1
channel:
2
ϩ
2
͑
NO͒ →NO͑A ⌺ ͒ϩNO͑X ⌸͒
2
amines the UV photodissociation of (NO) in the 222–213
2
⌬
Hϭ44 910 cmϪ1
.
͑I͒
nm region.
Our goal is to determine how the products’ scalar and vector
properties reflect the bonding characteristics, electronic
structure and the dynamics of the dissociation of the elec-
tronically excited NO dimer.
a͒Current address: Biological Imaging Center, Beckman Institute 139-74,
California Institute of Technology, 1200 E. California Blvd, Pasadena, CA
9
1125.
b͒
Electronic mail: reisler@usc.edu
0021-9606/2003/119(14)/7197/9/$20.00
7197
© 2003 American Institute of Physics
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1

7198
J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
Potter et al.
In previous work by Kajimoto et al., NO(A) product
In the present work, we extend our measurements to the
†
Ϫ1
quantum state distributions obtained via reaction I were de-
termined following 193 nm photolysis, and could be fit by a
constrained version of the statistical phase space theory
PST͒. In this version the fraction of products with aligned
orbital angular momentum vector L was treated as a param-
near threshold regime (E Ϸ200 cm ), and examine in de-
tail both scalar and vector properties of the dissociation prod-
ucts. We also carry out more extensive comparisons with
statistical treatments, including v"J correlations. Based on
the new results, we propose a mechanism in which UV ex-
citation accesses ͑directly or indirectly͒ a predominantly Ry-
dberg electronic state that is weakly bound and correlates
with channel I. The deviations from the statistical predictions
are thought to reflect restricted IVR involving the coupling
of the initial vibrational excitation to the N–N reaction co-
ordinate. The large mismatch between the different vibra-
tional modes renders the couplings state specific, influences
the nuclear dynamics that lead eventually to product forma-
tion, and may also be reflected in the multiple dissociation
time scales observed in the evolution of the excited dimer
into products.11
͑
eter that depended on the rotational energy of the NO
3
,5
products. The NO product possessed weak alignment and
vector correlations, and its recoil anisotropy parameter ␤eff
ranged from 1.0 to 1.4 for Nϭ7–20 levels of NO(A), where
1
0
N is the rotational level. These results, which corresponded
†
Ϫ1
to excess energy E ϭ6900 cm , were interpreted as an in-
dication of fast and direct dissociation, mostly within the
molecular plane. The authors concluded that the rotational
axis of the NO(A) fragment becomes more perpendicular to
the dimer plane as N increased.5
A different perspective of the dissociation was explored
in the time-resolved photoelectron spectroscopy measure-
11
II. EXPERIMENT
ments carried out at 210 nm. This study showed that (NO)
2
dissociation exhibited two time scales. The initially prepared
dimer state decayed in ϳ0.3 ps, while the NO(A)ϩNO(X)
products buildup time was ϳ0.7 ps. It was suggested that
nonadiabatic transitions might give rise to this behavior, al-
though no definitive conclusions about the participating
states could be reached.
The experiments are performed using (NO) generated
2
in a seeded molecular beam of NO. The (NO)2 dimer is
excited in a one-photon transition to above the threshold of
2
ϩ
2
the NO(A ⌺ )ϩNO(X ⌸) dissociation channel using
21.67 nm laser radiation. Following photolysis, the dimer
2
2
ϩ
undergoes fast dissociation, and NO(A ⌺ ,N) products are
In a recent study ͑Paper I͒,12 we examined in detail the
angular distributions obtained in the photodissociation of
detected by resonance enhanced multiphoton ionization
REMPI͒ and velocity map ion imaging, providing velocity
and angular distributions of state-selected products. The ex-
periments are similar to those carried out at 213 nm,12 and
therefore, only procedures that have changed are discussed in
detail.
͑
†
Ϫ1
(
NO) at 213 nm (E ϭ2038 cm ) for specific NO(A) rota-
2
tional states. Using the velocity map ion imaging technique,
we obtained speed-dependent recoil anisotropy parameters
␤eff from images of selected NO(A,N) states. The main re-
sult was that as the c.m. translational energy, E , of the
T
Nitric oxide dimer is formed in a free jet expansion of
NO in a 70% Ne: 30% He buffer. A doubly skimmed pulsed
molecular beam containing 7% NO seeded in 2.0 atm of the
carrier gas propagates through a hole in the repeller plate of
the ion optics assembly into the ionization region. The Ne:He
buffer gives better velocity resolution than pure He buffer by
slowing the molecular beam and enabling the skimmers to
better reduce the lateral components of the translational mo-
tion. Additionally, the greater cooling achieved in the Ne:He
mixtures minimizes the contribution of parent rotational an-
gular momentum to the overall angular momentum, which is
important for near-threshold experiments, since so few rota-
tional states of the fragments are accessible. By measuring
fragments decreased, ␤eff first decreased and then, at very
low E , increased abruptly again. This ␤-E correlation
T
T
could be simulated for all the monitored NO(A,N) states by
a classical model that related the decrease in ␤eff at low E to
T
the deviations from axial recoil mandated by angular mo-
mentum conservation. This model, referred to in what fol-
lows as the ␤-E correlation model, is applicable to cases
T
where the dissociation results from an in-plane electronic
transition. The model shows that for each NO(A,N) level,
high rotational states J of the NO(X) co-fragment are pro-
duced preferentially via planar dissociation, in agreement
5
with Naitoh et al., and the fragments’ angular momenta at-
2
ϩ
2
tain their final values at an interfragment separation of 2.6
Ϯ0.4 Å, close to the 2.24 Å N–N equilibrium bond length in
the ground state of the dimer. Except for very highly rotating
NO(X,J) states near the energetic limit, both co-rotating and
counter-rotating NO products are produced.
the REMPI spectrum of the NO A ⌺ � X ⌸ transition in
mixtures of 7% NO, we estimate that the rotational tempera-
ture in the beam is T ϭ2 K with the Ne:He buffer com-
rot
pared with 3 K with the previously used He buffer.
Further downstream, (NO) undergoes photolysis with
2
In addition, with 213 nm photolysis both the rotational
energy distributions of NO(X) co-fragments correlated with
specific NO(A,N) states, and the global rotational state dis-
tribution of NO(A) showed deviations from the predictions
of PST. This deviation was particularly prominent for high
rotational states of the NO(X) co-fragment. It was suggested
in Paper I that at E ϭ2038 cm , effects due to exit channel
dynamics likely influenced both the correlated and global
rotational state distributions of the NO fragments, but the
deviations were small and their origin was not revealed.
pulsed, linearly polarized, and mildly focused (f.l.
ϭ50 cm) UV laser radiation, which intersects the molecular
beam at a right angle. The photolysis laser pulse is obtained
by using the frequency-doubled output of an excimer laser
pumped dye laser system ͑Coumarin 440, 0.1–0.3 mJ͒. The
correspondence between the measured signal and (NO)2
†
Ϫ1
12
photolysis has been demonstrated previously.
The photolysis and probe lasers are both linearly polar-
ized and introduced coaxially at a right angle to the molecu-
2
ϩ
lar beam. NO(A ⌺ ) photofragments are probed state selec-
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J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
UV photodissociation of the NO dimer
7199
tively with the focused output of a Nd:YAG laser pumped
dye laser system ͓Rhodamine 640, 0.2–0.5 mJ; f.l.
ϭ30–50 cm lens depending on the NO(A,N) signal͔ by 1ϩ1
2
ϩ
2
ϩ
6,13
REMPI via the E ⌺ � A ⌺ transition at ϳ600 nm.
Probing the P and R branches of the transition gives identical
results. At the employed probe laser intensity, the monitored
transitions are saturated,14 but the results do not change when
the laser intensity is reduced. To minimize complications due
to vector correlations, the polarizations of the two lasers are
fixed parallel to each other, and we assume that changes in
the anisotropy parameter due to rotational alignment are
6
minimal. The time delay between the pump and probe lasers
is kept at 0Ϯ5 ns. Typical signals include the summation of
5
(
1Ϫ2)ϫ10 laser firings. The main source of background
ion signal is non-state-selective ionization of NO(A) frag-
ments by the pump laser radiation. Good spatial and tempo-
ral overlap of the two laser beams minimizes the background
due to ionization by the pump.
The velocity map imaging arrangement has been de-
scribed in detail elsewhere.1
5,16
In brief, it consists of an
ion-acceleration stage, a 60 cm long drift-tube, and a CCD
camera that monitors a phosphor screen coupled to a MCP
ion detector. Since there is less energy available for transla-
tion of the fragments than in Paper I, the electrode voltages
are reduced to expand the size of the image.
In acquiring images, the electric field vector, E, of the
photolysis laser is maintained parallel to the vertical direc-
tion of the image plane and the product recoil velocities are
aligned predominantly in the polar direction of the image.
After background subtraction, the images are symmetrized
and the two-dimensional ͑2D͒ projections are converted to
three-dimensional ͑3D͒ velocity distributions using the Basis
Set Expansion ͑BASEX͒ method.17 This image reconstruc-
tion method is based on expanding the projection in a basis
set of functions that are analytical projections of known well-
behaved functions. The fragment’s speed distribution is ob-
tained at each distance from the center by analytical integra-
tion of the reconstructed image, expressed as a linear
combination of basis functions, over all angles. The angular
distributions are directly obtained from the expression of the
image in polar coordinates.
III. RESULTS AND ANALYSIS
Figure 1 shows representative reconstructed images of
2
ϩ
NO(A ⌺ ,N) fragments following 221.67 nm photolysis.
2
ϩ
FIG. 1. 2D cuts of the reconstructed images of NO(A ⌺ ,Nϭ0,5,6) ob-
The total available energy with respect to the channel I
tained in photolysis of (NO)2 at 221.67 nm. The maximum energies avail-
able to the NO(X) fragment are 202.5, 142.5, and 118.5 cm , respectively.
The electric field vector of the photolysis laser is parallel to the vertical
direction of the image plane.
†
Ϫ1
threshold is E ϭ202.5 cm , and the maximum energies
available to the NO(X) fragments are Emaxϭ202.5, 142.5,
Ϫ1
Ϫ1
and 118.5 cm for Nϭ0, 5, and 6, respectively. From these
images we derive the binding energy of the NO dimer in its
Ϫ1
ground electronic state, 710Ϯ10 cm , in good agreement
with previous results.2
ϭ6) measurement (Emaxϭ118.5 cmϪ1), the only spin–orbit
state energetically accessible is NO(X ⌸1/2).
2
The speed distribution of each NO(A,N) state is con-
verted to a translational energy distribution P(E ) from
T
which the correlated NO(X,⍀,v,J) internal energy ͑spin–
orbit, vibrational, and rotational, respectively͒ distribution
P(E ) is derived. Figure 2 shows the P(E ) distributions
A. Angular distributions
The speed-dependent recoil anisotropy parameter,
␤ (V), is derived from the angular distributions using
eff
int
T
1
8
for the same NO(A,N) states. Note that in the NO(A,N
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7200
J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
Potter et al.
2
ϩ
2
ϩ
FIG. 3. Dependence of the anisotropy parameter, ␤(ET), of NO(A ⌺ , v
FIG. 2. Total c.m. translational energy (E ) distributions of NO(A ⌺ ,N
T
ϭ0, Nϭ0,5,6) on the c.m. translational energy (E ) following photodisso-
ciation at 221.67 nm. The rotational level of the NO(X ⌸⍀ϭ3/2,1/2 ,v
ϭ0,J) co-fragment is specified on the vertical lines as in Fig. 2. The open
and closed squares correspond to dissociation into the ⍀ϭ1/2 and ⍀ϭ3/2
spin–orbit states, respectively. The circles indicate the prediction of the
T
ϭ0,5,6) obtained in the photodissociation of (NO)2 at 221.67 nm. The
2
2
vertical lines mark the rotational levels of the NO(X ⌸
,J) co-
⍀
ϭ3/2,1/2
fragment. The long and short lines correspond to the ⍀ϭ1/2 and ⍀ϭ3/2
spin–orbit states, respectively. In the Nϭ6 measurement, only the
2
NO(X ⌸1/2) spin–orbit state is accessible.
␤
-ET model described in the text.
1
2
2
NO(X ⌸1 ,J) and NO(X ⌸ ,J) states, respectively. The
/2
3/2
P͑␪,V͒ϰͩ ͓ͪ1ϩ␤ ͑V͒P ͑cos ␪͔͒.
͑1͒
eff
2
†
Ϫ1
4
␲
maximum ␤eff value observed with E ϭ202.5 cm is 1.2
Ϯ0.1, somewhat lower than the value observed at E
ϭ2038 cm (␤ ϭ1.36Ϯ0.05).
†
␤eff(V) is determined using Eq. ͑1͒ at each distance from the
center of the image corresponding to an available NO(X,J)
state ͑i.e., a particular speed͒. Energy balance is given by
Ϫ1
eff
B. Correlated energy distributions
†
NO͑A͒
int
NO͑X͒
NO͑A͒
NO͑X͒
E ϭhvϪD ϭE
ϩEint ϩET
ϩET
,
͑2͒
0
The NO(X,J) rotational state distributions correlated
with specific NO(A,N) rotational states are shown in the left
hand panels of Fig. 4. To derive the correlated distributions,
the fragment speed distributions were fit by a set of Gaussian
NO(A,X)
where D is the dissociation threshold of channel I, E
0
T
NO(A,X)
are the c.m. recoil energies of the fragments; and Eint
are the corresponding internal energies, ͑i.e., spin–orbit, vi-
brational, and rotational energies͒. Each measured ␤eff is a
functions, each centered at the position of an
2
weighted average of the ␤ parameters associated with all the
NO(X ⌸1
,J) state. The widths of the Gaussian func-
/2,3/2
2
NO(X ⌸
,J) states whose Eint is complementary to ET .
The solid and open squares in Fig. 3 represent measured ␤eff
values at ET corresponding to the Eint of specific
tions were optimized to give the best fit for each speed dis-
tribution. The relative populations of the J states were then
determined by a least square fit, using Tikhonov regulariza-
1
/2,3/2
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J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
UV photodissociation of the NO dimer
7201
FIG. 4. Correlated distributions P(J)
of NO(X,J) rotational states for spe-
cific NO(A,N) states. The populations
extracted from the observed transla-
tional energy distributions, P(E ) are
T
indicated by circles, while the solid
curve depicts the corresponding PST
distribution. The left and right panels
show distributions with maximum
available energy of 202.5 and 2038
Ϫ1
cm , respectively.
tion to stabilize the coefficients in the overlapped region of
and angular momentum, which for the NO dimer distribu-
tions requires satisfying the condition set in Eq. ͑2͒ and also
1
7
low J states. The small separation between low J states
Jр3) in the energy distribution reduces the accuracy of
(
J͑NO͒2ϭJNO͑A͒ϩJNO͑X͒ϩL,
͑3͒
their extracted populations to Ϯ50%, while for higher J’s it
is about Ϯ10%. The error is greater than in our previous
where J(NO)2, and JNO(A,X) are the angular momenta of the
(
NO) experiments at 213 nm ͑shown for comparison on the
2
1
2
parent (NO)2 molecule, and the NO(A,X) fragments, re-
spectively; and L is the orbital angular momentum.
In our PST treatment of correlated rotational distribu-
right-hand side of Fig. 4͒, because of the smaller signal to
noise ratio. The extracted rotational distributions in the 213
nm photolysis experiments have shown that the two spin–
orbit states of NO(X) are approximately equally populated in
all the correlated distributions. Therefore, in the rotational
state distributions shown in Fig. 4, the spin–orbit levels are
suppressed for clarity of presentation.
tions in (NO) dissociation, N
is selected in the experi-
2
NO(A)
ment, the values of JNO(X) are determined by the available
energy, and J(NO)2 is determined by the rotational tempera-
1
0
ture of the parent in the molecular beam (T ϭ2 K). The L
rot
states are counted for each specific JNO(A) , JNO(X) , and
J(NO)2 combination allowed by the conservation of energy
and angular momentum, and the result for each J(NO)2 is
IV. DISCUSSION
weighted according to a 2 K Boltzmann distribution.
The correlated rotational state distributions obtained at
221.67 nm (E ϭ202.5 cm ) agree well with the statistical
A. Scalar properties
†
Ϫ1
In the PST description of bond breaking, the accessible
phase space is constrained only by conservation of energy
predictions shown in solid lines in Fig. 4. However, at the
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7202
J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
Potter et al.
higher available energy (E ϭ2038 cmϪ1), both the corre-
lated rotational distribution and the global NO(A) rotational
state distributions are overestimated by PST for high J states
†
͑
see Fig. 4 and Paper I͒.12 These deviations from PST pre-
dictions are fairly small but consistent, and from scalar prop-
erties alone we cannot elucidate their nature.
B. Vector properties
In previous papers,12,19 the ␤-ET correlation model, a
classical model based on energy and angular momentum
conservation, was used to explain the measured dependence
of the recoil anisotropy parameter ␤eff on the translational
energy of the recoiling fragments in the photodissociation of
1
9
12
tri-atomic and tetra-atomic species. In applying the
FIG. 5. PST prediction of the v"J correlation in the 213 nm (E†
model, a critical distance R where the rotational and orbital
C
Ϫ1
angular momenta were established was inferred from fits to
the data. For the NO dimer, RC was defined as the distance
between the centers-of-mass of the two NO fragments,12 and
it was, therefore, loosely related to the value of R at the
ϭ2038 cm
) photodissociation of (NO)2 for selected ͓NO(A,N),
NO(X,J)͔ pairs. The dotted, dashed, and solid lines represent dissociation
into Nϭ1, 11, and 19, respectively. The solid and dashed vertical lines
represent the lowest NO(X) co-fragment J level for which planar dissocia-
tion ͑v perpendicular to J; ␤ ϭϪ1/2) was inferred from the experiments
vJ
transition state (R уRTS). In simulating the dependence of
for pairs with Nϭ11 and 19, respectively. This is in contrast to the statistical
v"J calculation, which predicts no such correlation.
C
␤eff on E , we examined two models, one in which the
T
dissociation was constrained to the plane, and one in which a
constraint was not imposed. Based on comparisons with the
is convenient for calculating scalar product state distribu-
tions, it is not as well suited to describe v"J correlations.
These are more easily calculated by using the helicity state
count for PST developed by North and Hall.20 An advantage
of their method is that in the helicity basis, the projections of
the fragments angular momenta on the recoil axis are good
quantum numbers, while the orbital angular momentum L
has no projection on this axis.
experimental ␤eff versus E curves, we concluded that in 213
T
nm photolysis, dissociation into high rotational levels of
NO(X) must take place from a planar (NO) geometry and
2
the best fit was obtained for R ϭ2.6Ϯ0.4 Å. We assume that
C
both co-rotating and counter-rotating NO fragments are pro-
duced, except for the highest allowed J states, for which only
counter-rotating fragments satisfy both energy and angular
momentum conservation.12
To perform the helicity state count for the v"J correlation
͑without including a centrifugal barrier͒, the angular mo-
The results of the ␤-E correlation model obtained for
T
221.67 nm photolysis are depicted by circles in Fig. 3. The
menta of the individual fragments J are described by their
i
best fits are obtained for R ϭ3.0Ϯ0.4 Å, and the planar and
C
projections on the center-of-mass relative velocity vector,
unconstrained dissociation models fit the data equally well.
Evidently, in this case the model cannot serve to identify a
geometrical bias in the dissociation.
␭iϭϪJ ¯J ͓iϭNO(A),NO(X)͔. The total helicity, ⌳
i
i
ϭ␭
Ϫ␭
, is contstrained by J due to angular
͑NO)
2
NO(A)
NO(X)
momentum conservation such that ͉⌳͉рJ͑NO)2 . The statisti-
cal prediction of the v"JNO(A) correlation for dissociation into
The ␤-ET correlation model indicates that at E†
Ϫ1
ϭ2038 cm , dissociation into high NO(X,J) states prefer-
a given (JNO(A) ,JNO(X)) pair is given by the second Legendre
entially takes place in the NO dimer plane. In addition, com-
parisons with PST calculations show that the populations of
these high NO(X,J) fragments deviate from statistical pre-
dictions. It remains unclear, though, whether the deviation
from the statistical prediction of the rotational state distribu-
tion is associated with the requirement for planar dissocia-
20
moment of the normalized p(␭NO(A)) distribution
J
NO͑A͒
␤vJ,JNO͑A͒ ,JNO͑X͒ϭ
p͑␭NO͑A͒͒JNO͑X͒
͚
␭
ϭϪJ
NO͑A͒
NO͑A͒
␭NO͑A͒
ϫP2
ͩ
ͪ
,
͑4͒
tion derived from the ␤-E correlation model. Planarity im-
T
ͱ
JNO͑A͒͑JNO͑A͒ϩ1͒
plies that the NO velocity vector v, which lies in the plane,
must be perpendicular to J, and the question arises whether a
perpendicular v"J correlation for high J states is required by
statistical theories. For example, in dissociation of a nonro-
tating NO dimer into one nonrotating and one rotating frag-
ment ͑the pseudo-triatomic case͒, the rotational angular mo-
mentum of the rotating fragment has to be balanced mainly
by L, causing v to be perpendicular to J. In such a case, the
statistical prediction would indicate planar dissociation.
In order to determine if this is the case here, the statis-
tical prediction of the v"J vector correlation has been calcu-
lated. While the traditional PST calculation described above
where ␤vJ is the bipolar moment corresponding to the v"J
0
0
21
correlation ͓denoted elsewhere by ␤ (22)]. The limiting
values of ␤vJ are Ϫ1/2 and 1, corresponding to v perpendicu-
2
2
lar and parallel to J, respectively. The results of the statis-
tical calculations of ␤vJ for NO(A,Nϭ1,11,19) paired with
the allowed NO(X,J) states are shown in Fig. 5 for dissocia-
tion at 213 nm and T ϭ3 K ͑the rotational temperature of
rot
1
2
the NO dimer in the 213 nm experiments͒.
For NO(A,N) pairs associated with the Jϭ0 state of
NO(X), a perpendicular v"J correlation similar to that of a
triatomic molecule should be obtained. However, even in this
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J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
UV photodissociation of the NO dimer
7203
case ␤vJ can deviate from its limiting Ϫ1/2 value, because
some of the orbital angular momentum can be compensated
by parent molecule rotation, resulting in less negative values
of 1.36Ϯ0.05, 1.30Ϯ0.05, and 1.2Ϯ0.1, respectively, sug-
gesting that the lifetime increases as the available energy
decreases.
of ␤ . The effect of parent rotation diminishes as N in-
creases, because fewer of the allowed L states are balanced
by J(NO)2. Similarly, the deviations from the Ϫ1/2 limit in-
An important requirement for statistical dissociation is
that the internal energy of the parent molecule is redistrib-
uted randomly among its vibrational modes on a time scale
faster than bond breaking. At energies close to the dissocia-
tion threshold, the parent lifetime is longer, allowing more
vJ
crease at higher Trot
In general,
NO(A,N),NO(X,J)͔ pair have low rotational angular mo-
.
when
both
fragments
in
an
time for the (NO) internal energy to be randomized prior to
͓
2
†
dissociation. At higher E the dissociation may be too fast
menta, the parent rotational angular momentum makes a sig-
nificant contribution, causing the v"J correlation to be small.
When both have higher ͑but comparable͒ rotational angular
momenta, the fragments can balance each other’s angular
momenta by counter-rotating, and again the v"J correlation is
small. For example, when NϷJ the predicted value is ␤vJ
Ϸ0. The v"J correlation calculations predict that in general
when monitoring an intermediate NO(A,N) level such as
Nϭ11 or 19 (Jmaxϭ34), there will be a perpendicular v"J
correlation with associated low NO(X,J) levels, but not with
high J levels. This is clearly seen in Fig. 5. Although a cen-
trifugal barrier is not included in this calculation, its effect is
small and does not change the qualitative prediction. Its in-
clusion would drive the ␤vJ value of the highest NO(X,J)
states to slightly more positive values corresponding to a
decreased correlation. This has been described in detail
for all the modes to be populated, explaining why the corre-
†
Ϫ1
lated product state distributions at E ϭ2038 cm
appear
†
Ϫ1
less statistical than at E ϭ202.5 cm
.
With respect to intramolecular vibrational energy redis-
tribution ͑IVR͒, the dissociation of the NO dimer on the
excited state resembles vibrational predissociation of a van
der Waals complex.23 In both species the frequencies of the
intermolecular dimer modes are much lower than the fre-
quencies of the vibrational modes of the individual sub-units.
The large disparity between these frequencies leads to small
coupling matrix elements between the molecular modes of
the sub-units and the intermolecular modes, resulting in re-
stricted IVR.
The preference for planarity for the high NO(X,J) co-
fragments suggests a restricted involvement of the torsional
2
0
͑out-of-plane͒ mode in the excited NO dimer. The reduced
elsewhere.
participation of the torsional mode can be explained by the
following argument. If we assume that the initial excitation
involves the NO moiety,8 i.e., excitation of the NO stretch,
then for dissociation to occur, energy must flow into the
N–N bond. Assuming further that the vibrational frequencies
in the excited state are similar to those in the ground state
neutral and cation ͑which are comparable͒, we can use
From our perspective, the main conclusion to be drawn
from the v"J correlation calculations is that for all the
NO(A,N) states investigated in our work, the statistical cal-
culations do not predict a perpendicular v"J correlation.
Thus, the statistical prediction does not dictate the planar
dissociation inferred from the experiments of Paper I for
high NO(X,J) states. Again, it is important to emphasize that
,24
Ϫ1
ϳ1800, ϳ300, ϳ200, and ϳ100 cm for the NO stretch,
when applying the ␤-E correlation model to the dissocia-
T
NNO bend, NN stretch, and torsion, respectively.25 Conse-
quently, couplings are expected to be weak between the NO
stretch and all the other modes, strong between the NNO
bend and the NN stretch, and weakest to the torsion. It is
reasonable then that the high levels of the torsional modes,
which give rise to out-of-plane dissociation, are not effi-
ciently excited, in particular at high excess energies.
tion of (NO) we have not assumed a priori that there is a
2
preference for planar dissociation. The conclusion that pla-
narity is the preferred geometry for high JNO(X) pairs is based
1
2
on the fit of the curve of ␤eff versus E to the data. There-
T
fore, the discrepancy between the experimental findings and
the statistical predictions for both scalar and vector proper-
ties for pairs with high NO(X,J) states indicates that non-
statistical effects are important in the product state distribu-
tions obtained in the UV dissociation of the NO dimer.
D. The nature of the dissociative state
We have argued above that the decreased propensity for
out-of-plane dissociation for NO products in high J states
can reflect small coupling matrix elements to the low-
frequency torsional mode of the excited state. This excited
state, however, remains unassigned. Though we limited our
measurements to wavelengths where channel I predominates,
it should be remembered that more than one electronic state
of the dimer can give rise to this channel. Moreover, ab initio
calculations show that in the 1 eV energy range around the
C. Dissociation mechanism
Electronic structure considerations and experiments indi-
1
cate that the transition dipole moment of the (NO)2 B2
1
�
A1 system lies in the molecular plane, parallel to the
5
–7
N–N bond.
This geometry corresponds to the limiting
Ϫ1
value ␤ϭ2. As discussed in Paper I, the observed reduction
of the measured ␤eff from its limiting value is partly due to
dissociation lifetime, which is close to a picosecond at 210
threshold of channel I ͑i.e., ϳ50 000Ϯ5000 cm ͒, there are
8
4 singlet Rydberg states and 8 singlet valence states. The
8
group of 4 ion-pair states is not much higher in energy. It is
11
nm. Additional reduction in ␤ may be due to out-of-plane
motions and rotation of the recoil axis with change in the
molecular geometry during dissociation. Our measurements
at 213.00, 216.00, and 221.67 nm yield maximum ␤eff values
quite plausible, therefore, that the adiabatic electronic states
include contributions from several diabatic states, and that
the mixing among states varies along the N–N reaction co-
ordinate. This has been seen in other dissociating molecules
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7204
J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
Potter et al.
and radicals that have valence and Rydberg states in close
HOCl ground-state dissociation into HOϩCl following OH
overtone excitation.
2
6,27
30
proximity.
In our case, the initially excited state may
possess, for example, a large ns or npx,y,z Rydberg character
mixed with valence states that correlate asymptotically with
2
2
V. SUMMARY AND CONCLUSIONS
the NO(B ⌸)ϩNO(X ⌺) channel ͑whose threshold is only
Ϫ1
1
280 cm above channel I͒, and/or ion-pair states. This sce-
The UV photodissociation of the NO dimer has been
studied at the pair correlation level with emphasis on the
dynamics of the NO(X)ϩNO(A) channel. Both vector and
nario does not exclude, of course, nonadiabatic transitions.
If indeed the dissociative state has a predominantly Ry-
dberg character, its N–N bonding is probably intermediate
between that of the neutral and ionic ground states, which are
†
scalar properties have been examined from 221 nm (E
Ϫ1
†
Ϫ1
ϭ202 cm ) to 213 nm (E ϭ2038 cm ). The major find-
ings from this work, as well as from Paper I are summarized
below:
Ϫ1
32
bound by ϳ700 and ϳ5000 cm , respectively. By using
ϩ1 ionization of jet-cooled (NO) , we found that UV ab-
1
2
Ϫ1 31
sorption commences at 41 500Ϯ200 cm
.
If dissociation
͑1͒ At the higher excess energy, both the global NO(A)
distribution, and the correlated distributions display devia-
tions from the predictions of PST, especially for high
NO(X,J) rotational levels. Near threshold, the deviations are
insignificant.
͑2͒ The maximum value of ␤eff at each excess energy,
obtained from the measured angular distributions as a func-
tion of ET , is typical of fast dissociation following a parallel
transition, but is lower than the limiting value of 2.0. ␤eff
decreases with decreasing excess energy, and part of this
reduction is due to increased dissociation lifetime. This is
confirmed in the time-resolved measurements of Blanchet
and Stolow,11 which show a buildup time of ϳ1 ps for the
NO(A) product.
to channel I takes place on the initially excited state, this
Ϫ1
state would be bound by 3400Ϯ200 cm . Such a shallow
well in the N–N coordinate would explain the incomplete
IVR in the dissociation, which would become more severe
when ͑i͒ the dissociation is faster; and ͑ii͒ higher excitation
of the torsional mode is required.
Alternatively, one can look at the inverse process to dis-
sociation, i.e., the association of NO(X) and NO(A), and
gain insight by considering what is known about the quench-
ing of NO(A) in collisions with NO(X), a process which has
been studied extensively.28 The efficient quenching has been
attributed, at least in part, to strong electrostatic interactions
between NO(A) and NO(X), which are enhanced by the
large dipole moment of NO(A) ͑1.1 D͒.29 These attractive
͑3͒ The ␤-ET
correlation model indicates that for
͓
NO(A,N),NO(X,J)͔ pairs with high NO(X,J) rotational
interactions extend to long range, rationalizing the R value
C
†
levels planar dissociation is favored, at least at high E . This
of ϳ3.0 Å obtained in the near threshold photodissociation
experiments. This also helps explain the statistical behavior
observed near the threshold of reaction I. At shorter N–N
distances, the electrostatic attraction switches to a bonding
valence interaction.
result is in agreement with the findings of Naitoh et al. at
5
1
93 nm. This propensity for planarity, which corresponds to
v perpendicular to J, is compared with statistical calculations
of the v"J correlation. It is concluded that statistical consid-
erations cannot rationalize the observed preference for planar
dissociation for the high NO(X,J) states.
A mechanism involving vibrational predissociation with
restricted IVR is proposed to explain the observed scalar and
vector properties. Specifically, the low frequency torsional
Blanchet and Stolow, who carried out femtosecond pho-
toelectron spectroscopy experiments at 210 nm, inferred that
a nonadiabatic decay pathway may be involved in the
11
dissociation. This explained the faster disappearance of the
parent ion signal compared to the buildup of the photoelec-
tron spectrum of the NO(A) product. However, femtosecond
absorption can coherently excite a superposition of states,
which then dephases ͑e.g., s and p Rydberg states, or a Ry-
dberg and a valence state͒. In this regard, the first excitation
step in the femtosecond and nanosecond experiments may be
different.
͑out-of-plane͒ mode does not couple efficiently to the other
modes, especially at higher excess energies when the disso-
ciation is fast. On the other hand, the long-range attraction
between NO(A) and NO(X), which is revealed both in the
photodissociation dynamics of the dimer and in the quench-
ing of NO(A) by NO(X), encourages IVR and can explain
the more statistical rotational state distributions observed
near the threshold.
Last, we wish to comment on the issue of molecular
͑
cis-ONNO͒ versus complex ((NO) ) properties of the NO
2
Open questions still remain regarding the nature of the
initially excited state and the role of nonadiabatic transitions.
Our preliminary results on REMPI of the NO dimer in the
molecular beam place the threshold of the UV absorption at
dimer. There are similarities between our proposed dissocia-
tion mechanism of the NO dimer and that of nitrite mol-
ecules ͑RO–NO͒. In the dissociation of CH ONO(S ) into
3
1
Ϫ1
CH OϩNO, for example, excitation is initially localized in
3
41 500Ϯ200 cm , but do not reveal how many states are
the NO moiety, and there is a shallow well along the
involved in the dissociation. If dissociation to channel I takes
place directly on the initially excited state, this state would
–
O–NO coordinate. Because of the weak coupling between
Ϫ1
the initially excited mode and the dissociation mode, the life-
be bound by 3400Ϯ200 cm . This binding strength is inter-
time is long enough to allow oscillation in the CH ON–O
mediate between the ground states of the neutral ͑ϳ700
3
Ϫ1
Ϫ1
coordinate before sufficient energy accumulates in the
cm ͒ and the ion ͑ϳ5000 cm ͒, suggesting a large Ryd-
berg character for the excited state. Experiments are in
progress in our laboratory to further characterize the excited
state͑s͒.
2
3
CH O–NO coordinate for dissociation to occur. Restricted
3
IVR is illustrated also in molecules with low dissociation
thresholds and high frequency vibrational modes, such as the
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J. Chem. Phys., Vol. 119, No. 14, 8 October 2003
UV photodissociation of the NO dimer
7205
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1