775
J. Chem. Phys., Vol. 119, No. 2, 8 July 2003
Photolysis of N O
2
around 6000 msϪ1. On average about 65% of the energy
These expressions may be used in conjunction with Eq.
4͒ to obtain analytical expressions for the Fourier moments
of the measured images. Expressions for the relevant rota-
͑
appears as translational excitation of the photofragments.
3
Peak values of  are 0.82, 1.00 and 0.96 for O( P ),
0
tional moments were presented in Table I of Ref. 18 ͑note the
3
3
O( P ), and O( P ). Averaging  over the product velocity
distribution yields mean values of 0.33 for O( P ), 0.44 for
0
O( P ) and 0.37 for O( P ), as summarized in Table II. The
1
2
0
typographical error in the moment in the VH geometry;
3
0
0
this expression should be identical to that for the VV 0
3
3
1
2
moment͒.
trend of increasing  with increasing product velocity is very
In order to fit the data, a set of velocity-dependent basis
1
similar to that observed for the O( D) channel, indicating
K
0
functions is generated for the F (k ,k,qЈ;v ) dynamical
1
p
that the initial excitation is either to the same state or to a
triplet state with the same electron configuration and spatial
symmetry. As mentioned in the Introduction, the spin-
factors. In the present work, the velocity dependence of the
bipolar moments was treated by expanding them as a linear
combination of equally spaced Gaussian functions that span
1
1
allowed transition to the 2 AЈ component of the B͓ ⌬͔ state
3
the range of possible velocities for the O( P) product, i.e.,
is believed to be the dominant process at 193 nm, but there is
3
also the possibility of direct excitation to the b͓ ⌬͔ state,
K
b ͑k ,k;v͒ϭ
c ͑K,k ,k͒G ͑vϪv ͒,
͑9͒
3
3
0
1
͚i
i
1
i
i
Ј Љ
which splits into A and A components on bending, or to
3
Ϫ
the c͓ ⌺ ͔ state, which correlates with a state of AЉ sym-
metry on bending. The fact that  increases with increasing
velocity would suggest that a significant fraction of the re-
maining energy ͑about 35% of the total available͒ is released
where G (vϪv ) is a Gaussian centered at velocity v .
i
i
i
Equation ͑6͒ then becomes
ϱ
K
into rotation of the N cofragment, as is the case for the
F ͑k ,k,qЈ;v ͒ϭ
c ͑K,k ,k͒
͵
G ͑vϪv ͒
2
0
1
p
͚i
i
1
i
i
3
,13
v
higher energy product channel.
The highest values of 
p
1
/2
arise from near-linear geometries in which the dissociating
bond is aligned preferentially parallel to the electric vector of
the excitation light. Such processes would be expected to
v2
ϫC
͑ ,0͒
vpdv.
k q
T
ͩ ͪ
1
Ј
2
2
p
v Ϫv
impart little rotation to the departing N , and should there-
2
͑10͒
fore correspond to the highest product velocities. Conversely,
dissociation from bent geometries would give a much larger
ϱ
2
2
2
1/2
p
The functions
͐
G (vϪv )C
i
( ,0)(v /v Ϫv ) vpdv
vp
i
k1qЈ
T
may then be chosen as basis functions and the coefficients
degree of rotational excitation in the N cofragment, leading
2
c (K,k ,k) optimized in a global fit of the measured Fourier
to lower product velocities, and would also give rise to a
i
1
moments to the analytical expressions for the Fourier mo-
ments described above. The fitting procedure returns
smaller value of .
In spite of the similarities between ( ) for the singlet
and triplet channels, the velocity distribution for the triplet
channel is much broader. As noted above, the fraction of
v
K
velocity-dependent bipolar moments b (k ,k;v), or may be
0
1
modified to return other sets of alignment parameters using
the equivalences alluded to previously.1
8,22,24
In the present
3
energy released into translation is around 65% for the O( P)
work, the velocity dependence was described using a basis
set of 20 Gaussians, and alignment information was ex-
tracted in the form of the alignment anisotropy parameters
channel, significantly higher than the ϳ40% reported for the
1
2,3,5,7,13
O( D) channel.
If all of the internal excitation ob-
served here in the N coproducts ͑i.e., about 35% of the total
2
s , ␣ , ␥ , and . Error estimates for the alignment pa-
2
2
2
2
available energy͒ were rotational in origin, this would corre-
rameters were obtained from the standard deviation in the
returned velocity-dependent parameters relative to a polyno-
mial fit through the data. The polynomial fit had the effect of
smoothing out oscillations in the returned alignment param-
eters resulting from noise on the data and was used only for
the purposes of carrying out an error analysis.
spond to excitation to rotational levels with quantum num-
bers J ϳ100, which is in fact quite close to the excitation
N
2
3,13
observed for the singlet channel.
This suggests that the
average torques generated along the two dissociation path-
ways are similar. However, the broader distribution of trans-
lational energies in the present case implies a wider range of
internal quantum states are populated in the N coproducts in
2
the triplet channel compared with the singlet channel. If dis-
sociation occurs via spin-forbidden excitation to the
IV. RESULTS AND DISCUSSION
3
3
3
3
Ϫ 3
b͓ ⌬( AЈϩ AЉ)͔ or c͓ ⌺ ( AЉ)͔ states, these differences
in energy disposal may reflect the differences in the topology
of the triplet surfaces, coupled with the greater energy re-
lease in the triplet channel relative to the singlet. If excitation
Velocity-map images measured in the four experimental
geometries described in Sec. II are shown in Fig. 3. The
Fourier moments of the images are shown in Fig. 4, together
with fits to the data using the methodology described in the
previous section. In Fig. 5, the velocity distributions and
velocity-dependent anisotropy parameters (v) determined
from the fitting procedure are presented for the three product
spin–orbit states. The distributions show very similar behav-
ior in each case; the velocity distributions are fairly broad,
1
1
were to occur initially to the B͓ ⌬( AЉ)͔ state, followed by
crossing to a triplet state, the differences in the speed distri-
butions suggest that intersystem crossing to a dissociative
triplet surface is most likely to occur close to the Franck–
Condon region rather than a long way into the exit channel.
The measured alignment anisotropy parameters s , ␣ ,
Ϫ1
peaking at around 4850 ms , while the spatial anisotropy
2
2
3
3
increases more or less linearly with velocity, peaking at
␥ , and for the O( P ) and O( P ) fragments are small,
2 2 1 2
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