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J. Chem. Phys., Vol. 109, No. 11, 15 September 1998
Zhang, Marvet, and Dantus
nm region. Therefore, it is no surprise that certain spectral
features in the 260–290 nm region are due to the I2 f→A
fluorescence. Although we can not determine the exact iden-
tity of the fluorescent state responsible for the vibrational
coherence, the above analysis strongly suggests that the f
state is responsible.
during the first 500 fs after formation of the I2 photodisso-
ciation product. The fast decay implies a high degree of ro-
tational excitation in the I2 fragment.
A quantitative analysis of the rotational dephasing can
be performed on the pure rotational contribution presented in
Fig. 5͑b͒. A formulation of time-dependent rotational anisot-
ropy for the case of one-photon pump and one-photon probe
Since the I—I interatomic distance in the ground state of
CH2I2 is rather close to the bond lengths in the f, g and G
states of the I2 molecule,16,38,40,41 significant vibrational ex-
citation in the I2 fragment is not expected. However, because
the HCH angle in ground-state CH2I2 differs significantly
has been given by Baskin and Zewail32 for a ͑ , ͒ transition
ʈ ʈ
ʈ
case. Extension of the formulation to the ͑ ,Ќ͒ case yields
1
͚j Pj cos 2nt
͚j Pj
r t͒ϭϪ
͑
1ϩ3
,
͑21͒
ͩ
ͪ
from the bond angle of CH2 in the X and b states,16,42 vibra-
˜
˜
20
tional excitation should be expected in the CH2 photofrag-
where the symbols are defined as in Sec. II A. However,
analysis of the pure rotational contribution shown in Fig.
5͑b͒ using this formulation failed to reproduce the experi-
mental data in general and the observed r(0) value in par-
ticular. One can see from Fig. 5͑b͒ that the r(t) value at time
zero is close to Ϫ0.3, especially if one follows the trend of
the experimental trace. This is different from the expected
value of Ϫ0.2 for a situation where the pump and probe
transition dipoles are perpendicular to each other. We find
that this is due to the multiphoton nature of the pump tran-
sition. A three-photon pump transition would be expected to
produce a greater degree of alignment than is expected for a
one-photon transition because it produces a (cos )6 distribu-
tion in the nascent products rather than a (cos )2 distribu-
tion. This narrower initial alignment causes the dephasing of
rotational anisotropy to appear faster than it really is.
In order to model time-dependent rotational anisotropy
experiments in which the excitation is a multiphoton process,
we have extended the existing treatment32 for one-photon
pump and one-photon probe in Sec. II. A summary of the
model with specific application to the case of a three-photon
pump and one-photon probe follows. For this case, if all the
pump transition dipoles are aligned parallel to each other and
the probe dipole is perpendicular to the pump dipole at time
zero, we find from Eq. ͑15͒ that the rotational anisotropy can
be expressed as19
˜ ˜
ment if CH2 is produced in the X or b state. This could
represent a significant amount of energy, especially when
one considers the high vibrational frequencies of CH2.
The vibrational coherence decays over a period of ap-
proximately 500 fs. Under the experimental conditions of
this study, the mean collision time can be estimated to be
approximately 100 ns. Clearly, intermolecular collisions can
not be responsible for the observed dephasing of vibrational
coherence. The vibrational anharmonicity can also cause vi-
brational dephasing and loss of coherence. Although this
may be largely responsible for the observed dephasing, a
simulation with this as the only mechanism yields a very
wide vibrational distribution and a less satisfactory fitting
result. This indicates that other dephasing mechanisms play a
part.
The fitted vibrational phase factor, in Eq. ͑20͒, is
found to be nonzero. The uncertainty in determining the
value of this factor is significantly affected by the accuracy
of experimental determination of time zero. We have made
use of the fact that when collecting fluorescence at 340 nm, a
large spike can be observed at time zero ͑see paper I1͒. The
peak position of the spike can serve as a very good indication
of where the actual time zero is located. With this, the time
zero can be estimated to be within the resolution of the time
scan, which is less than 30 fs. This accounts for about 10%
of the ϳ300 fs vibrational period. Thus the uncertainty of the
phase factor can be estimated to be about ϳ36°, i.e., ϳ10%
of the phase of a full period, 360°. Thus even with this large
error, the fitted phase factor ϭ51°Ϯ36° for this molecular
detachment channel is quite different from that obtained for
1
͚j Pj cos 2nt
͚j Pj
r t͒ϭϪ
͑
1ϩ3
,
͑22͒
ͫ
ͬ
12
where the weighting factor Pj describes the rotational popu-
lation of the I2 fragment, in this case a Gaussian function
given by
the D dissociation pathway in paper I. An induction period,
Ј
while bond rearrangement takes place, is a possible explana-
tion for the observed nonzero phase factor.
1
2
2
͒ /͑⌬j͒
eϪ͑ jϪj
,
͑23͒
max
P ϭͱ
j
⌬j
B. Rotational analysis
and nϭ4Bj denotes the j-dependent nutational frequency
of the fragment being probed. The quantity B represents the
rotational constant of the I2 fragment. It is obvious from Eq.
͑22͒ that r(0)ϭϪ1/3. The discrepancy between this value
and the experimental value ͓see Fig. 5͑b͔͒ may be attributed
to finite signal to noise ratio. A least-squares fit of the ob-
served r(t) data using the above formulae is presented in
Fig. 5͑b͒ as the solid curve. As guided by the fitted curve, the
trend of the experimental trace is seen to approach the ex-
pected Ϫ1/3 value toward time zero. The fit gives rise to the
following parameters: the center of the rotational distribution
Examination of the data in Fig. 4 reveals that depletion
immediately after time zero is more efficient when the pump
and probe pulses are polarized perpendicular to each other
than when they are parallel. This is a strong indication that
the dipole of the probe transition is perpendicular to the di-
pole of the pump transition at time zero. The implication of
this observation to the symmetry of the excited states of the
parent and the I2 fragment will be explored in Sec. IV E. It is
also quite apparent from Fig. 4 that there is a considerable
degree of anisotropy in the data, most of which vanishes
138.251.14.35 On: Sun, 21 Dec 2014 14:52:12
Zhang, Qingguo
