Chemistry Reference
In-Depth Information
photofragments dissociate with kinetic energies much larger than the rotational
spacing are considered. The direction of the incident light coincides with the
x
-axis, and
i
,
j
, and
k
indicate the unit vectors in the directions of the
x
-,
y
-,
and
z
-axes, respectively. The transition moment
μ
and the electric vector
ε
are
represented by
μ
=
i
sin
χ
·
cos
φ
+
j
sin
χ
·
sin
φ
+
k
cos
χ
(1)
and
cos
θ
(2)
Assuming that the detector for the fragments lies on the
z
-axis, the angular distri-
bution of the photofragments in the
y
-
z
plane can be expressed as:
ε
=−
j
sin
θ
+
k
2
π
1
4
π
1
4
π
2
dφ
=
f
(
θ
)
=
|
μ
·
ε
|
[1
+
βP
2
(cos
θ
)]
(3)
0
(3
a
2
where
P
2
(
a
)
1)
/
2, which is the second Legendre polynomial. The co-
efficient
β
of
P
2
(cos
θ
) in Eq. (3) is the so-called anisotropic parameter, which is
given by the simple equation
=
−
β
=
2
P
2
(cos
χ
)
(4)
For a diatomic molecule, the direction of dissociation is matched with the internu-
clear axis and thus the angle
χ
can only be 0 or
π/
2. Here
P
2
(cos
θ
) vanishes at an
angle
θ
of 54.7
◦
, which is the so-called magic angle. The model leading to Eq. (4)
corresponds to that of a nonrotating molecule, where the so-called axial-recoil ap-
proximation is regarded as being fully satisfied. Note that the initial anisotropy is
simply reduced by a factor of four even in the case of slower dissociation compared
to the rotational period [36].
The theoretical treatments of molecular photodissociation under the axial-recoil
conditions were presented in 1972 by Zare [35], who derived the general expres-
sion for the angular distribution of neutral products from diatomic molecules, as
expressed by Eqs. (3) and (4), with both semiclassical and quantum mechanical
treatments. The extension of these results to a linear triatomic molecule was per-
formed by Busch and Wilson [36] in 1972. More systematic analyses of the angular
distribution of the photofragments for an arbitrary molecule were shown by Yang
and Bersohn [37] in 1974. The effects on the photofragment angular distributions
of excited-state symmetry, lifetime, angular momentum, and angular recoil distri-
bution relative to internal coordinates have been considered in these works.
The general expression for the photoion angular distribution in dissociative pho-
toionization of a diatomic molecule under the axial-recoil conditions was derived
by Dehmer and Dill [38] in 1978. The photoion angular distribution is determined
by the total symmetry of the final state (molecular ion and photoelectron), since the
photoionization process also involves the ejection of photoelectrons. It has been
