Chemistry Reference
In-Depth Information
(
A
,
B
)
−
,
(
A
B
)
AB
E
diss
AB
R
0
R
x
Internuclear distance
R
FIGURE 9.12
Schematic representation of the relevant potential energy surfaces for dis-
sociative attachment. For simplicity, it is assumed that the molecule
AB
is initially in the
vibrational ground state, although this is usually not the case. The electron is thus captured at
R
=
R
0
,where
R
0
is the equilibrium distance of the two nuclei (upward vertical arrow). The
thereby created
AB
−
compound is envisaged to be in an antibonding state whose potential
energy surface crosses that of the
AB
state at
R
=
R
x
.For
R
<
R
x
, the compound state has thus
a finite probability to decay (downward directed vertical arrows). However, provided the state
survives until the nuclear distance
R
>
R
x
, it asymptotically reaches the
(
A
−
,
B
)
dissociation
limit and dissociative attachment is completed.
cross section for dissociative attachment becomes
dR
)
∗
V
dk
(
mM
(
K
k
i
2
d
σ
D
ν
i
(
−
)
dE
=
(
R
R
)
χ
ν
i
(
R
)
d
K
,
(9.91)
2π
)
2
(
e
−
,
AB
)
where
m
and
k
arethereducedmassandtherelativemomentumofthe
system,
respectively,
M
and
K
are the corresponding quantities in the
(
A
−
,
B
)
system, χ
ν
i
(
R
)
(
−
)
dE
is the vibrational state of the molecule, and
(
R
)
is the scattering state satisfying
the complex conjugate of (9.79) with
V
d
(
the
interaction between the antibonding
AB
−
state and the electron-molecule scattering
continuum, and
J
R
)
=
V
AB
−
(
R
)
,
V
0
(
R
)
=
V
AB
(
R
)
,
V
dk
(
R
)
(
R
)
=[
V
d
(
∞
)
−
V
d
(
R
)
]
exp
[
iKR
]
. The total energy available for the
collision is
E
ω
B
, where ω
A
−
and ω
B
denote the
internal energies of the ion and atom, respectively, and ω
ν
i
is the vibrational energy
of the molecule.
In order to avoid additional indices, quantum numbers for the internal state of
=
k
2
/
2
+
ω
ν
i
=
K
2
/(
2
M
)
+
ω
A
−
+
the
system are suppressed and rotations of the molecule are also ignored.
Because the period of rotation is much longer than the collision time, rotations could
be included within the adiabatic approximation. Finally, provided the kinetic energy
of the incident electron,
k
2
(
A
−
,
B
)
2, is much larger than the vibrational energy of the target,
ω
ν
i
, the local approximation could be employed, that is, (9.86) could be used instead
of (9.79). Further details about the calculation of electron attachment cross sections
can be found in the review article by Chutjian et al. [76].
Bardsley et al. [60] have shown that within the semiclassical approximation
d
σ
ν
i
/
/
K
factorizes into a capture cross section, which describes the formation of the
compound state, and a survival probability for that state. The semiclassical calculation
d
