3. The vibrational wave functions of these states overlap quite effectively (see
(3.6.8) and Fig. 4.22a–c). Note that the implementation of point 2 of these
requirements contributes to the implementation of point 3 (Fig. 4.22).
As we have seen in Sect. 3.6, in a diatomic molecule, the intersection of the
PECs of states i and j is possible only if they have different species of the
electronic wave functions. These PECs are called diabatic. Otherwise, these
PECs are ‘repelled’ (adiabatic curves), and predissociation is called nonadiabatic [31], p. 519 (Fig. 4.22d) (see Sect. 4.6.1.1 and below).
In polyatomic molecules, an intersection always takes place, but not for all
coordinates (conical intersection), i.e., the PESs of these molecules intersect
even if the species of their wave functions coincide.
4.7.1 Predissociation of Diatomic Molecules
In Sect. 3.6, we examined the dependence of the predissociation rate on the characteristics of the molecule states in both the quantum mechanical and semiclassical
approximations. In the quantum mechanical approximation, the probability of
predissociation when passing the vicinity of the closest approximation of two PECs
depends on the matrix elements of the interaction of V ij , i.e., in a certain approximation, on the values of the electronic interaction matrix elements A el and the
vibrational wave function overlap integral, see (3.6.8). In the semiclassical
approximation, the dependence of the predissociation rate is given by the
Landau-Zener formula (3.6.21), which, in many cases, offers the same result as in
the quantum mechanical approach.
Let V 1 and V 2 operators cause mutual perturbation of the bound and repulsive
states, and their complete parity is the same (these are all operators that cause
predissociation except hyperfine and Stark ones (see below). The predissociation
rate is not equal to the sum of the predissociation rate caused by the operators V 1
and V 2 operators separately in this case. An interference effect is observed, that is, a
term appears, which includes the product of the V 1 and V 2 operators; most often its
value is relatively small. Maybe, this feature occurs in the case of the hyperfine and
gyroscopic predissociation of the bound state I 2 ðB0
þ
u Þ via the repulsive 1 u (
1 P) (see
below).
The most important types of electronic predissociation are the following:
Electrostatic predissociation. It occurs if both bound and repulsive states have
the same symmetry type. There are two types of interactions:
(a) Interactions between noncrossing (adiabatic) curves caused by the nuclear
kinetic energy operator b
T
N . This type of predissociation is called nonadiabatic.
The N
þ
2 (C
2 R
þ
u * B
2 R
þ
u Þ interaction is analysed in [31], p. 531) as an
example of nonadiabatic predissociation.
136
4 Photolysis of Free Molecules
(3.6.8) and Fig. 4.22a–c). Note that the implementation of point 2 of these
requirements contributes to the implementation of point 3 (Fig. 4.22).
As we have seen in Sect. 3.6, in a diatomic molecule, the intersection of the
PECs of states i and j is possible only if they have different species of the
electronic wave functions. These PECs are called diabatic. Otherwise, these
PECs are ‘repelled’ (adiabatic curves), and predissociation is called nonadiabatic [31], p. 519 (Fig. 4.22d) (see Sect. 4.6.1.1 and below).
In polyatomic molecules, an intersection always takes place, but not for all
coordinates (conical intersection), i.e., the PESs of these molecules intersect
even if the species of their wave functions coincide.
4.7.1 Predissociation of Diatomic Molecules
In Sect. 3.6, we examined the dependence of the predissociation rate on the characteristics of the molecule states in both the quantum mechanical and semiclassical
approximations. In the quantum mechanical approximation, the probability of
predissociation when passing the vicinity of the closest approximation of two PECs
depends on the matrix elements of the interaction of V ij , i.e., in a certain approximation, on the values of the electronic interaction matrix elements A el and the
vibrational wave function overlap integral, see (3.6.8). In the semiclassical
approximation, the dependence of the predissociation rate is given by the
Landau-Zener formula (3.6.21), which, in many cases, offers the same result as in
the quantum mechanical approach.
Let V 1 and V 2 operators cause mutual perturbation of the bound and repulsive
states, and their complete parity is the same (these are all operators that cause
predissociation except hyperfine and Stark ones (see below). The predissociation
rate is not equal to the sum of the predissociation rate caused by the operators V 1
and V 2 operators separately in this case. An interference effect is observed, that is, a
term appears, which includes the product of the V 1 and V 2 operators; most often its
value is relatively small. Maybe, this feature occurs in the case of the hyperfine and
gyroscopic predissociation of the bound state I 2 ðB0
þ
u Þ via the repulsive 1 u (
1 P) (see
below).
The most important types of electronic predissociation are the following:
Electrostatic predissociation. It occurs if both bound and repulsive states have
the same symmetry type. There are two types of interactions:
(a) Interactions between noncrossing (adiabatic) curves caused by the nuclear
kinetic energy operator b
T
N . This type of predissociation is called nonadiabatic.
The N
þ
2 (C
2 R
þ
u * B
2 R
þ
u Þ interaction is analysed in [31], p. 531) as an
example of nonadiabatic predissociation.
136
4 Photolysis of Free Molecules