How is the problem of CINAT cross-sections in a collision AB* + M solved
correctly? Ideally, it is necessary to calculate all the potential energy surfaces of the
AB*
… M complex correlating with the initial (input channel) and final (output
channel) states, calculate the dependences of the matrix elements of the interaction
of these states on the complex internal coordinates. Then one can solve the dynamic
problem of the image point motion along these surfaces, taking into account the
presence of non-adiabatic transitions between them. This ideal is unattainable even
to describe the collision of a light diatomic molecule with helium atom; in any case,
as we will see below, even the best of the existing models are unable to explain
some of the effects observed in the experiment.
You already know that a non-adiabatic transition between adiabatic PESs only
occurs when the matrix elements of the interaction of states corresponding to these
PESs are nonzero. Therefore, the CINATs selection (propensity) rules are determined by the symmetry of these states and the interaction operator. We met with
these interactions in Sect. 3.3. At small distances, these are exchange interactions,
then direct electrostatic (multipole-multipole) and polarization (calculated in the
second order of perturbation theory) interactions are ‘added’ to them (become
comparable in magnitude).
On the classification of CINATs. They can be divided into two large groups:
– CINATs between rovibronic levels of a molecule, the mixing of which is
allowed to one degree or another. These are the so-called perturbationfacilitated [21], p. 313, [22], p. 445 (perturbation-assisted [23]) processes. The
role of a species colliding with a molecule between which states the CINAT is
realized can be quite primitive: collisions lead to the fact that one or more
(many) of the mutually perturbed levels is populated as a result of R $ T or V,
R $ T processes, and then the non-adiabatic transition occurs.
– CINAT between rovibronic levels of a molecule, the mixing of which is either
weak, so that it does not affect the CINAT rate, or is rigorously forbidden. These
are perturbation-irrelevant [21], p. 313, [22], p. 447 (perturbation-independent
[23]) processes indifferent to perturbation in a free molecule. Here the partner’s
participation in the CINAT is fundamental: the transition cannot occur without
it. Just in the similar CINATs analysis, one cannot do anything without solving
the problem of an image point moving along the PES of the complex, which was
discussed above.
The cross-section dependences of these two types of processes on the level
characteristics between which the transitions occur and the colliding particle
properties are different. We will consider them separately. Let us start with the
perturbation-facilitated processes.
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5 Energy Transfer in Collisions
correctly? Ideally, it is necessary to calculate all the potential energy surfaces of the
AB*
… M complex correlating with the initial (input channel) and final (output
channel) states, calculate the dependences of the matrix elements of the interaction
of these states on the complex internal coordinates. Then one can solve the dynamic
problem of the image point motion along these surfaces, taking into account the
presence of non-adiabatic transitions between them. This ideal is unattainable even
to describe the collision of a light diatomic molecule with helium atom; in any case,
as we will see below, even the best of the existing models are unable to explain
some of the effects observed in the experiment.
You already know that a non-adiabatic transition between adiabatic PESs only
occurs when the matrix elements of the interaction of states corresponding to these
PESs are nonzero. Therefore, the CINATs selection (propensity) rules are determined by the symmetry of these states and the interaction operator. We met with
these interactions in Sect. 3.3. At small distances, these are exchange interactions,
then direct electrostatic (multipole-multipole) and polarization (calculated in the
second order of perturbation theory) interactions are ‘added’ to them (become
comparable in magnitude).
On the classification of CINATs. They can be divided into two large groups:
– CINATs between rovibronic levels of a molecule, the mixing of which is
allowed to one degree or another. These are the so-called perturbationfacilitated [21], p. 313, [22], p. 445 (perturbation-assisted [23]) processes. The
role of a species colliding with a molecule between which states the CINAT is
realized can be quite primitive: collisions lead to the fact that one or more
(many) of the mutually perturbed levels is populated as a result of R $ T or V,
R $ T processes, and then the non-adiabatic transition occurs.
– CINAT between rovibronic levels of a molecule, the mixing of which is either
weak, so that it does not affect the CINAT rate, or is rigorously forbidden. These
are perturbation-irrelevant [21], p. 313, [22], p. 447 (perturbation-independent
[23]) processes indifferent to perturbation in a free molecule. Here the partner’s
participation in the CINAT is fundamental: the transition cannot occur without
it. Just in the similar CINATs analysis, one cannot do anything without solving
the problem of an image point moving along the PES of the complex, which was
discussed above.
The cross-section dependences of these two types of processes on the level
characteristics between which the transitions occur and the colliding particle
properties are different. We will consider them separately. Let us start with the
perturbation-facilitated processes.
168
5 Energy Transfer in Collisions