3.5 Descriptions of Collisional Processes Using Potential
Energy Curves and Surfaces. Intramolecular
Vibrational Relaxation in Polyatomic Molecules
Let us discuss the potential energy of the system of atoms and how to describe the
collisional processes by the motion of an image point along the PES or PEC of the
system of atoms.
Let the author reminds once again that the basis for introducing the concepts of
PECs, PESs is the adiabatic approximation. Within the framework of this
approximation, each fixed configuration of atoms defined by the positions of their
nuclei corresponds to the set of eigenvalues of the solution of the wave equation for
the electron wave function namely adiabatic electronic terms U k (Q) = E
el
k + U N (Q),
where Q and U N (Q) are coordinates and the potential energy of interaction of
nuclei. Each of them corresponds to its electronic state, i.e., its k-th wave function.
If these terms are sufficiently separated in the entire Q range, then the Massey
parameter DUl= hu is large, and the adiabatic term can be considered as the PES
(PEC) of a system of atoms in the k-th electronic state. Within the framework of the
adiabatic approximation, the motion of atoms does not cause transitions between
PECs, PESs, and the elementary collision process (energy redistribution or chemical reaction) is described in terms of the motion of an image point, the point
corresponding to the current values of the coordinates of the system of atoms, along
this single PES, PEC. Going beyond the adiabatic approximation involves taking
into account the possibility of transitions between electronic states, which is the
subject of the theory of nonadiabatic transitions. At low kinetic energies of atoms
u (u is in the denominator of the Massey parameter (3.2.19)) adiabatic approximation quite satisfactorily describes the process on a significant part of a PEC or
PES. If the states approach the distance ‘dangerous for clean adiabaticity’ in any
region of a PEC or PES (again the Massey parameter), then one has to take into
account nonadiabatic effects, and in a large number of problems this gives a small
correction, which is correctly calculated in the framework of PT. Even if this is not
the case, and the ‘nonadiabatic effect’ is large, most often, the area where this takes
place is relatively small, and the description of the process outside it within the
framework of the adiabatic approximation is very instrumental. Nonadiabatic
processes, on the other hand, can be described as an instantaneous compared with
the characteristic times of motion of the nuclei (*10
–13 s) ‘jump’ (*10
–15 s) from
the surface to the surface. The author has discussed collision processes and their
description in the framework of motion along a PEC, PES, so far. All of the above
applies to the description of spontaneous unimolecular processes, in particular,
dissociation and predissociation.
We will consider nonadiabatic processes a little later; now, we will see how to
describe an elastic scattering, the energy redistribution processes, and chemical
reactions in the framework of the motion of an image point on a PEC or PES.
It is evident that to solve the problem of collision, dissociation, or predissociation as a motion of an image point on a PEC, PES, it is necessary to know these
3.5 Descriptions of Collisional Processes Using Potential Energy …
59
Energy Curves and Surfaces. Intramolecular
Vibrational Relaxation in Polyatomic Molecules
Let us discuss the potential energy of the system of atoms and how to describe the
collisional processes by the motion of an image point along the PES or PEC of the
system of atoms.
Let the author reminds once again that the basis for introducing the concepts of
PECs, PESs is the adiabatic approximation. Within the framework of this
approximation, each fixed configuration of atoms defined by the positions of their
nuclei corresponds to the set of eigenvalues of the solution of the wave equation for
the electron wave function namely adiabatic electronic terms U k (Q) = E
el
k + U N (Q),
where Q and U N (Q) are coordinates and the potential energy of interaction of
nuclei. Each of them corresponds to its electronic state, i.e., its k-th wave function.
If these terms are sufficiently separated in the entire Q range, then the Massey
parameter DUl= hu is large, and the adiabatic term can be considered as the PES
(PEC) of a system of atoms in the k-th electronic state. Within the framework of the
adiabatic approximation, the motion of atoms does not cause transitions between
PECs, PESs, and the elementary collision process (energy redistribution or chemical reaction) is described in terms of the motion of an image point, the point
corresponding to the current values of the coordinates of the system of atoms, along
this single PES, PEC. Going beyond the adiabatic approximation involves taking
into account the possibility of transitions between electronic states, which is the
subject of the theory of nonadiabatic transitions. At low kinetic energies of atoms
u (u is in the denominator of the Massey parameter (3.2.19)) adiabatic approximation quite satisfactorily describes the process on a significant part of a PEC or
PES. If the states approach the distance ‘dangerous for clean adiabaticity’ in any
region of a PEC or PES (again the Massey parameter), then one has to take into
account nonadiabatic effects, and in a large number of problems this gives a small
correction, which is correctly calculated in the framework of PT. Even if this is not
the case, and the ‘nonadiabatic effect’ is large, most often, the area where this takes
place is relatively small, and the description of the process outside it within the
framework of the adiabatic approximation is very instrumental. Nonadiabatic
processes, on the other hand, can be described as an instantaneous compared with
the characteristic times of motion of the nuclei (*10
–13 s) ‘jump’ (*10
–15 s) from
the surface to the surface. The author has discussed collision processes and their
description in the framework of motion along a PEC, PES, so far. All of the above
applies to the description of spontaneous unimolecular processes, in particular,
dissociation and predissociation.
We will consider nonadiabatic processes a little later; now, we will see how to
describe an elastic scattering, the energy redistribution processes, and chemical
reactions in the framework of the motion of an image point on a PEC or PES.
It is evident that to solve the problem of collision, dissociation, or predissociation as a motion of an image point on a PEC, PES, it is necessary to know these
3.5 Descriptions of Collisional Processes Using Potential Energy …
59