Chapter 3
Theory of Elementary Processes
Abstract The chapter deals with elementary processes, i.e., the simple processes
which proceed in one stage. The definitions of differential and total cross-sections,
microscopic rate constants, and probabilities of elementary processes are introduced. The detailed balance principle, adiabatic approximations, as well as potential
energy curves and surfaces, are discussed. Different types of intermolecular interactions, descriptions of collisional processes and reactions including nonadiabatic
transition using potential energy curves and surfaces are examined.
3.1 Cross-Sections, Rate Constants, and Probabilities
of Elementary Processes. The Detailed Balance
Principle
When species collide (below, in this section, we will consider the collision of two
species) two different results are possible (not according to the formal kinetics of
the process): either the chemical composition of the colliding species does not
change or it changes (i.e., a chemical reaction occurs). In general, the first option
can be presented as [1], p. 30:
AðiÞ þ BðjÞ ! AðlÞ þ BðmÞ þ DE ij;lm ;
ð3:1:1Þ
and the last one as
AðiÞ þ BðjÞ ! CðlÞ þ DðmÞ þ DE ij;lm
ð3:1:2Þ
where i, j and l, m are some sets of quantum numbers of the states of the species
before and after the collision, respectively, DE ij,lm is the change in the internal
energy of the colliding species, converting to their kinetic energies.
The above quantum numbers describe the electronic states of atoms and the
rovibronic states of two- and polyatomic species. It should be noted that to
© Springer Nature Switzerland AG 2021
A. Pravilov, Gas-Phase Photoprocesses, Springer Series in Chemical Physics 123,
https://doi.org/10.1007/978-3-030-65570-9_3
37
Theory of Elementary Processes
Abstract The chapter deals with elementary processes, i.e., the simple processes
which proceed in one stage. The definitions of differential and total cross-sections,
microscopic rate constants, and probabilities of elementary processes are introduced. The detailed balance principle, adiabatic approximations, as well as potential
energy curves and surfaces, are discussed. Different types of intermolecular interactions, descriptions of collisional processes and reactions including nonadiabatic
transition using potential energy curves and surfaces are examined.
3.1 Cross-Sections, Rate Constants, and Probabilities
of Elementary Processes. The Detailed Balance
Principle
When species collide (below, in this section, we will consider the collision of two
species) two different results are possible (not according to the formal kinetics of
the process): either the chemical composition of the colliding species does not
change or it changes (i.e., a chemical reaction occurs). In general, the first option
can be presented as [1], p. 30:
AðiÞ þ BðjÞ ! AðlÞ þ BðmÞ þ DE ij;lm ;
ð3:1:1Þ
and the last one as
AðiÞ þ BðjÞ ! CðlÞ þ DðmÞ þ DE ij;lm
ð3:1:2Þ
where i, j and l, m are some sets of quantum numbers of the states of the species
before and after the collision, respectively, DE ij,lm is the change in the internal
energy of the colliding species, converting to their kinetic energies.
The above quantum numbers describe the electronic states of atoms and the
rovibronic states of two- and polyatomic species. It should be noted that to
© Springer Nature Switzerland AG 2021
A. Pravilov, Gas-Phase Photoprocesses, Springer Series in Chemical Physics 123,
https://doi.org/10.1007/978-3-030-65570-9_3
37