Chapter 1
From the Phenomenology of Chemical
Reactions to the Study of Two-Body
Collisions
This chapter guides the reader through the phenomenology of the simplest kinetics
of chemical systems to the modeling of the rate coefficients governing their time evolution. From the analysis of the weakness of the transition state (TS) model approach
(that is phenomenologically valid but useless for predicting), the rate of chemical
processes is rationalized in terms of collisions of two structureless bodies using classical mechanics. In this way, it is possible to follow the space and time evolution of
the colliding partners. The machinery of the related classical mechanics equations
(Newton, Hamilton, and Lagrange) is explained and the numerical procedures for
associating classical trajectories starting from different initial conditions to the fate
of the chemical process is given once the interaction is known. Applications to various popular models of the interaction (hard sphere, repulsive Coulomb, attractive–
repulsive potentials, like the Lennard–Jones (LJ) and the Morse) are considered for
an analytical and numerical solution of the problem.
1.1 From Kinetics to Bimolecular Collisions
1.1.1 The Phenomenological Approach
In order to build a rigorous theoretical and computational ground for the description and understanding of chemical reactions, one has to scale the treatment of the
problem of chemical processes down from the macroscopic phenomenological level
(that refers to thermodynamics and kinetics treatments) to the microscopic one (that
refers to dynamics treatments). The scaling down starts from confining the analysis
to gas-phase homogeneous systems in order to more easily relate the parameters
characterizing the time evolution of the system to the variation of the intervening
species (say X of concentration [X] or partial pressure p X ) because, as is well known,
pressure p X is related to the concentration [X] and the temperature T by the equation
p X = [X]RT . The variation of the intervening species is usually quantified in terms
© Springer International Publishing AG 2018
A. Laganà and G. A. Parker (eds.), Chemical Reactions, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-62356-6_1
1
From the Phenomenology of Chemical
Reactions to the Study of Two-Body
Collisions
This chapter guides the reader through the phenomenology of the simplest kinetics
of chemical systems to the modeling of the rate coefficients governing their time evolution. From the analysis of the weakness of the transition state (TS) model approach
(that is phenomenologically valid but useless for predicting), the rate of chemical
processes is rationalized in terms of collisions of two structureless bodies using classical mechanics. In this way, it is possible to follow the space and time evolution of
the colliding partners. The machinery of the related classical mechanics equations
(Newton, Hamilton, and Lagrange) is explained and the numerical procedures for
associating classical trajectories starting from different initial conditions to the fate
of the chemical process is given once the interaction is known. Applications to various popular models of the interaction (hard sphere, repulsive Coulomb, attractive–
repulsive potentials, like the Lennard–Jones (LJ) and the Morse) are considered for
an analytical and numerical solution of the problem.
1.1 From Kinetics to Bimolecular Collisions
1.1.1 The Phenomenological Approach
In order to build a rigorous theoretical and computational ground for the description and understanding of chemical reactions, one has to scale the treatment of the
problem of chemical processes down from the macroscopic phenomenological level
(that refers to thermodynamics and kinetics treatments) to the microscopic one (that
refers to dynamics treatments). The scaling down starts from confining the analysis
to gas-phase homogeneous systems in order to more easily relate the parameters
characterizing the time evolution of the system to the variation of the intervening
species (say X of concentration [X] or partial pressure p X ) because, as is well known,
pressure p X is related to the concentration [X] and the temperature T by the equation
p X = [X]RT . The variation of the intervening species is usually quantified in terms
© Springer International Publishing AG 2018
A. Laganà and G. A. Parker (eds.), Chemical Reactions, Theoretical Chemistry
and Computational Modelling, https://doi.org/10.1007/978-3-319-62356-6_1
1