Essentials of Computational Chemistry

15
Adiabatic Reaction Dynamics
15.1 Reaction Kinetics and Rate Constants
Consider an arbitrary equilibrium system
A + B + C +···−−−⇀
↽−−− ···+X + Y + Z (15.1)
where no particular stoichiometry is implied. When the system is displaced from equilibrium,
by addition of more of a particular species, by a change in temperature and/or pressure, or
by any other influence, empirical observation has shown that the rate at which equilibrium
is reestablished may be expressed as
rate(t) = kφ(t) [A]a [B] b [C] c ···
···[X] x [Y] y [Z] z
(15.2)
where kφ is a phenomenological rate constant (distinguished from an elementary rate constant
as defined later on), [W] represents the concentration of species W (usually expressed in
units of molarity or partial pressure), and each concentration term has associated with it an
exponent that is sometimes referred to as the ‘molecularity’ of the species. Often, but not
always, molecularities have integral values, including zero. Note that since we are measuring
a return to equilibrium, all concentration terms are functions of time t, asarekφ and the rate
itself.
The apriori prediction of all of the variables appearing on the r.h.s. of Eq. (15.2) is
a challenging task, to say the least. This is particularly true because the equilibrium of
Eq. (15.1) may involve the simultaneous operation of a large number of individual chemical
reactions, with some possibly involving very low concentrations of reactive intermediates,
the presence of which may be difficult to establish experimentally. In order to make progress,
a critical simplification is to break the overall process down into so-called elementary steps.
To simplify matters a bit, we will consider only adiabatic reaction steps, that is, reactions
taking place on a single PES without any change in electronic state (the topic of non-adiabatic
dynamics is discussed briefly in Section 15.5). For practical purposes, there are only two
kinds of elementary reactions: unimolecular and bimolecular.
Essentials of Computational Chemistry, 2nd Edition Christopher J. Cramer
© 2004 John Wiley & Sons, Ltd ISBNs: 0-470-09181-9 (cased); 0-470-09182-7 (pbk)