6
1 From the Phenomenology of Chemical Reactions …
The thermodynamics treatment assumes the existence of an intermediate (X
‡ ) which
is in thermal equilibrium with the reactants. The intermediate can then dissociate to
form products
X − →
←X
‡
→ W.
(1.16)
The equilibrium constant K
‡ of such process defined as
K
‡
=
[X
‡
]
[X ]
(1.17)
can be related to k f via the relationship
k f =
k B T
h
K
‡
.
(1.18)
This allows us to relate the rate coefficient k f to the standard free energy change
k f =
k B T
h
e
−G
o‡ /RT
,
(1.19)
thanks to the relationship
G
o‡
= H
o‡
− T S
o‡
(1.20)
and the Van’t Hoff equation
∂ K
‡
∂T
=
H
o‡
RT 2
(1.21)
with the quantities G
o‡ , H
o‡ , and S
o‡ being the free energy, the enthalpy
(or heat), and the enthropy of activation thermodynamic functions, respectively. By
considering that H
o‡ is equivalent to the activation energy E
o
f at constant pressure,
one can write
k f =
k B T
h
e
−E
o
f /RT
.
(1.22)
For illustrative purposes, we sketch here (see Fig. 1.2) the simple reactive system
of an atom, A, and the diatom, BC, giving the diatom AB and the atom C.
From the basic assumptions of the TST approach, one has the following:
1. The reactive process occurs on a single potential energy surface (PES) on which
a path made of the local minima located on an arrangement continuity variable
(named minimum energy path (MEP) coordinate and represented as a solid line
in the plot of Fig. 1.2) connects reactants (A + BC) to products (AB + C);