Chemistry Reference
In-Depth Information
Table 2.2 Wigner
s
three threes
that characterise transition state theory Wigner (
1938
)
'
'
'
Three steps in theory of kinetics:
(WS1)
Determine potential energy surfaces
(WS2)
Determine elementary reaction rates
(WS3)
Solve rate equations for complex reaction mechanism
Three groups of elementary reactions:
(WE1)
Vibrationally/rotationally inelastic collisions (not a chemical reaction)
(WE2)
Reactive collisions on a single potential energy surface
(WE3)
Electronically non-adiabatic reactive collisions
Three assumptions:
(WA1) Electronic adiabaticity: the electronic configuration is in the lowest quantum state for
each configuration of the nuclei
(WA2)
The validity of classical mechanics for the nuclear motion
(WA3) Existence of a dividing surface that trajectories do not re-cross
After Miller (
1998
)
challenges, types of reactions and assumptions of the theory as a set of
three
'
.
14
The three threes are summarised in Table
2.2
, and translated into a
specific set of steps (WS), groups (WG) and assumptions (WA).
Wigner
threes
'
s three steps are: (WS1) The determination of potential energy surfaces,
whichgives,inthewordsofWigner,
'
the behaviour of all molecules present in the
system during the reaction, how they will move, and which products they will yield
when colliding with definite velocities, etc.
'
(p. 29). The solution of this problem
requires the calculation of a potential energy surface, which is a quantum chemistry
problem that was solved, somewhat unsatisfactorily, byBorn andOppenheimer (
1927
).
Wigner classifies the elementary reactions in three groups. Only the second type
of elementary reactions can be treated with transition state theory, hence, only
(WE2) is considered in the theory.
Finally, Wigner discusses three assumptions (WA). The first specific assumption
is the adiabatic assumption (WA1), which assumes that during the reaction the
molecular system
'
on the lowest possible potential energy surface, and there
is no change of electronic configuration. The second assumption, (WA2) is that the
motion of the nuclei can be described with classical mechanics, and hence entails
the Born-Oppenheimer separation between electronic and nuclear motion. The third
assumption, (WA3), is that the reaction does not go
'
backwards
'
, i.e. all systems
crossing the barrier are reacting systems. The consequence of this is that the step
from the reactants to the transition state is the rate determining step for the equation.
Once a set of reactants form a transition state, this transition state will fall apart to
form the end products of the reaction.
'
stays
'
14
Wigner refers to the theory in this paper as
. The paper by Laidler
and King (
1983
) contains a brief discussion of this conference and the role it played in the
subsequent adoption of the theory.
The Transition State Method
'
'
