Reviews in Computational Chemistry Volume 18

188 Charge-Transfer Reactions in Condensed Phases
∆z
1
0.8
0.6
0.4
0.4 0.6 0.8 1
∆e
Figure 14 Dependence of the occupation number difference z on the mixing
parameter e at E12=l I ¼ 0:2, FI s ¼ 0 (solid line); E12=l I ¼ 0:5, FI s ¼ 0 (dot–
dashed line); E12=l I ¼ 3:0, FI s =lI ¼ 1:0 (dashed line).
z increasingly deviates from e. In the inverted region, z is nearly 1 and is
almost independent of e.
The establishment of the invariant reorganization energy l I allows one
to use electrostatic models for the reorganization energy based on solvation
of fixed charges located at molecular sites 5 instead of using a more complicated
algorithm through the delocalized electronic density. 84 This ability to
use electrostatic fixed charge models instead of distributed density of quantum
mechanics is permitted because the invariant reorganization energy sets up the
characteristic length between centers of charge localization to be used in electrostatic
models of solvent reorganization 7
rCT ¼ e 1 m 2 12 þ 4m2 12
For self-exchange transitions, due to the relation 2m12 ¼ m ab, one gets
rCT ¼ r 2 12 þ r2 ab
1=2
1=2
½117Š
½118Š
where r ab is the distance between the centers of electron localization in the diabatic
representation.
The mixing parameter e makes the CT free energy surfaces dependent
on the gas-phase, adiabatic transition dipole moment. The standard extension
of the MH theory on the case of strong electronic overlap 85 assumes a nonzero
ET matrix element H ab, but neglects the diabatic transition dipole (or eliminates