Reviews in Computational Chemistry Volume 18

164 Charge-Transfer Reactions in Condensed Phases
The diabatic solvent reorganization energy is defined by the nuclear response
function w n and by the diabatic field difference
The free energy gap
l d ¼ 1
2 E ab w n E ab ½45Š
F d 0 ¼ Fd 0b F d 0a ¼ I ab þ F d s ½46Š
is composed of the gas-phase splitting I ab ¼ I b Ia and the solvation free
energy
F d s ¼ Eav w E ab ½47Š
where w ¼ w e þ w n is the total response function of the solvent.
Projection on the energy gap reaction coordinate in Eq. [18] is simple to
perform for the scalar reaction coordinate Y d
where
FCWD s ðXÞ ¼ X
k
Q ¼
and Y ðkÞ are all the roots of the equation
ðbQ E 0 ½Y ðkÞ ŠÞ 1 e bE ½YðkÞ Š
ð
e bE ðYd Þ dY d
In Eq. [48], E 0 ½Y ðkÞ Š denotes the derivative
½48Š
½49Š
X ¼ E½Y d Š ½50Š
E 0 Y ðkÞ ¼ d EðYd Þ
dY d
Y d ¼Y ðkÞ
where Y d ¼ Y ðkÞ indicates that the derivative is taken at the coordinate Y ðkÞ
obtained as a solution of Eq. [50].
Equations [41]–[50] provide an exact solution for the CT free energy surfaces
and Franck–Condon factors of a two-state system in a condensed medium
with quantum electronic and classical nuclear polarization fields. The
derivation does not make any specific assumptions about the off-diagonal
matrix elements of the Hamiltonian. It, therefore, includes the off-diagonal
½51Š