Reviews in Computational Chemistry Volume 18

λ i /eV
4
3
2
1
0
0 10 20 30 40
Both the free energy gap and the Stokes shift include two contributions: one
arising from the variation of the solute dipole (the first term) and one due to
the polarizability change (the second term). The Stokes shift is hence nonzero
even if the charge distribution does not change in the course of the transition
(m02 ¼ m01).
The polarizability difference determines the relative change in the
frequency of the solvent driving mode given by the parameter a1 of the Q
model
a1 ¼
fe1
2ap f1 ~a0
The fact that the parameter a1 is connected to spectroscopic moments for
absorption and emission transitions opens an interesting opportunity to derive
the polarizability change of optical chromophores from spectroscopic first and
second moments. The equation for the polarizability change is as follows:
~a0 ¼ 1
2l1
l
h nst þ l2
α 01
α 02 /Å 3
Beyond the Parabolas 179
Figure 8 Dependence of the solvent reorganization energy in the neutral (1, m01) and
charge-separated (2, m02) states on the polarizability of the final state a02. The solvent
response coefficients are estimated from the continuum dielectric model (Eq. [95]).
Solute and solvent parameters are m01 ¼ 0, m02 ¼ 15 D, a01 ¼ 20 A ˚ 3 , R0 ¼ 4A ˚ , E1 ¼ 2,
Es ¼ 30. In this and subsequent figures, some of the axes are labeled as the ratios shown
in order to make the quantities dimensionless. For example, the ordinate in this plot
is in units of electron volts, and the abscissa is in units of cubic angstroms.
h nst þ l1
~m02 ~m01
h nst þ l2
2
1
2
½99Š
½100Š