Reviews in Computational Chemistry Volume 18

178 Charge-Transfer Reactions in Condensed Phases
The parameter fei is defined by Eq. [90]. It scales the solute dipole moment and
the polarizability yielding the effective difference values
The parameter
~m0 ¼ fe2m02 fe1m01 ~a0 ¼ fe2a02 fe1a01 ½93Š
fi ¼ ½12a a0iŠ
1
represents the self-consistent reaction field of the solvent including both the
electronic and nuclear polarization components; a ¼ ae þ ap, where ae is the
solvent response coefficient of the solvent electronic polarization. The electronic
and total solvent response coefficients can be evaluated from the dielectric
cavity or explicit solvent models. 5,71,72 The dielectric continuum estimate
for a spherical solute yields
ae ¼ 1
R 3 0
E1 1
2E1 þ 1
a ¼ 1
R 3 0
Es 1
2Es þ 1
where E1 and Es are the high frequency and static dielectric constants of the
solvent. When the solute polarizability is constant, the reorganization energy
is the same in both reaction states ð f ¼ f1 ¼ f2; fe ¼ fe1 ¼ fe2Þ and is given by
the well-known relation 73
½94Š
½95Š
l ¼ ðaf ae feÞ
m 2 0 ½96Š
A polarizability change leads to a significant variation of the reorganization
energy, which is illustrated in Figure 8, where li are plotted against a02.
As can be seen, the reorganization energy approximately doubles with excitation
when the excited-state polarizability is about 50% higher than the
ground-state value. Such polarizability differences are not uncommon for optical
chromophores (Table 2). The effect of the negative polarizability variation
is much weaker, and l2 is only slightly smaller than l1.
From the Q model, the solvent-induced shift of the equilibrium free
energy gap F0i ¼ Ii þ Fs;i is given by the following relation:
Fs;i ¼ 2apfi ~m0 m0i þ apfi ~a0 m 2 0i ½97Š
Also, the solvent-induced Stokes shift between the absorption and emission
first spectral moments is
h nst ¼ hn abs hnem
¼ 2ap ~m0 ½f2m02 f1m01Šþ2a 2 p
~a0½ðf2m02Þ 2
ðf1m01Þ 2 Š ½98Š