Reviews in Computational Chemistry Volume 18

174 Charge-Transfer Reactions in Condensed Phases
and emission (i ¼ 2)
li ¼ 1 2 bh2 hdn 2 i i ¼ 1 2 bs2 i
where the Gaussian spectral width si is experimentally defined through the
half-intensity width i as
½80Š
s 2 i ¼ 2 i =ð8ln2Þ ½81Š
As is easy to see from Eq. [80] and Figure 7, the Q model predicts the breaking
of the symmetry between the absorption and emission widths (Eq. [11]) generated
by a statistical distribution of solvent configurations around a donor–
acceptor complex (inhomogeneous broadening). This fact may have a significant
application to the band shape analysis of optical transitions since unequal
absorption and emission width are often observed experimently. 65,66
The parameter a1 is defined through the Stokes shift and two reorganization
energies from optical widths
a1 ¼ l 1 ðhnst þ l2Þ
l ¼ l2 l1 ½82Š
Similarly, the equilibrium energy gap is (cf. to Eq. [8])
which is equivalent to
F0 ¼ hnm
F0 ¼ hnm þ l1 l
2
l1 a1
2 a2 2
h nst þ l2
½83Š
ðh nst þ l1Þ 2 ½84Š
The Stokes shift and two second spectral moments fully define the parameters
of the model. In addition, they should satisfy Eqs. [73] and [74]. The latter
feature establishes the condition of model consistency that is important for
mapping the model onto condensed-phase simulations that we discuss below.
The connection of the model parameters to the first and second spectral
cumulants enables one to build global, nonequilibrium free energy surfaces of
ET based on two cumulants obtained at equilibrium configuration of the system.
This allows one to apply the model to equilibrium computer simulations
data or to spectral modeling. Compared to the MH picture of intersecting
parabolas, the Q model predicts a more diverse pattern of possible system
regimes including (1) an existence of a one-sided band restricting the range
of permissible reaction coordinates, (2) singular free energies outside the fluctuation
band, and (3) a linear energy gap law at large activation barriers. The
main features of the Q and L models are compared in Table 1.