Reviews in Computational Chemistry Volume 18

m 12 /D
6
5.5
5
4.5
4
3.5
17 18 19 20 21 22
− νem /10 3 cm −1
the traditional formulation. It shows the dependence of m12 (circles) and
m12n0=nav (squares, n0 ¼ 25,400 cm 1 ) on the emission frequency nem for
the dye C153 measured in solvents of different polarity. 95 The two sets of
transition dipoles are noticeably divergent in strongly polar solvents.
Electron-Transfer Matrix Element
Optical Band Shape 197
Figure 16 The transition dipole m12 according to Eq. [139] (nav ¼ nem, circles) and
m12n0=nem (squares) versus nem for emission transitions in C153 in different solvents. 95
The dashed lines are regressions with the slopes 0.02 (squares) and 0.27 (circles).
The transition dipole between the free energy surfaces F ðXÞ is not the
only parameter that depends on the nuclear configuration of the solvent.
The effective ET matrix element H eff
ab ½PnŠ following from the trace of the
two-state Hamiltonian over the electronic degrees of freedom also depends
on the nuclear configuration of the solvent (Eq. [37]). In contrast to the case
of optical transitions where the dependence on the nuclear solvent configurations
is transformed into a frequency dependence of the transition dipole
~m12ðnÞ (Eq. [132]), the dependence of the ET matrix element H eff
ab ½PnŠ on the
nuclear field Pn should be fully included into the statistical average over Pn
when the ET rate constant is calculated in the Golden Rule perturbation
scheme over H eff
ab ½PnŠ. 11 The Pn dependence represents a non-Condon effect
of the solvent field on the rate preexponential factor. The result of the calculations
43 is the standard Golden Rule expression 9,11 for the nonadiabatic rate
constant
k ðiÞ
NA ¼ h 1 ðpb=lÞ 1=2 H MH 2 FCWDið0Þ ½140Š