Reviews in Computational Chemistry Volume 18

192 Charge-Transfer Reactions in Condensed Phases
below). The former route connects the spectral moments to ET activation
parameters (Table 1). The latter is applied to extract off-diagonal matrix elements,
most often the ET matrix element and the transition dipole. Band shape
analysis of optical spectra has been successfully used in ET research for many
years, and our present knowledge about mechanisms and energetics of ET originates
largely from spectroscopic measurements. 16 The understanding of electronic
and solvent effects on the ET kinetics has been recently supplemented
by extensive information about the intramolecular, vibronic envelope from
resonance Raman spectroscopy. 86
The fast growth of the field of ET research and, especially, the design of
new bridge-coupled donor–acceptor pairs imposes new demands on the theory
of optical spectra. Several major challenges are currently faced by the field.
They may be summarized as follows: (1) The presently existing band-shape
analysis has been created for ET transitions. 17 It has not anticipated strong
electronic coupling and thus fails when applied to transitions with high magnitudes
of the ET matrix element. 87 (2) The model is limited to two states only.
Mixing to higher excited states, resulting in intensity borrowing, is commonly
neglected. Extension to more then two states is especially important for photoinduced
CT where a CT state is formed from and is strongly coupled to a
locally exited state of either donor or acceptor unit. 17,88 (3) There are indications
in the literature that the common assumption of complete decoupling
between the intramolecular vibrational modes and solvent thermal motions
may fail for some systems. 89,90 Understanding the origin of and full account
for these effects should be incorporated into new models of optical bands.
The challenges outlined above still await a solution. In this section, we
show how some of the theoretical limitations employed in traditional formulations
of the band shape analysis can be lifted. We discuss two extensions of
the present-day band shape analysis. First, the two-state model of CT transitions
is applied to build the Franck–Condon optical envelopes. Second, the
restriction of only two electronic states is lifted within the band shape analysis
of polarizable chromophores that takes higher lying excited states into account
through the solute dipolar polarizability. Finally, we show how a hybrid model
incorporating the electronic delocalization and chromophore’s polarizability
effects can be successfully applied to the calculation of steady-state optical
band shapes of the optical dye coumarin 153 (C153). We first start with a general
theory and outline the connection between optical intensities and the ET
matrix element and transition dipole.
Optical Franck–Condon Factors
Absorption of light by molecules, resulting in electronic excitations, is
caused by the interaction of the bound molecular electrons with the electric
field of the radiation. In the dipolar approximation, the interaction of the
dipole operator of the solute ^m0 with the time-dependent electric field EðtÞ