Optical band shape

Anharmonic higher order terms gain importance for stronger solute-solvent couplings requiring 0 in Eq. [121]. The nonequilibrium solvent polarization can be considered as an ET reaction coordinate. The curvature of the corresponding free energy surface is 

When the electron is partially delocalized, one should switch to the adiabatic representation in which the upper and lower CT surface are split by an energy gap depending on P. If this energy gap is expanded in P with truncation after the second-order term, we come to the model of a donor-acceptor complex whose dipolar polarizabilities are different in the ground and excited states. The solute-solvent interaction energy then attains the energy of solute polarization that is quadratic in P 

The revision of characteristic frequencies of nuclear modes is a general result of electronic delocalization holding for both the intramolecular vibrational modes and the solvent modes. The fact that this effect shows up already in the harmonic expansion term makes it much stronger compared to nonlinear solvation in respect to nonparabolic distortion of the free energy surfaces. 

Spectral measurements open a door to access the rate constant parameters of ET. The connection between optical observables and ET parameters can be divided into two broad categories (1) analysis of the optical band profile (band shape analysis) and (2) the use of integrated spectral intensities (see 

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. 

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This chapter concerns the energetics of charge-transfer (CT) reactions. We will not discuss subjects dealing with nuclear dynamical effects on CT kinetics. " The more specialized topic of employing the liquid-state theories to calculate the solvation component of the reorganization parameters is not considered here. We concentrate instead on the general procedure of the statistical mechanical analysis of the activation barrier to CT, as well as on its connection to optical spectroscopy. Since the very beginning of ET research, steady-state optical spectroscopy has been the major source of reliable information about the activation barrier and preexponential factor for the ET rate. The main focus in this chapter is therefore on the connection between the statistical analysis of the reaction activation barrier to the steady-state optical band shape. 

The free energy gap, equal to the energy of the incident light, is basis independent. It defines the Franck-Condon factor entering the optical band shapes. The analysis below follows this general scheme (Figure 4). 

Equation [134], given in the form of a weighted sum of individual solvent-induced line shapes, provides an important connection between optical band shapes and CT free energy surfaces. Before turning to specific models for the Franck-Condon factor in Eq. [134], we present some useful relations, following from integrated spectral intensities, that do not depend on specific features of a particular optical line shape. 

D. V. Matyushov and M. D. Newton,/. Phys. Chem. A, 105, 8516 (2001). Understanding the Optical Band Shape Coumarin-153 Steady-State Spectroscopy. 

Optical spectroscopy has been employed for a long time as an effective tool to investigate molecular dynamics and relaxations in molecular impurity crystals. The spectroscopic methods work effectively in crystals because impurity bands have a well-resolved structure. Optical bands of such type can be treated with the help of the comprehensively developed theory for homogeneous optical band shape. The theory enables one to get information concerning both the electron-phonon interaction and the molecular dynamics in crystals. 

Within the scope of the stochastic approach, there is no strict boundary between homogeneous and inhomogeneous broadening. The boundary depends on the timescale of the experiment. This approach is convenient for considering the line broadening problem in vapour or liquid phases. However, stochastic theory cannot explain the optical band shape in solids. Therefore, we shall only use a dynamical approach to the line broadening problem. 

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