Vertical energy gap

The barrier to EE between n and c, where the two parabolas cross, is the point with one-fourth the vertical energy gap A, owing to the analytical geometry of a parabola. This value of was incorporated in Eq. (10-57) and is explicitly treated in Problem 10-22. Reference should be made to Fig. 10-11. 

The goal of theory and computer simulation is to predict S i) and relate it to solvent and solute properties. In order to accomplish this, it is necessary to determine how the presence of the solvent affects the So —> Si electronic transition energy. The usual assmnption is that the chromophore undergoes a Franck-Condon transition, i.e., that the transition occurs essentially instantaneously on the time scale of nuclear motions. The time-evolution of the fluorescence Stokes shift is then due the solvent effects on the vertical energy gap between the So and Si solute states. In most models for SD, the time-evolution of the solute electronic stracture in response to the changes in solvent environment is not taken into accoimt and one focuses on the portion AE of the energy gap due to nuclear coordinates. 

The vertical energy gap of the wells at the initial reaction coordinate is described as the reorganization energy, since it implies the rise in energy as the system moves towards the saddle point X along the reaction coordinate (see Fig. 2). Conceptually, the system starts to resemble the situation it will have when the products are finally formed. 

Even in the non-harmonic case, one may still define 17 as the vertical energy gap Gf — G [35,36], but 17 will no longer be linear in x >, in contrast to Equation (3.79). In this case, the relationship noted by Tachiya [37]... 

At any instant the fluorescence frequency u t) is given by the relation hu t) = AP + (( t)), where ( t)) is the nonequilibrium average (under the surrogate estimate of the solvent nonequilibrium distribution function) of the surrogate solvent contribution to the vertical energy gap = [compare with Eq. (3)]. The solvation time correlation... 

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