Coherent state prefactor

Finally, the coherent state prefactor is given by the expression... 

In this, the semiclassical coherent state prefactor has been eliminated. To compensate for its absence, the position, momentum and action jumps arising from the infinitesimal evolution with H have been rescaled. Thus, the trajectories must incur the following increments at time f ... 

Prefactor A (i.e., the Van Vleck determinant) in Eq. (448) relates to fluctuations around the classical path. It should be noted that the utilization of the singledomain approximation (445) partly ignores a contribution on the side of unordered spin configurations to wave functions of the ground states that is, any term similar to To in expression (442), the decoherence factor, is omitted. Thus, the spin-spin interaction results in the coherent behavior of a magnetic one-domain particle. 

We have presented several approaches to calculate the rate constants of electron transfer occurring in solvent from the weak to strong electronic couplings. In the fast solvent relaxation limit, the approach based on the nonadiabatic transition state theory can be adopted. It is related to the Marcus formula by a prefactor and referred as a modified Marcus formula. When the solvent dynamics begin to play a role, the quantum Kramers-like theory is applicable. For the case where the intramoleeular vibrational motions are much faster than the solvent motion, the extended Sumi-Mareus theory is a better ehoice. As the coherent motion of eleetron is ineorporated, such as in the organic semiconductors, the time-dependent wavepaeket diffusion approach is proposed. Several applications show that the proposed approaches, together with electronic structure calculations for the faetors eontrolling eleetron transfer, can be used to theoretically predict electron transfer rates correctly. 

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