COMPARISONS OF SEMICLASSICAL APPROXIMATIONS BY EXPANSION IN PLANCKS-CONSTANT

Fermi's golden rule is expanded in Planck's constant to study quantum effects of nuclear baths on transitions between electronic states. For six approximations, the second-order expansion of the transition rate s is compared with the exact expansion. The comparison provides the co nditions for agreement between the exact and approximate rate constant s in the second order. Two of the conditions show that the change in e lectronic states of the solute does not affect solvent structure much. The other concerns linearity of the reaction coordinate. Besides the comparison of analytical expressions, the expansion of approximations is numerically compared, using a simple model. Most approximations sho w similar values for a parameter set. The values approximate the value obtained by quantum molecular simulations. (C) 1998 American Institut e of Physics. [S0021-9606(98)00844-7].