| Abstract
| - Closed-form rate expressions are derived on the basis of the stationary-phase approximation for the Fermigolden rule expression of the quantum electron-transfer (ET) rate. First, on the basis of approximate solutionsof the stationary-phase points near ΔG = 0, −λ, and λ, where ΔG is the reaction free energy and λ is thereorganization energy, three closed-form rate expressions are derived, which are respectively valid near eachvalue of ΔG. Numerical tests for a model Ohmic spectral density with an exponential cutoff demonstrategood performance of the derived expressions in the respective regions of their validity. In particular, theexpression near ΔG = −λ, which differs from the semiclassical approximation only by a prefactor quadraticin ΔG, works substantially better than the latter. Then, a unified formula is suggested, which interpolates thethree approximate expressions and serves as a good approximation in all three regions. We have alsodemonstrated that the interpolation formula can serve as a good quantitative means for understanding thetemperature dependence of the quantum ET rate.
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