On the relationship between the dispersed polaron and spin-boson models

The dispersed polaron model [Warshel, Hwang, J. Chem. Phys. 84 (1986) 4938] provides a powerful way of using classical molecular dynamics simulation in evaluation of quantum mechanical rate constant for electron transfer and related processes. Similar application is provided by the so-called spin-boson Hamiltonian. Here we establish that both approaches are equivalent.