title: Electron transfer dynamics: Zusman equation versus exact theory.
abstract: The Zusman equation has been widely used to study the effect of solvent dynamics on electron transfer reactions. However, application of this equation is limited by the classical treatment of the nuclear degrees of freedom. In this paper, we revisit the Zusman equation in the framework of the exact hierarchical equations of motion formalism, and show that a high temperature approximation of the hierarchical theory is equivalent to the Zusman equation in describing electron transfer dynamics. Thus the exact hierarchical formalism naturally extends the Zusman equation to include quantum nuclear dynamics at low temperatures. This new finding has also inspired us to rescale the original hierarchical equations and incorporate a filtering algorithm to efficiently propagate the hierarchical equations. Numerical exact results are also presented for the electron transfer reaction dynamics and rate constant calculations.
authors.affiliation: Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China.
authors.forename: Qiang
authors.initials: Q
authors.lastname: Shi
authors.forename: Liping
authors.initials: L
authors.lastname: Chen
authors.forename: Guangjun
authors.initials: G
authors.lastname: Nan
authors.forename: Ruixue
authors.initials: R
authors.lastname: Xu
authors.forename: YiJing
authors.initials: Y
authors.lastname: Yan
mesh_terms: D000465:Algorithms; D004583:Electrons; D008956:Models, Chemical; D011789:Quantum Theory; D012997:Solvents / Q000737:chemistry*; D013816:Thermodynamics
chemical_list: D012997:Solvents