Can Surface Hopping sans Decoherence Recover Marcus Theory? Understanding the Role of Friction in a Surface Hopping View of Electron Transfer

Abstract

We compare the dynamics of Fewest Switches Surface Hopping (FSSH) in different parameter regimes of the spin-boson model. We show that for exceptional regions of the spin-boson parameter space, FSSH dynamics are in fact time-reversible. In these rare instances, FSSH does recover the correct Marcus rate scaling (as a function of diabatic coupling) without the addition of decoherence. In regions where dynamics are irreversible, however, FSSH does not recover the correct Marcus rate scaling. Finally, by comparing the friction dependence of rates predicted by various decoherence schemes to an analytic result by Zusman, we provide yet more evidence that the method of introducing decoherence has a qualitative effect on the accuracy of results and this effect must be treated carefully.

On the accuracy of surface hopping dynamics in condensed phase non-adiabatic problems

“…41,42 It should be noted, however, that there has been some debate as to just how pervasive this problem is. [43][44][45][46][47] One of the goals of the present work is to provide an in depth examination of this issue.…”

Surface hopping, transition state theory, and decoherence. II. Thermal rate constants and detailed balance

“…14is computed in reference to the diabatic barrier height whereas κ ad is an adiabatic transmission coefficient for barrier crossings over the ground state (which should correspond to an adiabatic barrier height). In the diabatic limit, SB theory and Zusman theory 40,66 are identical. An average of 5000 trajectories is used for this computation.…”

“…35 As an aside, it is interesting that, for the choice of parameters in this paper, including decoherence increases the FSSH rate of decay whereas, in previous papers, we have shown that including decoherence dramatically reduces the rate of decay (assuming a direct calculation with a stronger driving force). 28,29,40,53 In the adiabatic regime, the dynamics on the upper surface is less important, and hence there is little difference between the A-FSSH and the FSSH results.…”

“…Furthermore, we would also like to identify those regimes where the effects of decoherence are important and those regimes where these effects are not important. 40…”

Charge Transport in Molecular Materials: An Assessment of Computational Methods

“…They demonstrated that by adding a decoherence step, based on a propagation of the first moments of the positions and the momenta of the charge carrier, one can indeed recover the correct Marcus be-havior. 335 This step is indeed just a "collapse" of the wavefunction, that occurs with a probability proportional to the inverse of the so-called coherence time. 335 A further problem in practical applications of the original FSSH scheme is its insufficient treatment of so called trivial and "unavoided" crossings 336 between PESs.…”