Surface hopping outperforms secular Redfield theory when reorganization energies range from small to moderate (and nuclei are classical)

Abstract

We evaluate the accuracy of Tully's surface hopping algorithm for the spin-boson model in the limit of small to moderate reorganization energy. We calculate transition rates between diabatic surfaces in the exciton basis and compare against exact results from the hierarchical equations of motion; we also compare against approximate rates from the secular Redfield equation and Ehrenfest dynamics. We show that decoherence-corrected surface hopping performs very well in this regime, agreeing with secular Redfield theory for very weak system-bath coupling and outperforming secular Redfield theory for moderate system-bath coupling. Surface hopping can also be extended beyond the Markovian limits of standard Redfield theory. Given previous work [B. R. Landry and J. E. Subotnik, J. Chem. Phys. 137, 22A513 (2012)] that establishes the accuracy of decoherence-corrected surface-hopping in the Marcus regime, this work suggests that surface hopping may well have a very wide range of applicability.

Coherent exciton-vibrational dynamics and energy transfer in conjugated organics

“…Erhenfest and surface hopping 36 are examples of such methods allowing explicit treatment of large molecular systems for which fully quantum dynamics is prohibitively expensive 8 , 37 – 39 . Alternative perturbative approaches 40 – 42 usually treat nuclei as an effective bath, and the self-energy due to coupling of the nuclei and electrons is usually defined in frequency space and is estimated by averaging over the nuclear motion, thus losing the explicit correlation. Such approaches have been extensively applied, for example, to biological light-harvesting systems 43 , 44 .…”

An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability

“…28, the spin-boson Hamiltonian can be transformed through a change of basis into a different form whereby only a single, primary bath mode is coupled directly to the two-level system. However, that single bath mode (with position x and momentum p) is now coupled to an auxiliary nuclear bath (with positions ⃗ Q and momenta ⃗ P) whose net effect is to damp the motion of the primary bath mode while introducing a random force (i.e., the primary mode will experience Langevin dynamics 48 ).…”

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

“…A-FSSH has been used previously with success to compute rate constants directly. 29,53,54 The details of the A-FSSH algorithm are described in detail in the Appendix A of Paper I (which closely follows the details of Ref. 29).…”

“…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.…”