Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes

Abstract

We investigate the incorporation of the surface-leaking (SL) algorithm into Tully's fewest-switches surface hopping (FSSH) algorithm to simulate some electronic relaxation induced by an electronic bath in conjunction with some electronic transitions between discrete states. The resulting SL-FSSH algorithm is benchmarked against exact quantum scattering calculations for three one-dimensional model problems. The results show excellent agreement between SL-FSSH and exact quantum dynamics in the wide band limit, suggesting the potential for a SL-FSSH algorithm. Discrepancies and failures are investigated in detail to understand the factors that will limit the reliability of SL-FSSH, especially the wide band approximation. Considering the easiness of implementation and the low computational cost, we expect this method to be useful in studying processes involving both a continuum of electronic states (where electronic dynamics are probabilistic) and processes involving only a few electronic states (where non-adiabatic processes cannot ignore short-time coherence).

Surface hopping with a manifold of electronic states. III. Transients, broadening, and the Marcus picture

“…Besides the methods above, historically surface hopping (SH) 14,15 has been a widely used tool for treating electronphonon (e-ph) couplings for molecules or atoms if there are only a few electronic DOF. In the presence of a manifold of electronic DOF-for instance, the case of a loosely bound anion-Preston's surface leaking algorithm 16,17 is one possible approach. More generally, near a metal surface, Shenvi et al have suggested discretizing the electronic bath, and running SH on a large number of independent potential energy surfaces (PESs).…”

Nuclear Dynamics at Molecule–Metal Interfaces: A Pseudoparticle Perspective

“…The goal of this paper is to present such a derivation, which starts from the full quantum-mechanical description, and stepby-step derives equations suitable for implementation of the surface hopping algorithm for non adiabatic molecular dynamics at molecule-metal interfaces. The presented derivation extends recent considerations [44][45][46][47] by taking into account hybridization (broadening) of molecular states with those of the metal(s) in a rigorous way and by providing expressions suitable for implementation of the algorithm in current carrying molecular junctions.…”

“…Indeed the surface hopping procedure described in Refs. [44][45][46][47] is obtained in the limit where level broadening is disregarded. We also show that tracing out information on adiabatic surfaces leads to Ehrenfest dynamics (motion on the potential of mean force).…”

Lindblad equation and its semiclassical limit of the Anderson-Holstein model

“…There are two ways to get rid of the characteristic function: the first way is to assume that D = ∞, mentioned in [31]; the second way is to consider ǫ ↓ 0. In either way, we end up with the approximation…”