A Reciprocal-Space Formulation of Surface Hopping

Abstract

Surface hopping has seen great success in describing molecular phenomena where electronic excitations tend to be localized, but its application to materials with band-like electronic properties has remained limited. Here, we derive a formulation of fewest-switches surface hopping where both the quantum and classical equations of motion are solved entirely in terms of reciprocal-space coordinates. The resulting method is directly compatible with band structure calculations, and allows for the efficient description of band-like phenomena by means of a truncation of the Brillouin zone. Using the Holstein and Peierls models as examples, we demonstrate the formal equivalence between real-space and reciprocal-space surface hopping, and assess their accuracy against mean-field mixed quantum--classical dynamics and numerically-exact results.

13 pages, 9 figures

References in corpus (5)

• Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
• Exciton-phonon coupling strength in single-layer MoSe2 at room temperature
• On the Munn-Silbey approach to polaron transport with off-diagonal coupling
• An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry's phase and "magnetic" forces
• A Reciprocal-Space Formulation of Mixed Quantum-Classical Dynamics

Cited by in corpus (3)

• Spectral and thermodynamic properties of the Holstein polaron: Hierarchical equations of motion approach
• Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods
• Overcoming positivity violations for density matrices in surface hopping