Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects

Abstract

Adequate simulation of non-adiabatic dynamics through conical intersection requires account for a non-trivial geometric phase (GP) emerging in electronic and nuclear wave-functions in the adiabatic representation. Popular mixed quantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry a nuclear wave-function to be able to incorporate the GP into nuclear dynamics. Surprisingly, the MQC methods reproduce ultra-fast interstate crossing dynamics generated with the exact quantum propagation so well as if they contained information about the GP. Using two-dimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: 1) compensation for repulsive diagonal second order non-adiabatic couplings and 2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.

8 pages, 7 figures

References in corpus (3)

• Landau-Zener type surface hopping algorithms
• When do we need to account for the geometric phase in excited state dynamics ?
• Path integral formulation for quantum nonadiabatic dynamics and the mixed quantum-classical limit

Cited by in corpus (3)

• An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry's phase and "magnetic" forces
• Geometric phase effects in excited state dynamics through a conical intersection in large molecules: N-dimensional linear vibronic coupling model study
• High-order geometric integrators for representation-free Ehrenfest dynamics