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 (6)

• Landau-Zener type surface hopping algorithms
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• Geometric phase effects in low-energy dynamics near conical intersections: A study of the multidimensional linear vibronic coupling model
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• The adiabatic limit of the exact factorization of the electron-nuclear wave function
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• An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry's phase and "magnetic" forces
• A Demonstration of Consistency between the Quantum Classical Liouville Equation and Berry's Phase and Curvature
• 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
• Molecular Level-Crossing and the Geometric Phase Effect from the Optical Hanle Perspective
• Holonomy and vortex structures in quantum hydrodynamics
• Geometric Phase Effect in Thermodynamic Properties and in the Imaginary-Time Multi-Electronic-State Path Integral Formulation