Why Do Mixed Quantum-Classical Methods Describe Short-Time Dynamics through Conical Intersections So Well? Analysis of Geometric Phase Effects

Rami Gherib; Ilya G Ryabinkin; Artur F Izmaylov

doi:10.1021/acs.jctc.5b00072

Why Do Mixed Quantum-Classical Methods Describe Short-Time Dynamics through Conical Intersections So Well? Analysis of Geometric Phase Effects

J Chem Theory Comput. 2015 Apr 14;11(4):1375-82. doi: 10.1021/acs.jctc.5b00072.

Authors

Rami Gherib^{1

2}, Ilya G Ryabinkin^{1

2}, Artur F Izmaylov^{1

2}

Affiliations

¹ Department of Physical and Environmental Sciences, University of Toronto Scarborough , Toronto, Ontario M1C 1A4, Canada.
² Chemical Physics Theory Group, Department of Chemistry, University of Toronto , Toronto, Ontario M5S 3H6, Canada.

PMID: 26574349
DOI: 10.1021/acs.jctc.5b00072

Abstract

Adequate simulation of nonadiabatic dynamics through conical intersection requires accounting for a nontrivial 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 ultrafast 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 nonadiabatic couplings and (2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.