A diabatic definition of geometric phase effects

TL;DR

This paper introduces a new diabatic-based method to define and analyze geometric phase effects in quantum dynamics, providing insights into their influence on nuclear motion near conical intersections.

Contribution

It proposes a novel diabatic construction to remove geometric phases while preserving potential energy surfaces, enabling more accurate analysis of their dynamical effects.

Findings

GP effects are similar in both methods at low energies

New approach shows reduced GP effects in ultrafast excited state dynamics

Comparison highlights differences in GP influence depending on energy regimes

Abstract

Electronic wave-functions in the adiabatic representation acquire nontrivial geometric phases (GPs) when corresponding potential energy surfaces undergo conical intersection (CI). These GPs have profound effects on the nuclear quantum dynamics and cannot be eliminated in the adiabatic representation without changing the physics of the system. To define dynamical effects arising from the GP presence the nuclear quantum dynamics of the CI containing system is compared with that of the system with artificially removed GP. We explore a new construction of the system with removed GP via a modification of the diabatic representation for the original CI containing system. Using an absolute value function of diabatic couplings we remove the GP while preserving adiabatic potential energy surfaces and CI. We assess GP effects in dynamics of a two-dimensional linear vibronic coupling model both for ground and excited state dynamics. Results are compared with those obtained with a conventional removal of the GP by ignoring double-valued boundary conditions of the real electronic wave-functions. Interestingly, GP effects appear similar in two approaches only for the low energy dynamics. In contrast with the conventional approach, a new approach does not have substantial GP effects in the ultra-fast excited state dynamics.