Non-adiabatic coupling matrix elements in a magnetic field: Geometric gauge dependence and Berry phase

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• Non-adiabatic coupling matrix elements (NACMEs) are essential for molecular dynamics simulations, especially surface hopping methods.
• NACMEs exhibit gauge dependence, complicating calculations for complex-valued wave functions arising from magnetic fields or spin-orbit coupling.
• Berry curvature and Berry force are significant in magnetic field-influenced molecular dynamics and spin-orbit coupling contexts.

Purpose of the Study:

• To develop a robust scheme for calculating continuous, differentiable NACMEs for complex-valued wave functions as a function of molecular geometry.
• To compute ground- and excited-state Berry curvatures using high-level theory for the first time.
• To directly calculate Berry phases from diagonal NACMEs.

Main Methods:

• Development of a novel computational scheme for gauge-invariant NACME calculation.
• Application of the Full Configuration Interaction (FCI) level of theory for high accuracy.
• Demonstration using the H2 molecule as a test case.

Main Results:

• Successful calculation of continuous and differentiable NACMEs for complex-valued wave functions.
• First-ever computation of ground- and excited-state Berry curvatures at the FCI level.
• Direct computation of Berry phases from diagonal NACMEs.

Conclusions:

• The developed method provides a reliable way to compute NACMEs, Berry curvatures, and Berry phases for complex systems.
• This work advances the accuracy and applicability of molecular dynamics simulations involving non-adiabatic effects.
• The findings are particularly relevant for systems with magnetic fields or significant spin-orbit coupling.