Understanding molecular geometric phase effects with exact effective force: case study of a model system

Area of Science:

• Quantum Chemistry
• Molecular Dynamics
• Computational Physics

Background:

• Geometric phase effects are crucial in molecular dynamics.
• Existing methods struggle to accurately capture these effects.
• Exact factorization (EF) provides a theoretical framework.

Purpose of the Study:

• To investigate molecular geometric phase effects using EF.
• To analyze dynamics simulations of a two-state vibronic coupling model.
• To interpret results from Born-Huang expansion, exact time-dependent potential energy surface (TDPES), and exact effective force perspectives.

Main Methods:

• Employed exact factorization (EF) and exact effective force.
• Performed dynamics simulations for a two-state vibronic coupling model.
• Analyzed results using Born-Huang expansion, TDPES, and exact effective force.

Main Results:

• Periodic vanishing nuclear density can be explained by energy perspective via exact TDPES.
• Exact effective force with classical dynamics reproduces nuclear density better than adiabatic force.
• Discrepancies in nuclear density are most pronounced in interference regions.

Conclusions:

• The exact effective force offers a promising starting point for approximations.
• Improved trajectory-based methods can accurately describe geometric phase effects.
• EF provides a robust framework for understanding complex molecular phenomena.