Geometric Phase Effect in Thermodynamic Properties and in the Imaginary-Time Multi-Electronic-State Path Integral...

Area of Science:

• Quantum mechanics
• Theoretical chemistry
• Computational physics

Background:

• Geometric phase (GP) arises from conical intersections (CIs) and impacts vibronic energy levels.
• Standard Born-Oppenheimer path integral molecular dynamics (PIMD) neglects GP, causing errors in low-temperature thermodynamics.
• Accurate simulation of complex quantum systems requires accounting for GP.

Purpose of the Study:

• Demonstrate that multi-electronic-state path integral (MES-PI) formulation inherently includes GP.
• Quantify the impact of GP on thermodynamic properties by comparing rigorous and GP-excluded methods.
• Highlight MES-PIMD as the most general and accurate method for systems with unknown CI topology.

Main Methods:

• Utilized imaginary-time MES-PI formulation.
• Calculated GP through the electronic trace of overlap matrices between time slices.
• Developed an ad hoc GP-excluded MES-PI method using a geometric signature matrix and winding-number factor.
• Compared rigorous MES-PI with the ad hoc method to isolate GP effects.

Main Results:

• MES-PI naturally captures the geometric phase (GP) effect.
• The GP's impact on thermodynamic properties was unambiguously quantified.
• The study confirms the implicit GP inclusion in prior MES-PIMD simulations.
• A method to isolate GP effects was successfully implemented.

Conclusions:

• MES-PIMD is the most accurate and general method for simulating complex quantum systems, especially those with unknown conical intersection details.
• The study validates the importance of including GP in quantum simulations for thermodynamic accuracy.
• The developed methodology allows for precise quantification of GP's influence.