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

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The multi-electronic-state path integral (MES-PI) method naturally captures the geometric phase (GP) effect, crucial for accurate low-temperature quantum simulations. This approach corrects errors from standard methods lacking GP consideration.

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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.