Simulating vibronic spectra via Matsubara-like dynamics: Coping with the sign problem.

Area of Science:

• Quantum Chemistry
• Spectroscopy
• Theoretical Chemistry

Background:

• Vibronic spectra reveal molecular dynamics, but theoretical interpretation is complex for many-body systems with multiple electronic states.
• Classical-like approximations are often needed but challenging for multi-state systems.

Purpose of the Study:

• To develop a theoretical framework for simulating vibronic spectra using Matsubara dynamics.
• To generalize existing Matsubara dynamics to multiple potential energy surfaces (PESs).
• To propose a modified simulation method that overcomes the sign problem.

Main Methods:

• Expressing imaginary-time shifted time correlation functions and vibronic spectra using Matsubara dynamics.
• Applying the Matsubara approximation in the adiabatic limit to generalize the formalism to multiple PESs.
• Developing a modified Matsubara-like dynamics to simulate the standard correlation function.

Main Results:

• A generalized Matsubara dynamics for multiple PESs was derived, though it retains the sign problem.
• A novel modified method was proposed and mathematically analyzed for two shifted harmonic oscillators.
• The modified method accurately approximates vibronic absorption spectra for both harmonic and anharmonic systems without the sign problem by sampling the thermal Wigner function.

Conclusions:

• The developed modified Matsubara-like dynamics provides an accurate and computationally feasible approach for simulating vibronic spectra.
• This method offers a significant advancement for studying complex molecular systems where traditional methods face challenges.