Non-adiabatic ring polymer molecular dynamics with spin mapping variables.

Area of Science:

• Quantum Chemistry
• Molecular Dynamics
• Computational Physics

Background:

• Simulating quantum dynamics in complex molecular systems is computationally challenging.
• Existing methods often struggle with accurate sampling of quantum statistics and computational efficiency.

Purpose of the Study:

• To develop a novel, efficient, and accurate method for simulating non-adiabatic quantum dynamics.
• To introduce the spin mapping non-adiabatic ring polymer molecular dynamics (SM-NRPMD) approach.

Main Methods:

• Derivation of the path-integral partition function using spin coherent states and ring polymer formalism.
• Justification of a Hamiltonian for coupled spin mapping variables and nuclear ring polymer dynamics.
• Numerical validation using nuclear position and population auto-correlation functions.

Main Results:

• The SM-NRPMD method shows excellent agreement with numerically exact results for non-adiabatic model systems.
• Spin mapping variables provide nearly time-independent expectation values for equilibrium systems.
• SM-NRPMD demonstrates invariant dynamics under potential partitioning variations.

Conclusions:

• The SM-NRPMD method is a highly accurate and efficient tool for quantum dynamics simulations.
• It offers significant advantages over harmonic oscillator mapping for systems in thermal equilibrium.
• The method's robustness is confirmed by its invariance to potential partitioning schemes.