Quantum-classical path integral. II. Numerical methodology.

Area of Science:

• Physical Chemistry
• Quantum Mechanics
• Computational Chemistry

Background:

• Simulating quantum systems interacting with large environments is computationally challenging.
• Accurate modeling requires capturing both quantum system dynamics and environmental influence.

Purpose of the Study:

• To develop a novel quantum-classical methodology for propagating the density matrix of a system coupled to a polyatomic environment.
• To provide a computationally tractable approach for studying quantum dynamics in condensed phases.

Main Methods:

• A quantum-classical path integral (QCPI) approach is employed, treating the system with path integrals and the environment with classical trajectories.
• The methodology allows for state transitions in trajectories, governed by coupling strength and reorganization energy.
• An iterative scheme refines solvent quantum corrections by incorporating nonlocal "quantum memory" effects.

Main Results:

• The QCPI method accurately describes system-environment dynamics, particularly when environmental quantum effects are weak.
• A random hop approximation offers an inexpensive yet accurate alternative in such cases.
• The iterative scheme demonstrates convergence towards the full QCPI result as quantum memory effects are included.

Conclusions:

• The developed quantum-classical methodology provides an efficient and accurate tool for simulating dissipative quantum systems.
• The approach is applicable to various systems, including two-level systems, offering insights into chemical reaction dynamics and energy transfer.