A Road Map to Various Pathways for Calculating the Memory Kernel of the Generalized Quantum Master Equation

Area of Science:

• Quantum chemistry
• Theoretical chemistry
• Computational physics

Background:

• The generalized quantum master equation (GQME) is crucial for simulating molecular dynamics, including energy, charge, and coherence transfer.
• Nuclear degrees of freedom influence electronic dynamics via a memory kernel, but its calculation is non-unique and sensitive to approximations.

Purpose of the Study:

• To systematically map out the 30 distinct pathways for calculating the memory kernel in GQME.
• To compare the performance of these pathways using approximate methods for projection-free inputs.
• To identify the most accurate and numerically stable method for calculating the memory kernel.

Main Methods:

• Development of a systematic roadmap detailing 30 pathways for memory kernel calculation.
• Application of the mapping Hamiltonian linearized semiclassical method to obtain projection-free inputs.
• Comparative analysis of pathway performance using the spin-boson benchmark model.

Main Results:

• The study maps 30 pathways for memory kernel calculation within the GQME framework.
• Performance evaluation reveals sensitivity to pathway choice when using approximate projection-free inputs.
• Expressing the memory kernel with a specific operator ordering (projection operator preceding Liouvillian) yields optimal accuracy and stability.

Conclusions:

• The choice of pathway significantly impacts the accuracy and numerical stability of electronic dynamics simulations using GQME with approximate methods.
• A specific formulation of the memory kernel, involving an exponential operator with a preceding projection operator, is identified as superior.
• This work provides crucial guidance for selecting appropriate computational methods in molecular dynamics simulations.