Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Chemical Dynamics

Background:

• Solving the time-dependent Schrödinger equation requires evaluating integrals over the potential energy surface (PES).
• Standard methods approximate the PES using Taylor expansions, which can be computationally expensive and less accurate.

Purpose of the Study:

• To introduce a novel method for approximating PES matrix elements using Gaussian process regression (GPR).
• To demonstrate the efficiency and accuracy of GPR compared to Taylor expansion methods in quantum dynamics.

Main Methods:

• PES interpolation using Gaussian process regression (GPR).
• Single-point PES evaluations at limited configurations per time-step, avoiding Hessian matrix calculations.
• Application to 2-, 5-, and 10-dimensional benchmark models with non-linear coupling.

Main Results:

• GPR method yields PES matrix elements with significantly reduced average error compared to Taylor expansions.
• Achieved accuracy comparable or superior to Taylor methods without additional computational cost.
• Demonstrated effectiveness in complex multi-dimensional systems.

Conclusions:

• GPR provides a computationally simpler and more accurate alternative for PES matrix element evaluation.
• The GPR methodology is recommended to replace Taylor expansion methods in quantum dynamics simulations.
• Further refinements of the GPR procedure hold promise for enhanced computational efficiency.