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Adrián Gómez Pueyo1, Sergio Blanes2, Alberto Castro1,3

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This study introduces a unified numerical method for quantum-classical molecular dynamics. By adapting Magnus expansions for nonlinear systems, it enhances accuracy and stability in simulations involving both quantum electrons and classical nuclei.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Molecular Dynamics

Background:

  • Simulating systems with both quantum and classical components (e.g., electrons and nuclei) is crucial in chemistry and physics.
  • Existing quantum-classical molecular dynamics (QCMD) models often use separate numerical methods for quantum and classical parts, potentially compromising accuracy and stability.
  • Developing unified, accurate, and stable propagation techniques for QCMD remains a significant challenge.

Purpose of the Study:

  • To propose and evaluate a novel numerical method for the accurate and stable propagation of hybrid quantum-classical molecular dynamics models.
  • To address the limitations of existing methods that use disparate propagation techniques for quantum and classical degrees of freedom.
  • To adapt efficient numerical methods, originally developed for linear systems, to handle the inherent nonlinearity of quantum-classical systems.

Main Methods:

  • The study proposes employing (quasi)-commutator free Magnus expansions, a technique efficient for linear Schrödinger-like equations, for both quantum and classical particles in QCMD.
  • To overcome the nonlinearity of the quantum-classical system, where the Hamiltonian depends on the system's state, a higher-order extrapolation is used to approximate the unknown Hamiltonian at intermediate points.
  • This approach results in a multistep technique or a predictor-corrector formula for nonlinear quantum-classical dynamics.

Main Results:

  • The adapted Magnus expansion method provides a unified approach for propagating both quantum (e.g., time-dependent density-functional theory for electrons) and classical (nuclei) components.
  • The extrapolation technique effectively handles the nonlinear dependence of the Hamiltonian, maintaining accuracy and stability.
  • The proposed method offers improved preservation of geometrical structures and accuracy order compared to traditional approaches.

Conclusions:

  • The (quasi)-commutator free Magnus expansion, adapted with extrapolation for nonlinear systems, presents a robust and efficient method for quantum-classical molecular dynamics.
  • This unified approach overcomes limitations of using separate propagation schemes, leading to more reliable simulations of complex molecular systems.
  • The technique offers a promising direction for advancing the accuracy and stability of computational modeling in quantum chemistry and condensed matter physics.