Geometric integration in Born-Oppenheimer molecular dynamics

Area of Science:

• Computational chemistry
• Molecular dynamics
• Theoretical physics

Background:

• Extended Lagrangian methods offer a framework for simulating molecular systems.
• Self-consistent field (SCF) convergence issues can introduce numerical noise in simulations.
• Geometric integration schemes are crucial for accurate and stable molecular dynamics.

Purpose of the Study:

• To develop and analyze geometric integration schemes for extended Lagrangian Born-Oppenheimer molecular dynamics.
• To investigate the impact of weak dissipation on numerical noise reduction.
• To evaluate the performance of different integration schemes regarding energy conservation, accuracy, and stability.

Main Methods:

• Development of extended Lagrangian schemes for coupled nuclear and electronic degrees of freedom.
• Implementation and analysis of three geometric integration methods: Verlet, second-order symplectic, and third-order symplectic.
• Systematic investigation of energy conservation, accuracy, and stability under varying dissipation levels, time steps, and SCF convergence criteria.

Main Results:

• The extended Lagrangian framework allows for stable and energy-conserving simulations even with approximate SCF convergence.
• Inclusion of weak dissipation in symplectic integration methods effectively damps numerical noise.
• Third-order optimal symplectic integration demonstrated superior performance in conserving energy and maintaining stability.

Conclusions:

• Geometric integration schemes, particularly third-order optimal symplectic with dissipation, provide efficient and robust simulations for extended Lagrangian molecular dynamics.
• Weak dissipation is a key component for managing numerical artifacts in reversible dynamics.
• These methods enhance the reliability and efficiency of large-scale molecular simulations.