Time-Reversible Velocity Predictors for Verlet Integration with Velocity-Dependent Right-Hand Side

Area of Science:

• Computational Chemistry
• Molecular Dynamics Simulations
• Physical Chemistry

Background:

• Accurate simulations of molecular systems are crucial for understanding chemical and physical processes.
• Existing methods for molecular dynamics, such as the Gear integrator and MTTK method, have limitations in handling velocity-dependent forces and constraints.
• The Verlet integrator is a popular choice for molecular dynamics but requires careful treatment of constraints and velocities.

Purpose of the Study:

• To develop and evaluate time-reversible velocity predictors (TRVPs) for use with the Verlet integrator.
• To assess the performance of TRVPs in molecular dynamics simulations involving velocity-dependent forces and constraints.
• To compare TRVPs with existing methods like the Gear integrator and MTTK for accuracy and efficiency.

Main Methods:

• Development of TRVPs with increasing orders of time-reversibility error.
• Application of TRVPs with the Verlet integrator, independent of SHAKE or RATTLE algorithms for bond length constraints.
• Testing TRVPs with the Nosé-Hoover thermostat on various model systems, including oscillators, liquid argon, SPC/E water, and a peptide.
• Comparison with the Gear integrator, MTTK method, and velocity iteration method.

Main Results:

• TRVP method demonstrates performance comparable to the velocity iteration method.
• Leapfrog velocities were identified as the optimal kinetic energy formula for Verlet/SHAKE algorithms.
• Proposed modifications to the MTTK method and suggested improvements for thermostat integration.

Conclusions:

• TRVPs offer a viable and accurate alternative for molecular dynamics simulations with velocity-dependent forces.
• The developed TRVP method simplifies constraint handling without compromising accuracy.
• Methodological improvements, including optimal kinetic energy formulas and thermostat strategies, can further enhance simulation accuracy.