Shadow Hamiltonian in classical NVE molecular dynamics simulations involving Coulomb interactions

Area of Science:

• Computational Chemistry
• Materials Science
• Statistical Mechanics

Background:

• Accurate molecular dynamics (MD) simulations are crucial for understanding material properties.
• Simulating systems with Coulomb interactions and constraints in the microcanonical ensemble (NVE) traditionally faces challenges with energy drift.
• Achieving long simulation times is essential for capturing rare events and accurate thermodynamic properties.

Purpose of the Study:

• To develop and validate a new methodology for highly accurate NVE molecular dynamics simulations.
• To minimize energy drift in simulations of systems with Coulomb interactions and complex constraints.
• To enable millisecond timescale simulations without the need for system thermostatting.

Main Methods:

• Modified Ewald summation method with smoothed real space terms.
• Development of numerical tools for assessing simulation drift.
• Calculation of standard Ewald errors and perturbation errors, including charge correlation effects.
• Improved shadow Hamiltonian expressions accounting for higher-order time step terms.

Main Results:

• Achieved negligible energy drift rates of 10⁻⁶ K/μs, six orders of magnitude lower than typical values.
• Demonstrated millisecond timescale simulations in the NVE ensemble.
• Successfully calculated diffusion coefficients for room temperature ionic liquids with high accuracy.
• Validated the strict conservation of the shadow Hamiltonian (E_s) with errors of 1 part in 10¹⁰.

Conclusions:

• The new methodology significantly enhances the accuracy and timescale of NVE MD simulations.
• This approach is suitable for complex systems, including molten salts, polar liquids, and ionic liquids.
• The ability to perform long, drift-free simulations opens new avenues for computational materials discovery and chemical process modeling.