Shadow Hamiltonian in classical NVE molecular dynamics simulations: A path to long time stability

Area of Science:

• Computational physics
• Molecular dynamics simulations
• Statistical mechanics

Background:

• The microcanonical ensemble (NVE) is crucial for molecular dynamics (MD) simulations.
• Shadow energy (E_s) is a conserved quantity in NVE MD simulations using the position Verlet algorithm.
• Accurate energy conservation is vital for reliable simulation results, especially during phase transitions or structural rearrangements.

Purpose of the Study:

• To introduce a novel methodology for precise and accurate calculation of shadow energy (E_s).
• To demonstrate that E_s, not total energy (E), remains constant during structural changes in supercooled liquids.
• To enable long-timescale (microsecond) NVE simulations with negligible energy drift without thermostats.

Main Methods:

• Development and application of a new method for calculating shadow energy (E_s).
• Analysis of energy drift using block averaging and novel drift functions for shadow energy.
• Implementation of strategies for preparing and conducting bulk-phase NVE simulations with minimal drift.
• Extension of the methodology to polyatomic systems with flexible degrees of freedom and SHAKE constraints.

Main Results:

• E_s is shown to be constant during structural changes in supercooled liquids, a finding not observed for total energy (E).
• Microsecond-range NVE simulations were achieved with essentially zero energy drift.
• Extremely small standard errors (≈10^-10 in reduced units) for E_s, E, and temperature (T) were obtained.
• A temperature drift of ≈10^-6 K/μs was achieved, six orders of magnitude better than typical protein simulation standards.
• The method was successfully extended to complex polyatomic systems with constraints.

Conclusions:

• The presented methodology allows for highly accurate and precise calculation of shadow energy in NVE MD simulations.
• This approach enables long-timescale simulations with unprecedentedly low energy drift, crucial for studying dynamic processes.
• The findings significantly advance the capability of molecular dynamics for simulating complex systems with high fidelity.