On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration...

Area of Science:

• Computational Chemistry
• Biophysics
• Molecular Modeling

Background:

• Verlet and leapfrog algorithms are standard for molecular dynamics simulations.
• These algorithms exhibit less accurate velocity propagation compared to position propagation.
• Accurate calculation of squared velocities is essential for temperature and pressure determination.

Purpose of the Study:

• To derive a more accurate expression for squared particle velocity in the leapfrog scheme.
• To identify and correct systematic biases in temperature and pressure calculations.
• To improve the accuracy of molecular dynamics (MD) simulations for biomolecular systems.

Main Methods:

• Derivation of an improved formula for squared particle velocity at full time steps.
• Comparative analysis of kinetic energy calculation methods (average of half-step energies vs. square of average velocity).
• Investigation of the impact of the improved method on systems coupled to thermostats and barostats.

Main Results:

• A novel, more accurate expression for squared particle velocity in the leapfrog scheme was derived.
• Computing kinetic energy as the average of half-step energies is more accurate than squaring the average velocity.
• The standard method introduces a systematic bias in instantaneous temperature and pressure calculations.

Conclusions:

• The derived expression enhances the accuracy of molecular dynamics simulations.
• Correcting the squared velocity calculation improves the reliability of thermodynamic property estimations.
• This work offers a more precise approach for analyzing biomolecular systems using MD simulations.