Newton's algorithm for discrete classical dynamics.

Area of Science:

• Computational Physics
• Chemical Physics
• Classical Mechanics

Background:

• Molecular Dynamics (MD) simulations are crucial in computational physics and chemistry.
• Commonly used algorithms like velocity-Verlet and position-Verlet are debated regarding their distinctness.
• These algorithms are foundational in simulating the dynamics of molecules and materials.

Purpose of the Study:

• To clarify the relationship between different discrete algorithms used in Molecular Dynamics (MD) simulations.
• To demonstrate that widely used algorithms are reformulations of Newton's original discrete dynamics.
• To highlight persistent errors in MD simulation software and advocate for corrections.

Main Methods:

• Analysis of discrete algorithms used in Molecular Dynamics (MD) simulations.
• Comparison of velocity-Verlet and position-Verlet integrators with Newton's original discrete dynamics.
• Review of published MD simulation results and their reported energy conservation properties.

Main Results:

• Velocity-Verlet and position-Verlet algorithms are mathematically equivalent formulations of the same underlying discrete algorithm.
• All discussed discrete algorithms in MD are reformulations of Newton's 1687 discrete dynamics.
• These reformulations produce identical dynamics, conserving momentum, angular momentum, and energy.

Conclusions:

• The distinction between velocity-Verlet and position-Verlet integrators in MD is a misconception.
• MD simulations based on Newton's discrete dynamics are fundamentally sound but suffer from software implementation errors.
• Correction of public MD software is necessary to ensure accurate simulation results for energy, temperature, and heat capacity.