# Effective conservation of energy and momentum algorithm using switching potentials suitable for molecular dynamics simulation of thermodynamical systems

## TL;DR

This paper introduces an energy and momentum conserving algorithm for molecular dynamics simulations that effectively manages energy violations during potential switching, ensuring stable thermodynamical properties.

## Contribution

The novel algorithm maintains energy and momentum conservation during potential switching in MD simulations, improving accuracy over traditional methods.

## Key findings

- The algorithm preserves system coordinates during moves.
- It reduces energy violations during potential crossover.
- Thermodynamical properties remain stable with the algorithm.

## Abstract

During a crossover via a switching mechanism from one 2-body potential to another as might be applied in modeling (chemical) reactions in the vicinity of bond formation, energy violations would occur due to finite step size which determines the trajectory of the particles relative to the potential interactions of the unbonded state by numerical (e.g. Verlet) integration. This problem is overcome by an algorithm which preserves the coordinates of the system for each move, but corrects for energy discrepancies by ensuring both energy and momentum conservation in the dynamics. The algorithm is tested for a hysteresis loop reaction model with an without the implementation of the algorithm. The tests involve checking the rate of energy flow out of the MD simulation box; in the equilibrium state, no net rate of flows within experimental error should be observed. The temperature and pressure of the box should also be invariant within the range of fluctuation of these quantities. It is demonstrated that the algorithm satisfies these criteria.