NVE ensemble

Summary

The NVE ensemble (microcanonical ensemble) conserves number of atoms, volume, and energy in a molecular dynamics simulation (1). It is used by classical Hamiltonian dynamics simulations under the ergodicity assumption. Use for equilibration is inadvisable since unstable/strained molecules transfer their energy to kinetic energy, leading to higher temperatures.

Details

General formula:

$$d\mathbf{x}=M^{-1}\mathbf{p}dt\text{\hspace{1em}(1)}$$ $$d\mathbf{p}=-{\nabla }_{x}U(\mathbf{x})dt\text{\hspace{1em}(2)}$$

Discrete time step approximation:

$$\delta \mathbf{x}=M^{-1}\mathbf{p}\delta t\text{\hspace{1em}(3)}$$ $$\delta \mathbf{p}=-{\nabla }_{\mathbf{x}}U(\mathbf{x})\delta t\text{\hspace{1em}(4)}$$

Total energy: $\mathcal{H}={\sum }_{i=1}^N\frac{{\mathbf{p}}_i^2}{2m}+U({\mathbf{r}}^N)$

See Mathematical terms in MD for notation. Cites (1,2)

1.

Hénin J, Lelièvre T, Shirts MR, Valsson O, Delemotte L. Enhanced Sampling Methods for Molecular Dynamics Simulations [Article v1.0]. Living Journal of Computational Molecular Science. 2022;4(1):1583. Available from: https://doi.org/10.33011/livecoms.4.1.1583

2.

Understanding Molecular Simulation. 2002; Available from: https://doi.org/10.1016/b978-0-12-267351-1.x5000-7