# Accelerating Variable Cell Shape Molecular Dynamics with a Position-Dependent Mass Matrix

## TL;DR

This paper introduces a new method in molecular dynamics simulations that increases time steps by using a position-dependent mass matrix, allowing faster and more efficient simulations.

## Contribution

The novel contribution is adapting MTMD with a position-dependent mass matrix for variable cell shape systems and demonstrating its efficiency.

## Key findings

- The method increased the time step by a factor of 4.4 in molecular crystal simulations.
- An acceleration factor of 2.8 was achieved in liquid water simulations at the density function theory level.

## Abstract

In molecular dynamics (MD), the accessible time scales
are limited
by the necessity to choose sufficiently small time steps so that the
fastest vibrations of the system can still be modeled. Mass tensor
molecular dynamics (MTMD) aims to increase the time step by augmenting
the Hamiltonian with a position-dependent mass matrix. Higher masses
are assigned to modes with fast vibrations. These modes are identified
by using an approximate Hessian matrix. The approximate Hessian matrix
presented in this paper is applicable to the simulation of molecular
systems, where no changes in the bonding pattern occur. We have adapted
the MTMD method to variable cell shape systems and present a suitable
symplectic integrator. The efficiency of the method is demonstrated
for a system of molecular crystals consisting of N-(4-Methylbenzylidene)-4-methylaniline, where we could sample transitions
between two polymorphs and thereby increase the time step by a factor
of 4.4 to speed up the simulation. We have also simulated liquid water
at the density function theory level, where we have achieved an acceleration
by a factor of 2.8.