# Maximum Entropy-Mediated Liquid-to-Solid Nucleation and Transition

## TL;DR

This paper introduces a new algorithm that uses maximum entropy to adjust molecular dynamics simulations, enabling better modeling of liquid-to-solid transitions and improving atomic structure predictions.

## Contribution

A novel algorithm that biases molecular dynamics simulations using radial distribution functions under maximum entropy principles to guide nucleation and transitions.

## Key findings

- The algorithm successfully adjusts the radial distribution function of liquid models to match target models.
- It can initiate crystallization in liquids, forming stable and metastable crystalline states.
- The method is useful for improving interaction models and interpreting experimental data.

## Abstract

Molecular dynamics (MD) simulations are a powerful tool
for studying
matter at the atomic scale. However, to simulate solids, an initial
atomic structure is crucial for the successful execution of MD simulations
but can be difficult to prepare due to insufficient atomistic information.
At the same time, wide-angle X-ray scattering (WAXS) measurements
can determine the radial distribution function (RDF) of atomic structures.
However, the interpretation of RDFs is often challenging. Here, we
present an algorithm that can bias MD simulations with RDFs by combining
the information on the MD atomic interaction potential and the RDF
under the principle of maximum relative entropy. We show that this
algorithm can be used to adjust the RDF of one liquid model, e.g.,
the TIP3P water model, to reproduce the RDF and improve the angular
distribution function (ADF) of another model, such as the TIP4P/2005
water model. In addition, we demonstrate that the algorithm can initiate
crystallization in liquid systems, leading to both stable and metastable
crystalline states defined by the RDF, e.g., crystallization of water
to ice and liquid TiO2 to rutile or anatase. Finally, we
discuss how this method can be useful for improving interaction models,
studying crystallization processes, interpreting measured RDFs, or
training machine-learned potentials.