Thermodynamic Integration for Dynamically Unstable Systems Using Interatomic Force Constants without Molecular Dynamics

TL;DR

This paper introduces a fast, accurate first-principles method for calculating anharmonic vibrational free energy and phase transition temperatures without molecular dynamics, using interatomic force constants and statistical sampling.

Contribution

The authors develop a novel thermodynamic integration approach that replaces AIMD with force constant-based sampling, achieving four orders of magnitude speedup while maintaining accuracy.

Findings

Successfully predicts phase transition temperatures within 25% error for various materials.

Enables large-scale predictive mapping of phase transitions.

Significantly reduces computational cost compared to traditional AIMD methods.

Abstract

We demonstrate an efficient and accurate, general-purpose first-principles blueprint for calculating anharmonic vibrational free energy and predicting structural phase transition temperatures of solids. Thermodynamic integration is performed without molecular dynamics using only interatomic force constants to model analogues of the true potential and generate their thermal ensembles. By replacing \textit{ab initio} molecular dynamics (AIMD) with statistical sampling of ensemble configurations and trading density-functional theory (DFT) energy calculations on each configuration for a set of matrix operations, our approach enables a faster thermodynamic integration by 4 orders of magnitude over the traditional route via AIMD. Experimental phase transition temperatures of a variety of strongly anharmonic materials with dynamical instabilities including shape-memory alloys are recovered to largely within 25% error. Such a combination of speed and accuracy enables the method to be deployed at a large-scale for predictive mapping of phase transition temperatures.