Temperature dependent effective potential method for accurate free energy calculations of solids

TL;DR

The paper introduces the TDEP method, combining ab initio molecular dynamics with a model Hamiltonian, to accurately compute anharmonic free energies of solids across temperatures.

Contribution

It presents a detailed formalism and practical implementation of TDEP, demonstrating its effectiveness through first-principles and classical simulations on various materials.

Findings

Force constants in Zr become more localized upon stabilization.

TDEP accurately predicts phase diagrams for helium.

Results align well with experimental data and established methods.

Abstract

We have developed a thorough and accurate method of determining anharmonic free energies, the temperature dependent effective potential technique (TDEP). It is based on \emph{ab initio} molecular dynamics followed by a mapping onto a model Hamiltonian that describes the lattice dynamics. The formalism and the numerical aspects of the technique are described in details. A number of practical examples are given, and results are presented, which confirm the usefulness of TDEP within \emph{ab initio} and classical molecular dynamics frameworks. In particular, we examine from first-principles the behavior of force constants upon the dynamical stabilization of body centered phase of Zr, and show that they become more localized. We also calculate phase diagram for $^4$He modeled with the Aziz \emph{et al.} potential and obtain results which are in favorable agreement both with respect to experiment and established techniques.