Harmonic-to-anharmonic thermodynamic integration made simple using REG TI

TL;DR

This paper introduces REG TI, a regularization method that simplifies harmonic-to-anharmonic thermodynamic integration by removing singularities, improving accuracy and enabling automation in free energy calculations for solids.

Contribution

The paper presents a novel regularization technique, REG TI, that addresses singularities in standard TI, facilitating more accurate and automated free energy computations for solids with diffusive degrees of freedom.

Findings

REG TI effectively removes singularities in TI integrands.

Demonstrated on a model system and paracetamol polymorphs.

Enables more accurate and potentially automated free energy calculations.

Abstract

Standard harmonic-to-anharmonic thermodynamic integration (TI) is known to develop a near singularity in the integrand for solids exhibiting diffusive degrees of freedom, such as rotating functional groups or migrating defects. This pathology results in numerical challenges for estimating absolute free energies within a single thermodynamic cycle. In this work, we introduce a simple regularization that removes this singularity and yields a well-behaved integrand that can be accurately evaluated on a uniform grid. The approach -- termed Regularized End-point Gradient (REG) TI -- is demonstrated on a model system and on predicting the relative stability of paracetamol polymorphs for which quasi-free methyl rotations lead to a near singularity in standard TI. We expect REG TI to simplify anharmonic free energy calculations for solids and to potentially enable their automation.