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This paper addresses the singularity issue in harmonic-to-anharmonic thermodynamic integration (TI) for solids with diffusive degrees of freedom, which hinders accurate free energy estimation. The authors introduce a regularization technique called Regularized End point Gradient (REG) TI to eliminate the singularity and produce a well-behaved integrand. They demonstrate the effectiveness of REG TI on a model system and in predicting the relative stability of paracetamol polymorphs, showcasing its ability to simplify anharmonic free energy calculations.
REG TI offers a simple fix for the singularity that plagues free energy calculations of solids with rotating functional groups or migrating defects, potentially unlocking automated workflows.
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.