Harmonic-to-anharmonic thermodynamic integration made simple using REG TI
The state-of-the-art method to predict the free energy of solids (a central thermodynamic quantity) is thermodynamic integration. Unfortunately, this approach has a failure mode for systems with local or global diffusive degrees of freedom: in harmonic-to-anharmonic thermodynamic integration (TI), the integrand becomes near-singular at the endpoint, making numerical evaluation difficult.
Existing approaches either sample this endpoint behavior brute-force on a highly non-uniform grid (with results that can depend on grid choice) or use carefully designed TI paths to avoid the singularity, which requires prior knowledge of the entropy associated with the diffusive mode.
In this work, the author analyzes this problem in simple model systems and introduces a straightforward regularization of the TI integrand that removes the endpoint singularity and allows the integral to be evaluated on a uniform grid. The resulting regularised TI method is demonstrated analytically and numerically on both model and realistic systems that are challenging for standard TI, with the goal of improving the automation of anharmonic free-energy calculations for complex solids.
Authors: Venkat Kapil