Thermodynamic Integration Using Interatomic Force Constants without Molecular Dynamics

We demonstrate an efficient and accurate, general-purpose first-principles blueprint for calculating anharmonic vibrational free energy of solids, capable of predicting structural phase transition temperatures of materials. Thermodynamic integration is performed using interatomic force constants without molecular dynamics to model analogues of the true potential and generate their thermal ensembles. By replacing ab initio molecular dynamics (AIMD) with statistical sampling of ensemble configurations and trading density-functional theory (DFT) calculations on each configuration for a set of matrix multiplications, 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 mostly within 10% 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.