Stochastic Sampling for Quantum-Anharmonic Property Prediction in Solids

Computationally predicting the thermodynamic properties of solids (e.g., free energy and entropy) requires a trade-off between the level of physics captured (e.g., quantum vs. classical statistics) and the computational cost. While thermodynamic integration is the gold standard for predicting classical free energies, this method requires path-integral approaches to capture quantum effects and can be prohibitively expensive to compute. We propose and validate a cumulant-expansion approach to estimate thermodynamic properties that does not require dynamics, captures zero-point motion, and can predict free energy, entropy, internal energy, and heat capacity. Instead of directly simulating dynamics, thermally-excited atomic configurations are sampled for a harmonic crystal. This sampling-based technique captures zero-point motion and avoids the computational cost of simulating dynamics while still converging to the true value. We validate the approach through comparison with results obtained from thermodynamic integration for materials including Lennard-Jones argon as well as other materials exhibiting greater structural and chemical complexity.