Uncertainty Quantification of Total Energy Tight Binding Models for van der Waals Materials

Interatomic potentials can range greatly in complexity, accuracy, and transferability. Understanding the uncertainty of an interatomic potential is crucial for any application area. Thus, uncertainty quantification (UQ) for interatomic potentials has become an important area of research. Total Energy Tight Binding (TETB) models, which are semi-empirical potential energy descriptions constructed with information about the electronic degrees of freedom in a material, are often more computationally scalable than fully ab initio methods. However, little has been done to quantify uncertainty in TETB models. In this work, we develop Markov-chain Monte Carlo methods for uncertainty quantification in TETB models. We apply our methods to twisted bilayer graphene systems because of their strong dependence on electronic degrees of freedom in lattice reconstruction, and the use of models in these systems that span multiple energy scales. We use our UQ methods to determine uncertainties in particular quantities of interest such as corrugation of twisted bilayer graphene, bandwidths of relaxed structures, and magic angle Fermi velocities. Comparisons to UQ in classical interatomic potentials are made throughout.