Use of Chebyshev Clustering for Systematic Determination of Semi-empirical Quantum Models

Semi-empirical quantum models such as Density Functional Tight Binding (DFTB) are attractive methods for obtaining accurate simulation data at longer time and length scales than possible with standard quantum approaches such as Kohn-Sham Density Functional Theory (DFT). However, DFTB models have not been parameterized for significant portions of the periodic table, thus hindering their use for a wide array of application areas including materials under extreme conditions. Here, we present a systematic approach for DFTB model development whereby DFT training data is generated through sampling of up to four-body atomic clusters at distances corresponding to Chebyshev quadrature nodes. This yields a small and rapidly computed training set without the traditional reliance on computationally intensive molecular dynamics simulations. We then optimize the Chebyshev Interaction Model for Efficient Simulation (ChIMES) to determine the empirical (non-quantum mechanically computed) parts of DFTB, allowing for down selection of DFTB model hyerparameters. We use our Chebyshev clustering method to create DFTB models for condensed phase hydrogen, and solid phases of carbon and silicon. Validation against ground-state and cold curve data as well as shock Hugoniot data indicates strong transferability of our models over a broad set of conditions. Our developments thus provide a way to create accurate DFTB models in a semi-automated and less computationally intensive fashion, potentially extending its use to elements as well as mixture and alloys beyond its current capability. Prepared by LLNL under Contract DE-AC52-07NA27344.