We report here on the creation of a multi-center semi-empirical local basis set approach (MSEL) for long time scale (e.g., > 1 ns) simulation of experiments under extreme thermodynamic conditions. Density Functional Theory (DFT) has been shown to accurately reproduce the high pressure-temperature chemistry, phase boundaries, and EOS of many materials. DFT simulations, though, scale poorly with computational effort and thus are generally limited to nanometer system sizes and picosecond time-scales.
In contrast, chemical kinetic effects and phase changes observed in experiments can span up to nanosecond timescales and significantly longer length scales. MSEL holds promise as a high throughput simulation capability by providing orders of magnitude increase in computational efficiency while retaining most of the accuracy of Kohn-Sham DFT. Our approach is based on density functional tight binding with self-consistent charges, with improved determination of both quantum mechanical electronic states and empirical functions. We show that MSEL interaction potentials can be created by expanding on density functional tight binding in two different ways:
An extended atomic basis set is used in order to maintain transferability between different material phases and conditions, (e.g., up to d-orbital interactions for carbon)
The many-site DFT Hamiltonian is approximated as a sum of two and three-center terms, and is mapped onto a combination of radial grids and empirical functions for efficient calculation.
Here, we develop MSEL models for carbon at pressures up to 2000 GPa and temperatures up to 20,000 K. Our new interaction potential for carbon yields accurate material properties for diamond, graphite, the BC8 phase, and simple cubic carbon, as well as for the shock Hugoniot of diamond compressed up to the conducting liquid. Our results provide a straightforward method by which the MSEL approach can be made to provide equation of state and long-time scale chemical kinetic data at a similar accuracy to standard quantum codes. Our methods could be extended to any number of materials related to geology and materials science, including iron oxides, SiO, and hydrocarbon systems.