(695d) Development of Non-Empirical Tight Binding Theory for Efficient Quantum Chemical Calculations

Computational predictions of structures and chemical reactivities of molecules and materials are limited by the high cost of state-of-the-art ab initio methods, such as density functional theory (DFT) and coupled cluster theory. The tight binding (TB) approximation reduces the computational burden by replacing many complicated integrals with simplified empirical functional forms. Such integral approximations, however, involve data-fitted parameters that often sacrifice accuracy and suffer from poor transferability across the chemical space. Consequently, applications of TB models in chemistry remain restricted, despite the significant demand for low-cost energy calculators that can accelerate computational discoveries.

Previously, we introduced a non-empirical tight binding model (NTB) that is free of parameters. The model generalizes the Hückel electronic structure problem and is based on a new ansatz of atom-centered, non-interacting, hydrogenic electron states, which we refer to as H-ansatz. Surprisingly, the method surpasses the accuracy of Kohn-Sham DFT for certain molecules. For H₂, NTB exhibits absolute errors of 0.002 Å, 0.08 eV/atom, and 13 cm^-1 in equilibrium bond length, electronic binding energy, and vibrational frequency with respect to experimentally derived values. Remarkably, NTB achieves this accuracy using an on-the-fly-optimized minimal basis set and no parameters.

In this work, we discuss our efforts toward the generalization of the NTB theory to larger H_x systems and extension toward main group elements. We report sensitivity testing of the total energy to different physically motivated forms of the H-ansatz Hamiltonian and evaluate the connection of NTB to the empirical electronegativity equalization principle. Finally, we assess the viability of NTB in calculating energy barriers of model chemical reactions. We anticipate that development of NTB will enable rapid characterization of a wide array of materials and reaction mechanisms, paving a way toward more rapid discoveries.