The atomic density based tight-binding (aTB) model: A robust and accurate semi-empirical method parameterized for H-Ra; applied to structures, vibrational frequencies, noncovalent interactions, and excited states

This work introduces a semi-empirical method, named aTB, based on the tight-binding model and named for its zero-order Hamiltonian that utilizes density-fitting atomic densities. This method can calculate the molecular structure, vibrational frequencies, non-covalent interactions, and excited states of large molecular systems. The parameters of aTB cover elements from Hydrogen (H) to Radium (Ra), and for ground state calculations, it supports the analysis of first- and second-order derivatives. The Hamiltonian of aTB contains a zero-order Hamiltonian, Coulomb term, an explicit second- and third-order expansion of the exchange-correlation term, and a spin-polarization term with only one additional parameter. A series of extensive tests were conducted to compare aTB with existing semi-empirical methods.