The Atomic Density-Based Tight-Binding (aTB) Model: A Robust and Accurate Semiempirical Method Parametrized for H–Ra; Applied to Structures, Vibrational Frequencies, Noncovalent Interactions, and Excited States

This work introduces a semiempirical 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, noncovalent 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 semiempirical methods.