  Semi-empirical quantum mechanical methods traditionally expand the electron
density in a minimal, valence-only electron basis set. The minimal-basis
approximation causes molecular polarization to be underestimated, and hence
intermolecular interaction energies are also underestimated, especially for
intermolecular interactions involving charged species. In this work, the
third-order self-consistent charge density functional tight-binding method
(DFTB3) is augmented with an auxiliary response density using the
chemical-potential equalization (CPE) method and an empirical dispersion
correction (D3). The parameters in the CPE and D3 models are fitted to
high-level CCSD(T) reference interaction energies for a broad range of chemical
species, as well as dipole moments calculated at the DFT level; the impact of
including polarizabilities of molecules in the parameterization is also
considered. Parameters for the elements H, C, N, O and S are presented. The
RMSD interaction energy is improved from 6.07 kcal/mol to 1.49 kcal/mol for
interactions with one charged specie, whereas the RMSD is improved from 5.60
kcal/mol to 1.73 for a set of 9 salt bridges, compared to uncorrected DFTB3.
For large water clusters and complexes that are dominated by dispersion
interactions, the already satisfactory performance of the DFTB3-D3 model is
retained; polarizabilities of neutral molecules are also notably improved.
Overall, the CPE extension of DFTB3-D3 provides a more balanced description of
different types of non-covalent interactions than NDDO type of semi-empirical
methods (e.g., PM6-D3H4) and PBE-D3 with modest basis sets.
