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Semi-empirical quantum mechanical methods traditionally expand the electrondensity in a minimal, valence-only electron basis set. The minimal-basisapproximation causes molecular polarization to be underestimated, and henceintermolecular interaction energies are also underestimated, especially forintermolecular interactions involving charged species. In this work, thethird-order self-consistent charge density functional tight-binding method(DFTB3) is augmented with an auxiliary response density using thechemical-potential equalization (CPE) method and an empirical dispersioncorrection (D3). The parameters in the CPE and D3 models are fitted tohigh-level CCSD(T) reference interaction energies for a broad range of chemicalspecies, as well as dipole moments calculated at the DFT level; the impact ofincluding polarizabilities of molecules in the parameterization is alsoconsidered. Parameters for the elements H, C, N, O and S are presented. TheRMSD interaction energy is improved from 6.07 kcal/mol to 1.49 kcal/mol forinteractions with one charged specie, whereas the RMSD is improved from 5.60kcal/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 dispersioninteractions, the already satisfactory performance of the DFTB3-D3 model isretained; polarizabilities of neutral molecules are also notably improved.Overall, the CPE extension of DFTB3-D3 provides a more balanced description ofdifferent types of non-covalent interactions than NDDO type of semi-empiricalmethods (e.g., PM6-D3H4) and PBE-D3 with modest basis sets.

Improving intermolecular interactions in DFTB3 using extended polarization from chemical-potential equalization