Improving intermolecular interactions in DFTB3 using extended polarization from chemical-potential equalization Anders S. Christensen, ∗ , † Marcus Elstner, ‡ and Qiang Cui ∗ , † University of Wisonsin-Madison, Department of Chemsitry, 1101 University Ave, Madison, WI 53706, USA, and Universit¨at Karlsruhe, Theoretische Chemische Biologie, Kaiserstr. 12, 76131 Karlsruhe, Germany E-mail: [email protected]; [email protected] Abstract Semi-empirical quantum mechanical methods traditionally expand the electron den- sity in a minimal, valence-only electron basis set. The minimal-basis approximation causes molecular polarization to be underestimated, and hence intermolecular interac- tion energies are also underestimated, especially for intermolecular interactions involv- ing charged species. In this work, the third-order self-consistent charge density func- tional 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 fi tted 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 ∗ To whom correspondence should be addressed † University of Wisonsin-Madison ‡ Universit¨at Karlsruhe 1 arXiv:1507.00370v1 [physics.chem-ph] 1 Jul 2015
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 di ff erent types of non-covalent interactions than NDDO type of semi-empirical methods (e.g., PM6-D3H4) and PBE-D3 with modest basis sets. Introduction Semi-empirical (SE) quantum mechanical (QM) methods have enabled QM to be used where ab initio methods are too computationally expensive. Conceptually, the SE methods are approximations to ab initio QM methods, but introduce parameters that must be fi tted empirically based on either ab initio or experimental data. SE methods has been discussed and benchmarked thoroughly, as most recently reviewed in Refs. 1–5. In the NDDO/MNDO-based methods, the formalism is derived from Hartree-Fock theory, but with several approximations in both the matrix algebra and integral calculation. 6,7 In the density functional tight-binding (DFTB) methods, 8,9 the formalism is derived from a Taylor expansion of the DFT energy in terms of density ﬂ uctuation with respect to a reference, and the matrix elements are calculated from fi rst-principles DFT. 10,11
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