Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications

We report the parametrization of the approximate density functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of organic and biologically relevant molecules. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of molecules of biological relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these molecules; vibrational frequencies are also examined, although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, especially for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant reduction of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calculations, DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination number of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary solution; this suggests that the current DFTB3 methodology has limited transferability for complex phosphorus chemistry at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodology are needed for a reliable method that describes phosphorus chemistry without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calculations for studying phosphorus/sulfur chemistry in condensed phase systems, especially as a low-level method that drives the sampling in a dual-level QM/MM framework.