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.

本报告介绍了针对硫和磷的近似密度泛函紧束缚方法DFTB3的参数化。该参数化工作遵循与我们先前为氧、氮、碳和氢建立的3OB集合相一致的理论框架，因此所得参数可广泛应用于描述各类有机及生物相关的分子。参数化中纳入了3d轨道，且电子参数的选择旨在最大限度地减少原子化能的错误。参数通过一组生物相关分子的多种分子进行测试，重点关注这些分子的几何结构、反应能、质子亲和力和氢键相互作用；同时，也考察了振动频率，尽管这一方面的工作不够系统。DFTB3/3OB的结果与DFT（B3LYP和PBE）、从头算（MP2、G3B3）以及多种流行的半经验方法（PM6和PDDG）的结果进行了比较，以及与旧参数化（MIO集合）的DFTB3预测结果。总体而言，DFTB3/3OB相较于之前的参数化（DFTB3/MIO）有显著的提升，在大多数测试案例中，也优于PM6和PDDG，尤其在结构性质、振动频率、氢键相互作用和质子亲和力方面。在反应能方面，DFTB3/3OB相较于DFTB3/MIO有显著的改进，这主要归因于原子化能错误的显著降低；与PM6和PDDG相比，DFTB3/3OB通常表现更好，尽管改进的幅度较小。与高级计算相比，DFTB3/3OB在预测几何结构方面最为成功；在能量方面存在较大的误差，但通过使用DFTB3几何结构在高级计算中计算单点能量，可以大幅提高结果。DFTB3/3OB方法存在一些尚未解决的问题，最显著的是在描述涉及磷配位数变化的磷酸水解反应时的困难，为此，特开发了特定参数化（3OB/OPhyd）作为临时解决方案；这表明，当前的DFTB3方法在复杂磷化学领域，特别是在需要详细机制研究精度的层面上，具有有限的迁移性。因此，为了获得一个无需临时参数即可可靠描述磷化学的方法，DFTB3方法需要进行根本性的改进。尽管如此，DFTB3/3OB有望成为研究凝聚相系统中磷/硫化学的量子力学/分子力学（QM/MM）计算中具有竞争力的量子力学方法，尤其是在作为低级方法驱动双水平QM/MM框架中采样方面。