Müller Marcel, Hansen Andreas, Grimme Stefan
Mulliken Center for Theoretical Chemistry, Clausius-Institute for Physical and Theoretical Chemistry, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstraße 4, 53115 Bonn, Germany.
J Chem Phys. 2023 Oct 28;159(16). doi: 10.1063/5.0172373.
Many low-cost or semiempirical quantum mechanical-based electronic structure methods suffer from the use of unpolarized minimal atomic orbital (AO) basis sets. In this work, we overcome this limitation by a fully DFT variationally optimized, adaptive minimal basis set consistently available for the elements up to radon (Z = 86). The new key feature is to make the linear coefficients of the primitive Gaussians in a contracted AO dependent on the effective atomic charge of the atom in the molecule, i.e., each symmetry-unique atom obtains its "own" specifically adapted basis functions. In this way, the physically important "breathing" of the AOs in a molecule with (a) atomic charge (expansion/contraction for anionic/cationic states) and (b) the number of close-lying bonded neighbor atoms is accounted for. The required atomic charges are obtained from a specially developed extended Hückel type Hamiltonian and the coordination numbers from the molecule geometry. Proper analytical derivatives of the resulting adaptive basis functions can easily be derived. Moreover, the basis functions are electric field-dependent, thus improving the description of, e.g., dipole moments and polarizabilities. The new basis set termed q-vSZP (charge dependent valence single-ζ, polarized) is thoroughly benchmarked for atomic/molecular and thermochemical properties compared to standard minimal and double-ζ basis sets at the DFT level with the accurate ωB97X-D4 functional. It is shown that q-vSZP is clearly superior to existing minimal basis sets, often reaching double-ζ quality or even better results. We expect it to be the optimal choice in future semiempirical quantum mechanical methods.
许多基于低成本或半经验量子力学的电子结构方法都存在使用非极化最小原子轨道（AO）基组的问题。在这项工作中，我们通过一种完全基于密度泛函理论（DFT）变分优化的自适应最小基组克服了这一限制，该基组可始终如一地用于直至氡（Z = 86）的元素。新的关键特性是使收缩AO中原始高斯函数的线性系数取决于分子中原子的有效原子电荷，即每个对称唯一的原子都获得其“自己”专门适配的基函数。通过这种方式，考虑了分子中AO随（a）原子电荷（阴离子/阳离子状态下的膨胀/收缩）和（b）相邻紧密键合原子数量的物理上重要的“呼吸”现象。所需的原子电荷从专门开发的扩展休克尔型哈密顿量中获得，配位数从分子几何结构中获得。由此产生的自适应基函数的适当解析导数可以很容易地推导出来。此外，基函数与电场有关，从而改善了例如偶极矩和极化率的描述。与标准最小基组和双ζ基组相比，在DFT水平上使用精确的ωB97X-D4泛函，对新的基组q-vSZP（电荷依赖价单ζ，极化）的原子/分子和热化学性质进行了全面的基准测试。结果表明，q-vSZP明显优于现有的最小基组，常常达到双ζ质量甚至更好的结果。我们预计它将成为未来半经验量子力学方法的最佳选择。
