Segmented Contracted Error-Consistent Basis Sets of Double- and Triple‑ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations

Segmented contracted
Gaussian basis sets optimized at the one-electron
exact two-component (X2C) level – including a finite size model
for the nucleus – are presented for elements up to Rn. These
basis sets are counterparts for relativistic all-electron calculations
to the Karlsruhe “def2” basis sets for nonrelativistic
(H–Kr) or effective core potential based (Rb–Rn) treatments.
For maximum consistency, the bases presented here were obtained from
the latter by modification and reoptimization. Additionally we present
extensions for self-consistent two-component calculations, required
for the splitting of inner shells by spin–orbit coupling, and
auxiliary basis sets for fitting the Coulomb part of the Fock matrix.
Emphasis was put both on the accuracy of energies of atomic orbitals
and on the accuracy of molecular properties. A large set of more than
300 molecules representing (nearly) all elements in their common oxidation
states was used to assess the quality of the bases all across the
periodic table.

分段收缩型高斯基组：本文报道了在单电子精确二分量（exact two-component, X2C）计算级别下优化得到、且纳入原子核有限尺寸模型的高斯基组，覆盖直至氡（Rn）的所有元素。该基组是相对论全电子计算的对应版本，对应于面向非相对论计算（覆盖H~Kr元素）或基于有效核势（effective core potential, ECP）处理（覆盖Rb~Rn元素）的卡尔斯鲁厄"def2"基组。为保证最高程度的一致性，本文报道的基组通过对上述卡尔斯鲁厄"def2"基组进行修改与重新优化得到。此外，本文还提供了用于自旋轨道耦合引发内壳层劈裂的自洽二分量计算扩展基组，以及用于拟合福克（Fock）矩阵库仑部分的辅助基组。本研究同时兼顾了原子轨道能级精度与分子性质精度两方面的要求。本文采用包含近全部元素常见氧化态的300余种分子组成的大型测试集，对全元素周期表范围内该基组的性能进行了评估。