Reduced Serially Improved GTOs for Molecular Applications from H to Ar: Efficient Diffuse Functions in Augmented Basis Sets

A new family of Serially
Improved Gaussian-type Orbitals for Molecular
Applications (SIGMA) has been developed for hydrogen to argon and
is available in both standard and augmented versions. This new basis
set features a reduced number of primitive functions compared to the
original SIGMA set and eliminates the constraint of shared exponents
across different angular momentum shells. Its composition is similar
to that of the Dunning correlation-consistent basis sets. In the augmented
version of this novel SIGMA family, termed reduced SIGMA, the diffuse
primitive functions are contracted with others bearing higher exponents,
unlike in the corresponding Dunning sets, where they are added to
the set without contraction. This feature makes the reduced SIGMA
basis sets less susceptible to linear dependencies in large and compact
systems, which is reflected in better convergence of the minimization
process and has a positive impact on energy optimization procedures.
The improved performance of the augmented reduced SIGMA basis sets
over Dunning and other commonly used basis sets is demonstrated through
atomic and molecular calculations at various computational levels
across a broad set of systems.

面向分子应用的系列改进型高斯型轨道（Serially Improved Gaussian-type Orbitals, SIGMA）新家族已开发完成，适用于氢至氩元素，并提供标准型与扩充型两种版本。相较于原始SIGMA基组，该新型基组的原始基函数数量更少，且消除了不同角动量壳层共享指数的约束。其组成与邓宁（Dunning）相关一致基组相似。在该新型SIGMA家族的扩充型版本——即约化SIGMA（reduced SIGMA）中，弥散原始基函数会与高指数基函数进行收缩组合；而在对应的邓宁基组中，弥散基函数仅被直接添加至基组中，无需进行收缩。这一特性使得约化SIGMA基组在大尺寸与紧凑体系中更不易产生线性依赖问题，具体表现为极小化过程的收敛性更优，同时对能量优化程序具有积极作用。相较于邓宁基组与其他常用基组，扩充型约化SIGMA基组的更优性能，已通过覆盖广泛体系的多种计算级别下的原子与分子计算得到验证。