混合斜坡高斯基组对Li-Ne核相关性质的研究：STO-RG和STO-R2G
Mixed ramp-Gaussian basis sets for core-dependent properties: STO-RG and STO-R2G for Li-Ne
摘要：
现代量子化学中使用的传统高斯基组缺乏电子-核尖点，因此难以准确描述核心电子的性质。最近引入的一种新类型的基集，混合斜坡高斯，引入了一个新的原始函数称为斜坡函数，解决了这个问题。本文介绍了三个新的混合斜坡高斯基组- STO-R，STO-RG和STO-R2 G，从斜坡和高斯原始函数的线性组合-这是来自单核zeta斯莱特基组的元素Li到Ne。该推导以与著名的STO- $n$ G基组类似的方式进行。STO-RG基函数的性能优于STO-3G基函数和STO-R2 G优于STO-6 G，无论是在波函数拟合和其他关键量，如单电子能量和电子-核尖点。本文的第二部分对如何通过修改核心基函数将标准的全高斯基函数转换为斜坡高斯基函数进行了初步的研究。使用碳的6- 31 G基组的测试用例，我们确定第二高斯基元在将斜坡高斯核心基函数直接拟合到全高斯核心基函数时比拟合到斯莱特基函数时不那么重要。此外，我们确定了单核zeta的基集，因此在将来应该最直接地转换为混合斜坡高斯基集。
英文摘要：
The traditional Gaussian basis sets used in modern quantum chemistry lack an electron-nuclear cusp, and hence struggle to accurately describe core electron properties. A recently introduced novel type of basis set, mixed ramp-Gaussians, introduce a new primitive function called a ramp function which addresses this issue. This paper introduces three new mixed ramp-Gaussian basis sets - STO-R, STO-RG and STO-R2G, made from a linear combination of ramp and Gaussian primitive functions - which are derived from the single-core-zeta Slater basis sets for the elements Li to Ne. This derivation is done in an analogous fashion to the famous STO-$n$G basis sets. The STO-RG basis functions are found to outperform the STO-3G basis functions and STO-R2G outperforms STO-6G, both in terms of wavefunction fit and other key quantities such as the one-electron energy and the electron-nuclear cusp. The second part of this paper performs preparatory investigations into how standard all-Gaussian basis sets can be converted to ramp-Gaussian basis sets through modifying the core basis functions. Using a test case of the 6-31G basis set for carbon, we determined that the second Gaussian primitive is less important when fitting a ramp-Gaussian core basis function directly to an all-Gaussian core basis function than when fitting to a Slater basis function. Further, we identified the basis sets that are single-core-zeta and thus should be most straightforward to convert to mixed ramp-Gaussian basis sets in the future.
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