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Atomic orbitals revisited: generalized hydrogen-like basis sets for 2nd-row elements

机译：重新判断的原子轨道：2个元素的广义氢化基础组

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In the present work, we revisit the problem of atomic orbitals from the positions mostly dictated by semiempirical approaches in quantum chemistry. To construct basis set, having proper nodal structure and simple functional form of orbitals and representing atomic properties with reasonable accuracy, authors propose an Ansatz based on gradual improvement of hydrogen atomic orbitals. According to it, several basis sets with different numbers of variable parameters are considered and forms of orbitals are obtained for the 2nd-row elements either by minimization of their ground state energy (direct problem) or by extracting from atomic spectra (inverse problem). It is shown that so-derived three- and four-parametric basis sets provide accurate description of atomic properties, being, however, substantially provident for computational requirements and, what is more important, simple to handle in analytic models of quantum chemistry. Since the discussed Ansatz allows a generalization for heavier atoms, our results may be considered not only as a solution for light elements, but also as a proof of concept with possible further extension to a wider range of elements.
机译：在目前的工作中，我们重新审视了大多数由量子化学中的半透明方法决定的地点的原子轨道问题。为了构建基础集，具有适当的节点结构和简单的功能形式的轨道，代表具有合理精度的原子特性，作者提出了一种基于氢原子轨道的逐渐改善的Ansatz。根据它，考虑具有不同数量的可变参数的几个基集，并且通过最小化其地位能量（直接问题）或通过从原子谱（逆问题）中提取来获得2nd-行元素的轨道形式。结果表明，所以衍生的三个和四个参数基集提供了原子特性的准确描述，然而，用于计算要求的基本上公积地，更重要的是，在量子化学的分析模型中更重要。由于所讨论的ANSATZ允许较重的原子允许推广，因此我们的结果不仅可以作为光元素的解决方案，而是作为具有可能进一步延伸到更广泛的元件的概念证明。

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