This work presents the formalism for evaluating molecular SCF equations, adapted to four-component Dirac spinors, which in turn reduce to Slater-type orbitals with non-integer principal quantum numbers in the non-relativistic limit. If Slater-type spinor orbitals are used in the algebraic approximation to solve the Dirac equation, the “catastrophe” previously noted for atomic numbers \(Z>137\), in Dirac equation resolution with a potential corresponding to a point-charge no longer applies. It is observed that, ground-state energy of hydrogen-like atoms reaches the negative-energy continuum \(\left( -mc^2 \right)\) with super-critical nuclear charge \(Z_{c}\), about \(Z_{c}=160\). The difficulty associated with finding relations for molecular integrals over Slater-type spinors which are non-analytic in the sense of complex analysis at \(r = 0\), is eliminated. Unique numerical accuracy is provided by solving the molecular integrals through Laplace expansion of the Coulomb interaction and prolate spheroidal coordinates. New convergent series representation formulae are derived. The technique draws on previous work by the author. The general formalism is presented in this paper.

中文翻译：

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在Dirac–Hartree–Fock方法中，Slater型自旋轨道的优势。具有超临界核电荷的类氢原子的结果

这项工作提出了用于评估分子SCF方程的形式主义，该方程适用于四组分Dirac旋子，这些旋子又被还原为在非相对论范围内具有非整数主量子数的Slater型轨道。如果在代数逼近中使用Slater型自旋轨道来求解Dirac方程，则以前在Dirac方程分辨率中为原子数\（Z> 137 \）记录的“灾难”不再具有与点电荷相对应的电势适用。可以看出，氢原子的基态能量达到了具有超临界核电荷\（Z_ {c} \）的负能量连续体\（\ left（-mc ^ 2 \ right）\），\（Z_ {c} = 160 \）。消除了在Slater型旋子上找到分子积分关系的困难，这种复杂性在\（r = 0 \）的复杂分析意义上是非解析的。通过对库仑相互作用的拉普拉斯展开和长球体坐标求解分子积分，可以提供独特的数值精度。推导了新的收敛级数表示公式。该技术借鉴了作者先前的工作。本文介绍了一般形式主义。