This work presents the formalism for evaluating molecular SCF equations, as 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. The "catastrophe" which emerges for a charge numbers $Z>137$, in solving the Dirac equation with a potential corresponding to a point$-$charge is avoided through using Slater$-$type spinor orbitals in the algebraic approximation. It is observed that, ground$-$state energy of hydrogen$-$like atoms reaches the negative$-$energy continuum $\left(-mc^2 \right)$ while critical nuclear charge $Z_{c}$, about $Z_{c}=160$. The difficulty associated with finding relations for molecular integrals over Slater$-$type spinors which are not$-$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 Coulomb interaction and prolate spheroidal coordinates. New convergent series representation formulae are derived. The technique draws on previous work by the author and the general formalism is presented in this paper.
Combined theory of two- and four- component complete orthonormal sets of spinor wave functions and Slater type spinor orbitals in position, momentum and four-dimensional spaces
Optimizing single Slater determinant for Electronic Hamiltonian with Lagrange multipliers and Newton-Raphson methods as an alternative to ground state calculations via Hartree-Fock self consistent field
Expansion and one-range addition theorems for complete orthonormal sets of spinor wave functions and Slater spinor orbitals of arbitrary half-integral spin in position, momentum and four-dimensional spaces
Use of Combined Hartree-Fock-Roothaan Theory in Evaluation of Lowest States of K [Ar]4s^0 3d^1 and Cr+ [Ar]4s^0 3d^5 Isoelectronic Series Over Noninteger n-Slater Type Orbitals
Combined theory of complete orthonormal sets of quasirelativistic and relativistic sets of wave functions, and Slater orbitals of spin -1/2 particles in position, momentum and four dimensional spaces
Unsymmetrical and symmetrical one-range addition theorems for Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices
Evaluation of potential energy of interaction between molecules using one-range addition theorems for Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials
Straightforward and accurate automatic auxiliary basis set generation for molecular calculations with atomic orbital basis sets
密度拟合（英语：Density fitting，DF），又称恒等式解析（英语：Resolution of the identity，RI），是一种在量子化学计算中广泛使用的技术，使用各种类型的原子基组-高斯型轨道、斯莱特型轨道以及数值原子轨道-来加速密度泛函、哈特里-福克和后哈特里-福克计算。传统上，自定义辅助基组是手工优化每个轨道基组，但是，也有人提出了一些自动方案。在这项工作中，我们提出了一个简单的，但数值稳定的自动化计划，形成辅助基集的帮助下，枢轴Cholesky分解，这是适用于任何类型的原子基函数。我们使用高斯基组进行概念验证计算，证明了该方案，并表明当与至少极化三重$ζ$质量的轨道基组一起使用时，所提出的方法导致W 4 -17测试集的非多参考部分的Hartree-Fock（HF）和二阶Møller-Plesset（MP2）总能量的DF/RI误差可以忽略不计。结果是有前途的未来应用采用斯莱特型轨道或数值原子轨道，以及计划的基础上使用本地拟合方法。也可以使用全局拟合方法，在这种情况下，可以截断由本方案产生的高角动量函数以使计算成本最小化。
Evaluating two-electron-repulsion integrals over arbitrary orbitals using Zero Variance Monte Carlo: Application to Full Configuration Interaction calculations with Slater-type orbitals
Quantum chemistry with Coulomb Sturmians: Construction and convergence of Coulomb Sturmian basis sets at Hartree-Fock level
首次讨论了由指数衰减的库仑Sturmian函数组成的基组，用于模拟电子结构。所提出的基组构造使用其原理、角动量和磁量子数的单独上限来选择库仑Sturmian函数。它们共同的库仑-斯特米安指数被作为第四个参数。在Hartree-Fock水平上研究了第二和第三行原子的基组的收敛性质。因此，重要的基组参数的值和电子结构的物理性质之间的关系被确认。例如，在不受限制的哈特里-福克计算中，角动量量子数的一个异常大的极限可以与这种情况下的球对称破缺联系起来。此外，最佳的，即最小能量，库仑Sturmian指数和平均斯莱特指数值之间的联系得到的Clementi和Raimondi（E。Clementi和D. L. Raimondi，J.Chem.Phys.38，2686（1963））。这些功能的库仑Sturmian基集强调他们的能力，正确地再现物理特性的Hartree-Fock波函数。
Fully numerical calculations on atoms with fractional occupations. Range-separated exchange functionals
最近发展的一种全数值原子结构计算的有限元方法[S. Lehtola，Int. J. Quantum Chem. 119，e25945（2019）]扩展到通过分数占据轨道描述具有球对称密度的原子。专门版本的Hartree-Fock以及局域密度和广义梯度近似密度泛函的开发，允许非常快速的计算在基组限制的地面和低洼的激发态，甚至重原子。还描述了基于Yukawa或互补误差函数（erfc）内核的范围分离的实现，允许现代范围分离混合泛函的整数或分数占用数的完整基组基准。最后，在局域密度或广义梯度近似水平上，计算了原子有效势的叠加原子势方法[S。Lehtola，J. Chem. Theory Comput. 15，1593（2019）]，其已被证明是初始化电子结构计算的简单且有效的方式。本数值方法提供超越microhartree精度与少量的数值基函数，并重现文献结果的基态原子和它们的阳离子$1 \leq Z \leq 86 $。我们的研究结果表明，文献值偏离了10 μEh从完整的基组极限。数值方案的erfc内核的工作比较从大高斯基组计算的结果从文献中。自旋限制基态的报告Hartree-Fock和Hartree-Fock-Slater计算与分数占用$1 \leq Z \leq 118$。
