Bağcı A, Hoggan P E
Institute Pascal, UMR 6602 CNRS, University Blaise Pascal, 24 Avenue des Landais, BP 80026, 63177 Aubiere Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):043301. doi: 10.1103/PhysRevE.92.043301. Epub 2015 Oct 2.
Previous papers by the authors report that they obtained compact, arbitrarily accurate expressions for two-center, one- and two-electron relativistic molecular integrals expressed over Slater-type orbitals. In the present study, accuracy limits of expressions given are examined for three-center nuclear attraction integrals, which are one-electron, three-center integrals with no analytically closed-form expression. In this work new molecular auxiliary functions are used. They are obtained via Neumann expansion of the Coulomb interaction. The numerical global adaptive method is used to evaluate these integrals for arbitrary values of orbital parameters and quantum numbers. Several methods, such as Laplace expansion of Coulomb interaction, single-center expansion, and the Fourier transformation method, have previously been used to evaluate these integrals considering the values of principal quantum numbers in the set of positive integer numbers. This study of three-center integrals places no restrictions on quantum numbers in all ranges of orbital parameters.
作者之前的论文报告称，他们获得了关于斯莱特型轨道上两中心、单电子和双电子相对论分子积分的紧凑且任意精确的表达式。在本研究中，对给定表达式的精度极限进行了检验，这些表达式针对的是三中心核吸引积分，它是单电子、三中心积分，没有解析封闭形式的表达式。在这项工作中使用了新的分子辅助函数。它们是通过库仑相互作用的诺伊曼展开得到的。数值全局自适应方法用于评估这些积分在轨道参数和量子数任意值时的情况。此前曾使用几种方法，如库仑相互作用的拉普拉斯展开、单中心展开和傅里叶变换方法，来评估这些积分，这些方法考虑的是正整数集中的主量子数的值。本研究对三中心积分在轨道参数的所有范围内的量子数没有限制。
