Dirac方程中分子三中心积分的基准值
Benchmark values for molecular three-center integrals arising in the Dirac equation
摘要：
作者在他们以前的论文中得到了紧凑的，任意精确的表达式，两个中心的单电子和双电子相对论分子积分表示Slater型轨道。本文研究了三中心核引力积分的精确极限，这类积分是第一个不具有解析封闭形式关系的积分集。它们通过新的分子辅助函数表示，通过库仑相互作用的诺依曼展开。数值全局自适应方法被用来计算这些积分的任意值的轨道参数，量子数。采用库仑相互作用的拉普拉斯展开、单中心展开、傅里叶变换等方法，计算了主量子数在正整数集合中的取值。这是第一次尝试在不限制量子数的条件下，研究三中心积分在所有轨道参数范围内的性质。
英文摘要：
The authors in their previous papers obtained compact, arbitrarily accurate expressions for two-center one- and two-electron relativistic molecular integrals expressed over Slater-type orbitals. In this present study, the accuracy limits of given expressions is examined for three-center nuclear attraction integrals, which are the first integral set do not have analytically closed form relations. They are expressed through new molecular auxiliary functions obtained via Neumann expansion of Coulomb interaction. The numerical global adaptive method is used to evaluate these integrals for arbitrarily values of orbital parameters, quantum numbers. Several methods, such as Laplace expansion of Coulomb interaction, single-center expansion, Fourier transformation method, have been performed in order to evaluate these integrals considering the values of principal quantum numbers in the set of positive integer numbers. This is the first attempts to study the three-center integrals without any restrictions on quantum numbers and in all ranges of orbital parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
