论文标题
关于电子排斥积分的评估
On the Evaluation of the electron repulsion integrals
论文作者
论文摘要
考虑了具有非全能主量子数的Slater型轨道上的电子排斥积分。这些积分可用于多电子系统的非权威主义和相对论计算。它们涉及高几何功能。由于用于定义它们的无限序列的非平凡结构，因此实际上很难计算高几何函数。其系列的收敛性严格取决于参数的值。出现了诸如取消或圆形错误之类的计算问题。与Hyper $ - $几何函数无关的关系，用于coulomb电位$ \ left的期望值（r_ {21}^{ - 1} \ right）$。这些关系是新的，并表明来自拉普拉斯扩张的两范围性质的并发症已消除。这些积分还为具有任意力的电势的期望值构成了初始条件。电子排斥积分由有限系列的功率函数表达。此处给出的电子排斥积分的方法适用于多中心积分。
The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. These integrals are useful in both non-relativistic and relativistic calculations of many-electron systems. They involve hyper-geometric functions. Due to the non-trivial structure of infinite series that are used to define them the hyper-geometric functions are practically difficult to compute. Convergence of their series are strictly depends on the values of parameters. Computational issues such as cancellation or round-off error emerge. Relationships free from hyper$-$geometric functions for expectation values of Coulomb potential $\left(r_{21}^{-1}\right)$ are derived. These relationships are new and show that the complication coming from two-range nature of Laplace expansion for the Coulomb potential is removed. These integrals also form an initial condition for expectation values of a potential with arbitrary power. The electron repulsion integrals are expressed by finite series of power functions. The methodology given here for evaluation of electron repulsion integrals are adapted to multi-center integrals.
