2022/12/26 by Bağcı, A., Aucar, Gustavo A.
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2212.13911
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 (r21-1) 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.