On the Evaluation of the electron repulsion integrals

• URL: http://arxiv.org/abs/2212.13911v3
• Date: Wed, 4 Jan 2023 14:28:20 GMT
• Title: On the Evaluation of the electron repulsion integrals
• Abstract summary: The electron repulsion integrals over the Slater-type orbitals with non-integer principal quantum numbers are considered. They are useful in both non-relativistic and relativistic calculations of many-electron systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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