Academic Journal
A Bi−directional method for evaluating integrals involving higher transcendental functions. HyperRAF: A Julia package for new hyper−radial functions
| Τίτλος: | A Bi−directional method for evaluating integrals involving higher transcendental functions. HyperRAF: A Julia package for new hyper−radial functions |
|---|---|
| Συγγραφείς: | Bağcı, A., Aucar, G.A. |
| Στοιχεία εκδότη: | Elsevier B.V. |
| Έτος έκδοσης: | 2024 |
| Συλλογή: | Pamukkale University Repository / Pamukkale Üniversitesi Açık Erişim Arşivi |
| Θεματικοί όροι: | Coulomb potential, Bi−directional method, Hyper−radial functions, Laplace expansion, Non−integer Slater−type orbitals, Algebra, Computer programming languages, Electric fields, Electrons, Function evaluation, Laplace transforms, Quantum theory, Bi-directional, Geometric functions, Higher transcendental functions, Hyper−radial function, Laplace expansions, Non−integer slater−type orbital, Radial functions, Slater-type orbitals, Quantum chemistry |
| Περιγραφή: | The electron repulsion integrals over Slater−type orbitals with non−integer principal quantum numbers are investigated. These integrals are useful in both non−relativistic and relativistic calculations of many−electron systems. They involve hyper−geometric functions that are practically difficult to compute. 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. This is achieved by utilizing auxiliary functions represented in finite power series. They serve as essential components in deriving straightforward recurrence relationships for electron repulsion integrals. In the context of computing the expectation values of potentials with arbitrary power, the methodology presented here for evaluation of these integrals forms the initial condition. It is also adapted to multi−center integrals. Program summary: Program Title: HyperRAF CPC Library link to program files: https://doi.org/10.17632/6pbv2y7s42.1 Developer's repository link: https://github.com/abagciphys/HyperRAF.git Licensing provisions: MIT Programming language: Julia Programming Language [1] Supplementary material: An exploratory variant of the software program written in the Mathematica Programming Language [2]. External routines/libraries: Nemo, a computer algebra package for the Julia programming language [3], JRAF, a Julia package for computation of relativistic molecular auxiliary functions [4]. Nature of problem: Definite integrals involving higher transcendental functions given by, fmn1(a,b,x)=xm−1e−bxΓ[n,ax], and fmn2(a,b,x)=xm−1e−bxγ[n,ax] are frequently encountered in atomic physics, with the electron repulsion integral being a notable illustration. For exclusive solutions to these integrals, one can refer to Erdélyi's [5] or Gradshteyn and Ryzhik's [6] books. The solutions are obtained by using the series representation of incomplete gamma ... |
| Τύπος εγγράφου: | article in journal/newspaper |
| Γλώσσα: | English |
| Relation: | Computer Physics Communications; Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı; https://hdl.handle.net/11499/56069; http://dx.doi.org/10.1016/j.cpc.2023.108990; 295; WOS:001111374000001 |
| DOI: | 10.1016/j.cpc.2023.108990 |
| Διαθεσιμότητα: | https://hdl.handle.net/11499/56069 https://doi.org/10.1016/j.cpc.2023.108990 |
| Rights: | none |
| Αριθμός Καταχώρησης: | edsbas.14078FAE |
| Βάση Δεδομένων: | BASE |
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