Analytical evaluation of relativistic molecular integrals: III. Computation and results for molecular auxiliary functions

Bağcı, A.; Hoggan, Philip E.

doi:10.1007/s12210-020-00953-3

Cited by 6 publications

(15 citation statements)

References 102 publications

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“…The analytical expression to be used for computation of the Eq. ( 9) based on the vectorization procedure, were suggested explicitly in [27] as,…”

Section: A Convergent Series Representation For Rafmentioning

confidence: 99%

“…( 13) and the Algorithm 1, it is easy to clarify which functions are used in the content of these vectors. In order to store elements of B and L 3 vectors, the derived recurrence relationships in previous paper [27] make it sufficient instead of three or four to use only two sum indices. The Algorithm 1 is accordingly, not for direct computation of the J vector but to properly re−shape and collect all its stored elements.…”

Section: Package Overviewmentioning

confidence: 99%

“…( 18). The symmetry properties found in previous studies [24,26,27] allow avoiding computation of hyper−geometric functions and enable the recurrence relations with only two sum indices to be derived. The derived relationships are also consistent with the vectorization procedure followed as a method in the present study.…”

Section: Package Overviewmentioning

confidence: 99%

“…A computer program based on the analytical methods of computation, described in the previous series of papers [24,26,27] by the author for relativistic molecular auxiliary functions, is presented here. It is unique inasmuch as it is the only computer program code that enables highly accurate calculation of the molecular integrals involving power functions with non−integer exponents.…”

Section: Introductionmentioning

confidence: 99%

“…It has been successful among the enormous number of attempts. The history of non−integer principal quantum number usage comprehensively discussed in [27].…”

Section: Introductionmentioning

confidence: 99%

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JRAF: A Julia Package for Computation of the Relativistic Molecular Auxiliary Functions

Bagci

2021

Preprint

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Evaluation of relativistic molecular integrals over exponential−type spinor orbitals require using the relativistic auxiliary functions in prolate spheroidal coordinates. They have derived recently by the author [Physical Review E 91, 023303 (2015)]. They are used in solution of the molecular Dirac equation for electrons moving around Coulomb potential. A series of papers on a method for fully analytical evaluation of relativistic auxiliary functions in following, published [2, 3, 4]. From the computational physics point of view, these works also demonstrate how to deal with the integrals involve product of power functions with non−integer exponents and incomplete gamma functions. The computer program package to calculate these auxiliary functions in high accuracy is presented. It is designed in Julia programming language. It is capable of yielding highly accurate results for molecular integrals over a wide range of orbital parameters and quantum numbers. Additionally, the program package provides numerous tools such as efficient calculation for the angular momentum coefficients arising in the product of two normalized associated Legendre functions centered on different atomic positions, the rotation angular functions used for both complex and real spherical harmonics. Sample calculations are performed for two−center one−electron integrals over non−integer Slater−type orbitals. The results prove that the package is robust.

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“…The analytical expression to be used for computation of the Eq. ( 9) based on the vectorization procedure, were suggested explicitly in [27] as,…”

Section: A Convergent Series Representation For Rafmentioning

confidence: 99%

Section: Package Overviewmentioning

confidence: 99%

Section: Package Overviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…It has been successful among the enormous number of attempts. The history of non−integer principal quantum number usage comprehensively discussed in [27].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations