Advantages of Slater-type spinor orbitals in the Dirac–Hartree–Fock method. Results for hydrogen-like atoms with super-critical nuclear charge

Bağcı, A.

doi:10.1007/s12210-020-00899-6

Cited by 7 publications

(4 citation statements)

References 93 publications

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“…The additional computer program code written for the molecular integrals [Eqs. (28−30)] is based on the formulas given in [9,25]. The results show that code presented in this study for the relativistic auxiliary functions based on the analytical method via the series representation of the beta functions allows arbitrary precision floating point calculations.…”

Section: Resultsmentioning

confidence: 89%

“…Dropping the restriction on principal quantum number leads to new features [9,25,27] (see also references therein) and wide range of application in physics and chemistry. The analytical method used for computation of molecular auxiliary functions is of course open for improvement.…”

Section: Resultsmentioning

confidence: 99%

“…The above procedure by the author improved to a general set of functions where the parameters are free from any restriction [14]. A symmetry feature for two−center two−electron molecular integrals that pointed out and identified by a criterion in [24,25], eliminates the necessity for immediate expansion for incomplete gamma functions or using the relations for the normalized complementary incomplete and the normalized incomplete gamma functions as [20,22] cause some restrictions for the set of functions to be used.…”

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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Section: Resultsmentioning

confidence: 89%

Section: Resultsmentioning

confidence: 99%

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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“…Note that the domain for the integrals given in this form of molecular auxiliary functions is more advantageous in terms of numerical calculations. The Riemann-Liouville type integrals may be derived via the equation (78). Similarly to the equation ( 77) we change the ξ variable this time, to:…”

Section: Relationship Between Riemann-liouville Type Integrals and Re...mentioning

confidence: 99%

Complete and orthonormal sets of exponential-type orbitals with non-integer quantum numbers

Bağcı

Hoggan

2023

J. Phys. A: Math. Theor.

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Atomic and molecular orbitals show exponential decrease at long range. Complete orthonormal basis sets for atoms should satisfy this criterion. A number of such bases have been used in physics (e.g. Coulomb Sturmians). The challenge of this work is first adapting Slater type Orbitals for this role, as they are not radially orthogonal. Even more important is their generalisation to non-integer quantum numbers that have applications for configuration interaction (CI). This generalisation requires the whole apparatus of non-integer calculus that is presented using the Riemann-Liouville approach.

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Are B functions with nonintegral orders a computationally useful basis set?

Weniger

2021

New Electron Correlation Methods and Their Applications, and Use of Atomic Orbitals With Exponential Asymptotes

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Advantages of Slater-type spinor orbitals in the Dirac–Hartree–Fock method. Results for hydrogen-like atoms with super-critical nuclear charge

Cited by 7 publications

References 93 publications

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

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

Complete and orthonormal sets of exponential-type orbitals with non-integer quantum numbers

Are B functions with nonintegral orders a computationally useful basis set?

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