Direct minimization of Hartree-Fock-Roothaan energy functionals using derivative-free optimization algorithms: a case study on the use of noninteger Slater-type orbitals.
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| Title: | Direct minimization of Hartree-Fock-Roothaan energy functionals using derivative-free optimization algorithms: a case study on the use of noninteger Slater-type orbitals. |
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| Authors: | BAĞCI, Ali1 abagci@pau.edu.tr |
| Source: | Turkish Journal of Physics. 2026, Vol. 50 Issue 3, p148-169. 22p. |
| Subjects: | Simplex algorithm, Atomic models, Heuristic, Radial basis functions, Nonsmooth optimization |
| Abstract: | This study presents an evaluation of derivative-free optimization algorithms for the direct minimization of Hartree-Fock-Roothaan energy functionals involving nonlinear orbital parameters and noninteger-order quantum numbers. The analysis focuses on atomic calculations employing noninteger Slater-type orbitals. Analytic derivatives of the energy functional are not readily available for these orbitals. Four methods are investigated under identical numerical conditions: Powell's conjugate-direction method, the Nelder-Mead simplex algorithm, coordinate-based pattern search, and a model-based algorithm utilizing radial basis functions for surrogate-model construction. Performance analysis is first carried out using the Powell singular function, a well-established test case exhibiting challenging properties, including Hessian singularity at the global minimum. The algorithms are then applied to Hartree-Fock-Roothaan self-consistent-field energy functionals, which define a highly nonconvex optimization landscape due to the nonlinear coupling of orbital parameters. Illustrative examples are provided for closed-shell atomic configurations, specifically the He and Be isoelectronic series, with calculations performed for energy functionals involving up to eight nonlinear parameters. This work presents the first systematic investigation of derivative-free optimization methods for Hartree-Fock-Roothaan energy minimization with noninteger Slater orbitals. [ABSTRACT FROM AUTHOR] |
| Copyright of Turkish Journal of Physics is the property of Scientific and Technical Research Council of Turkey and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194891115 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Direct minimization of Hartree-Fock-Roothaan energy functionals using derivative-free optimization algorithms: a case study on the use of noninteger Slater-type orbitals. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22BAĞCI%2C+Ali%22">BAĞCI, Ali</searchLink><relatesTo>1</relatesTo><i> abagci@pau.edu.tr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Turkish+Journal+of+Physics%22">Turkish Journal of Physics</searchLink>. 2026, Vol. 50 Issue 3, p148-169. 22p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Simplex+algorithm%22">Simplex algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Atomic+models%22">Atomic models</searchLink><br /><searchLink fieldCode="DE" term="%22Heuristic%22">Heuristic</searchLink><br /><searchLink fieldCode="DE" term="%22Radial+basis+functions%22">Radial basis functions</searchLink><br /><searchLink fieldCode="DE" term="%22Nonsmooth+optimization%22">Nonsmooth optimization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study presents an evaluation of derivative-free optimization algorithms for the direct minimization of Hartree-Fock-Roothaan energy functionals involving nonlinear orbital parameters and noninteger-order quantum numbers. The analysis focuses on atomic calculations employing noninteger Slater-type orbitals. Analytic derivatives of the energy functional are not readily available for these orbitals. Four methods are investigated under identical numerical conditions: Powell's conjugate-direction method, the Nelder-Mead simplex algorithm, coordinate-based pattern search, and a model-based algorithm utilizing radial basis functions for surrogate-model construction. Performance analysis is first carried out using the Powell singular function, a well-established test case exhibiting challenging properties, including Hessian singularity at the global minimum. The algorithms are then applied to Hartree-Fock-Roothaan self-consistent-field energy functionals, which define a highly nonconvex optimization landscape due to the nonlinear coupling of orbital parameters. Illustrative examples are provided for closed-shell atomic configurations, specifically the He and Be isoelectronic series, with calculations performed for energy functionals involving up to eight nonlinear parameters. This work presents the first systematic investigation of derivative-free optimization methods for Hartree-Fock-Roothaan energy minimization with noninteger Slater orbitals. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Turkish Journal of Physics is the property of Scientific and Technical Research Council of Turkey and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.55730/1300-0101.2810 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 148 Subjects: – SubjectFull: Simplex algorithm Type: general – SubjectFull: Atomic models Type: general – SubjectFull: Heuristic Type: general – SubjectFull: Radial basis functions Type: general – SubjectFull: Nonsmooth optimization Type: general Titles: – TitleFull: Direct minimization of Hartree-Fock-Roothaan energy functionals using derivative-free optimization algorithms: a case study on the use of noninteger Slater-type orbitals. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: BAĞCI, Ali IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 13000101 Numbering: – Type: volume Value: 50 – Type: issue Value: 3 Titles: – TitleFull: Turkish Journal of Physics Type: main |
| ResultId | 1 |
