OPERATOR SPECTRUM TRANSFORMATION IN HARTREE–FOCK AND KOHN–SHAM EQUATIONS
- Авторлар: Danshin A.1, Kovalishin A.1
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Мекемелер:
- National Research Center “Kurchatov Institute”
- Шығарылым: Том 509, № 1 (2023)
- Беттер: 23-27
- Бөлім: МАТЕМАТИКА
- URL: https://journals.rcsi.science/2686-9543/article/view/142165
- DOI: https://doi.org/10.31857/S2686954322600598
- EDN: https://elibrary.ru/CQRWAR
- ID: 142165
Дәйексөз келтіру
Аннотация
The paper proposes a method for preliminary transformation of the spectrum of the equation operator both in the Hartree–Fock method and in density functional theory. This method makes it possible to solve a partial eigenvalue problem instead of the complete one, and the eigenfunctions turn out to be ordered in a way convenient for calculation. The transformation makes an old idea of grid approximation of a solution competitive in terms of computational speed as compared to widely used approaches based on basis sets methods.
Негізгі сөздер
Авторлар туралы
A. Danshin
National Research Center “Kurchatov Institute”
Хат алмасуға жауапты Автор.
Email: danshin_aa@nrcki.ru
Russian Federation, Moscow
A. Kovalishin
National Research Center “Kurchatov Institute”
Хат алмасуға жауапты Автор.
Email: kovalishin_aa@nrcki.ru
Russian Federation, Moscow
Әдебиет тізімі
- Hohenberg P., Kohn W. Inhomogeneous Electron Gas // Phys. Rev. 1973. V. 136. P. B864–B871.
- Kohn W., Sham L.J. Self-Consistent Equations Including Exchange and Correlation Effects // Phys. Rev. 1965. V. 140. P. A1133–A1138.
- Kohn W. Nobel Lecture: Electronic structure of matter–wave functions and density functionals // Rev. Mod. Phys. 1999. V. 71. P. 1253–1266.
- Фок В.А. Приближенный способ решения квантовой задачи многих тел // Успехи физических наук. 1967. Т. 93. С. 342–363.
- Pople J.A. Nobel Lecture: Quantum chemical models // Rev. Mod. Phys. 1999. V. 71. P. 1267–1274.
- Payne M.C., Teter M.P., Allan D.C., Arias T.A., Joannopoulos J.D. Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients // Rev. Mod. Phys. 1992. V. 64. P. 1045–1097.
- Kresse G., Furthmuller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set // Phys. Rev. B. 1996. V. 54. P. 11169–11186.
- Koch W., Holthausen M.C. A Chemist’s Guide to Density Functional Theory, 2nd Edition. Wiley-VCH, Weinheim, 2001. 313 p.
- Martin R.M. Electronic Structure: Basic Theory and Practical Methods. Cambridge University Press, 2004. 624 p.
- Beck T.L. Real-space mesh techniques in density-functional theory // Rev. Mod. Phys. 2000. V. 72. P. 1041–1080.
- Torsti T. et al. Three real-space discretization techniques in electronic structure calculations // physica status solidi (b). 2006. V. 243. P. 1016–1053.
- Marques M., Castro A., Bertsch G., Rubio A. octopus: a first-principles tool for excited electron-ion dynamics // Computer Physics Communications. 2003. V. 151. P. 60–78.
- Kronik L. et al. PARSEC – the pseudopotential algorithm for real-space electronic structure calculations: recent advances and novel applications to nano-structures // physica status solidi (b). 2006. V. 243. P. 1063–1079.
- Zhou Y., Saad Y., Tiago M., Chelikowsky J. Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration // Phys. Rev. E. 2006. V. 74. P. 066704.
- Zhou Y., Chelikowsky J., Saad Y. Chebyshev-filtered subspace iteration method free of sparse diagonalization for solving the Kohn-Sham equation // Journal of Computational Physics. 2014. V. 274. P. 770–782.
- Шихов С.Б. Вопросы математической теории реакторов. Линейный анализ. М.: Атомиздат, 1973. 376 с.
- Крянев А.В., Шихов С.Б. Вопросы математической теории реакторов: Нелинейный анализ. М.: Энергоатомиздат, 1983. 280 с.
- Марчук Г.И., Лебедев В.И. Численные методы в теории переноса нейтронов. М.: Атомиздат, 1981. 456 с.
- Самарский А.А., Гулин А.В. Численные методы. М.: Наука, 1989. 432 с.
- Лебедев В.И. Функциональный анализ и вычислительная математика. М.: Физматлит, 2005. 296 с.
- Bunge C.F., Barrientos J.A., Bunge A.V., Cogordan J.A. Hartree-Fock and Roothaan-Hartree-Fock energies for the ground states of He through Xe // Phys. Rev. A. 1992. V. 46. P. 3691–3696.
- Koga T., Tatewaki H., Thakkar A. Roothaan-Hartree-Fock wave functions for atoms with Z54 // Phys. Rev. A. 1993. V. 47. P. 4510–4512.
- Koga T., Thakkar A. Roothaan-Hartree-Fock wave functions for atoms from Cs through U // Phys. Rev. A. 1993. V. 48. P. 4775–4777.