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Парадигма конечно-разностного наискорейшего спуска: новый численный метод спектральной задачи Фокиана

Страницы / Pages
90-103

Аннотация

Предложен новый численный метод, объединяющий конечно-раз­ност­ный метод и метод парадигм наискорейшего спуска. Это поз­во­ля­ет избежать деления пространства волновых функций и спиновых пе­ре­менных, что приводит к суперпозиции в стационарных состояниях спи­новой проекции. Подход проверен путем сравнения с традици­онны­ми методами.

Abstract

A new numerical method that unify finite-difference and the method of steepest descent paradigms is suggested. It allows to avoid the wavefuncions spa­ce and spin variables division, that leads to superposition in spin projec­tion stacionary states. The approach is verified by comparison with conven­tio­nal methods.

Список литературы

1. Fock V. An Approximate Method for Solving the Quantum Many-Body Problem // Zs. Phys. 1930. Bd. 61, № 1—2. S. 126—148.

2. Fock V. The Fundamental Significance of Approximate Methods in Theoretical Physics // UFN. 1936. Vol. 16, iss. 8. 1070.

3. Pople J., Gill P., Johnson B. Kohn-Sham density-functional theory within a finite basis set // Chemical Physics Letters. 1992. Vol. 199, iss. 6. P. 557—560.

4. Laaksonen L. Fully numerical Hartree-Fock methods for molecules. Finnish State Computer Center // Computer Physics Reports. 1986. № 4. P. 313—344.

5. Gineityte V. Block Diagonalization Problem for a Fockian Matrix of Molecule and Its Solution by Means of Noncommutative Rayleigh-Schrödinger Perturbation Theory // International Journal of Quantum Chemistry. 1988. Vol. 68. P. 119—127.

6. Shukla A., Dolg M., Stoll H. Wannier-function-based ab initio Hartree-Fock approach extended to polymers: Applications to the LiH chain and trans-polyace­tyle­ne // Phys. Rev. B. 1998. № 58. 4325.

7. Evarestov R. Quantum Chemistry of Solids: The LCAO First Principles Treat­ment of Crystals. Springer, 2007.

8. Griffiths D. Introduction to Quantum Mechanics. Pearson Education, 2005.

9. NIST Atomic Spectra Database Ionization Energies Data. Gaithersburg, MD: NIST, 2009.

10. Marzari N., David D. Vanderbilt. Maximally localized generalized Wannier func­tions for composite energy bands // Phys. Rev. B. 1997. № 56. 12847.

11. Dahl J. Introduction to The Quantum World of Atoms and Molecules. World Scientific Publishing, 2001.

12. Quantum Mechanical ab-initio calculations of the properties of crystalline ma­te­rials. Lecture Notes in Chemistry / ed. by C. Pisam. Springer, 1996.

13. Kobus J. Overview of finite difference Hartree-Fock method algorithm, imple­men­tation and application //AIP Conference Proceedings. 2012. Vol. 1504, iss. 1. 189. doi: 10.1063/1.4771715.

14. Zhendong Fu. Spin Correlations and Excitations in Spin-frustrated Molecular and Molecule-based magnets. Jülich, 2012.

15. Kohn W. Nobel Lecture: Electronic structure of matter—wave functions and density functionals // Rev. Mod. Phys. 1991. № 71. 1253.