Method of local-scaling transformations and density-functional theory in quantum chemistry
Ivan Zh. Petkov
Institute of Nuclear Research and Nuclear Energy, Sofia 13, Bulgaria
Search for more papers by this authorMario V. Stoitsov
Institute of Nuclear Research and Nuclear Energy, Sofia 13, Bulgaria
Search for more papers by this authorCorresponding Author
Eugene S. Kryachko
Institute of Theoretical Physics, Kiev, USSR 252130
Institute of Theoretical Physics, Kiev, USSR 252130Search for more papers by this authorIvan Zh. Petkov
Institute of Nuclear Research and Nuclear Energy, Sofia 13, Bulgaria
Search for more papers by this authorMario V. Stoitsov
Institute of Nuclear Research and Nuclear Energy, Sofia 13, Bulgaria
Search for more papers by this authorCorresponding Author
Eugene S. Kryachko
Institute of Theoretical Physics, Kiev, USSR 252130
Institute of Theoretical Physics, Kiev, USSR 252130Search for more papers by this authorAbstract
The method of local-scaling transformations is developed with a view to applications of the nonrelativistic quantum mechanical variational principle in quantum chemistry. Some properties of local-scaling transformations are studied. The method presented links local-scaling transformations and one-electron densities via the ordinary differential equation that provides a proof of the theorem on the existence of the energy density functional within any given orbit and its universality in a sense of the general theory of ordinary differential equations, and allows the construction of this functional explicitly.
Bibliography
- 1 K. B. Wolf, Rev. Mex. Fis. 22, 45 (1973).
- 2 R. F. W. Bader and T. T. Nguyen-Dang, Advances in Quantum Chemistry, P.-O. Löwdin, Ed. (Academic, New York, 1981), vol. 14, p. 63.
- 3 E. A. Hylleraas, Z. Phys. 54, 347 (1929); Z. Phys. 65, 209 (1930).
- 4
V. Fock,
Z. Phys.
63, 855
(1930).
10.1007/BF01339281 Google Scholar
- 5 J. C. Slater, J. Chem. Phys. 1, 687 (1933).
- 6 P.-O. Löwdin, in Proceedings of Nikko Symposium on Molecular Physics, Maruzen, Tokyo, 1954 (unpublished) p. 116.
- 7 G. G. Hall, Proc. Phys. Soc. London 75, 575 (1960).
- 8 S. T. Epstein and J. O. Hirschfelder, Phys. Rev. 123, 1495 (1961).
- 9 S. T. Epstein, A. C. Hurley, R. E. Wyatt, and R. G. Parr, J. Chem. Phys. 47, 1275 (1967).
- 10 C. A. Coulson and J. C. Nash, J. Phys. B 7, 657 (1974).
- 11 P.-O. Löwdin, J. Mol. Spectrosc. 3, 46 (1959).
- 12 M. S. Gopinathan, Int. J. Quantum Chem. 10, 975 (1976).
- 13 G. Hunter, J. Chem. Phys. 64, 3213 (1976).
- 14 S. Wilson, J. Phys. B 12, L599 (1979).
- 15 B. Simon, Phys. Lett. 71A, 211 (1979).
- 16 R. Gáspár, Int. J. Quantum Chem. 23, 1017 (1983).
- 17 E. S. Kryachko, Int. J. Quantum Chem. 25, 637 (1984).
- 18
E. S. Kryachko,
in Local Density Approximation in Quantum Chemistry and Solid State Physics,
J. P. Dahl and
J. Avery, Eds.
(Plenum, New York,
1984),
p. 207.
10.1007/978-1-4899-2142-0_11 Google Scholar
- 19 I. Zh. Petkov and M. V. Stoitsov, JINR Preprint P4–82–349, JINR, Dubna, 1982; Teor. Mat. Fiz. 55, 407 (1983).
- 20 I. Zh. Petkov and M. V. Stoitsov, JINR Preprint P4–82–385, JINR, Dubna, 1982; Yad. Fiz. 37, 1167 (1983).
- 21 I. Zh. Petkov and M. V. Stoitsov, JINR Preprint E4–83–282, JINR, Dubna, 1983; M. V. Stoitsov, JINR Preprint P4–82–418, JINR, Dubna, 1982.
- 22 P. Hohenberg and W. Kohn, Phys. Rev. 136B, 864 (1964).
- 23 S. T. Epstein, The Variational Method in Quantum Chemistry (Academic, New York, 1974).
- 24
N. M. Witriol,
Int. J. Quantum Chem. Symp.
6, 145
(1972).
10.1002/qua.560060616 Google Scholar
- 25 L. S. Pontrjagin, Ordinary Differential Equations (Nauka, Moscow, 1974).
- 26 T. L. Gilbert, Phys. Rev. B 12, 2111 (1975).
- 27 J. E. Harriman, Phys. Rev. A 24, 680 (1981).
- 28 E. V. Ludeña, J. Chem. Phys. 79, 6174 (1983).
- 29 E. S. Kryachko, Int. J. Quantum Chem. 18, 1029 (1980).
- 30 V. Mikolas and A. Tomaśek, Phys. Lett. 64A, 109 (1977).
- 31 M. Levy, Proc. Nat. Acad. Sci. U.S.A. 76, 6062 (1979).
- 32 K. Freed and M. Levy, J. Chem. Phys. 77, 396 (1982).
- 33 S. M. Valone, J. Chem. Phys. 73, 4653 (1980).
- 34 T. Kato, Commun. Pure Appl. Math. 10, 151 (1957).
- 35 E. H. Lieb, Int. J. Quantum Chem. 24, 243 (1983).
- 36 E. S. Kryachko, I. Zh. Petkov, and M. V. Stoitsov, ITP Preprint ITP-84–109R, ITP, Kiev, 1984; Acta Cryst. A (to be published). I. Zh. Petkov, M. V. Stoitsov, and E. S. Kryachko, Ukrainian Fiz. J. (in press).
