- Access by Xinjiang University
Atomic Bethe-Goldstone Equations. III. Correlation Energies of Ground States of Be, B, C, N, O, F, and Ne
Phys. Rev. 175, 2 – Published 5 November, 1968
DOI: https://doi.org/10.1103/PhysRev.175.2
Abstract
A variational formulation of Brueckner's theory has been used to solve Bethe-Goldstone equations and to compute electronic pair-correlation energies for the atoms listed in the title. One-electron effective correlation energies, needed for open-shell atomic states, are also computed. An approximate Hartree-Fock function is used for the reference state in each case. Individual pair-correlation energies are computed to an expected accuracy of 0.001 Hartree a.u. The total correlation energies range from 98.5 to 100.3% of the empirical correlation energy. For comparison with many-particle perturbation theory, definitions of the hierarchy of -order Bethe-Goldstone equations and of the concepts of gross and net mean-value increments used in this work are restated in terms of linked Goldstone diagrams.
See Also
Atomic Bethe-Goldstone Equations. I. The Be Atom
References (44)
- K. A. Brueckner, Phys. Rev. 96, 508 (1954) ibid.97, 1353 (1955) ibid.100, 36 (1955) The Many-Body Problem, edited by B. deWitt (John Wiley & Sons, Inc., New York, 1959), pp. 47-241
- K. M. Watson, Phys. Rev. 89, 575 (1953)
- H. A. Bethe and J. Goldstone, Proc. Roy. Soc. (London) A238, 551 (1957)
- J. Goldstone, Proc. Roy. Soc. (London) A239, 267 (1957)
- D. J. Thouless, The Quantum Mechanics of Many-Body Systems (Academic Press Inc., New York, 1961)
- K. Kumar, Perturbation Theory and the Nuclear Many Body Problem (Interscience Publishers, Inc., New York, 1962)
- W. Brenig, Nuc. Phys. 4, 363 (1957)
- L. S. Rodberg, Ann. Phys. (N. Y.) 2, 199 (1957)
- R. K. Nesbet, Phys. Rev. 109, 1632 (1958)
- L. C. Gomes, J. D. Walecka, and V. F. Weisskopf, Ann. Phys. (N. Y.) 3, 241 (1958)
- R. Brout, Phys. Rev. 111, 1324 (1958)
- L. Szasz, Z. Naturforsch. 14a, 1014 (1959)
- V. A. Fock, M. H. Veselov, and M. E. Petrashen, Zh. Eksperim. i Teor. Fiz. 10, 723 (1940)
- R. K. Nesbet, Advan. Chem. Phys. 9, 321 (1965)
- O. Sinanoǧlu, J. Chem. Phys. 36, 706, 3198 (1962) Advan. Chem. Phys. 6, 315 (1964)
- M. Geller, H. S. Taylor, and H. B. Levine, J. Chem. Phys. 43, 1727 (1965)
- D. F. Tuan and O. Sinanoǧlu, J. Chem. Phys. 41, 2677 (1964)
- R. K. Nesbet, in Quantum Theory of Atoms, Molecules, and the Solid State, edited by P.-O. Löwdin (Academic Press Inc., New York, 1966), pp. 157-165 Colloq. Intern. Centre Nat. Rech. Sci., Paris 164, 87-94 (1967) to be published
- R. K. Nesbet, Phys. Rev. 155, 51 (1967)
- R. K. Nesbet, Phys. Rev. 155, 56 (1967)
- H. P. Kelly, Phys. Rev. 131, 684 (1963) ibid.136, B896 (1964) Perturbation Theory and its Applications in Quantum Mechanics, edited by C. H. Wilcox (John Wiley & Sons, Inc., New York, 1966), pp. 215-141 Universit of California Radiation Laboratory Technical Report No. UCRL-10971, 1962 (unpublished)
- H. P. Kelly, Phys. Rev. 144, 39 (1966)
- R. K. Nesbet, Proc. Roy. Soc. (London) A230, 312 (1955) Rev. Mod. Phys. 33, 28 (1961)
- H. A. Bethe, Phys. Rev. 138, B804 (1965)
- R. Rajaraman and H. A. Bethe, Rev. Mod. Phys. 39, 745 (1967)
- R. K. Nesbet, in Advances in Quantum Chemistry, edited by P. -O. Löwdin (Academic Press Inc., New York, 1967), pp. 1-24 M. Krauss, National Bureau of Standards Technical Note No. 438 (1967)
- E. Clementi, J. Chem. Phys. 38, 2780 (1963) ibid.39, 487 (1963)
- R. K. Nesbet, J. Chem. Phys. 36, 1518 (1962) A. D. McLean, ibid. 39, 2653 (1963) K. D. Carlson and P. N. Skancke, ibid. 40, 613 (1964) R. K. Nesbet, ibid. 43, S30 (1965)
- R. K. Nesbet, J. Chem. Phys. 40, 3619 (1964)
- G. Verhaegen, W. G. Richards, and C. M. Moser, J. Chem. Phys. 47, 2595 (1967)
- R. K. Nesbet, Rev. Mod. Phys. 35, 552 (1963)
- R. K. Nesbet, J. Chem. Phys. 43, 311 (1965)
- C. C. J. Roothaan, Rev. Mod. Phys. 23, 69 (1951)
- E. Clementi, J. Chem. Phys. 40, 1944 (1964)
- A. Veillard and E. Clementi, IBM Technical Report No. RJ447, 1967 (unpublished) E. Clementi, J. Chem. Phys. 38, 2248 (1963)
- V. McKoy and O. Sinanoǧlu, J. Chem. Phys. 41, 2689 (1964)
- E. Clementi and A. Veillard, J. Chem. Phys. 44, 3050 (1966)
- I. I. Glembotskii, V. V. Kibartas, and A. P. Iutsis, Zh. Eksperim. i Teor. Fiz. 29, 617 (1955) [English transl.: Soviet Phys.—JETP 2, 476 (1956)]
- J. Hinze and C. C. J. Roothaan, Progr. Theoret. Phys. (Kyoto) 40, 37 (1967)
- P. S. Bagus and C. M. Moser, Phys. Rev. 167, 13 (1968)
- H. F. Schaefer, III, and F. E. Harris, Phys. Rev. 167, 67 (1968)
- A. P. Iutsis, Ya. I. Vizbaraite, T. D. Strotskite, and A. A. Bandzaitis, Opt. i Spektroskopiya 12, 157 (1962) [English transl.: Opt. Spectry. (USSR) 12, 83 (1962)]
- R. K. Nesbet, Phys. Rev. 100, 228 (1955) ibid.109, 1632 (1958) L. Szasz, ibid. 132, 936 (1963)
- S. F. Boys, Proc. Roy. Soc. (London) A217, 235 (1953)