Hartree-Fock Procedure for Some <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ns</mi><mrow><msup><mrow><mi>n</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow><mi>s</mi><mi></mi><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><mrow></mrow><mrow><mn>1</mn></mrow><mrow></mrow><mrow></mrow></mmultiscripts></mrow></math></span> Configurations

C. Froese

doi:10.1103/PhysRev.150.1

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Hartree-Fock Procedure for Some $ns n^{'} s {}^{1}S$ Configurations

C. Froese

Department of Mathematics, University of British Columbia, Vancouver, Canada

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Phys. Rev. 150, 1 – Published 7 October, 1966

DOI: https://doi.org/10.1103/PhysRev.150.1

Abstract

A numerical Hartree-Fock procedure is described for computing wave functions for $ns n^{'} s {}^{1}S$ configurations in which the radial functions for the two $s$ electrons are not assumed to be orthogonal. When the two $s$ electrons are equivalent, this approach corresponds to the unrestricted Hartree-Fock approximation. The procedure was applied to some 2- and 4-electron systems. Results are reported for $1 s 1 s^{'} {}^{1}S$ of He, ${Li}^{+}$ , and ${Be}^{2 +}$ as well as $1 s 1 s^{'} ({}^{1}S) 2 sns {}^{1}S$ , $n = 2, 3, 4$ of Be. The total energies are compared with those of other approximations, and the transition integrals for the unrestricted approximation are shown to differ only slightly from those of the Hartree-Fock approximation.

References (16)

D. Layzer, Z. Horák, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N. Y.) 29, 101 (1964)
D. R. Hartree, The Calculation of Atomic Structure (John Wiley & Sons, Inc., New York, 1957)
V. Fock, Z. Physik 61, 126 (1930)
C. S. Sharma and C. A. Coulson, Proc. Phys. Soc. (London) 80, 81 (1962)
J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Company, Inc., New York, 1960), Vol. II, p. 17
C. Froese, Phys. Rev. 137, A1644 (1965)
C. Froese, Can. J. Phys., 41, 1895 (1963)
E. Trefftz, A. Schlüter, K.-H. Dettmar, and K. Jorgens, Z. Astrophys. 44, 1 (1957)
E. A. Hylleraas, Z. Physik 54, 347 (1929) C. Eckart, Phys. Rev. 36, 878 (1930)
H. Shull and P. O. Löwdin, J. Chem. Phys. 25, 1035 (1956)
R. P. Hurst, J. D. Gray, G. H. Brigman, and F. A. Matsen, Mol. Phys. 1, 189 (1958)
A. L. Stewart, Proc. Phys. Soc. (London) 83, 1003 (1964)
C. A. Coulson, Proc. Phys. Soc. (London) 84, 511 (1964)
C. L. Pekeris, Phys. Rev. 112, 1649 (1948) ibid.115, 1216 (1959)
G. H. Brigman, R. P. Hurst, J. D. Gray, and F. A. Matsen, J. Chem. Phys. 29, 251 (1958)
R. E. Watson, Ann. Phys. (N. Y.) 13, 250 (1961)

[c1] D. Layzer, Z. Horák, M. N. Lewis, and D. P. Thompson, Ann. Phys. (N. Y.) 29, 101 (1964)

[c2] D. R. Hartree, The Calculation of Atomic Structure (John Wiley & Sons, Inc., New York, 1957)

[c3] V. Fock, Z. Physik 61, 126 (1930)

[c4] C. S. Sharma and C. A. Coulson, Proc. Phys. Soc. (London) 80, 81 (1962)

[c5] J. C. Slater, Quantum Theory of Atomic Structure (McGraw-Hill Book Company, Inc., New York, 1960), Vol. II, p. 17

[c6] C. Froese, Phys. Rev. 137, A1644 (1965)

[c7] C. Froese, Can. J. Phys., 41, 1895 (1963)

[c8] E. Trefftz, A. Schlüter, K.-H. Dettmar, and K. Jorgens, Z. Astrophys. 44, 1 (1957)

[c9] E. A. Hylleraas, Z. Physik 54, 347 (1929) C. Eckart, Phys. Rev. 36, 878 (1930)

[c10] H. Shull and P. O. Löwdin, J. Chem. Phys. 25, 1035 (1956)

[c11] R. P. Hurst, J. D. Gray, G. H. Brigman, and F. A. Matsen, Mol. Phys. 1, 189 (1958)

[c12] A. L. Stewart, Proc. Phys. Soc. (London) 83, 1003 (1964)

[c13] C. A. Coulson, Proc. Phys. Soc. (London) 84, 511 (1964)

[c14] C. L. Pekeris, Phys. Rev. 112, 1649 (1948) ibid.115, 1216 (1959)

[c15] G. H. Brigman, R. P. Hurst, J. D. Gray, and F. A. Matsen, J. Chem. Phys. 29, 251 (1958)

[c16] R. E. Watson, Ann. Phys. (N. Y.) 13, 250 (1961)

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Hartree-Fock Procedure for Some $ns n^{'} s {}^{1}S$ Configurations

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Hartree-Fock Procedure for Some nsn′sS1 Configurations

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References (16)

Hartree-Fock Procedure for Some $ns n^{'} s {}^{1}S$ Configurations