Calculation of the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mmultiscripts><mrow><mi>S</mi></mrow><mprescripts></mprescripts><mrow></mrow><mrow><mn>1</mn></mrow><mrow></mrow><mrow></mrow></mmultiscripts></mrow></math></span> State of the Beryllium Atom in Hylleraas Coordinates

R. F. Gentner; E. A. Burke

doi:10.1103/PhysRev.176.63

Access by Xinjiang University

Calculation of the ${}^{1}S$ State of the Beryllium Atom in Hylleraas Coordinates

R. F. Gentner^*

E. A. Burke^*,†

Department of Physics, Adelphi University, Garden City, New York
Department of Chemistry, St. John's University, Jamaica, New York

Department of Physics, Adelphi University, Garden City, New York
Department of Physics, Brookhaven National Laboratory, Upton, New York

^*Supported in part by U. S. Army Research Office, Durham, North Carolina.
^†Supported by U. S. Atomic Energy Commission.

PDF

Phys. Rev. 176, 63 – Published 5 December, 1968

DOI: https://doi.org/10.1103/PhysRev.176.63

Abstract

The ${}^{1}S$ state of the Be atom is calculated in Hylleraas coordinates using a 25-term single-determinant wave function having the proper spin-angular-momentum symmetry. A ground-state energy of -29.3158 Ry is obtained, as compared with the experimentally observed value of -29.337 Ry and the best Hartree-Fock value of -29.145 96 Ry, indicating that the application of the procedure to larger systems should be fruitful. Suggestions are given to improve the accuracy of the present method and to extend it to atoms of higher atomic number. Solutions of the integrals and procedures for manipulating them in storage are presented.

References (33)

A. W. Weiss, Phys. Rev. 122, 1826 (1961)
C. Schwartz, Phys. Rev. 126, 1015 (1962)
Oktay Sinanoğlu, Phys. Rev. 122, 493 (1960)
L. Szasz, Z. Naturforsch. 14a, 1014 (1959) ibid.15a, 909 (1960) J. Chem. Phys. 35, 1072 (1961) Phys. Rev. 126, 169 (1962) J. Math. Phys. 3, 1147 (1962) Phys. Rev. 132, 936 (1963) Z. Naturforsch. 22, 2109 (1967)
E. A. Hylleraas, Z. Physik 54, 347 (1929)
T. Kinoshita, Phys. Rev. 105, 1490 (1957) ibid.115, 336 (1959)
C. L. Pekeris, Phys. Rev. 112, 1649 (1958) ibid.115, 1216 (1959)
H. M. James and A. S. Coolidge, Phys. Rev. 49, 688 (1936)
H. M. James and A. S. Coolidge, Phys. Rev. 55, 873 (1939)
E. A. Burke, Phys. Rev. 130, 1871 (1963)
K. F. Berggren and R. F. Wood, Phys. Rev. 130, 198 (1963)
V. H. Smith, Jr., and S. Larsson, Uppsala University Quantum Chemistry Group Technical Report No. 186, 1967 (unpublished)
R. K. Nesbet, Phys. Rev. 155, 51 (1967)
[8]
S. S. Kuo, Numerical Methods and Computers (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965), Chap. 9
Atomic Energy Levels, National Bureau of Standards Circular No. 467, edited by C. E. Moore (U. S. Government Printing Office, Washington, D. C., 1949), Vol. 1 C. W. Scherr, J. N. Silverman, and F. A. Matsen, Phys. Rev. 127, 830 (1962)
C. C. J. Roothaan, L. M. Sachs, and A. W. Weiss, Rev. Mod. Phys. 32, 186 (1960)
S. F. Boys, Proc. Roy. Soc. (London) A217, 136 (1953)
V. V. Kibartas, V. I. Kavetskis, and A. P. Iutsis, Zh. Eksperim. i Teor. Fiz. 29, 623 (1955) [English transl.: Soviet Phys. — JETP 2, 481 (1956)]
R. E. Watson, Phys. Rev. 119, 170 (1960)
A. Kotchoubey and L. H. Thomas, J. Chem. Phys. 45, 3342 (1966)
H. P. Kelly, Phys. Rev. 131, 684 (1963) ibid.136, B896 (1964)
D. F. Tuan and O. Sinanoğlu, J. Chem. Phys. 41, 2677 (1964)
M. Geller, H. S. Taylor, and H. B. Levine, J. Chem. Phys. 43, 1727 (1965)
O. Sinanoğlu and E. Mortenson, J. Chem. Phys. 34, 1078 (1961)
L. Szasz and J. Byrne, Phys. Rev. 158, 34 (1967)
J. Linderberg and H. Shull, J. Mol. Spectry 5, 1 (1960)
Omitted endnote
Y. Öhrn and J. Nordling, J. Chem. Phys. 39, 1864 (1963)
H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (John Wiley & Sons, Inc., New York, 1944), p. 369
E. A. Burke, J. Math. Phys. 6, 1691 (1965)
R. A. Bonham, J. Mol. Spectry 15, 112 (1965)
P. J. Roberts, Proc. Phys. Soc. (London) 88, 53 (1966)

[c1] A. W. Weiss, Phys. Rev. 122, 1826 (1961)

[c2] C. Schwartz, Phys. Rev. 126, 1015 (1962)

[c3] Oktay Sinanoğlu, Phys. Rev. 122, 493 (1960)

[c4] L. Szasz, Z. Naturforsch. 14a, 1014 (1959) ibid.15a, 909 (1960) J. Chem. Phys. 35, 1072 (1961) Phys. Rev. 126, 169 (1962) J. Math. Phys. 3, 1147 (1962) Phys. Rev. 132, 936 (1963) Z. Naturforsch. 22, 2109 (1967)

[c5] E. A. Hylleraas, Z. Physik 54, 347 (1929)

[c6] T. Kinoshita, Phys. Rev. 105, 1490 (1957) ibid.115, 336 (1959)

[c7] C. L. Pekeris, Phys. Rev. 112, 1649 (1958) ibid.115, 1216 (1959)

[c8] H. M. James and A. S. Coolidge, Phys. Rev. 49, 688 (1936)

[c9] H. M. James and A. S. Coolidge, Phys. Rev. 55, 873 (1939)

[c10] E. A. Burke, Phys. Rev. 130, 1871 (1963)

[c11] K. F. Berggren and R. F. Wood, Phys. Rev. 130, 198 (1963)

[c12] V. H. Smith, Jr., and S. Larsson, Uppsala University Quantum Chemistry Group Technical Report No. 186, 1967 (unpublished)

[c13] R. K. Nesbet, Phys. Rev. 155, 51 (1967)

[c14] [8]

[c15] S. S. Kuo, Numerical Methods and Computers (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1965), Chap. 9

[c16] Atomic Energy Levels, National Bureau of Standards Circular No. 467, edited by C. E. Moore (U. S. Government Printing Office, Washington, D. C., 1949), Vol. 1 C. W. Scherr, J. N. Silverman, and F. A. Matsen, Phys. Rev. 127, 830 (1962)

[c17] C. C. J. Roothaan, L. M. Sachs, and A. W. Weiss, Rev. Mod. Phys. 32, 186 (1960)

[c18] S. F. Boys, Proc. Roy. Soc. (London) A217, 136 (1953)

[c19] V. V. Kibartas, V. I. Kavetskis, and A. P. Iutsis, Zh. Eksperim. i Teor. Fiz. 29, 623 (1955) [English transl.: Soviet Phys. — JETP 2, 481 (1956)]

[c20] R. E. Watson, Phys. Rev. 119, 170 (1960)

[c21] A. Kotchoubey and L. H. Thomas, J. Chem. Phys. 45, 3342 (1966)

[c22] H. P. Kelly, Phys. Rev. 131, 684 (1963) ibid.136, B896 (1964)

[c23] D. F. Tuan and O. Sinanoğlu, J. Chem. Phys. 41, 2677 (1964)

[c24] M. Geller, H. S. Taylor, and H. B. Levine, J. Chem. Phys. 43, 1727 (1965)

[c25] O. Sinanoğlu and E. Mortenson, J. Chem. Phys. 34, 1078 (1961)

[c26] L. Szasz and J. Byrne, Phys. Rev. 158, 34 (1967)

[c27] J. Linderberg and H. Shull, J. Mol. Spectry 5, 1 (1960)

[c28] Omitted endnote

[c29] Y. Öhrn and J. Nordling, J. Chem. Phys. 39, 1864 (1963)

[c30] H. Eyring, J. Walter, and G. E. Kimball, Quantum Chemistry (John Wiley & Sons, Inc., New York, 1944), p. 369

[c31] E. A. Burke, J. Math. Phys. 6, 1691 (1965)

[c32] R. A. Bonham, J. Mol. Spectry 15, 112 (1965)

[c33] P. J. Roberts, Proc. Phys. Soc. (London) 88, 53 (1966)

Physical Review Journals Archive

Export citation

Export citation

Calculation of the ${}^{1}S$ State of the Beryllium Atom in Hylleraas Coordinates

Abstract

References (33)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Calculation of the S1 State of the Beryllium Atom in Hylleraas Coordinates

Abstract

References (33)

Calculation of the ${}^{1}S$ State of the Beryllium Atom in Hylleraas Coordinates