Core Polarization and Hyperfine Structure of the B, C, N, O, and F Atoms

William A. Goddard, III

doi:10.1103/PhysRev.182.48

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Core Polarization and Hyperfine Structure of the B, C, N, O, and F Atoms

William A. Goddard, III^*

Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91109

^*Alfred P. Sloan Research Fellow.

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Phys. Rev. 182, 48 – Published 5 June, 1969

DOI: https://doi.org/10.1103/PhysRev.182.48

Abstract

Calculations on the hyperfine-splitting constants for the atoms B, C, N, O, and F have been carried out by both the unrestricted Hartree-Fock (UHF) method and a method corresponding to optimizing the orbitals of a Slater determinant after spin projection (the GF method). This is equivalent to one form of Löwdin's extended Hartree-Fock method. These calculations account for core-polarization contributions to the spin density but not for any significant part of the electron correlation. It is found that the core-polarization term is significantly larger (for N about 65% larger) than the experimental value, indicating that the remaining correlation effects significantly decrease the magnitude of the spin density at the nucleus.

Since these calculations used analytic expansions, an extensive set of basis sets was examined in order to determine what type of basis set is required in order to obtain accurate values for various properties.

On the basis of these calculations and the observed hyperfine structure, we obtain a magnetic moment (in nuclear magnetons) of $μ_{N} = \pm 0.97$ for ${}^{11}C$ and electric quadrupole moments (in barns) of $Q = 0.037$ for ${}^{11}B$ , $Q = 0.031$ for ${}^{11}C$ (assuming $μ_{N}$ for ${}^{11}C$ to be negative), and $Q = - 0.025$ for ${}^{17}O$ .

References (64)

S. M. Blinder, Advan. Quantum. Chem. 2, 47 (1965)
A. J. Freeman and R. E. Watson, in Magnetism, edited by G. T. Rado and H. Suhl (Academic Press, Inc., New York, 1965), Vol. IIA, p. 167
B. Bleaney, in Hyperfine Interactions, edited by A. J. Freeman and R. B. Frankel (Academic Press, Inc., New York, 1967), p. 1
R. E. Watson and A. J. Freeman, in Hyperfine Interactions, edited by A. J. Freeman and R. B. Frankel (Academic Press, Inc., New York 1967) p. 53
C. M. Moser, in Hyperfine Interactions, edited by A. J. Freeman and R. B. Frankel (Academic Press, Inc., New York, 1967) p. 95
A. Abragam, J. Horowitz, and M. H. L. Pryce, Proc. Roy. Soc. (London) A230, 169 (1955)
G. W. Pratt, Jr., Phys. Rev. 102, 1303 (1956)
V. Heine, Phys. Rev. 107, 1002 (1957) J. H. Wood and G. W. Pratt, ibid. 107, 995 (1957) M. H. Cohen, D. A. Goodings, and V. Heine, Proc. Phys. Soc. (London) 73, 811 (1959)
R. E. Watson and A. J. Freeman, Phys. Rev. 120, 1125 (1960) J. Appl. Phys. 32, 118S (1961) D. A. Goodings and V. Heine, Phys. Rev. Letters 5, 370 (1960)
L. M. Sachs, Phys. Rev. 117, 1504 (1960)
D. A. Goodings, Phys. Rev. 123, 1706 (1961)
N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. 124, 1124 (1961)
N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. 128, 213 (1962)
N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. 130, 1441 (1963)
N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. Mod. Phys. 35, 548 (1963)
N. Bessis et al. Phys. Rev. 135, A588 (1964)
Omitted endnote
P. O. Löwdin, Advan. Chem. Phys. 2, 207 (1959)
([12–16])
W. Marshall, Proc. Phys. Soc. (London) 78, 113 (1961)
P. O. Löwdin, Phys. Rev. 97, 1509 (1955)
P. O. Löwdin, in Quantum Theory of Atoms, Molecules and Solid-State (Academic Press, Inc., New York, 1966) p. 601
W. A. Goddard III, Phys. Rev. 157, 81 (1967)
W. A. Goddard III, J. Chem. Phys. 48, 450 (1968)
W. A. Goddard III, Phys. Rev. 157, 93 (1967)
W. A. Goddard III, Phys. Rev. 176, 106 (1968)
W. A. Goddard III, J. Chem. Phys. 48, 5337 (1968)
C. C. J. Roothaan, Rev. Mod. Phys. 23, 69 (1951)
Omitted endnote
Omitted endnote
E. Clementi and D. L. Raimonde, J. Chem. Phys. 38, 2686 (1963) E. Clementi, 40, 1944 (1964) [IBM Technical Report No. RJ-256, 1963 (unpublished)] P. S. Bagus, T. L. Gilbert, H. D. Cohen, and C. C. J. Roothaan, to be published E. Clementi, C. C. J. Roothaan, and M. Yoshimine, Phys. Rev. 127, 1618 (1962) N. Bessis, H. Lefebvre-Brion, and C. M. Moser, [11–15]
Omitted endnote
Omitted endnote
C. C. J. Roothaan and P. S. Kelly, Phys. Rev. 131, 1177 (1963)
Omitted endnote
Omitted endnote
Omitted endnote
Omitted endnote
P. S. Bagus and B. Liu, Phys. Rev. 148, 79 (1966)
Omitted endnote
[S. Huzinaga, J. Chem. Phys. 42, 1293 (1965)]
Omitted endnote
J. S. M. Harvey, Proc. Roy. Soc. (London) A285, 581 (1965)
Omitted endnote
H. F. Schaefer III, R. A. Klemm, and F. E. Harris, Phys. Rev., 176, 49 (1968)
R. A. Haberstroh, W. J. Kossler, O. Ames, and D. R. Hamilton, Phys. Rev. 136, B932 (1964)
G. Wessel, Phys. Rev. 92, 1581 (1953)
R. M. Sternheimer, Phys. Rev. 164, 10 (1967)
S. M. Blinder, Bull. Am. Phys. Soc. 5, 14 (1960)
T. P. Das and A. Mukherjee, J. Chem. Phys. 33, 1808 (1960)
Omitted endnote
R. K. Nesbet, in La Structure Hyperfine Magnétique des Atomes et des Molécules (Centre National de la Recherche Scientifique, Paris, 1967), p. 87
U. Kaldor, J. Chem. Phys. 49, 6 (1968)
S. Larsson, Phys. Rev. 169, 49 (1968)
S. Lunell, Phys. Rev. 173, 85 (1968)
R. C. Ladner and W. A. Goddard, J. Chem. Phys. (to be published)
W. A. Goddard III, Phys. Rev. 157, 73 (1967)
Omitted endnote
([24])
D. E. Rutherford, Substitutional Analysis (Edinburgh University Press, London, 1948)
Omitted endnote
N. F. Ramsey, Molecular Beams (Oxford University Press, London, 1956), p. 172
E. R. Cohen and J. W. M. Dumond, Rev. Mod. Phys. 37, 537 (1965)
B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill Book Co., Inc., New York, 1963) V. Heine, Group Theory in Quantum Mechanics (Pergamon Press, Ltd., New York, 1960)

[c1] S. M. Blinder, Advan. Quantum. Chem. 2, 47 (1965)

[c2] A. J. Freeman and R. E. Watson, in Magnetism, edited by G. T. Rado and H. Suhl (Academic Press, Inc., New York, 1965), Vol. IIA, p. 167

[c3] B. Bleaney, in Hyperfine Interactions, edited by A. J. Freeman and R. B. Frankel (Academic Press, Inc., New York, 1967), p. 1

[c4] R. E. Watson and A. J. Freeman, in Hyperfine Interactions, edited by A. J. Freeman and R. B. Frankel (Academic Press, Inc., New York 1967) p. 53

[c5] C. M. Moser, in Hyperfine Interactions, edited by A. J. Freeman and R. B. Frankel (Academic Press, Inc., New York, 1967) p. 95

[c6] A. Abragam, J. Horowitz, and M. H. L. Pryce, Proc. Roy. Soc. (London) A230, 169 (1955)

[c7] G. W. Pratt, Jr., Phys. Rev. 102, 1303 (1956)

[c8] V. Heine, Phys. Rev. 107, 1002 (1957) J. H. Wood and G. W. Pratt, ibid. 107, 995 (1957) M. H. Cohen, D. A. Goodings, and V. Heine, Proc. Phys. Soc. (London) 73, 811 (1959)

[c9] R. E. Watson and A. J. Freeman, Phys. Rev. 120, 1125 (1960) J. Appl. Phys. 32, 118S (1961) D. A. Goodings and V. Heine, Phys. Rev. Letters 5, 370 (1960)

[c10] L. M. Sachs, Phys. Rev. 117, 1504 (1960)

[c11] D. A. Goodings, Phys. Rev. 123, 1706 (1961)

[c12] N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. 124, 1124 (1961)

[c13] N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. 128, 213 (1962)

[c14] N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. 130, 1441 (1963)

[c15] N. Bessis, H. Lefebvre-Brion, and C. M. Moser, Phys. Rev. Mod. Phys. 35, 548 (1963)

[c16] N. Bessis et al. Phys. Rev. 135, A588 (1964)

[c17] Omitted endnote

[c18] P. O. Löwdin, Advan. Chem. Phys. 2, 207 (1959)

[c19] ([12–16])

[c20] W. Marshall, Proc. Phys. Soc. (London) 78, 113 (1961)

[c21] P. O. Löwdin, Phys. Rev. 97, 1509 (1955)

[c22] P. O. Löwdin, in Quantum Theory of Atoms, Molecules and Solid-State (Academic Press, Inc., New York, 1966) p. 601

[c23] W. A. Goddard III, Phys. Rev. 157, 81 (1967)

[c24] W. A. Goddard III, J. Chem. Phys. 48, 450 (1968)

[c25] W. A. Goddard III, Phys. Rev. 157, 93 (1967)

[c26] W. A. Goddard III, Phys. Rev. 176, 106 (1968)

[c27] W. A. Goddard III, J. Chem. Phys. 48, 5337 (1968)

[c28] C. C. J. Roothaan, Rev. Mod. Phys. 23, 69 (1951)

[c29] Omitted endnote

[c30] Omitted endnote

[c31] E. Clementi and D. L. Raimonde, J. Chem. Phys. 38, 2686 (1963) E. Clementi, 40, 1944 (1964) [IBM Technical Report No. RJ-256, 1963 (unpublished)] P. S. Bagus, T. L. Gilbert, H. D. Cohen, and C. C. J. Roothaan, to be published E. Clementi, C. C. J. Roothaan, and M. Yoshimine, Phys. Rev. 127, 1618 (1962) N. Bessis, H. Lefebvre-Brion, and C. M. Moser, [11–15]

[c32] Omitted endnote

[c33] Omitted endnote

[c34] C. C. J. Roothaan and P. S. Kelly, Phys. Rev. 131, 1177 (1963)

[c35] Omitted endnote

[c36] Omitted endnote

[c37] Omitted endnote

[c38] Omitted endnote

[c39] P. S. Bagus and B. Liu, Phys. Rev. 148, 79 (1966)

[c40] Omitted endnote

[c41] [S. Huzinaga, J. Chem. Phys. 42, 1293 (1965)]

[c42] Omitted endnote

[c43] J. S. M. Harvey, Proc. Roy. Soc. (London) A285, 581 (1965)

[c44] Omitted endnote

[c45] H. F. Schaefer III, R. A. Klemm, and F. E. Harris, Phys. Rev., 176, 49 (1968)

[c46] R. A. Haberstroh, W. J. Kossler, O. Ames, and D. R. Hamilton, Phys. Rev. 136, B932 (1964)

[c47] G. Wessel, Phys. Rev. 92, 1581 (1953)

[c48] R. M. Sternheimer, Phys. Rev. 164, 10 (1967)

[c49] S. M. Blinder, Bull. Am. Phys. Soc. 5, 14 (1960)

[c50] T. P. Das and A. Mukherjee, J. Chem. Phys. 33, 1808 (1960)

[c51] Omitted endnote

[c52] R. K. Nesbet, in La Structure Hyperfine Magnétique des Atomes et des Molécules (Centre National de la Recherche Scientifique, Paris, 1967), p. 87

[c53] U. Kaldor, J. Chem. Phys. 49, 6 (1968)

[c54] S. Larsson, Phys. Rev. 169, 49 (1968)

[c55] S. Lunell, Phys. Rev. 173, 85 (1968)

[c56] R. C. Ladner and W. A. Goddard, J. Chem. Phys. (to be published)

[c57] W. A. Goddard III, Phys. Rev. 157, 73 (1967)

[c58] Omitted endnote

[c59] ([24])

[c60] D. E. Rutherford, Substitutional Analysis (Edinburgh University Press, London, 1948)

[c61] Omitted endnote

[c62] N. F. Ramsey, Molecular Beams (Oxford University Press, London, 1956), p. 172

[c63] E. R. Cohen and J. W. M. Dumond, Rev. Mod. Phys. 37, 537 (1965)

[c64] B. R. Judd, Operator Techniques in Atomic Spectroscopy (McGraw-Hill Book Co., Inc., New York, 1963) V. Heine, Group Theory in Quantum Mechanics (Pergamon Press, Ltd., New York, 1960)

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Core Polarization and Hyperfine Structure of the B, C, N, O, and F Atoms

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