Born-Mayer-Type Interatomic Potential for Neutral Ground-State Atoms with <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo>=</mo><mn>2</mn><mn></mn></math></span> to <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo>=</mo><mn>105</mn><mn></mn></math></span>

Adolf A. Abrahamson

doi:10.1103/PhysRev.178.76

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Born-Mayer-Type Interatomic Potential for Neutral Ground-State Atoms with $Z = 2$ to $Z = 105$

Adolf A. Abrahamson

Department of Physics, The City College of the City University of New York, New York 10031

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Phys. Rev. 178, 76 – Published 5 February, 1969

DOI: https://doi.org/10.1103/PhysRev.178.76

Abstract

Born-Mayer parameters are given which permit, with good accuracy (to within 6%), a greatly simplified computation of a previously derived interatomic potential, $U (R)$ , based on the Thomas-Fermi-Dirac (TFD) approximation. The numerical values of $A$ and $b$ appearing in $U (R) = A \exp (- b R)$ are tabulated in two sets of commonly used units for 104 homonuclear pairs of neutral ground-state atoms having $Z = 2$ to $Z = 105$ . Approximate lower and upper limits of applicability, $R_{l}$ and $R_{u}$ , are also listed, as is the magnitude of the maximum percent error ( $ε$ ) for each fit. $R_{l}$ is generally $\sim 1.5 a_{0} (a_{0} = 0.529 17 Å)$ , while $R_{u} \sim 3.5 a_{0}$ . The effective upper limit probably lies at $\sim 6 - 8 a_{0}$ . Also, with the aid of the given table and the combining rule $U_{12} ≃ {(U_{11} U_{22})}^{\frac{1}{2}}$ , the interaction energies of a total of 5356 heteronuclear diatoms can readily be obtained.

References (25)

L. H. Thomas, Proc. Cambridge Phil Soc. 23, 542 (1927)
E. Fermi, Z. Physik 48, 73 (1928)
P. A. M. Dirac, Proc. Cambridge Phil. Soc. 26, 376 (1930)
(a) P. Gombas, Die Statistische Theorie des Atoms und thre Anwendungen (Springer-Verlag, Vienna, 1949) (b) in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, Germany, 1956), Vol. 36
A. A. Abrahamson, R. D. Hatcher, and G. H. Vineyard, Phys. Rev. 121, 159 (1961)
A. A. Abrahamson, Phys. Rev. 130, 693 (1963)
A. A. Abrahamson, Phys. Rev. 133, A990 (1964)
Omitted endnote
M. Born and J. E. Mayer, Z. Physik 75, 1 (1932)
M. Born, Atomic Physics (Hafner Publishing Co., New York, 1946), p. 262
[13,17], 26, 60-67, 70 [6]
I. Amdur and J. E. Jordan, in Advances in Chemical Physics, edited by J. Ross (Interscience Publishers, New York, 1966), Vol. X
J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, Phys. Rev. 120, 1229 (1960)
A. N. Goland, Ann. Rev. Nucl. Sci. 12, 243 (1962)
E. V. Kornelsen, Can. J. Phys. 42, 364 (1964)
G. Leibfried, Bestrahlungseffekte in Festkörpern; eine Einführung in die Theorie (B. G. Teubner Verlagsgesellschaft, Stuttgart, 1965)
D. K. Nichols and V. A. J. Van Lint, in Solid State Physics (Academic Press, Inc., New York, 1966), Vol. 18
H. Pauly and J. P. Toennies, in Advances in Atomic and Molecular Physics, edited by D. R. Bates and I. Estermann (Academic Press, Inc., New York, 1965), Vol. I
F. J. Zehr and H. W. Berry, Phys. Rev. 159, 13 (1967)
Handbook of Physics, edited by E. U. Condon and H. Odishaw (McGraw-Hill, New York, 1958), p. 7-12; p. 10
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954)
I. Amdur and E. A. Mason, Phys. Fluids 1, 370 (1958) J. Chem. Phys. 25, 632 (1956)
I. Amdur, E. A. Mason, and A. L. Harkness, J. Chem. Phys. 22, 1071 (1954)
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[4], pp. 140 and 162 J. W. Sheldon, Phys. Rev. 99, 1291 (1955) E. Teller, Rev. Mod. Phys. 34, 627 (1962)

[c1] L. H. Thomas, Proc. Cambridge Phil Soc. 23, 542 (1927)

[c2] E. Fermi, Z. Physik 48, 73 (1928)

[c3] P. A. M. Dirac, Proc. Cambridge Phil. Soc. 26, 376 (1930)

[c4] (a) P. Gombas, Die Statistische Theorie des Atoms und thre Anwendungen (Springer-Verlag, Vienna, 1949) (b) in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, Germany, 1956), Vol. 36

[c5] A. A. Abrahamson, R. D. Hatcher, and G. H. Vineyard, Phys. Rev. 121, 159 (1961)

[c6] A. A. Abrahamson, Phys. Rev. 130, 693 (1963)

[c7] A. A. Abrahamson, Phys. Rev. 133, A990 (1964)

[c8] Omitted endnote

[c9] M. Born and J. E. Mayer, Z. Physik 75, 1 (1932)

[c10] M. Born, Atomic Physics (Hafner Publishing Co., New York, 1946), p. 262

[c11] [13,17], 26, 60-67, 70 [6]

[c12] I. Amdur and J. E. Jordan, in Advances in Chemical Physics, edited by J. Ross (Interscience Publishers, New York, 1966), Vol. X

[c13] J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vineyard, Phys. Rev. 120, 1229 (1960)

[c14] A. N. Goland, Ann. Rev. Nucl. Sci. 12, 243 (1962)

[c15] E. V. Kornelsen, Can. J. Phys. 42, 364 (1964)

[c16] G. Leibfried, Bestrahlungseffekte in Festkörpern; eine Einführung in die Theorie (B. G. Teubner Verlagsgesellschaft, Stuttgart, 1965)

[c17] D. K. Nichols and V. A. J. Van Lint, in Solid State Physics (Academic Press, Inc., New York, 1966), Vol. 18

[c18] H. Pauly and J. P. Toennies, in Advances in Atomic and Molecular Physics, edited by D. R. Bates and I. Estermann (Academic Press, Inc., New York, 1965), Vol. I

[c19] F. J. Zehr and H. W. Berry, Phys. Rev. 159, 13 (1967)

[c20] Handbook of Physics, edited by E. U. Condon and H. Odishaw (McGraw-Hill, New York, 1958), p. 7-12; p. 10

[c21] J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (John Wiley & Sons, Inc., New York, 1954)

[c22] I. Amdur and E. A. Mason, Phys. Fluids 1, 370 (1958) J. Chem. Phys. 25, 632 (1956)

[c23] I. Amdur, E. A. Mason, and A. L. Harkness, J. Chem. Phys. 22, 1071 (1954)

[c24] E. A. Mason, J. Chem. Phys. 23, 49 (1955)

[c25] [4], pp. 140 and 162 J. W. Sheldon, Phys. Rev. 99, 1291 (1955) E. Teller, Rev. Mod. Phys. 34, 627 (1962)

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Born-Mayer-Type Interatomic Potential for Neutral Ground-State Atoms with $Z = 2$ to $Z = 105$

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Born-Mayer-Type Interatomic Potential for Neutral Ground-State Atoms with Z=2 to Z=105

Abstract

References (25)

Born-Mayer-Type Interatomic Potential for Neutral Ground-State Atoms with $Z = 2$ to $Z = 105$