Abstract
It has been recognized 1-16 that electrostatic potentials at the nuclei of atoms and molecules play key roles in determining total energies. (For an overview, see the preceeding chapter by Politzer). It has also been recognized that the Hellmann-Feynman theorem provides a fundamental link between an energy change and the electrostatic potential at the nucleus caused by the electrons. The latter will be called the EPN.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. L. Foldy, A note on atomic binding energies, Phys. Rev. 83: 397 (1951).
E. B. Wilson, Four-dimensional electron density function, J. Chem. Phys. 36: 2232 (1962).
S. Fraga, Non-relativistic self-consistent-field theory. II, Theoret. Chim. Acta 2: 406 (1964).
R. Gâspdr, Many-electron problems. I. Energy relations in the theory of neutral atoms, Int. J. Quantum Chem. 1: 139 (1967).
P. Politzer and R. G. Parr, Some new energy formulas for atoms and molecules, J. Chem. Phys. 61: 4258 (1974).
P. Politzer, Some approximate energy relationships for molecules, J. Chem. Phys. 64: 4239 (1976).
R. G. Parr, R. A. Donnelly, M. Levy and W. E. Palke, Electronegativity; the density functional viewpoint, J. Chem. Phys. 68: 3801 (1978).
P. Politzer, Observations on the significance of the electrostatic potentials at the nuclei of atoms and molecules, in: “The Theory of Molecular Structure and Bonding,” R. Pauncz and E. A. Halevi, eds., Israel J. Chem. (Special issue) 19:224 (1980).
P. Politzer, Electrostatic potential-electronic density relationships in atoms, J. Chem. Phys. 72: 3027 (1980).
M. Levy, Variational energy functionals involving one-electron operator, J. Chem. Phys. 67: 724 (1977).
M. Levy, An energy-density equation for isoelectronic changes in atoms, J. Chem. Phys. 68: 5298 (1978).
M. Levy, On approximate energy differences from average electron densities, J. Chem. Phys. 70: 1573 (1979).
K. D. Sen, The isoelectronic energy-density relationship in atoms, J. Chem. Phys. 71: 3551 (1979).
M. Levy and Y. Tal, Atomic binding energies from fundamental theorems involving the electron density, r-1, and the Z-1 perturbation expansion, J. Chem. Phys. 72: 3416 (1980).
Y. Tal and M. Levy, Rigorous and approximate relations between expectation values of atoms, J. Chem. Phys. 72: 4009 (1980).
M. Levy and Y. Tal, Energy-density relations and screening constants in atoms, J. Chem. Phys., in press.
J. K. Percus, The role of model systems in the few-body reduction of the N-fermion problem, Int. J. Quantum Chem. 13: 89 (1978).
E. R. Davidson, “Reduced Density Matrices Quantum Chemistry,” Academic Press, New York (1976).
L. J. Schaad, B. H. Robinson and B. A. Hess, Jr., The relation between orbital SCF energies and total SCF energies in molecules, J. Chem. Phys. 67: 4616 (1977).
A. J. Thakkar and V. H. Smith, Jr., Compact and accurate integral-transform wave functions, Phys. Rev. A 15: 1 (1977).
G. G. Hall, The stability of a wave function under a perturbation, Phil. Mag. 62: 249 (1961).
P. Politzer and K. C. Daiker, Some potential-energy relationships for isoelectronic atomic series, Int. J. Quantum Chem. 14: 245 (1978).
E. A. Hylleraas, The Schrödinger two-electron problems, in: “Advances in Quantum Chemistry,” Vol. 1, P.-0. Löwdin, ed., Academic Press, New York (1964), p. 1.
J. Linderberg and H. Shull, Electronic correlation energy in Sand 4-electron atoms, J. Mol. Spectrosc. 5: 1 (1960).
J. O. Hirschfelder, W. Byers Brown and S. T. Epstein, Recent developments in perturbation theory, in: “Advances in Quantum Chemistry,” Vol. 1, P.-0. Löwdin, ed., Academic Press, New York (1964), p. 256.
P. 0. Löwdin, Scaling problems, virial theorem and connected relations in quantum mechanics, J. Mol. Spectrosc. 3: 46 (1959).
M. Cohen, On the systematic linear variation of atomic expectation values, J. Phys. B 12: L219 (1979).
R. P. Iczkowski and J. L. Margrave, J. Am. Chem. Soc. 83: 3547 (1961).
M. Levy, Y. Tal and S. Clement, to be published.
G. C. Lie and E. Clementi, Study of the electronic structure of molecules. XXI. Correlation energy corrections as a functional of the Hartree-Fock density and its application to the hydrides of the second row atoms, J. Chem. Phys. 60: 1275 (1974).
M. Levy, S. Clement and J. P. Perdew, Total electron binding energies in atoms from zero-order wave functions, Bull. Am. Phys. Soc. 24: 626 (1979).
E. H. Lieb and B. Simon, Thomas-Fermi theory revisited, Phys. Rev. Lett. 31: 631 (1973).
N. H. March, The Thomas-Fermi approximation in quantum mechanics, Adv. Phys. 6: 1 (1957).
J. Goodisman, Modified quantum-statistical calculations for atomic electron densities, Phys. Rev. A 2: 1193 (1970).
J. Goodisman, Energy levels in modified quantum statistical potentials, Theoret. Chim. Acta 24: 1 (1972).
N. H. March, “Self-Consistent Fields in Atoms,” Pergamon Press, Oxford (1975).
N. H. March and R. J. White, Non-relativistic theory of atomic and ionic binding energies for large atomic number, J. Phys. B 5: 466 (1972).
C. F. Fischer, “The Hartree-Fock Method for Atoms,” John Wiley and Sons, New York (1972).
R. G. Parr, S. R. Gadre and L. J. Bartolotti, Local density functional theory of atoms and molecules, Proc. Nat. Acad. Sci. U.S.A. 76: 2522 (1979).
J. Sucher, Ground-state energy of any atom, J. Phys. B 11: 1515 (1978).
K. D. Sen, An approximate density equation for isoelectronic changes in atoms, J. Chem. Phys. 70: 5334 (1979).
Y. Tal and M. Levy, Expectation values of atoms and ions: The Thomas-Fermi limit, Phys. Rev. A, accepted for publication.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1981 Springer Science+Business Media New York
About this chapter
Cite this chapter
Levy, M., Clement, S.C., Tal, Y. (1981). Correlation Energies from Hartree-Fock Electrostatic Potentials at Nuclei and Generation of Electrostatic Potentials from Asymptotic and Zero-Order Information. In: Politzer, P., Truhlar, D.G. (eds) Chemical Applications of Atomic and Molecular Electrostatic Potentials. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9634-6_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-9634-6_3
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4757-9636-0
Online ISBN: 978-1-4757-9634-6
eBook Packages: Springer Book Archive