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Electronegativity: The density functional viewpoint
1.P. Hohenberg and W. Kohn, Phys. Rev. Sec. B 136, 864 (1964).
2.S. Fraga, Theor. Chim. Acta 2, 406 (1964).
3.Hohenberg‐Kohn theory does not require the ground state to be nondegenerate. The result is stated without proof by W. Kohn, in Proceedings of the 1966 Midwest Conference on Theoretical Physics (Indiana U., Bloomington, IN, 1967), p. 14. The proof follows the lines of the proof for the nondegenerate case (Ref. 1), requiring only the additional observation that if ρ is a ground state density for two distinct potentials υ and some elgenfunction ψ among the degenerate solutions for υ, and some eigenfunction among the degenerate solutions for both produce the same ρ.
4.We expect that the smallest μ ordinarily will go with the smallest E, but this may not always be the case—see Eq. (22). This is like the situation in Hartree‐Fock theory, where the sum of orbital energies is almost always a minimum for the ground state. See W. H. Adams, Phys. Rev. 127, 1650 (1962).
5.Term coined by Professor E. G. Larson at the Boulder Theoretical Chemistry Conference, June, 1975.
6.T. L. Gilbert, Phys. Rev. B 12, 2111 (1975).
7.Footnote 12 of Ref. 1.
8.For example, I. M. Gelfand and S. V. Fomin, Calculus of Variations (Prentice‐Hall, Englewood Cliffs, NJ, 1963).
9.M. B. Einhorn and R. Blankenbecler, Ann. Phys. 67, 480 (1971). For this reason, Lagrange multipliers often are called sensitivity coefficients.
10.R. P. Iczkowski and J. L. Margrave, J. Am. Chem. Soc. 83, 3547 (1961).
11.R. S. Mulliken, J. Chem. Phys. 2, 782 (1934);
11.R. S. Mulliken, 3, 573 (1935)., J. Chem. Phys.
12.R. Pariser, J. Chem. Phys. 21, 568 (1953).
13.It is assumed that the form of admits this operation.
14.A principal part of Q may be written in the form where P is an appropriately defined local pressure in the electron gas. This point of view is being studied in this laboratory by Dr. L. Bartolotti.
15.W. J. Gordy, J. Chem. Phys. 19, 792 (1951).
16.For example, P. Gombas, Die Statistische Theorie des Atoms und Ihre Anwendung (Springer, Vienna, 1949).
17.Essentially the same analysis may be found in R. Gáspár, Int. J. Quantum Chem. 1, 139 (1967). Eq. (5)–(9).
17.See also N. H. March, J. Chem. Phys. 67, 4618 (1977).
18.Reference 2; and S. Fraga and J. Karwowski, “Tables of Hartree‐Fock Atomic Data,” Tech. Rep. Dept. of Chem. Univ. of Alberta, Edmonton, 1973, p. 26.
19.Compare P. Politzer and R. G. Parr, J. Chem. Phys. 61, 4258 (1974).
20.J. Hinze and H. H. Jaffe, J. Am. Chem. Soc. 84, 540 (1962).
21.R. T. Sanderson, Science 121, 207 (1955).
22.P.‐O. Löwdin, Phys. Rev. 97, 1474 (1955).
23.The quantities and determine the entire first‐order density matrix and hence T through a standard formula. Correct functionals could be either explicit density matrix functionals or trivial transcriptions of the density functional using the relation The latter viewpoint is emphasized in the present paper, the former in Ref. 28.
24.D. W. Smith, Phys. Rev. 147, 896 (1966).
25.Since the squares of the natural orbitals form a linearly dependent set, a given density might have more than one natural orbital resolution. For a ground state there can be only one wavefunction, however. In any case, Eq. (53) would be valid for every trial set in the neighborhood of
26.Reference 6, p. 2118, text after Eq. (3.26).
27.Communicated by RGP to several persons in January, 1975, and by letter from RGP to E. B. Wilson, Jr., February 10, 1975.
28.R. A. Donnelly, doctoral dissertation. University of North Carolina, 1977;
28.R. A. Donnelly and R. G. Parr (submitted to J. Chem. Phys.).
29.This property is implicit in the earliest discussions of electronegativity and bonding.
30.L. Pauling, The Nature of the Chemical Bond (Cornell U.P. Ithaca, NY, 1960), 3rd ed. Eq. (3–10), p. 91.
31.For example, W.‐P. Wang, R. G. Parr, D. Murphy, and G. Henderson, Chem. Phys. Lett. 43, 409 (1976);
31.W.‐P. Wang and R. G. Parr, Phys. Rev. A 16, 891 (1977).
32.For example, S. T. Epstein and C. M. Rosenthal, J. Chem. Phys. 64, 247 (1976).
33.R. F. W. Bader and P. M. Beddall, J. Chem. Phys. 56, 3220 (1972).
34.Reference 21, and also R. T. Sanderson, Chemical Bonds and Bond Energy, (Academic, New York, 1976), 2nd ed.
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