Abstract
The realization of Harrison's first-principles pseudopotential concept is re-analyzed. It is shown that the most critical and at the same time most fundamental step is the separation of the electronic system into two subsystems, tightly-bound core-electrons and quasi-free valence-electrons. Different varieties of the local statisticalX α-exchange and correlation approximation are used to describe the core-core and valence-core many-body interactions. Many-body effects among the conduction-electrons are taken into account by using different modified forms of the dielectric screening function. The different potentials are applied to a calculation of phonon-dispersion relations and mode-Grüneisen parameters, of the cohesive properties (equilibrium lattice constant, binding energy, compressibility, equation of state), of the crystal structure, the thermodynamic properties, the interionic pair potential and of some electronic properties (liquid resistivity as a function of temperature, Fermi-surface data). It is shown that a careful description of the many-body interactions, both in the formulation of the electron-ion potential and in the screening process, allows a quantitatively accurate unified and fundamental analysis of a wide range of different properties.
Similar content being viewed by others
References
Useful references may be found in the following reviews: (a) Harrison, W.A.: Pseudopotentials in the Theory of Metals, New York: Benjamin 1966; (b) Heine, V., Weaire, D.: Solid State Physics, ed. Seitz, F., Turnbull, D., and Ehrenreich, H., New York: Academic Press 1970, vol. 24, p. 242; Cohen, M.H., Heine, V.: ibid p. 50; (c) Joshi, S.K., Rajagopal, A.K.: Solid State Physics, ed. Seitz, F., Turnbull, D., and Ehrenreich, H., New York: Academic Press 1969, vol. 22, p. 159
Hafner, J., Schmuck, P.: Phys. Rev. B9, 4138 (1974)
Hafner, J.: Z. Physik B22, 351 (1975)
Hafner, J., Eschrig, H.: phys. stat. solidi (b)72, 179 (1975)
Hafner, J.: J. Phys. F5, 1439 (1975)
Lindgren, I.: Int. J. Quantum Chem. S5, 411 (1971)
Herman, D., Skillman, S.: Atomic Structure Calculations. Englewood Cliffs, N.J.: Prentice Hall 1963
Hafner, J.: J. Phys. F5, L 150 (1975)
Singwi, K.S., Sjölander, A., Tosi, M.P., Land, R.H.: Phys. Rev. B1, 1044 (1970)
Hubbard, J.: Proc. Roy. Soc. (London) A240, 539 (1957); A243, 356 (1957) Sham, L.J.: Proc. Roy. Soc. (London) A283, 33 (1965) Geldart, D.J.W., Vosko, S.H.: Can. J. Phys.44, 2137 (1966) Ashcroft, N.W.: J. Phys. C1, 232 (1968)
Toigo, F., Woodruff, T.O.: Phys. Rev. B2, 3958 (1971)
Vashishta, P., Singwi, K.S.: Phys. Rev. B6, 875 (1972)
Pearson, W.B.: A Handbook of Lattice Spacing and Structures Metals and Alloys, London: Pergamon 1958
King, W.F., Cutler, P.H.: Phys. Rev. B8, 1303 (1973)
Latter, E.O.: Phys. Rev.99, 510 (1955)
Pauling, L.: The Nature of the Chemical Bond, Ithaca-New York: Cornell University Press 1948
Hafner, J.: Phys. Letters50A, 271 (1974)
Hedin, L., Lundqvist, S.: Solid State Physics, ed. Seitz, F., Turnbull, D., Ehrenreich, H., vol. 23, p. 2ff. New York: Academic Press 1969
Ernst, G.: Acta Physica Austriaca33, 27 (1971)
Copley, J.R.D., Rotter, C.A., Smith, H.G., Kamitakahara, W.A.: Phys. Rev. Letters33, 365 (1969)
Martinson, R.H.: Phys. Rev.178, 902 (1969)
Ho, P.S., Ruoff, A.L.: J. Phys. Chem. Solids29, 2101 (1968)
Daniels, W.B.: in Lattice Dynamics, ed. Wallis, R.F., p. 273. New York: Pergamon Press 1965
Copley, J.R.D.: Can. J. Phys.51, 2564 (1973)
Wallace, D.C.: Thermodynamics of Crystals, New York: Wiley 1972
Smith, H.G., Dolling, G., Nicklow, R.M., Vijayaraghavan, P.R., Wilkinson, M.K.: Neutron Inelastic Scattering, Symp. Copenhagen 1968 (IAEA Vienna 1968), vol. 1, p. 149
Woods, A.D.B., Brockhouse, B.N., March, R.H., Stewart, A.T.: Phys. Rev.128, 1112 (1962)
Cowley, R.A., Woods, A.D.B., Dolling, G.: Phys. Rev.150, 487 (1966)
Copley, J.R.D., Brockhouse, B.N.: Can. J. Phys.51, 667 (1966)
Hafner, J.: phys. stat. sol. (b)56, 579 (1973);57, 107 (1973);57, 479 (1973)
Landolt-Börnstein, Vol. I, part 1, p. 211, Berlin-Göttingen-Heidelberg: Springer 1950 Gschneider, K.A.: in Solid State Physics (ed. Seitz, F., Turnbull, D., and Ehrenreich, H.) vol. 16, New York: Academic Press 1964
Day, J.P., Ruoff, A.L.: phys. stat. sol. (a)25, 205 (1974)
Marquardt, W.R., Trivisonno, J.: J. Phys. Chem. Solids28, 805 (1967)
Smith, P.A., Smith, C.S.: J. Phys. Chem. Solids26, 279 (1965)
Gutmann, E.J., Trivisonno, J.: J. Phys. Chem. Solids28, 805 (1967)
Schramm, K.H.,: Z. Metallkunde63, 148 (1972)
Vaidya, S.N., Getting, I.C., Kennedy, G.C.: J. Phys. Chem. Solids32, 2545 (1971)
Barett, C.S.: Acta Crystallogr.9, 671 (1956)
Basanski, Z.S., Verdini, I.L.: Phil. Mag.4, 1311 (1959)
Moriarty, J.A.: Phys. Rev. B8, 1338 (1973)
Houston, W.V.: Rev. Mod. Phys.20, 161 (1948) Horton, G.K., Schiff, H.: Proc. Roy. Soc. (London) A250, 248 (1959)
Bhetts, D.B., Bhatia, A.B., Horton, G.K.: Phys. Rev.104, 43 (1956)
Pynn, R., Ebbsjö, I.: J. Phys. F (Metal Physics)1, 744 (1971)
Filby, J.D., Martin, D.L.: Proc. Roy. Soc. (London) A284, 83 (1965)
Martin, D.L.: Proc. Roy. Soc. (London) A254, 433 (1960)
Filby, J.D., Martin, D.L.: Proc. Roy. Soc. (London) A276, 187 (1963)
Lee, M.J.G.: Proc. Roy. Soc. (London) A295, 440 (1966)
Lee, M.J.G., Falicov, L.M.: Proc. Roy. Soc. (London) A304, 319 (1969)
Shoenberg, D., Stiles, P.J.: Proc. Roy. Soc. (London) A281, 62 (1964)
Ziman, J.: Phil. Mag.6, 1013 (1961)
Greenfield, A.J., Wellendorf, J., Wiser, N.: Phys. Rev. A4, 1607 (1971)
Liquid Metals Handbook, ed. Jackson, J., Atomic Energy Commission, Washington 1955
Smithels, C.J.: Metals Reference Book, London/Washington 1962
Ashcroft, N.W., Lekner, J.: Phys. Rev.145, 83 (1966)
Slater, J.C., Johnson, K.H.: Phys. Rev. B5, 844 (1972) Lindgren, I., Schwarz, K.: Phys. Rev. A5, 542 (1972)
Author information
Authors and Affiliations
Additional information
Work sponsored by the Fonds zur Förderung der wissenschaftlichen Forschung in Österreich unter Contract No. 2029
Rights and permissions
About this article
Cite this article
Hafner, J. Unified analysis of static, dynamic and electronic properties of the alkali metals. Z Physik B 24, 41–52 (1976). https://doi.org/10.1007/BF01312872
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01312872