Abstract
The main concepts of the pseudopotential theory are first discussed (equivalency, core states elimination, orthogonalization hole, transferability). The perturbative approach is used to derive the (sp-bonded) metal structural energy. The significance and limitations of the resulting volume plus pair force expression are next discussed. Finally, a few non perturbative approaches are presented.
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References
Drude, P. (1900) “Electronic theory of metals”, Ann. Physik 1, 566–578.
Phillips, J.C. and Kleinman, L. (1959) “New method for calculating wave function in crystals and molecules”, Phys. Rev. 116, 287–293.
Herring, C. (1940) “Orthogonalized plane waves method for band structure calculation”, Phys. Rev. 126, 1169–1182.
[43 Harrison, W. A. (1967) Pseudopotentials in the Theory of Metals, Benjamin, New-York.
Ehrenreich, H. and Cohen, M.H. (1959) “Selfconsistent field approach to the many electrons problem”, Phys. Rev. 115, 786–790.90.
Abarenkov, I. and Heine, V. (1965) “The model potential for positive ions”, Phil. Mag. 12, 529–537.
Shaw, R.W. (1968) “Optimum form of a modified Heine-Abarenkov model potential”, Phys. Rev. 174, 769–781.
Ashcroft, N.W. (1966) “Electron-ion pseudopotentials in metals”, Phys. Letters 23, 48–49.
Hamann, D.R., Schlüter, M. and Chiang, C. (1979) “Norm-conserving pseudopotentials”, Phys. Rev. Lett. 43, 1494–1497.
Cohen, M. L. and Heine, V. (1970) “The fitting of pseudopotentials to experimental data”, Solid State Physics 24, Academic, New-York, pp. 38–249.
Heine, V. and Weaire, D. (1970) “Pseudopotential theory of cohesion and structure”, Solid State Physics 24, Academic, New-York, pp. 250–464.
Hohenberg, P. and Kohn, W. (1964) “Inhomogeneous electron gas”, Phys. Rev. 136, B864–871.
Kohn, W. and Sham, L.J. (1965) “Self-consistent equations including exchange and correlation effects”, Phys. Rev. 140, A1133–1138.
Dagens, L. (1977) “The resonant model potential: II. Total energy : application to Cu, Ag, Au and Ca”, J. Phys. F: Metal Phys. 7, 1167.
Moriarty, J.A. (1972) “Total energy of Copper, Silver and Gold”, Phys. Rev. 6, 1239–1252.
Moriarty, J.A. (1974) “Zero order pseudoatoms and the generalized pseudopotential theory”, Phys. Rev. 10, 30753091.
Carr, R. and Parrinello, M. (1985) “Uniform approach for molecular dynamics and density-functional theory”, Phys. Rev. Lett. 55, 2471–2474.
Shaw, R.W. and Harrison, W.A. (1967) “Reformulation of the screened Heine-Abarenkov model potential”, Phys. Rev. 163, 604–611.
Austin, B.J., Heine, V. and Sham, L.J. (1962) “General theory of pseudopotentials”, Phys. Rev. 127, 267–282.
Natapoff, M. (1976) “Calculation of the atomic radius”, J. Phys. Chem. Solids 37, 59–62.
Natapoff, M. (1978) “Pseudopotentials and the radius of the atomic core”, J. Phys. Chem. Solids 39, 1119–1123.
Heine, V. and Abarenkov, I. (1964). “The model potential method”, Phil. Mag. 9, 451–460.
Hamann, D.R. (1989) “Generalized norm conserving pseudopotentials”, Phys. Rev. B 40, 2980–2987.
Ziman, J.M. (1964) “The method of neutral pseudo-atoms in the theory of metals”, Adv. Phys. 13, 89–138.
Dagens, L. (1972) “The ion-electron-ion interaction according to the neutral atom model”, J. Phys. C: Solid State Phys. 5, L213–215.
Dagens, L. (1972) “A selfconsistent calculation of the neutral atom density according to the neutral atom model”, J. Phys. C : Solid State Phys. 5, 2333–2344.
Dagens, L. (1973) “Application de la méthode de l’atome neutre au calcul de l’énergie des métaux simples”, J. Physique 34, 879–889.
Norskov, J.K. and Lang, N.D. (1980) “Effective medium theory of chemical binding”, Phys. Rev. B 21, 2131-2136.Puska, M.J., Nieminen, R.N. and Manninen, M. (1981) “Atoms embedded in a electron gas : immersion energy”, Phys. Rev. B 24, 3037-3047.Jacobsen, K.W., Norskov, J.K. and Puska, M. J. (1987) “Interatomic interactions in the effective-medium theory”, Phys. Rev. B35, 7423-7442.
Puska, M.J., Nieminen, R.N. and Manninen, M. (1981) “Atoms embedded in a electron gas : immersion energy”, Phys. Rev. B 24, 3037–3047.
Jacobsen, K.W., Norskov, J.K. and Puska, M. J. (1987) “Interatomic interactions in the effective-medium theory”, Phys. Rev. B35, 7423–7442.
Ceperley, D.M. and Adler, B. J. (1980) “Ground state of the electron gas by a stochastic method”, Phys. Rev. Lett. 45, 566–569.
Perdew, J. and Zunger, A. (1981) “Self-interaction correction to the density-functional approximation for many electron systems”, Phys. Rev. 23, 5048.
Geldart, D.J.W. and Taylor, R. (1970) “Wave-number dependence of the static screening function. I.”, Can. J. Phys. 48, 155–165.
Geldart, D.J.W. and Taylor, R. (1970) “Wave-number dependence of the static screening function. II.”, Can. J. Phys. 48, 167–181.
Dagens, L. (1971) “Un calcul variationnel de 1’énergie d’échange d’un gaz d’electrons”, J. Physique 32, 719–728.
Brovman, E.G. and Kagan, Y (1970) “Long wave phonons in metals”, Sov. Phys.-JETP 30, 721–727.
Brovman, E.G., Kagan, Y. and Kholas, A. (1970) “The compressibility problem and violation of the Cauchy relation”, Sov. Phys.-JETP 30, 883–888.
Pettifor, D. C. and Ward, M. A. (1984) “An analytic pair potential for simple metals”, Solid State Com. 29, 291–294.
Dagens, L. (1974) “The effect of pressure on the pair potential for liquid sodium”, Phys. Stat. Sol. (b) 62, K109–113.
Rosenfeld, A.M. and Stott, M.J. (1987) “Density dependent potential and the compressibility problem”, J. Phys. F: Metal Phys. 17, 605–627.
Carlsson, A.E. and Ashcroft, N.W. (1983) “Pair potentials from band theory : vacancy formation energies”, Phys. Rev. B 27, 2101-2110.
Carlsson, A.E.(1990) “Beyond pair potentials in transition metals”, Solid State physics 43, Academic, New-York, pp. 1–91.
Dagens, L. (1984) “Effective interatomic forces in liquid metals”, Phys. Letters 101A, 283–285.
Dagens, L. (1986) “Effective interatomic potentials in strong scattering open shell metals”, J. Phys. Ft Metal Phys. 16, 1705–1724.
Finnis, M.W. and Sinclair, J.E. (1984) “A simple empirical N-body potential for transition Metal”, Phil. Mag. A 50, 45–55.
Daw, M.S. and Baskes, M.I. (1983) “Semi empirical quantum mechanical calculation of hydrogen embrittement in metals”, Phys. Rev. Lett. 50, 1285–1288.
Daw, M.S. and Baskes, M.I. (1984) “Embedded atom method : derivation and application to defects in metals”, Phys. Rev. B 29, 6443–6453.
Moriarty, J.A. (1977) “Density-functional formulation of the generalized pseudopotential theory”, Phys. Rev. B 16, 2537–2555.
Moriarty, J.A. (1990) “Multi-ion interatomic potentials in transition metals”, Phys. Rev. B 42, 1609–1628.
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© 1991 Springer Science+Business Media Dordrecht
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Dagens, L. (1991). The Pseudopotential Approach to the Interatomic Interaction Problem. In: Meyer, M., Pontikis, V. (eds) Computer Simulation in Materials Science. NATO ASI Series, vol 205. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3546-7_10
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DOI: https://doi.org/10.1007/978-94-011-3546-7_10
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