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By A. Baldereschi, R. Resta (auth.), J. T. Devreese, V. E. Van Doren, P. E. Van Camp (eds.)

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In recent years a large number of calculations [5-14] have utilized the local density functional (LDF) approximation [2,15,16] with remarkable results, predicting accurate structural energies of solids with no adjustable parameters. In the LDF approximation the solutions of the variational equations can be cast in the form of self-consistent field independent electron equations. The form of the equations is summarized in Section II to establish the basis for the remainder of the paper. In the opinion of the authors, it has not yet been understood why the LDF calculations have been so successful or, in other words, what will be the limits of the LDF approximations.

The structure of semiconductor surfaces [8,17] and interfaces [11,18]. The primary purpose of the paper is to discuss relations among different methods of calculation that can be used to develop the most efficient and physically meaningful techniques. This is discussed in Section IV where we compare and contrast two methods: 1) the "direct" method [7-14,19] where independent self-consistent 51 STRUCTURAL ENERGIES OF SEMICONDUCTORS solutions for different atomic positions are compared directly and 2) the perturbation (or dielectric function £) method [20-25] in which the self-consistent solutions for small displacements from equilibrium can be simplified by linearization of the equations.

C. Phillips, "Covalent Bonding in Crystals, Molecules and Polymers", Chicago University Press (1969). 27. G. , Vienna (1963), vol. II, p. 37. 28. J. Hubbard, Proc. Roy. Soc. A243, 336 (1958). J. Sham, Proc. Roy. Soc. A283, 33 (1965). 29. E. E. T. Devreese, J. de Physique (Paris), 42, C6-625 (1981). 48 P. E. VAN CAMP ET AL. E. E. T. Rev. B, to be published. 30. R. Resta and A. Baldereschi, J. de Physique (Paris) 42, C6-661 (1981); Phys. Rev. B23, 6615 (1981); Phys. Rev. B24,~839 (1981). A. Baldereschi and ~Resta, this proceedings.

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