Ab Initio Methods for Electronic Structures of Crystalline Solids

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Abstract

Two approaches have been dominant in theoretical studies of the electronic structures and properties of crystalline solids. The first and older approach involves the use of an independent-electron formalism, but with a semi-empirically determined effective Hamiltonian designed to reproduce the effects of electron exchange and correlation. A variety of effective Hamiltonians have been used, ranging from pseudopotentials, chosen mainly on the basis of agreement with experiment, to a priori choices such as the highly popular Xα method (Slater, 1970, 1971; Johnson and Smith, 1971), where the exchange-correlation potential is based on studies of the uniform electron gas (Slater, 1951; Gaspar, 1954; Kohn and Sham, 1965). This approach, although highly successful for many problems, leaves certain questions unanswered; among these are detailed assessments of the quality of the Hartree-Fock wavefunction, the quantitative roles of exchange and correlation, and the elucidation of collective phenomena inherently ruled out by an independent-electron model.