Independent-electron models local-density approximation

For direct Af-electron variational methods, the computational effort increases so rapidly with increasing N that alternative simplified methods must be used for calculations of the electronic structure of large molecules and solids. Especially for calculations of the electronic energy levels of solids (energy-band structure), the methodology of choice is that of independent-electron models, usually in the framework of density functional theory [189, 321, 90], When restricted to local potentials, as in the local-density approximation (LDA), this is a valid variational theory for any A-electron system. It can readily be applied to heavy atoms by relativistic or semirelativistic modification of the kinetic energy operator in the orbital Kohn-Sham equations [229, 384],... 

Molecular quantum chemistry and quantum mechanical simulation of solids have followed substantially independent paths and strategies for many years, with almost no reciprocal influence. In the implementation of computational schemes and formalisms, they started from different elementary models either the hydrogen or helium atom like, for example, the parameterization of a correlation functional based on accurate He atom calculations by Colle and Salvetti, or the electron gas, which is the reference system of the local density approximation "" (LDA) to density functional theory (DFT). Moreover, if we compare the simplest real crystals, like lithium metal or sodium chloride, with the smallest molecule, H2, the much greater complexity of the solid system is... 

As in the simpler jellium model, we retain the simple description of independent electrons, each moving in a confining potential U(r). Here however, that potential is not an arbitrary, made-up model potential chosen to fit data or to make a calculation convenient this potential includes such effects as the exchange interaction with the other electrons. In this, the present approach is quite reminiscent of the Hartree-Fock self-consistent procedure, which will be described next. There is one essential difference. Unlike the Hartree-Fock procedure, here the exchange term is approximated as a local function, depending only on the one-electron density. This approximation yields fast convergence to a self-consistent density. As in the Hartree-Fock... 

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