Many-electron local potential calculation

Though not discussed above, in all the studies mentioned the trial wavef unctions included pair correlation functions. J j. as prescribed by Reynolds et al. ( ). Moskowitz et al. (48.49) have shown that the product of a relatively simple multiconfiguration wavefunction with pair correlation functions can provide a rather accurate approximation to the exact wavefunction. In our calculations and in those of Hammond et al. (59) the many-electron local potential, has been obtained by allowing the REP to... 

It is not absolutely necessary to have accurate interatomic potentials to perform reasonably good calculations because the many collisions involved tend to obscure the details of the interaction. This, together with the fact that accurate potentials are only known for a few systems makes the Thomas-Fermi approach quite attractive. The Thomas-Fermi statistical model assumes that the atomic potential V(r) varies slowly enough within an electron wavelength so that many electrons can be localized within a volume over which the potential changes by a fraction of itself. The electrons can then be treated by statistical mechanics and obey Fermi-Dirac statistics. In this approximation, the potential in the atom is given by ... 

Methods for calculating collisions of an electron with an atom consist in expressing the many-electron amplitudes in terms of the states of a single electron in a fixed potential. In this chapter we summarise the solutions of the problem of an electron in different local, central potentials. We are interested in bound states and in unbound or scattering states. The one-electron scattering problem will serve as a model for formal scattering theory and for some of the methods used in many-body scattering problems. 

We have seen that many-body-based methods provide an ab-initio way to treat the Coulomb correlation in an N electron system without the expensive cost of QMC calculations. However, they are computationally more demanding than routine LDA-KS calculations and, hence, the feasibility of their application to complex systems is unclear, especially in the context of ab-initio molecular dynamics calculations, where many total-energy evaluations are required. As described in Sect. 5.3, the main problem when constructing approximations to E c [n] is related to its inherent non-analytical character which is due to the specific way in which the KS mapping between the real and the fictitious systems is done. However, this is not the only possible realisation of DFT and recently, new DFT methods have been proposed [112,113]. In these generalised Kohn-Sham schemes (GKS) the actual electron system is mapped onto a fictitious one in which particles move in an effective non-local potential. As a result of this, it is possible to describe structmal properties at the same (or better) level than LDA/GGA but improving on its description of quasiparticle properties. 

For the conduction electrons, it is reasonable to consider that the inner-shell electrons are all localized on individual nuclei, in wave functions very much like those they occupy in the free atoms. The potential V should then include the potential due to the positively charged ions, each consisting of a nucleus plus filled inner shells of electrons, and the self-consistent potential (coulomb plus exchange) of the conduction electrons. However, the potential of an ion core must include the effect of exchange or antisymmetry with the inner-shell or core electrons, which means that the conduction-band wave functions must be orthogonal to the core-electron wave functions. This is the basis of the orthogonalized-plane-wave method, which has been successfully used to calculate band structures for many metals.41... 

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

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