Ab-initio pseudopotential calculations

The local-density approximation describes the electronic many-body system in terms of a single-particle-like Schrddinger equation for each occupied state In the system. The electrons are, besides external nuclear Coulomb potentials, subjected to Coulomb repulsion from the other electrons (Hartree potential) and to exchange and correlation (x-c) potentials. The latter describe the interaction of each electron with its own surrounding x-c hole (see, e.g., von Barth and Williams, 1983). 

Having formulated the Schrddinger equation to be solved by iteration until selfconsistency, it is necessary to select a practical method for performing actual calculations. Among the 

A crucial development in pseudopotential theory is the formulation of normconserving pseudopotentials (Hamann et al., 1979 Kerker, 1980). From a local-density calculation of the allelectron free atom, the relatively weak pseudopotentials which bind only the valence electrons are constructed. The valence pseudo-wavefunctions do not contain the oscillations necessary to orthogonalize to the core, but are instead smooth functions which are much easier to handle in calculations on real solids. The features of such potentials are discussed in detail by, e.g., Bachelet et al. (1982), who also present pseudopotentials for all atoms from H to Pu. 

The normconserving pseudopotentials have proven to work well for many systems, notably semiconductors (see, e.g., Kune, this volume) and their surfaces (see, e.g., Morthrup and Cohen, 1982), ionic compounds (Froyen and Cohen, 1984), and simple metals (see, e.g., Lam and Cohen, 1981). Applications to transition metals also exist (see, e.g., Greenside and Schluter, 1983). The pseudopotential approximation becomes less satisfactory when valence and core electrons begin to have large overlap, both because of the pseudo-wavefunctions lacking nodes, and because the x-c potential ih the core region should also account for the presence of the core electrons. The latter problem can in many cases be treated well by nonlinear pseudopotentials (Louie et al., 1982). 

With plane-wave representation of wavefuntions the method for calculation of total energy has been described by Wendel and Martin (1978, 1979). Explicit expressions covering also nonlocal (angular momentum dependent) pseudopotentials and forces were given by Ihm, Zunger and Cohen (1979)- The method is described by Martin (this volume). 

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Figure Al.3.22. Spatial distributions or charge densities for carbon and silicon crystals in the diamond structure. The density is only for the valence electrons the core electrons are omitted. This charge density is from an ab initio pseudopotential calculation [27].

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Figure Al.3.27. Energy bands of copper from ab initio pseudopotential calculations [40].

Highlights in the chemistry of cyclopentadienyl compounds have been reviewed.65 Trends in the metallation energies of the gas-phase cyclopentadienyl and methyl compounds of the alkali metals have been studied by ab initio pseudopotential calculations. Whereas there is a smooth increase in polarity of M-(C5H5) bonds from Li to Cs, lithium appears to be less electronegative than sodium in methyl derivatives. The difference between C5H5 and CH3 derivatives is attributed to differences in covalent contributions to the M-C bonds. In solution or in the solid state these trends may be masked by the effects of solvation or crystal packing.66 The interaction between the alkali metal ions Li+-K+ and benzene has also been discussed.67... 

The equilibrium geometries of Cp2M (M = Yb, Eu, Sm) were studied by ab initio pseudopotential calculations at the Hartree-Fock (HF), MP2 and CSID levels. In the Hartree-Fock calculations [118] all the metallocenes favoured regular sandwich-type equilibrium structures with increasingly shallow potential energy surfaces for the bending motions along the series, M = Ca, Yb, Sr, Eu, Sm, and Ba. 

Table 3.9. Static structural properties for C, Si, and Ge obtained from the ab initio pseudopotential calculations of density-functional band theory compared with experiment...

Les, A., and Ortega-Blake, I. (1985). Inti. J. Quantum Chem. 27, 567—semiempirical (PCILO.MNDO) and ab initio pseudopotential calculations for relative stabilities of tautomers of 2- and 4-oxopyrimidine. 

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation...

Fig. 35. Side view of the atomic structure of Si(100)2xl-Bi as determined using ab initio pseudopotential calculations [98G8]. Si atoms are shown in white and Bi atoms in black. Distances are given in A.

Ab initio pseudopotential calcul ons at the Hartree-Fodr (HF), MP2 and CISD levels have been conductedi on the equilibrium geom es of q>2M (M=Ca, Sr or Ba). At the HF level, linear sandwkh-type equilibrium structures were indicated. Large-scale MP2... 

Table 4.1-32 Phonon wavenumbers/frequencies of boron compounds. Values for hexagonal boron nitride (BNhex) obtained from infrared reflectivity values for boron phosphide (BP) from ab initio pseudopotential calculations...

Ab initio pseudopotential calculation. First-order Raman scattering. 

Fig. 4.1-112 InSb. Phonon dispersion curves (left panel) and density of states (right panel). Experimental neutron data (circles) [1.21] and ab initio pseudopotential calculations (solid curves) [1.60]. From [1.60]...

Kumar, V. 2009. Coating of a layer of Au on A113 The findings of icosahedral Al A112Au20- and A112Au202 — fuUerenes using ab initio pseudopotential calculations. Phys. Rev. B 79 085423. 

In this work we have performed ab initio pseudopotential calculations of the electronic and magnetic properties of pure and mixed Fe systems with the Siesta method. We have compared our results with available data obtained through different well known ab initio methods in order to demonstrate the capabilities of this method for describing magnetic systems. 

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