Self-consistent pseudopotential

Vanderbilt D 1990 Soft self-consistent pseudopotentials in a generalized eigenvalue formalism Phys. Rev. B 41 7892-5... 

Let us now construct a representation of the electronic structure of SiOj. There have been many early studies of Si02, principally aimed at interpreting various experimental spectra these have been reviewed recently by Ruffa (1968, 1970). More recently, studios based upon calculations for large clusters of atoms have been made by Reilly (1970), Bennett and Roth (1971a,b), Gilbert ct al. (1973), and Yip and Fowler (1974). Most recently, a full, self-consistent pseudopotential calculation on quartz was made by trhelikowsky and Schliitcr (1977). Here, we shall... 

It is a somewhat formidable undertaking to make an energy-band calculation for a crystal such as a-quartz with nine atoms per primitive cell a full calculation has only recently been completed by Chelikowsky and Schliiter (1977), who used a self-consistent pseudopotential method. The results of this calculation are shown... 

Chelikowsky, J. R., and M. Schluter (1977). Electron states in a-quartz a self-consistent pseudopotential calculation. Phys. Rev. B15, 4020-29. 

In (a) are shown the energy bands of a-quartz obtained by Chelikowsky and Schliiter (1977) froi a self-consistent pseudopotential calculation. In part (b) are shown the bands of the simpler /1-cristobalite structure (Pantelides and Harrison, 1976) from an LCAO calculation and a Bond Orbital Approximation that calculation was restricted to the valence bands. The corresponding density of states is shown to the right. Because the symmetry of the structures is different, different symmetry points are indicated below each figure. [Part (a) after Chelikowsky and Schliiter, 1977 part (b) after Pantiledes and Harrison, 1976.]... 

Vaidehi N, Goddard WA (2000) Domain motions in phosphoglycerate kinase using hierarchical NEIMO molecular dynamics simulations. J Physl Chem A 104 2375-2383 Vanderbilt D (1990) Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B-Con Mat 41 7892-7895... 

Furthermore, for treating semiconductors (and also the stucture of simple metals), one has to leave the second order perturbation theory. The self-consistent pseudopotentials which are then needed, are not discussed in these lecture notes at all. They wOl be discussed by several lecturers at this ASI, in connection with several other topics, not even mentioned in these notes. 

In fact, the self-consistent pseudopotentials form an important subject... 

The starting point in this chain of equations is the Hartree (H) approximation, in which case 2 =0. An approximate "Hartree" calculation is shown in Fig.4 for Si. This calculation is "approximate" in that it is not a self-consistent H calculation, but in-stead -S based on a self-consistent pseudopotential-LDA calculation. After achieving selfconsistency the LDA exchange-correlation V was dropped in the extraction of the eigenvalues and... 

Fig. Al.l Ionic pseudopotentials of Fig. 2.1 plotted in direct space (broken line) and compared with the full nuclear potential -Z/r (solid line) when used for self-consistent determination of the (pseudo-)atomic charge densities, the screening converts them into, respectively, self-consistent pseudopotential (broken line) and self-consistent potential (solid line). The exchange factor a = 0.8 and spherical averaging of the charge density of incomplete shells were used in solving self-consistently the equations of DF, as described in Ref. 78.

Anderson, P. W. (1968). Self-consistent pseudopotentials and ultralocalized functions for energy bands. Phys. Rev. Lett. 21,13 ibid. (1969). Localized Orbitals for Molecular Quantum Theory. I. The Htlckel Theory. Phys. Rev. 181,25-32. 

P. W. Anderson, Self-consistent pseudopotentials and ultralocalized functions for energy bands, Phys. Rev. Letters 21, 13-16 (1968). 

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