Pseudopotential calculation

Figure Al.3.17. Modulated reflectivity spectrum of silicon. The theoretical curve is obtained from an empirical pseudopotential calculation [25], The experimental curve is from a wavelength modulation experiment from [32],...

Figure Al.3.20. Real part of the dielectric function for silicon. The experimental work is from [31]. The theoretical work is from an empirical pseudopotential calculation [25].

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].

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT teclmiques [M]- PAW, however, provides all-electron one-particle wavefiinctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in tenns of a pseudo-wavefiinction (easily expanded in plane waves) tenn that describes mterstitial contributions well, and one-centre corrections expanded in tenns of atom-centred fiinctions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential fonnalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [, ]. PAW is also fonnulated to carry out DFT dynamics, where the forces on nuclei and wavefiinctions are calculated from the PAW wavefiinctions. (Another all-electron DFT molecular dynamics teclmique using a mixed-basis approach is applied in [84].)... 

Pulci O, Onida G, Shkrebtii A I, Del Sole R and Adolph B 1997 Plane-wave pseudopotential calculation of the optical properties of GaAs Phys. Rev. B 55 6685... 

G.P. Francis and M.C. Payne, Finite basis set corrections to total energy pseudopotential calculations, J. 

Pyykko, P. and Stoll, H. (2000) Relativistic pseudopotential calculations, 1993-June 1999. in R.S.C. Specialist Periodical Reports, Chemical Modelling, Applications and Theory, Vol. 1, pp. 239-305. 

Fernandez, E.M., Soler, J.M. and Baibas, L.C. (2006) Planar and cagelike structures of gold clusters Density-functional pseudopotential calculations. Physical Review B - Condensed Matter, 73, 235433-1-235433-8. 

The model was also extended11 to single-crystal surfaces of silver. Although the calculated inner-layer capacitances varied in the right way from one face to another, the values were much too low. The problem was suspected to be due to the importance of the d electrons. What is still needed in this model is a better treatment of the solvent phase, valid at higher charge density, and a better way of deriving the repulsive potential of the solvent on the electrons, perhaps by a direct pseudopotential calculation, as done by Price and Halley.98,99... 

One of the most conspicuous differences between computational results is in the degree to which a normal H—Si chemical bond is formed. In the local-density pseudopotential calculations, the Si—H separation is about 1.6 A. This is much larger than the predictions of MNDO, Hartree-Fock, or PRDDO calculations, which are much closer to the molecular Si—H distance. It is not clear at this point whether the H—Si bond is, in fact, weaker than a conventional bond when in this configuration and therefore is overestimated by the Hartree-Fock-like calculations, or whether the strength is being underestimated in the local-density calculations. 

Fig. 5. Contour plot of the adiabatic potential-energy surface of an H atom in the (110) plane for the neutral H—B pair from a local-density pseudopotential calculation. The boron atom is at the center. For every hydrogen position, the B and Si atoms are allowed to relax, but only unrelaxed positions are indicated in the figure (Reprinted with permission from the American Physical Society, Denteneer, P.J.H., Van de Walle, C.G., and Pantelides, S.T. (1989). Phys. Rev. B 39, 10809.)...

The hydrogen frequency appropriate to the H—B pair was supported by the local-density pseudopotential calculations of Chang and Chadi (1988)... 

Figure 21 shows the photoelectron spectra of 34 (M = Ge) at 42 and 272 °C. The evident change in the shape of the spectrum clearly indicates the decomposition of the trimer. Band 1 was attributed to ionization of the sulphur lone pair of the monomeric species 33 (M = Ge), band 2 is related to the ji Ge=S bond, bands 4 and 6 to the a Ge—S and a Ge—C bonds respectively. Bands 3 and 5 were assigned to the ionization of a dimeric species. The assignment was supported by pseudopotential calculations. Also, the photoelectron spectrum of the dimeric species ( -Bu2GeS)2 was detected. 

Gernot Frenking, Iris Antes, Marlis Bohme, Stefan Dapprich, Andreas W. Ehlers, Volker Jonas, Arndt Neuhaus, Michael Otto, Ralf Stegmann, Achim Veldkamp, and Sergei F. Vyboishchikov, Pseudopotential Calculations of Transition Metal Compounds Scope and Limitations. 

Fig. 7.17 Plot of the calculated dielectric constant in silicon crystallites of different size. The broken curve corresponds to calculations based on the Penn model [Tsl], the dotted line corresponds to pseudopotential calculations [Wa5], while the full line is based on self-consistent linear screening calculation of hydrogenic impurities [AI4]. Redrawn from [AI4].

Tables 1 and 2 show the lowest torsional energy levels of hydrogen peroxide and deuterium peroxide which have been determined variationally using as basis functions the rigid rotor solutions. Experimental data are from Camy-Peiret et al [15]. The first set of leval data are from Camy-Peiret et al [15]. The first set of levels (SET I) has been calculated without including the pseudopotential V = 0). The levels corresponding to the other sets (SET II, SET III and SET IV) were obtained including pseudopotentials calculated with different numerical and analytical algorithms. Finally, the zero point vibration energy correction was introduced in the SET V [14],...

M. Fuchs, J. F. F. Da Silva, C. Stampfl, J. Neugebauer, and M. Scheffler, Cohesive Properties of Group-Ill Nitrides A Comparative Study of All-Electron and Pseudopotential Calculations Using the Generalized Gradient Approximation, Phys. Rev. B 65 (2002), 245212. 

Recent GGA first principles pseudopotential calculations conclude that Aun clusters adopt planar structures up to larger sizes than silver and copper, particularly the anionic species, due to relativistic effects. Specifically, Fernandez and coworkers obtain planar structures for the ground state of anionic v=l), neutral v=0), and cationic (z/=+l) species of Au(( clusters... 

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