Pseudopotentials structure

There are a variety of other approaches to understanding the electronic structure of crystals. Most of them rely on a density functional approach, with or without the pseudopotential, and use different bases. For example, instead of a plane wave basis, one might write a basis composed of atomic-like orbitals ... 

Figure Al.3.14. Band structure for silicon as calculated from empirical pseudopotentials [25],...

It is possible to identify particular spectral features in the modulated reflectivity spectra to band structure features. For example, in a direct band gap the joint density of states must resemble that of critical point. One of the first applications of the empirical pseudopotential method was to calculate reflectivity spectra for a given energy band. Differences between the calculated and measured reflectivity spectra could be assigned to errors in the energy band... 

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.3.24. Band structure of LiF from ab initio pseudopotentials [39],...

Figure B3.2.1. The band structure of hexagonal GaN, calculated using EHT-TB parameters detemiined by a genetic algorithm [23]. The target energies are indicated by crosses. The target band structure has been calculated with an ab initio pseudopotential method using a quasiparticle approach to include many-particle corrections [194].

The pseudopotential is derived from an all-electron SIC-LDA atomic potential. The relaxation correction takes into account the relaxation of the electronic system upon the excitation of an electron [44]- The authors speculate that ... the ability of the SIRC potential to produce considerably better band structures than DFT-LDA may reflect an extra nonlocality in the SIRC pseudopotential, related to the nonlocality or orbital dependence in the SIC all-electron potential. In addition, it may mimic some of the energy and the non-local space dependence of the self-energy operator occurring in the GW approximation of the electronic many body problem [45]. 

Needs R J and Mujica 1995. First-principles Pseudopotential Study of the Structural Phases of Silicon. Physical Review B51 9652-9660. 

Table 2 shows that in the case of ratile the GGA overestimation of lattice constants is less important in the present calculation than in Ref. 3. Most likely explanation is that the GGA functional is used here only for solid state calculations and not for the pseudopotential generation from the free atom. This procedure has been shown to give more accurate structural results than with the GGA applied both in the potential generation and solid state... 

The obtained static structure factors agree well with the experimental ones [4], all trends of the peak positions are reproduced correctly. There are only small deviations from the experiments (i) due to the pseudopotential (slighly too small bond lengths which correspond to slightly too large peak positions in the reciprocal lattice) and (ii) correct positions but a wrong trend in the heights of the prepeaks. For a detailed description see Ref. [7]. 

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. 

For H at T in Ge, Pickett et al. (1979) carried out empirical-pseudopotential supercell calculations. Their band structures showed a H-induced deep donor state more than 6 eV below the valence-band maximum in a non-self-consistent calculation. This binding energy was substantially reduced in a self-consistent calculation. However, lack of convergence and the use of empirical pseudopotentials cast doubt on the quantitative accuracy. More recent calculations (Denteneer et al., 1989b) using ab initio norm-conserving pseudopotentials have shown that H at T in Ge induces a level just below the valence-band maximum, very similar to the situation in Si. The arguments by Pickett et al. that a spin-polarized treatment would be essential (which would introduce a shift in the defect level of up to 0.5 Ry), have already been refuted in Section II.2.d. 

Recent calculations of hyperfine parameters using pseudopotential-density-functional theory, when combined with the ability to generate accurate total-energy surfaces, establish this technique as a powerful tool for the study of defects in semiconductors. One area in which theory is not yet able to make accurate predictions is for positions of defect levels in the band structure. Methods that go beyond the one-particle description are available but presently too computationally demanding. Increasing computer power and/or the development of simplified schemes will hopefully... 

Physical and Structural Aspects.—Perhaps the most significant theoretical paper comes from an application of pseudopotential SCF methods to PX3 molecules.1 This method neglects core orbitals, and hence shortens computer-time requirements, in comparison with more conventional SCF calculations. The results1 are really most encouraging, and compare favourably with standard SCF results, in relation to experimental values for bond angles and lengths, and for dipole moments. 

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