First-principles electronic structure results

In contrast to the case of bulk properties, very few ab initio calculations have been done for lanthanide or actinide surfaces. Although there has been much interest in the valence state at the surface of lanthanides, this has been treated by other means than first-principles electronic-structure calculations (Johansson and Martensson 1987). However, Hong et al. (1992) considered the Sm surface and applied the FLAPW method to a five-layer fee (100) slab in order to investigate theoretically the possibility of a valence change relative to the bulk. Although the results were not conclusive, this demonstrates the type of problems which can now be addressed by means of the present computational techniques. 

The final results of the electronic structure of the nanocrystals depend on the type of the orbital basis chosen to build the TB Hamiltonian. The first-principle band structure calculation of the bulk material gives a good indication of the choice of the basis set and the interactions. For example, the density of states (DOS) and the partial DOS (PDOS) for the bulk system clearly illustrate the various orbitals involved in bonding at any given energy. The character of various bands in the band dispersions can also be analyzed to obtain similar, but even more detailed information. Thus, one can appropriately select the orbital basis to perform the TB... 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

The electron density distribution of a known surface structure can be calculated from first-principles. Thus, the He diffraction data can be compared with theoretical results, in particular, to verify different structural models. Hamann (1981) performed first-principles calculations of the charge-density distributions of the GaAs(llO) surface, for both relaxed and unrelaxed configurations. The He diffraction data are in excellent agreement with the calculated charge-density distributions of the relaxed GaAs(llO) surface, and are clearly distinguished from the unrelaxed ones (Hamann, 1981). 

The problem of first-principles calculations of the electronic structure of solid surface is usually formatted as a problem of slabs, that is, consisting of a few layers of atoms. The translational and two-dimensional point group symmetry further reduce the degrees of freedom. Using modern supercomputers, such first-principles calculations for the electronic structure of solid surfaces have produced remarkably reproducible and accurate results as compared with many experimental measurements, especially angle-resolved photoemission and inverse photoemission. 

In the most elementary models of orbital structure, the quantities that explicitly define the potential V are not computed from first principles as they are in so-called ab initio methods (see Section 6). Rather, either experimental data or results of ab initio calculations are used to determine the parameters in terms of which V is expressed. The resulting empirical or semi-empirical methods discussed below differ in the sophistication used to include electron-electron interactions as well as in the manner experimental data or ab initio computational results are used to specify V. 

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