Conductance theories empirical corrections

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

As described in the preceding sections, fundamental studies of heterogeneous catalysis at the surface of catalysts are important for understanding reaction pathways and for the development of new or improved catalysts and processes. There have been earlier hypotheses proposed for selective oxidation catalysis for example, the multiplet theory which suggests that the activity depends upon correctly spaced groups (multiplets) of atoms to accommodate the reactant molecule (Balandin, 1969) and electronic theory based on the nature of adsorption on semiconductors and empirical correlations between activity, work function and electrical conductivity (Wolkenstein 1960). The importance... 

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