Spin polarized band energy

Figure 2. The structural energy difference (a) and the magnetic moment (b) as a function of the occupation of the canonical d-band n corresponding to the Fe-Co alloy. The same lines as in Fig. 1 are used for the different structures. In (b) the concentration dependence of the Stoner exchange integral Id used for the spin-polarized canonical d-band model calculations is shown as a thin dashed line with the solid circles. The value of Id for pure Fe and Co, calculated from LSDA and scaled to canonical units, are also shown in (b) as solid squares.

In a previous work we showed that we could reproduce qualitativlely the LMTO-CPA results for the Fe-Co system within a simple spin polarized canonical band model. The structural properties of the Fe-Co alloy can thus be explained from the filling of the d-band. In that work we presented the results in canonical units and we could of course not do any quantitative comparisons. To proceed that work we have here done calculations based on the virtual crystal approximation (VGA). In this approximation each atom in the alloy has the same surrounding neighbours, it is thus not possible to distinguish between random and ordered alloys, but one may analyze the energy difference between different crystal structures. 

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. 

When the cores are approached, the sub-bands split, acquiring a bandwidth, and decreasing the gap between them (Fig. 14 a). At a definite inter-core distance, the subbands cross and merge into the non-polarized narrow band. At this critical distance a, the narrow band has a metallic behaviour. At the system transits from insulator to metallic (Mott-Hubbard transition). Since some electrons may acquire the energies of the higher sub-band, in the solid there will be excessively filled cores containing two antiparallel spins and excessively depleted cores without any spins (polar states). 

The energy of the 5 f electrons consists of their band-energy Ef and of a spin polarization term Asp. Ajp has an atomic origin, and tends to localize the itinerant 5f... 

In Fig. 7 the results of the model for the cohesive energy are given, and compared with the experimental values and with the results of band calculations. The agreement is satisfactory (at least of the same order as for similar models for d-transition metals). For americium, the simple model yields too low a value, and one needs spin-polarized full band calculations (dashed curve in Fig. 7) to have agreement with the experimental value. 

The trend in lattice parameter across the actinide nitride series is reproduced by an energy band theory in which it is assumed that the f-electrons are itinerant. The results with and without spin polarization do not differ greatly until AmN is reached but in this... 

DV-Xa molecular orbital calculation is demonstrated to be very efficient for theoretical analysis of the photoelectron and x-ray spectroscopies. For photoelectron spectroscopy, Slater s transition state calculation is very effective to give an accurate peak energy, taking account of the orbital relaxation effect. The more careful analysis including the spin-polarized and the relativistic effects substantially improves the theoretical results for the core level spectrum. By consideration of the photoionization cross section, better theoretical spectrum can be obtained for the valence band structure than the ordinary DOS spectrum. The realistic model cluster reproduce very well the valence state spectrum in details. 

The calculation of the ground-state energy of the Wigner electron crystal necessitates the self-consistent solution of the Slater-Kohn-Sham equations for the Bloch orbitals of a single fully occupied energy band, since there is one electron per unit cell and one is concerned with the spin-polarized state [45], This was accomplished by standard computational routines for energy band-... 

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