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Extra resources for Electronic and Magnetic Properties of Metals and Ceramics
For selfconsistent calculations the electron density is needed; it is not hard to obtain in the ASA and will be discussed in the next section in connection with the augmented spherical wave method to which we now turn. 6 Augmented Spherical Waves (ASW) The augmented spherical wave method (ASW) was developed by Williams et al. (1979), and without Andersen's LMTO technique it would not have been conceived. There are essentially two differences: a different choice of the envelope function and a different and simpler method for augmenting the basis functions.
After these preliminaries we are now in a position to define the energy-independent orbital xjk(r) (Ecl- (1-154)) for the whole crystal given the functions (j) and (j) in the spheres. 0 h- e 0 r/S 1 Figure 1-10. Radial d function, P, and energy derivatives, P, P, of Y as given by Andersen (1975). case of / = 0, for which ,,_ A sin(V^r) r sa where x jk( ) * so-called envelope function that is defined to be nonzero only outside the spheres, and we have appended the angular momentum index, L, and the site index, T, to
This fact substantially reduces the number of band calculations required for total self-consistency. We add that these virtues unfortunately disappear to a large extend if the atomic sphere approximation and the shape approximation for the potential are abandoned. f d D% = \r — The preceding discussion was exclusively based on the Schrodinger equation and non-relativistic quantum mechanics. The spin of the electron was therefore largely ignored except when states were counted invoking the Pauli principle.