Augmented spherical-wave calculations

Williams, A.R., Kiibler, K. and Gelatt, C.D. (1979). Cohesive properties of metallic compounds Augmented-spherical-wave calculations, Phys. Rev. B 19,... 

There has been less interest in phases of the heavier homologs of the group-14 elements. There are indications that )5-NaSn, which contains tetrahedral S114 imits, is metallic and augmented spherical-wave calculations reveal a small indirect... 

The results of our band structure calculations for GaN crystals are based on the local-density approximation (LDA) treatment of electronic exchange and correlation [17-19] and on the augmented spherical wave (ASW) formalism [20] for the solution of the effective single-particle equations. For the calculations, the atomic sphere approximation (ASA) with a correction term is adopted. For valence electrons, we employ outermost s and p orbitals for each atom. The Madelung energy, which reflects the long-range electrostatic interactions in the system, is assumed to be restricted to a sum over monopoles. 

The augmented spherical-wave method of Williams et al. [1.20] appeared in 1979 and is an efficient computational scheme to calculate self-consistent electronic structures and ground-state properties of crystalline solids. According to its inventors it is a "direct descendant of the LMTO technique", and a comparison will show that the two methods are indeed very similar. 

The authors of [20] used the method of augmented spherical waves (ASW) for calculation of bulk moduH and cohesive energies of metals. Figure 8.7 (lower part) shows the augmented spherical waves that are applied for simulating of interatomic electron waves. 

Self-consistent ab initio band-structure calculations using the augmented-spherical-wave method have been carried out by Coehoom (1990) for hypothetical YFen and YFei2-jM t (M=Ti, V, Cr, Mo, and W). The calculated value of magnetic moment per Fe atom is 2.02 Ub, in good agreement with experiment, particularly if one takes into account that the experimental total moment also contains a small orbital contribution. 

Magnetoacoustic quantum oscillations were obtained for LaAg (Niksch et al. 1987). Two kinds of ellipsoidal Fermi surfaces, denoted by a and ji, were observed, as shown in fig. 17. The solid lines are theoretical ones based on relativistic self-consistent Augmented Spherical Wave (ASW) calculations. 

As stated, the lattice parameter in ZrN shows an unusual dependence on the composition. It shows a decrease in the N-rich side and remains constant in the Zr-rich side (I). The augmented spherical wave (ASW) calculations of Schwarz et al. show the lattice parameter around 4.52 A in ZrsN4, where 25% of Zr sites are left vacant (13). The progressive decrease of the lattice parameter down to 4.556 A in the N-implanted ZrN films at HT, therefore, suggests incorporation of most of the implanted N atoms in the substitutional sites, leaving vacancies at Zr sites, whereas the increase of the lattice parameter in the samples implanted at RT could be due to... 

Various methods for the calculation of band structures have been devised. The augmented plane wave (APW) method (23,24) and the Green s function (GF) method of Korringa, Kohn, and Rostocker (KKR) (25-28) were used for most of the early calculations of the band structures of transition metal compounds. A common approximation in both methods is the use of the so-called muffin tin potential. In this approximation it is assumed that the crystal potential is spherically symmetric within nonoverlapping spheres around the atomic sites and constant in the region between the atomic spheres. 

Since the angular basis of Yim serves just for projecting to /-subspaces and since for any kind of atomic-like radial calculations (including the Environment-Reflecting Pseudopotentials and Projector Augmented Waves) the wavefunctions and all the quantities can be considered real, we can reach considerable simpliflcation by using real spherical harmonics i instead of Yim so that all the vectors for rank-n update also remain real ... 

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