LAPW method calculations

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT teclmiques [M]- PAW, however, provides all-electron one-particle wavefiinctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in tenns of a pseudo-wavefiinction (easily expanded in plane waves) tenn that describes mterstitial contributions well, and one-centre corrections expanded in tenns of atom-centred fiinctions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential fonnalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [, ]. PAW is also fonnulated to carry out DFT dynamics, where the forces on nuclei and wavefiinctions are calculated from the PAW wavefiinctions. (Another all-electron DFT molecular dynamics teclmique using a mixed-basis approach is applied in [84].)... 

The theoretical description of the electronic structure has been obtained by means of the LAPW method on an ab-initio basis1101. The electronic potential is determined self-consistently for the elementary cell of the bare host structure, which consists of 44 atoms. More complicated systems, where the tubes are filled with water molecules are also taken into account. Recent self-consistent full-potential calculations (FLAPW) are performed to refine the results 11 . 

For transition elements like Pt and Au the linear orbital extension to the LAPW method [43] has been used. We have employed the procedure proposed in [20], in which the 5p-states for Au and Pt are included in the core for total energy calculations, but corresponding local orbitals are also included in the basis for the valence states in order to allow the basis functions for the actual valence electrons to orthogonalize to the extended core states. 

The relativistic LMTO and LAPW methods were used to calculate [77-80] the Fermi surface of UPta. This is a heavy fermion compound, and its physical properties axe strongly influenced the presence of the narrow U-/ bands at the Fermi level. The shape of the Fermi surface is then sensitive to relativistic effects, in particular the SO-coupling. The results of the calculations [78] were surprising since they showed that the topology of the Fermi surface was well described by these band structures although they were obtained within the LDA. A similar precision was not found for the effective cyclotron masses which were off by up to a factor of 30 when compared to experiments. The crystal potential enters in the LMTO via the potential parameters [30,73] for each (or each j in the relativistic version [4]), including the mass parameters fi (eq.(49)). A convenient way... 

There is, however, a price for this versatility. The LMTO method is one of several linear methods, and like all the other linear techniques it is accurate only in a certain energy range. The present technique in particular should not be used for states too far above the Fermi level. If such states are required one may still solve the self-consistency problem by the LMTO technique and then turn to the Linear Augmented Plane Wave (LAPW) method for accurate calculation of the unoccupied high-lying levels. Furthermore, in... 

The basic calculational techniques utilized by Norman (1985) and Norman et al. (1985a) are all well documented so this description is quite brief. All calculations were performed using a self-consistent linearized augmented-plane-wave (LAPW) method (Koelling and Arbman 1975). The warped muffin-tin (WMT) shape approximation was used. In this approximation, the potential is spherieally averaged about... 

However, the Fermi surface depends sensitively on details of the E-k relation, and the determination of the Fermi surface demands a more precise calculation for the eigenvalues than that for the cohesive energy. Therefore, for studies of the Fermi surface, these linearized methods should be applied carefully. Errors originating from linearized approximations should be minimized. Nevertheless, the LAPW method is valuable for calculations of the electronic structure in lanthanide compounds with complex crystal structures, such as LaCufi. 

As mentioned above, Harima et al. (1990b) calculated the band structure of LaCus with the orthorhombic structure by an LAPW method. The Cu-3d band and La-4f band are... 

Fig. 1. Band structures of (a) CeRhj and (b) CePdj calculated using a fully relativistic LAPW method. Note how the narrow f bands in CeRhj (about 0.05 Ry above the Fermi energy) pull down to touch the Fermi energy in CePdj which would be consistent with a tetravalent-mixed valent picture of alloys between these materials. However, it should be noted that CeRhj has very nearly a full f electron occupied through hybridization.

Blaha and Schwarz (59) also performed a band structure calculation for VN by means of the full-potential LAPW method. The authors compared the band structures, densities of states, and partial charges obtained by this method with the results of the earlier APW calculations (17,19), in which the muffin-tin approximation was used. The main differences between the two methods were outlined. It was found that the non-muffin-tin effects in this highly coordinated compound are very small. 

Figure 3 Band structure of TiC, calculated by means of the full-potential LAPW method. The energy (Ryd) refers to the mean value of the potential in the region between the atomic spheres as energy zero. The Fermi energy, indicated by a horizontal line, is at 0.64172 Ryd. (From Ref. 58.)...

Figure 12 LAPW total, g E), and local partial /-like densities of states, g (E), for TiC in units of states of both spin directions per Ryd and unit cell, calculated by means of the full-potential LAPW method...

LCAO partial Mike DOSs and the LAPW local partial /-like DOSs (4), because the LCAO partiai /-like DOSs refer to the whole unit cell, whereas the LAPW local partial /-like DOSs refer to specific muffin-tin spheres. As an example of this difference, the partition of the d-like DOS of TiC in the range of the p bands may be mentioned. According to the LCAO calculation the /js component of the partial t/-like DOS is higher than the eg component, as can be inferred from Fig. 9. However, the local partial /jj-like DOS obtained by means of the LAPW method is smaller than the eg component, as can be gathered from Fig. 14. 

Calculations of the valence electron densities (VEDs) by means of the LAPW method for TiC, TIN, and TiO (57), for TiC (73), and for VN (59,74), as well as by means of the FLAPW method for TiC and TiN (58), form the basis for an extensive discussion of the mechanism of chemical bonding in these substances. The theoretical electron densities (EDs) were compared... 

The VEDs for the four compounds MX (with M = Zr, Nb and X = C, N) have been calculated by Schwarz (4), again using the LAPW method. The main difference between the Ad metals (Zr, Nb) and the 3d metals (Ti, V) is the existence of an additional nodal surface in the VED of the former, leading to a spatially more diffuse electron density distribution. 

Self-consistent, scalar relativistic energy band calculations for hexagonal WC in bulk and thin-film forms were performed by Mattheiss and Hamann (86) by means of the LAPW method. 

The electric field gradients at the boron and metal sites for various transition metal diborides MB2 (M = Ti, V, Cr, Zr, Nb, Mo, and Ta) were calculated by Schwarz et al. (172) by means of the full-potential LAPW method as embodied in the Wien 95 code (45) in a scalar relativistic version. 

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