Full-potential augmented plane-wave FLAPW

One of the most accurate approaches to solve the LDF equations for the single slab geometry is the full-potential linearized augmented plane wave (FLAPW) method (10). Here, we highlight only the essential characteristics of this approach for further details the reader is referred to a recent review article (11). 

TABLES 1 and 2 show the calculated and measured results of splitting energies in WZ and ZB structures, respectively. Suzuki et al derived the values of A and Ar for WZ and ZN GaN and AIN from a full-potential linearised augmented plane wave (FLAPW) and band calculation [3,4], Another result with LAPW calculation was given by Wei and Zunger [5], Kim et al [6] determined them by the linear muffm-tin orbital (LMTO) method within the atomic sphere approximation (ASA). Majewski... 

The calculated and measured electron effective mass m c and its k-dependency for WZ and ZB GaN and AIN are summarised in TABLES 1 and 2, respectively. Suzuki et al derived them with a full-potential linearised augmented plane wave (FLAPW) band calculation [4,5], Miwa et al used a pseudopotential mixed basis approach to calculate them [6]. Kim et al [7] determined values for WZ nitrides by the full-potential linear muffin-tin orbital (FP-LMTO) method. Majewski et al [8] and Chow et al [9,10] used the norm-conserving pseudo-potential plane-wave (PPPW) method. Chen et al [11] also used the FLAPW method to determine values for WZ GaN, and Fan et al obtained values for ZB nitrides by their empirical pseudo-potential (EPP) calculation [12],... 

There are a number of band-structure methods that make varying approximations in the solution of the Kohn-Sham equations. They are described in detail by Godwal et al. (1983) and Srivastava and Weaire (1987), and we shall discuss them only briefly. For each method, one must eon-struct Bloch functions delocalized by symmetry over all the unit cells of the solid. The methods may be conveniently divided into (1) pesudopo-tential methods, (2) linear combination of atomic orbital (LCAO) methods (3) muffin-tin methods, and (4) linear band-structure methods. The pseudopotential method is described in detail by Yin and Cohen (1982) the linear muffin-tin orbital method (LMTO) is described by Skriver (1984) the most advanced of the linear methods, the full-potential linearized augmented-plane-wave (FLAPW) method, is described by Jansen... 

Full-potential linearized augmented plane wave (FLAPW)... 

As shown in Table 19, calculations [88] using the full-potential linearised augmented plane wave (FLAPW) method for the Al(lOO)—c(2 x 2)—Li phase formed by adsorption of 0.5 ML Li at room temperature con rm quantitatively the results of the LEED analysis described in Sec. 4.3 where, as shown in Fig. 15, Li was found to adsorb in a four-fold, substitutional site. 

We illustrate the spatially varying LDOS by means of the ( /7 x /7) R19.1° layer of sulfur on Pd(l 11) [209]. Figure 60 shows characteristic curves that are taken at different positions in the S layer. Within the empty states (<0 V) a lower current and dHU)/dU is found when measured on S atoms. This reduced electron density can be understood by means of the LDOS calculated by the full potential linear augmented plane wave (FLAPW) method [209]. 

The band structures of y-BN and (3-BN have been calculated (In context with that of a-BN) by a full-potential, linear, augmented-plane-wave (FLAPW) treatment. This Is the first ab Initio calculation for y-BN. The obtained energy band structure for y-BN is depicted In Fig. 4-22. Like a-BN (see Section 4.1.1.5, p. 38), y-BN is also an indirect gap Insulator. The gap of 4.9 eV Is produced by the valence band maximum at T and the conduction band minimum at K. The direct band gap (T-T) is 8.2 eV. The Brillouin zone of y-BN corresponds to that of a-BN [1]. 

Local density full potential linearized augmented plane wave (FLAPW) calculations (Ruquian Wu et al. 1991) and a local spin density approximation (LSDA) calculation... 

Electronic To have access to electronic properties, electronic structure and band symmetries, atomic orbitals approximation are no longer valuable [69]. EHian et al. used the full-potential linear-augmented plane-wave (FLAPW) method and the exchange-correlation potential treated in GGA, to reveal electronic properties... 

E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, Phys. Rev. B 24, 864 (1981). Full-potential linear augmented plane-wave (FLAPW)... 

Pressure variation of the electric field gradient (e.f.g.) in highly pure powdered samples of As and Sb has been followed up to 2.0 GPa at 293 K via pulsed NQR determination of the appropriate As, Sb or Sb resonance frequencies. The results were compared with theoretical calculations of the total e.f.g. by means of full-potential linearized augmented plane wave (FLAPW) calculations. The theoretical values were approximately 70% of the measured ones, but comparison was limited to some extent by the accuracy of the values used for the quadrupolar moments of As and Sb. Additional uncertainties arose from the... 

In the 1980s, methods were introduced that permit dealing with a crystal potential of completely general shape ( full-potential methods). The full-potential linearized augmented plane wave (FLAPW) method was developed by Wimmer et al. (43) in 1981. Another version of the FLAPW method was elaborated by Blaha et al. (44,45). A full-potential linear muffin tin orbital method has also been introduced (46,47). 

Classical simulations often lack the crucial insight into the problem, because one cannot simply use the force to characterize all the possible interactions. Fortunately, with decades of development, theoretical calculations have become quite sophisticated for crystals and molecules, although not yet for realistic nanometer-sized materials. For solids, the pseudopotential as well as the full-potential linearized augmented plane-wave (FLAPW) method within the density functional theory are well developed. Modern quantum chemical techniques (Gaussian98 [5] and MOLPRO [6]) are quite efficient to compute the potential surfaces for a given molecule. In order to illustrate those possibilities, we show some of our own results in simulating the reaction path for a segment of the retinal molecule in rhodopsin [7]. 

FLAPW Full potential linearised augmented plane wave Jansen and Freeman (1984)... 

As mentioned earlier, the existence of surface shifted core levels has been questioned.6 Calculated results for TiC(lOO) using the full potential linearized augmented plane wave method (FLAPW) predicted6 no surface core level shift in the C Is level but a surface shift of about +0.05 eV for the Tis levels. The absence of a shift in the C Is level was attributed to a similar electrostatic potential for the surface and bulk atoms in TiC. The same result was predicted for TiN because its ionicity is close to that of TiC. This cast doubts on earlier interpretations of the surface states observed on the (100) surface of TiN and ZrN which were thought to be Tamm states (see references given in Reference 4), i.e. states pulled out of the bulk band by a shift in the surface layer potential. High resolution core level studies could possibly resolve this issue, since the presence of surface shifted C Is and N Is levels could imply an overall electrostatic shift in the surface potential, as suggested for the formation of the surface states. 

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