FLAPW plane-wave

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].)... 

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). 

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. 

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],... 

FAB FEA FEB FET FFP FIB FIELO FIR FLAPW FP FP-LMTO FWHM fast atom beam free A exciton free B exciton field effect transistor far field pattern focused ion beam facet-initiated epitaxial lateral overgrowth far infrared reflectance full-potential linearised augmented plane wave Fabry-Perot full-potential linear muffin-tin orbital full wave at half maximum... 

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. 

In order to describe the wave functions decaying from a single crystal surface into the vacuum, the FLAPW method has been applied which gave the justification to expand the wave functions into 2D basis functions as symmetrized plane waves parallel to the surface (so called star functions, ) with their corresponding z-dependent star coefficients... 

These back-of-the-envelope calculations may be compared with the results of full-potential electronic-structure calculations of the FLAPW type (WIEN2k) based on the generalized gradient approximation (GGA) for the exchange-correlation potential. On purpose, we use a very accurate DFT method. Figure 3.1 shows the results of these quantum-mechanical calculations as a plot of the total energy as a function of the volume per formula unit for all three structure types. The calculations are based on 482/266/289 plane waves for... 

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]. 

FLAPW Fully linearized augmented plane wave GGA Generalized gradient approximation... 

Plane waves (FLAPW) Spherical waves (LMTO, ASW)... 

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]. 

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