LAPW method

Figure B3.2.4. A schematic illustration of an energy-independent augmented plane wave basis fimction used in the LAPW method. The black sine fimction represents the plane wave, the localized oscillations represent the augmentation of the fimction inside the atomic spheres used for the solution of the Sclirodinger equation. The nuclei are represented by filled black circles. In the lower part of the picture, the crystal potential is sketched.

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 authors would like to thank Professor P E Blochl, Dr H Eckstein, Professor W Schattke, Professor K E Smith and T Strasser for making figures available for this publication. FS thanks Dr E E Krasovskii for introducing him to the LAPW method. 

Singh D J 1994 Planewaves, Pseudopotentials and the LAPW Method (Norweii, MA Kiuwer)... 

Diffraction patterns from thin polycrystalline Ge films were measured by the eleetron diffraetometer. After refinement of scale and thermal factors and corrections for the primary extinetion within the two-beam approximation, the parameters k (spherieal deeompression of valence eleetron shell) and multipoles P32- and P40 (anisotropy of electron density) were ealeulated (Table 4). The residual faetor R ealeulated from the experimental and theoretical amplitudes (the latter were ealeulated by the LAPW method, Lu Z.W., et al. Phys.Rev. 1993, B47, 9385) is 2.07% and proofs the high quality of the experimental. 

D. J. Singh, Planewaves, Pseudopotentials, and the LAPW Method (Kluwer, Boston, 1994). 

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 first principles molecular dynamics simulation has been applied, based on the linearized-augmented-plane-wave (LAPW) method, to Seg and Seg+ clusters. The equilibrium structures have been obtained for Se8 and Se8+ clusters for the ionized cluster Seg-, a remarkable change from that for the neutral cluster has been found, which reflects the strong electron-lattice coupling in the cluster <1997MI1660, 1997MI75, 1997MI472>. 

D. Singh Plane waves, pseudopotentials and the LAPW method, Kluwer, Dordrecht, 1991 ... 

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... 

This monograph is based almost entirely on the work of O.K. Andersen. It is therefore appropriate to reveal the sources of the material presented, and at the same time give a brief history of the development of linear methods. At present several types of such methods are used, e.g. the linear muffin-tin orbitals (LMTO) method [1.19], the linear augmented plane-wave (LAPW) method [1.19], the augmented spherical-wave (ASW) method [1.20], and the linear rigorous cellular (LRC) method [1.15]. Of these the LMTO method, which was the earliest, will be our main concern. 

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