The spline augmented plane wave method

The recent methods to calculate the electronic structure of solids generate a more or less limited number of Bloch states which does not make a complete set. As a consequence for example the sum rule of Thomas-Reiche-Kuhn is not fulfilled. To overcome this deficiency a new method to solve the Schrödinger equation is proposed which uses far more trial functions than other methods. Similar to the APW-scheme the wave-functions are superpositions of plane waves and, within the APW-sphere, of spherical waves. Contrary to the APW-scheme the radial dependence of the spherical waves is expressed in a basis of localized spline functions determined for each k using the variational scheme. The new method is expected to be especially appropriate for non-warpedmuffin-tin potentials. Our tests showed that the method is very accurate and the sum rule involving the momentum operator is now well satisfied.     

Energy band structure of aluminium by the augmented plane wave method

The band structure of metallic aluminium has been calculated by the augmented plane wave method. The energy values and wave functions were computed for the equivalent of 2048 points in the Brillouin zone and for energies ranging from the bottom of the conduction band (3s, 3p) to approximately 0.4 Ry above the Fermi energy. The density of states and the Fermi energy were determined using a variant of an accurate method developed by Gilat and Rauben heimer (Phys. Rev.144 (1966), 390). The results are discussed and compared with earlier results.     

Iterative diagonalization in augmented plane wave based methods in electronic structure calculations

Due to the increased computer power and advanced algorithms, quantum mechanical calculations based on Density Functional Theory are more and more widely used to solve real materials science problems. In this context large nonlinear generalized eigenvalue problems must be solved repeatedly to calculate the electronic ground state of a solid or molecule. Due to the nonlinear nature of this problem, an iterative solution of the eigenvalue problem can be more efficient provided it does not disturb the convergence of the self-consistent-field problem. The blocked Davidson method is one of the widely used and efficient schemes for that purpose, but its performance depends critically on the preconditioning, i.e. the procedure to improve the search space for an accurate solution. For more diagonally dominated problems, which appear typically for plane wave based pseudopotential calculations, the inverse of the diagonal of (H ? ES) is used. However, for the more efficient “augmented plane wave + local-orbitals” basis set this preconditioning is not sufficient due to large off-diagonal terms caused by the local orbitals. We propose a new preconditioner based on the inverse of (H ? λS) and demonstrate its efficiency for real applications using both, a sequential and a parallel implementation of this algorithm into our WIEN2k code.     

Linearized augmented plane wave method utilizing the quadratic energy expansion of radial wave functions

Conclusions The developed version of the augmented plane wave method yields eigenvalues and eigenfunctions with higher accuracy than the standard LAPW, preserving its computational efficiency.The approximation of the exact radial solution by the Taylor expansion involving also the second energy derivative of the radial function, except for the first derivative, has two advantages. First, the energy dependence of the logarithmic derivatives atr=R is better described and, therefore, the method is less sensitive to the choice of the centre of expansionE ₀ or, equivalently, acceptably accurate eigenvalues are obtained for the broader energy region aroundE ₀. The other and probably more important advantage is that the approximate radial solutions are remarkably closer to the exact radial functions inside the muffin-tin sphere. This can be of use when evaluating the measurable quantities depending on the wave functions.     

Quadratic augmented plane wave method for self-consistent band structure calculations

Recently linearized versions of the augmented plane wave (APW) method have been introduced. The quadratic-APW (QAPW) method is presented which is a more general formulation of the linear-APW (LAPW) methods. Here the exact radial solution inside the muffin-tin (MT) sphere is replaced by its Taylor expansion with respect to the energy, truncated after the quadratic term, i.e. with higher accuracy when compared with the standard LAPW method which uses only the linear term. The standard LAPW method is obtained as a special case from our formulation. Similarly to the standard LAPW method, the energy independent APW's are formed from approximate radial wave functions which lead to the secular equations linear in energy. The analysis of the solution inside the MT-sphere shows that the eigenvalue error is proportional to (E-E ₀)⁶ in the method suggested as compared with (E-E ⁰)⁴ for the standard LAPW method. As an application both non-self-consistent and self-consistent calculations are presented for the band structure of FCC copper metal.     

Calculation of VLEED spectra with the extended linear augmented plane wave kp method

We describe a new method to calculate the VLEED (very low energy electron diffraction) spectra within the Bloch waves approach. The method is based on the variational solution of the Schr?dinger equation for a semi-infinite crystal. Inside the solid the trial LEED functionΦ is a linear combination of propagating and evanescent Bloch waves, which are generated by the inverse ELAPW (extended linear augmented plane waves)-kp method. The trial function is smoothly continuous over the whole space, and it satisfies by construction the equation (Ĥ − E)Φ=0 both in the crystal and in the vacuum half-spaces. In the surface layer the equation δ‖(Ĥ − E)Φ‖=0 is solved. To illustrate the properties of the method we discuss its application to the 1D case. We have performed a self-consistent band structure calculation of the 1T chalcogenide VSe₂ and obtained from the first principles the normal-incidence target current spectrum (TCS) for its (0001) surface. Presented at the VIII-th Symposium on Surface Physics, Třešt’ Castle, Czech Republic, June 28 – July 2, 1999.     

Viable improvement of the full potential linearized augmented plane wave (FLAPW) method

A characteristic feature of the Full Potential Linearized Augmented Plane Wave (FLAPW)-method consists in the spatial subdivision of the charge density analogous to that of the one-particle wavefunctions, i.e. into a portion that is expanded in terms of spherical harmonics Y_lm inside the muffin-tin spheres and into a plane wave expansion of the interstitial charge density. To obtain the Hartree potential inside the spheres one is hence forced to solve a boundary value problem at the sphere surface. In addition, in all non-equivalent spheres each (l,m)-component of the charge density is mapped onto 300-400 radial grid points. To ensure an accelerated convergence of the calculation, the pertinent schemes require this rather large data set to be stored and mixed within 3-6 iteration steps. We show and illustrate for the example of a spin-polarized Ni-film with and without an oxygen overlayer and for bulk Si that this data set can be compressed by at least two orders of magnitude if one partitions the charge density in a different way so that the relevant portion determining the interatomic bonding can be Fourier expanded throughout the lattice cell. One thereby arrives at a modified FLAPW-scheme that combines favorable features of the original method with virtues of the pseudopotential method which consist in the simple construction of the Hartree potential and the efficient way of achieving self-consistency. These advantages can be exploited to the fullest by using Fast Fourier Transform. Moreover, forces that atoms experience in off-equilibrium positions attain a particularly simple form in terms of the charge density expansion coefficients. Received: 31 May 1997 / Revised: 12 December 1997 / Accepted: 18 December 1997     

The electronic bandstructure of rhodium and the effects of change of volume

The electronic bandstructures of fcc rhodium have been calculated for the normal value of the lattice constant and one 5% smaller, using the nonrelativistic symmetrized augmented plane wave method. The results of the first calculation are in good agreement with those of other workers. Under pressure the d-bands shift and broaden appreciably, resulting in a slight increase in d-occupation.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.     

A plane wave generation method by wave number domain point focusing

A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications.     

The bandstructure of NiSb

The electronic bandstructure and the calculation of the density of states of NiSb using the APW-method have been performed. Some suggestions are given about d-like states and the position of the Fermi-energy. A new interpretation of the existing experimental data is made.     

The bandstructure and optical properties of PtBi

By means of the APW-method the electronic bandstructure and the density of states of PtBi have been calculated. The spatial behaviour of the d-states has been investigated and the Fermi-level calculated. Experimental data, e.g. XPS, were used to test the results. Also a comparison was made with two closely related compounds PdSb and PtSn. Finally the optical properties of PtBi have been calculated from the collected numerical data, using the joint density of states and density—density correlation formalism.     

Improved fake mode free plane wave expansion method

We analyze the origin of the fake modes introduced by the plane wave expansion method with three-dimension (3D) supercell approximation. Through the detailed analysis of the energy distribution of fake modes and real modes, we propose the plane wave expansion-three planar-slab waveguides method to remove the fake modes and obtain the fake mode free band structure of a two-dimensional air hole photonic crystal slab. To the best of our knowledge, this is the first time that such a fake mode free photonic crystal band structure is presented. Our method is also definitely useful in designing other 3D devices.     

On the mechanism of electronic transport in polycrystalline CdO thin films

Cadmium Oxide (CdO) thin films (d = 0.16−0.62 μm) were deposited onto glass substrates by thermal evaporation under vacuum (quasi closed volume technique) of high purity (99.99%) CdO polycrystalline powders. The substrate temperature was 300 and 473 K, respectively. After a post-deposition heat treatment, the temperature dependence of the electrical conductivity becomes reversible. The electronic transport mechanism in studied samples is explained in terms of Seto’s model for polycrystalline semiconducting films. The values of optical bandgap have been determined from absorption spectra.     

Solution of the three-dimensional problem of plane wave diffraction by a two-period plane grating

Using the discrete source method, we develop an algorithm for solving the three-dimensional problem of wave scattering by a plane grating consisting of acoustically soft or acoustically stiff bodies. An efficient algorithm is proposed for determining the periodic Green’s function of the grating. Numerical results are obtained for different geometries of the grating elements. The fulfillment of the energy conservation law is verified along with the fulfillment of the boundary condition at the surface of the central grating element.     

Waveguiding losses of micro-structured fibres—plane wave method revisited

We present a numerical method for the analysis of translationally invariant systems with anisotropic and dispersive electric and magnetic properties. This material model enables us to calculate the mode structure of photonic devices such as photonic crystal fibres (PCF) containing inclusions with anisotropic, conducting, magnetic, or negative index materials. The method is based on the popular plane wave (PWM) discretisation scheme applied to the generalised vectorial transmission line equations. The analysis is focused on the calculation of radiation losses. For this purpose we consider a uniaxial perfectly matched layer (UPML) termination of the otherwise periodic system. We asses the accuracy of the method and the properties of spurious modes created inside the UPML.     

The bandstructure of the copperoxide-plane including the singlet band

The effects of the Zhang-Rice singlet are included into the RPA-treatment of the Emery model by considering an additional singlet operator. The Fermi level of the doped, paramagnetic case is found within the singlet band. In agreement with the experiments, the dispersion of this band is similar to ordinary bandstructure calculations but it has a reduced bandwidth and is mainly of oxygen character.     

Approximate method of solving the problem of diffraction of a plane electromagnetic wave by a thin chiral layer covering a perfectly conducting plane

One-sided approximate impedance-type boundary conditions for a thin chiral layer placed on a perfectly conducting plane are derived. With these conditions, the problem of incidence of a plane electromagnetic wave on a chiral structure is solved. Approximate formulas for the coefficients of reflection of the fundamental and depolarized components are derived for the case of the perpendicular polarization of the electromagnetic wave (the electric field strength is normal to the plane of incidence). A comparison with an exact solution to the problem of diffraction by this chiral structure is made.     

磁各向异性介质中的平面电磁波

讨论了磁各向异性理想介质中平面电磁波的一般特性,继而推证了这种介质中平面波的对偶关系,导出了磁晶体中的“菲涅耳方程”,并利用此方程分析了这种理想介质中的平面波的结构、传播及其偏振特性．