An overview of high-performance computing (HPC) is given. Different types of computer architectures used in HPC are discussed: vector supercomputers, high-performance RISC processors, various parallel computers like symmetric multiprocessors, workstation clusters, massively parallel processors. Software tools and programming techniques used in HPC are reviewed: vectorizing compilers, optimization and vector tuning, optimization for RISC processors; parallel programming techniques like shared-memory parallelism, message passing and data parallelism; and numerical libraries.

A method for solving the coupled channel equation for potentials with a Coulomb singularity is presented: At small r, where the Coulomb term is dominant, the solution is expressed by using the variation of constants method in terms of the Coulomb functions F(l) and G(l). At large r, where the Coulomb potential is no longer important, one returns to the usual variable phase method which ''presses the solution in terms of Bessel functions and Neumann functions. Furthermore, the use of an interpolation scheme for the energy dependence considerably reduces the amount of computation. The advantages of this approach when used in conjunction with the point group symmetry are illustrated by using a realistic potential taken from a full potential linearized augmented plane wave (FLAPW) calculation for Cu.

An expansion is derived for the regular (power series) part of the Coulomb function, G0(η, ρ), in terms of Whittaker functions, which are closely related to the regular Coulomb functions F1 (η, ρ). The expansion coefficients are given as a sum of three terms; each of the terms obeys a simple three-term recurrence relation. In conjunction with the downward recurrence method for the regular functions (which is also discussed), this expansion is very useful for computing the irregular Coulomb functions G1(η, ρ), in particular for an attractive potential (η < 0) and for small or moderately large values of ρ

The Neumann series representation for the Bessel functions and Neumann functions is generalized for the regular and irregular solutions of the Kummer equation. This representation results in a convenient algorithm for the computation of a large family of special functions, e.g., most of the soluble cases of the Schrödinger equation, including complex energies or a complex (optical) potential.

Korringa-Kohn-Rostoker (KKR) calculations are performed for the high-temperature superconductor compound Bi2Sr2Ca1Cu2O8 both semi-relativistically and fully relativistically in order to investigate the influence of spin-orbit interaction. While the overall features of the two band structures turn out to be very similar, a small dropping of the Fermi energy leads to better agreement with angle-resolved photoemission experiments. However, the deviation from angle- integrated photoemission experiments remains unchanged.

A certain series of Bessel functions-recently discussed by Lee (1988)-is an asymptotic expansion of an integral of a Bessel function. Here the asymptotic properties of the series are investigated in more detail, and it is shown that the series is not only asymptotic, but also convergent under suitable restrictions. For large positive real arguments finite numbers of terms of the series give good approximations to the integral, but the infinite sum is different from the integral.

Angle-integrated photoemission, inverse photoemission, and x-ray emission spectra were calculated for ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$Ca${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8}$ and ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10}$. All spectra are based on densities of states obtained from local-density full-potential linearized augmented plane-wave (FLAPW) calculations. For the photoemission and inverse photoemission spectra, the single-scatterer final-state approximation was applied. For low photon energies mainly O $p$ states show up in the spectra, and there are appreciable differences between the two compounds. For high photon energies the spectra of both compounds are very similar and show Cu and Tl contributions. The unoccupied states probed by inverse photoemission have mainly O $p$ character with some Tl and Ba contributions. The Cu ${L}_{\mathrm{III}}$ x-ray emission spectra of both compounds reflect the Cu $d$ density of states (DOS) and closely resemble each other, whereas the O $K\ensuremath{\alpha}$ x-ray-emission spectra are narrower than the corresponding DOS because of differences in the core levels of inequivalent O atoms.

A formalism is derived to calculate the intensities of core-core-valence Auger spectra using results of band-structure calculations. The spectra obtained can be interpreted in terms of local partial densities of states. This method is applied to the ${L}_{3}$${M}_{2}$,3V transitions of Ti in the systems Ti-C, Ti-N, and Ti-O for ordered and disordered structures. In the case of Ti-C and Ti-O, a comparison with experimental spectra shows good agreement, especially concerning the influence of nonstoichiometry on the line shapes of the spectra.

Angle-integrated photoemission and inverse photoemission (IP) spectra of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ were calculated using the single-scatterer final-state approximation and densities of states obtained from a highly precise local-density band calculation. The photoemission spectra of the valence band show mainly Cu d states for high photon energies, and an increasing O p contribution with decreasing photon energies, which brings about qualitative changes in the spectra. The Bi contribution is small in all valence-band spectra, but the unoccupied Bi p states give rise to a peak in the IP spectrum. The calculated O-K\ensuremath{\alpha} x-ray emission spectrum (XES) is found to be narrower than might be expected from the O p density of state (DOS) alone due to the different core-level positions for the inequivalent oxygen atoms. By contrast, the calculated Cu ${L}_{\mathrm{III}}$ XES closely resembles the Cu d contribution to the DOS.

The electronic structure of Au rich Au-x-Pd-1-x alloys is investigated experimentally in terms of Au-N-6, 7 soft X-ray emission spectra and theoretically in terms of the fully relativistic KKR-CPA method. It is found that the theoretically calculatedN-6, 7 spectra agree rather well with the experimental data. It is also found that the calculated Fermi vectors in the direction [110] match very well the data obtained in diffuse electron scattering experiments.

Korringa-Kohn-Rostoker-Coherent-Potential-Approximation (KKR-CPA) calculations were performed on FeAl and NiAl in the CsCl structure with various concentrations of vacancies on the transition metal sublattice and antistructure atoms on both sublattices. It is found that transition metal vacancies only bring about minor changes in the density of states, whereas Fe atoms on the Al sublattice give rise to additional states near the Fermi energy. X-ray photoelectron spectra were calculated and-in the case of NiAl-compared with experiment.

Using a single site approximation for the final state (LEED function) and classical electron-photon interaction the intensity of XPS spectra is calculated for UIr3, UPt3 and UAu3 in terms of relativistic LMTO partial densities of states and relativistic partial cross sections. For UPt3 and UAu3 the theoretical intensities compare very well with the available experimental data.

Based on relativistic formulas derived in an earlier paper and on fully relativistic self-consistent linear augmented plane-wave band results for the densities of states and potentials, the x-ray photoemission intensity for ${\mathrm{UBe}}_{13}$ has been calculated. The results support the experimental finding of very low Be intensity at the Fermi energy. The agreement between the calculations and the data suggests that the highly correlated 5f states seen below 20 K may be condensing out of normal one-electron band states.

Al−Kα XPS intensities are calculated for Au x Pt1−x, Ag x Au1−x, Ag x Pt1−x and Au x Ni1−x using partial local densities of states as obtained from the fully relativistic KKR-CPA (GF) method and fully relativistic partial cross sections. It is found that the calculated spectra agree rather well with available angle integrated photoemission data.

A self-consistent LAPW band structure calculation of Cu2O is presented. Total and partial densities of states and electron densities were calculated and are used to give an interpretation of chemical bonding. It is found that there are significant deviations from a simple ionic picture due to a depletion of the valence band of Cu-3d electrons leading to a non-spherical charge density around Cu. A critical discussion of theoretical and experimental work on Cu2O is given.

The influence of metal vacancies on the electronic structure of zirconium nitride is studied by means of the KKR-CPA method. Besides lowering the Fermi energy, the vacancies do not change profoundly the density of states. The contribution of the vacancy subcell to the density of states is analysed in terms of the resonance condition for virtual bound states. In particular it is found that contrary to the case of vacancies on the nonmetal sublattice, where a sharp a1g-like virtual bound state was found, for metal vacancies there is only a somewhat weak eg-like virtual bound state, but no t2g-like peak. In the case of vacancies on both sublattices, the a1g-like virtual bound state is present, but the eg-like peak vanishes almost completely.

The Korringa-Kohn-Rostoker--coherent-potential-approximation (KKR-CPA) and the Korringa-Kohn-Rostoker--Green's-function (KKR-GF) methods are applied to study the electronic structure of substoichiometric ${\mathrm{TiC}}_{\mathrm{x}}$, ${\mathrm{TiN}}_{\mathrm{x}}$, ${\mathrm{VC}}_{\mathrm{x}}$, and ${\mathrm{VN}}_{\mathrm{x}}$. The introduction of vacancies in the nonmetal sublattice influences the electronic structure of all these compounds in a similar way: an additional sharp ``vacancy peak'' appears in the density of states, which, with increasing vacancy concentration, is broadened and shifted to higher energies. The Fermi energy is generally lowered by the introduction of vacancies.

The electronic structures of ${\mathrm{ZrC}}_{\mathrm{x}}$, ${\mathrm{ZrN}}_{\mathrm{x}}$, ${\mathrm{NbC}}_{\mathrm{x}}$, and ${\mathrm{NbN}}_{\mathrm{x}}$ for several concentrations x were investigated by means of the Korringa-Kohn-Rostoker coherent-potential approximation and the Korringa-Kohn-Rostoker Green's-function methods. The influence of vacancies on the electronic structure of these compounds is quite similar to the case of substoichiometric carbides and nitrides of 3d metals: near the minimum in the density of states between the nonmetal p and the metal d subbands additional ``vacancy peaks'' appear, and (except for ${\mathrm{ZrC}}_{\mathrm{x}}$) the Fermi energy is lowered. It is argued that similar properties may be expected for other d- and f-metal carbides, pnictides, and chalcogenides.

The Ti K emission band from TiN and substoichiometric ${\mathrm{TiN}}_{\mathrm{x}}$ (0.35\ensuremath{\le}x<1) has been investigated. The Ti p--like states are very strongly hybridized with the N 2p states located \ensuremath{\sim}6 eV below the Fermi level (${E}_{F}$) in TiN. In the presence of nitrogen vacancies, p-like nonbonding states are detected \ensuremath{\sim}2 eV below ${E}_{F}$. As x decreases, the intensity of the nonbonding structure increases, that of the \ensuremath{\sim}6 eV peak decreases, and the valence-band states move closer to ${E}_{F}$ reflecting the decrease in cohesion. Theoretical x-ray spectra have been obtained with use of the Korringa-Kohn-Rostoker coherent-potential-approximation densities of states and appropriate transition-matrix elements. The theory is shown to account for all the trends observed experimentally.