We describe the screened Korringa-Kohn-Rostoker (KKR) method and the third-generation linear muffin-tin orbital (LMTO) method for solving the single-particle Schrödinger equation for a MT potential. In the screened KKR method, the eigenvectors CRL,i are given as the non-zero solutions, and the energies εi as those for which such solutions can be found, of the linear homogeneous equations: , where Ka (ε) is the screened KKR matrix. The screening is specified by the boundary condition that, when a screened spherical wave is expanded in spherical harmonics YR′L′ (ȓR′) about its neighboring sites R′, then each component either vanishes at a radius, rR′=aR′L′, or is a regular solution at that site. When the corresponding “hard” spheres are chosen to be nearly touching, then the KKR matrix is usually short ranged and its energy dependence smooth over a range of order 1 Ry around the centre of the valence band. The KKR matrix, K (εν), at a fixed, arbitrary energy turns out to be the negative of the Hamiltonian, and its first energy derivative, K (εν), to be the overlap matrix in a basis of kinked partial waves, φRL (εν, rR), each of which is a partial wave inside the MT-sphere, tailed with a screened spherical wave in the interstitial, or taking the other point of view, a screened spherical wave in the interstitial, augmented by a partial wave inside the sphere. When of short range, K (ε) has the two-centre tight-binding (TB) form and can be generated in real space, simply by inversion of a positive definite matrix for a cluster. The LMTOs, χRL (εν), are smooth orbitals constructed from φRL(εν, rR) and φRL(εν, rR), and the Hamiltonian and overlap matrices in the basis of LMTOs are expressed solely in terms of K (εν) and its first three energy derivatives. The errors of the single-particle energies εi obtained from the Hamiltonian and overlap matrices in the φ(εν)- and χ(εν) bases are respectively of second and fourth order in εi – εi. Third-generation LMTO sets give wave functions which are correct to order εi – εν, not only inside the MT spheres, but also in the interstitial region. As a consequence, the simple and popular formalism which previously resulted from the atomic-spheres approximation (ASA) now holds in general, that is, it includes downfolding and the combined correction. Downfolding to few-orbital, possibly short-ranged, low-energy, and possibly orthonormal Hamiltonians now works exceedingly well, as is demonstrated for a high-temperature superconductor. First-principles sp3 and sp3d5 TB Hamiltonians for the valence and lowest conduction bands of silicon are derived. Finally, we prove that the new method treats overlap of the potential wells correctly to leading order and we demonstrate how this can be exploited to get rid of the empty spheres in the diamond structure.

Generalized functionals are constructed from the exchange-correlation energy by a Legendre transformation which makes the new functionals stationary at the electronic charge density, potential, and wave functions for the ground-state. Using generalized functionals, the density, potential, and wave functions can be independently parameterized and varied to determine the ground-state energy-surface for a system of atoms. This eliminates the computationally awkward steps of constructing densities from wave functions or potentials from densities, and is particularly well suited to parameterizations using tight-binding orbitale together with atomic-like densities and potentials. For each choice of parameters, the only quantities which must be computed are the electron-electron energy for the density, the integral of the potential over the density, and the band structure energy for the wave functions. To second order in the density, potential, and wave functions, the energy for a configuration of atoms is given by the generalized functional evaluated at a superposition of atomic densities, a potential made by stitching together the atomic potentials where they are equal, and atomic wave functions. For more accurate stationary energies the densities, potentials, and wave functions can be improved by one or more conjugate gradient steps.

We present a selfconsistent LCAO approach for describing the electronic properties of materials. This method introduces many-body effects by means of a new approach, whereby a local orbital potential is defined by calculating the exchange-correlation energy as a function of the different orbital occupancies. A LCAO-pseudopotential is also introduced, keeping all the calculations within the context of the local orbital basis. We have applied the method to the calculation of simple molecules and crystals, in both cases we find results that confirm the validity of our approach.

Tight binding is often seen as a middle ground method, lying between accurate ab iniiio methods, and fast empirical potential methods. The challenge is to make tight binding both as fast and as accurate as possible. One way to achieve this is to take established ab initio methods, and apply systematic approximations and efficient numerical techniques to obtain the greatest possible speed. A recently developed method, employing this approach, is described results presented for silicon, and recent developments (including fully self-consistent extensions) are reported.

The energetics of metallic alloys, their surfaces or interfaces, and magnetic multilayers is studied in terms of effective interatomic (or interlayer) interactions that are determined from ab initio electronic structure calculations using the TB-LMTO method combined with the coherent potential approximation and the method of surface Green functions. First the theoretical background (force theorem, Lloyd formula, generalized perturbation method for bulk and surfaces, vertex cancellation theorem, method of infinitesimal rotations) is discussed, and then the applications to the phase stability of bulk alloys, surface segregation in disordered alloys, magnetism-induced ordering in two- and three-dimensional systems, phase diagram of two-dimensional alloys, interlayer exchange coupling in metallic multilayers, and the construction of Heisenberg-like Hamiltonians for magnetic systems are presented.

We present two tight-binding linear muffin-tin orbitals (TB-LMTO) techniques for electronic structure calculations of extended defects (such as grain boundaries, interphase interfaces, surface layers etc.) in metals. The first is based on the first-principles self-consistent surface Green's function approach within the atomic-sphere approximation (ASA) utilizing two-dimensional periodicity in the layers parallel to the interface. In the second approach the Hamiltonian is constructed within the TB-LMTO-ASA as well, but semiempirical terms are employed to characterize the repulsive part of the interaction and the effect of electrons in interstitial space. While the adjustable parameters have only been fitted to the properties of ideal ground state structure, the semiempirical approach describes correctly the structural energy differences, phonon frequencies etc. Two examples are presented: the electronic structure of the Σ = 5(210)/[001] tilt grain boundary in tungsten is determined and the sensitivity of 4d magnetic moments in thin films to local environment is discussed. A comparison of the semiempirical TB-LMTO-ASA with the first-principles full-potential LMTO results is performed along the trigonal deformation path connecting the bcc, simple cubic and fee structures and the applicability of the semiempirical approach for simulating atomic structure of extended defects is assessed.

We describe the ab initio construction of two-center tight-binding (TB) hamiltonians, which at a properly chosen input density upon non-selfconsistent solution of the related Kohn-Sham equations transform the energy within density-functional theory (DFT) into a tight-bindinglike expression. In cases, where the electron density of the interacting many-atom structure in good approximation may be represented as a sum of atomic-like densities, the method has been shown to operate highly transferable, being particularly successful in determining the properties of low-energy silicon clusters, in predicting the structure and vibrational signatures of fullerene oligomers, amorphous carbons and carbon nitrides and in simulating elementary growth reactions on diamond surfaces. The uncertainties within the standard non-SCF DF-TB-variant, however, increase if the chemical bonding is controlled by a delicate charge balance between different atomic constituents, as e.g. in organic molecules and in polar semiconductors. Therefore, we extend the standard TB-approach to the operation in a selfconsistent-charge mode (SCC-DFTB) in order to improve total energies, forces, and transferability in the presence of considerable long-range Coulomb interactions. By using a variational technique, we derive a transparent and readily calculable expression for the iterative modification of Hamiltonian matrix elements and show, that the final energy is a second order approximation to the total energy in density-functional theory, see M. Elstner et al., this Symposium. First successful applications to surface studies of GaAs and dislocation modeling in GaN will be presented.

We discuss various aspects of calculating the electronic structure of liquid and amorphous metals using the recursion method and the tight-binding linear muffin-tin orbitals (TB-LMTO) basis. Resistivity calculations for such systems based on the Kubo-Greenwood formula and the TB-LMTO-recursion method are presented and compared with similar calculations based on the linear combination of atomic and atomic-like orbitals (LCAO) and the chemical pseudopotential approach. Results for amorphous Fe and Co and liquid Hg, Pd, and some 3d transition metals are presented. Sources of error in the calculation and ways to improve upon the present calculations are discussed.

In the present paper different tunneling mechanisms in conventional and half-metallic ferromagnetic tunnel junctions are analyzed within the same general method. Theoretically calculated direct tunneling in iron group systems leads to about a 30% change in resistance, which is close but lower than experimentally observed values. It is shown that the larger observed values of the TMR might be a result of tunneling involving surface polarized states. We find that tunneling via resonant defect states in the barrier radically decreases the TMR (down to 4% with Fe-based electrodes), and a resonant tunnel diode structure would give a TMR of about 8%. With regards to inelastic tunneling, magnons and phonons exhibit opposite effects: one-magnon emission generally results in spin mixing and, consequently, reduces the TMR, whereas phonons are shown to enhance the TMR. The inclusion of both magnons and phonons reasonably explains an unusual bias dependence of the TMR.

The model presented here is applied qualitatively to half-metallics with 100% spin polarization, where one-magnon processes are suppressed and the change in resistance in the absence of spin-mixing on impurities may be arbitrarily large. Even in the case of imperfect magnetic configurations, the resistance change can be a few 1000 percent. Examples of half-metallic systems are CrO2/TiO2 and CrO2/RuO2, and an account of their peculiar band structures is presented. The implications and relation of these systems to CMR materials, which are nearly half-metallic, are discussed.

We present an extension to the tight-binding (TB) approach to improve total energies, forces and transferability in the presence of considerable long-range Coulomb interactions. We derive an approximate energy expression in terms of charge density fluctuations δn at a reference (input) density n0, which is a second order approximation to the total energy expression in density functional theory (DFT). With the choice of n0 as a superposition of densities of neutral atomic fragments, we can define a repulsive potential as in standard TB theory, which is pairwise, short ranged and transferable. The zero order terms in the total energy expression are recoverd as the standard terms of our density-functional based tight-binding (DF-TB). For the second order terms, the charge density fluctuations δn are approximated by the total charge fluctuation Δqα at atom α, which is qualitatively estimated by employing the Mullikan charge analysis. Within this approximations the total energy expression contains new parameters, which are related to ab-intio DFT calculations. Finally, by introducing localized basis functions and applying the variational principle we arrive at the Hamilton matrix elements, wich themselves depend on the charge fluctuations and, therefore, the general eigenvalue problem has to be solved self-consistently. To obtain forces for efficient geometry relaxation and molecular-dyamics, we calculated analytical derivatives of the total energy with respect to the atomic sites. In order to demonstrate the strenghts of our self-consistent-charge tight-binding (SCC-TB), we calculated reaction energies, geometries and vibrational frequencies for a large set of molecules and compare the results to semi-empirical methods, density-functional calculations and experiment.

The central ideas and the advantages of the difference equation Green's function approach for layered systems with 2D-periodicity are presented. The tight-binding linear muffin-tin orbital and other practical aspects of the implementation are discussed. Preliminary test results are presented.

A real-space TB-LMTO-recursion method for electronic structure calculations is applied to the study of interacting extended and point defects in NiAl. Results of calculations for the pure intermetallic and with ternary additions (within a supercell model) show good agreement with band structure results. Further, electronic structure and total energy calculations of point (single impurity, M=Ti, V, Cr, Mn, Fe and Co) and planar defects such as anti-phase boundaries (APB) were carried out and the interaction between them was determined. We found that for the ½〈111〉{110} APB in NiAl, ternary additions occupy exclusively the 3d-metal sublattice and decrease the APB energy (except for Co). Finally, we employ TB-LMTO-REC to study the electronic structure of the most complex extended defect, a dislocation. We demonstrate for the 〈100〉{010} edge dislocation in NiAl that: (i) quasi-localized states may exist as a result of specific lattice distortions in the dislocation core with a type of “broken” bonds; (ii) the electronic structure changes appreciably in the process of dislocation motion; (iii) van-Hove singularities present in the ideal crystal may be shifted to E;r as a result of the dipolar character of the deformations in the dislocation core.

We have calculated the cohesive energies, bulk moduli and equilibrium volumes of Be and Mg oxides, sulphides and selenides, in both zincblende and rocksalt structures. The calculations have been performed with the Discrete-Variational-Method (DVM), a real space first-principle local-density-functional approach. Comparisons with the experiment and with other first-principles approaches show that the electronic and structural properties of solids can be computed with DVM at least as accurately as with the usual plane-wave pseudopotential methods. This result is especially interesting in view of the fact that an order N implementation of DVM, based on the W. Yang's divide and conquer method, has been recently developed.

Over the last decade, Quantum Monte Carlo (QMC) calculations for tight binding Hamiltonians like the Hubbard and Anderson lattice models have made the transition from addressing abstract issues concerning the effects of electron-electron correlations on magnetic and metal-insulator transitions, to concrete contact with experiment. This paper presents results of applications of “determinant” QMC to systems with disorder such as the conductivity of thin metallic films, the behavior of the magnetic susceptibility in doped semiconductors, and Zn doped cuprate superconductors. Finally, preliminary attempts to model the Kondo volume collapse in rare earth materials are discussed.

The tight-binding model with repulsive Hubbard interactions represents an ideal prototype for the study of strong correlations. While exact numerical methods have been used with some success, they are typically limited by the size of the clusters that can be investigated or by the temperatures that can be reached. Variational methods, on the other hand, often require considerable advance knowledge of ground-state properties. The method presented here alleviates this problem by augmenting the variational approach with a scheme similar to Lanczos iterations thus bridging the gap between exact diagonalization and variational approaches. For the t-J model, the low-energy effective Hamiltonian of the Hubbard model, material properties like broken translational invariance or superconducting correlations are then investigated and a region of stability of a superconducting phase is found.

We present the results of a recently developed approach where the interplay between the itinerant and localized character of electrons in narrow band materials is described by adding on-site correlation effects to a realistic band calculation: the single particle band states are treated as mean field solutions of a multi-orbital Hubbard Hamiltonian and the many-body term associated with localized e-e interaction is described in a configuration-interaction scheme. Quasi-particle states of nickel and CuGe03 have been calculated and compared with spectroscopical results.

A real-space method has been used to solve the generalized Hubbard Hamiltonian for a system with few electrons. The method is based on mapping the correlated many-body problem onto an equivalent tight-binding one in a higher dimensional space. For a linear chain, we have obtained an exact solution of the problem of three non-parallel electrons. The three-body correlation are studied by examining the binding energy in the ground state, for different values of the hopping parameters and of the on-site (U) and nearest-neighbor (V) interactions.

Self-energy corrections to the DFT-LDA HOMO-LUMO gap for clusters have been calculated through an efficient method based on ΔSCF theory. Total energies for the clusters are obtained via discrete variational method (DVM). Good results in comparison with experiments and available theoretical data for the sodium tetramer Na4 and C60 have been obtained. The localization properties of DVM basis-functions play a fundamental role in obtaining the above results with a strongly reduced computational effort in comparison with ab-initio schemes. For the two systems under study an estimate of the first excitonic transition energy is also given.

We calculate ab initio values of tight-binding parameters for the /-electron metal Ce and various phases of Si, from local-density functional one-electron Hamiltonian and overlap matrix elements. Our approach allows us to unambiguously test the validity of the common minimal basis and two-center approximations as well as to determine the degree of transferability of both nonorthogonal and orthogonal hopping parameters in the cases considered.

We have developed a tight-binding model which goes beyond the traditional two-center approximation and allows the tight-binding parameters to scale according to the bonding environment. Our studies show that this environment-dependent tight-binding model improves remarkably the accuracy and transferability of the potential to describe the structures and properties of higher coordinated metallic systems in addition to those of low coordinated covalent systems.