We demonstrate that our tight-binding method - which is based on fitting the energy bands and the total energy of first-principles calculations as a function of volume - can be easily extended to accurately describe carbon and silicon. We present equations of state that give the correct energy ordering between structures. We also show that quantities that were not fitted, such as elastic constants and the band structure of C60, can be reliably obtained from our scheme.

The mathematical theory of orthogonal polynomials and continued fractions provides efficient tools, via the recursion and related methods, for calculating diagonal elements of Green's function of tight-binding Hamiltonians. We present two recent generalizations of this formalism. The first one allows the calculation of conductivity and other linear response coefficients. The second one provides a new approach to the solution of mean-field theories of alloys. In particular it is shown that the self-consistent CPA equations can be easily solved, through a real-space calculation, for multi-component alloys based on periodic or non periodic lattices.

Empirical tight-binding theory is generalized to incorporate time-dependent electromagnetic fields in a systematic and gauge-invariant manner that does not introduce any extra adjustable parameters. It is shown that this approach successfully predicts a wide range of solid state properties that have not been accessible within the tight binding method so far. We present applications such as optical constants, luminescence in heterostructures, properties in ultra-high magnetic fields and lattice dynamics in polar materials.

This paper reviews recent progress in the theory of the atomic and electronic structure of disordered metallic alloys containing transition metals (TM). Realistic structural models are obtained using molecular dynamics simulations based on pair interatomic forces derived from a tight-binding-bond method. This approach describes quantitatively compositional trends in chemical and topological short-range order in agreement with diffraction experiments.

Until recently, tight-binding has been applied to either covalent or metallic solid state systems, or charge transfer treated in a simple point charge framework. We present a self-consistent tight-binding model which, for the first time, includes electrostatic ion polar-isabihty and crystal field splitting. The tight-binding eigenvectors are used to construct multipole moments of the ionic charges which are used to obtain angular momentum components of the electrostatic potential in structure constant expansions. Our first test of the model is to study the phase stability in zirconia; in particular the instability of the fluorite phase to a spontaneous symmetry breaking, and its interpretation in terms of band effects and ion polarisability. This new formalism opens up the way to apply the tight-binding approximation to problems in which polarisation of atomic charges is important, for example oxides and other ceramic materials and surfaces of metals.

Modelling in a realistic way both equilibrium and dynamical processes on bimetallic surfaces requires the availability of interatomic potentials sufficiently simple (i.e. analytical) although derived from the electronic structure. This is possible in the framework of Tight-Binding formalism. We present here a review of the applications of such potentials, together with some reflexions about their limitations.

Complex defects in Si and SiC such as coincidence tilt boundaries, planar defects and self-interstitial clusters were dealt with by using the transferable tight-binding method for Si and the self-consistent tight-binding method for SiC. These results have been compared with ab initio calculations of similar configurations. Essential features of the tight-binding results have been supported by the ab initio results. Especially, the agreement on stable atomic configurations is good, although there exits a tendency that energy increases are somewhat overestimated by the tight-binding methods. Serious faults have been found for the electronic structure by the tight-binding method for SiC.

The calculation of the electronic structure of silicon nanostructures is used to discuss the accuracy of results obtained by the tight-binding method. We first show that the level of refinement of the tight-binding approximation must be adapted to the calculated property. For example, an accurate description of both the valence and conduction bands which can be achieved with a 3rd-nearest neighbor approximation is necessary to calculate the variation of the gap energy with the silicon crystallite size. The sp3s* model which gives a bad description of the conduction band underestimates the confinement energy but can give good results when it is used to determine the variation of the crystallite band gap with pressure. To study Si-III (BC-8) nanocrystallites, we show that a good description of the bulk band structure can be obtained with non-orthogonal tight-binding but due to the large number of nearest neighbors one must take analytical variations of the parameter with interatomic distances. The parameters involved in these expressions can be easily fitted to the bulk band structures using the k-point symmetry without requiring the use of group theory. Finally we discuss the effect of increasing the size of the minimal-basis set and we show that it would be possible to get the values of the tight-binding parameters from a first-principles localized states band structure calculation avoiding the fit to the energy dispersion curves.

We point out that the predictive power of tight binding potentials is not limited to obtaining fairly accurate total energy calculations and very satisfactory structural evolutions by molecular dynamics simulations. They also allow for a nice physical picture of the links between bonding and stability in different structures, which is particularly helpful in the case of binary suicides

A simple spd tight-binding scheme for atomistic simulations in transition metals is developed using an orthogonal basis set in the two-center approximation. The purpose of the present approach is to cope with the limitations of the canonical d-band model for elements at the beginning or at the end of the transition metal series while keeping a reduced number of parameters, and simple decay-functions. The parameters for the hopping integrals are fitted to FP-LMTO calculations of the volume dependence of band energies and band structures for several selected structures. Constant values are taken for the on-site energies, and the Born-Mayer pair potential is used for the repulsive term. Two approaches are compared for the total energy: the band model and the bond model. First applications are presented in the case of zirconium, where the difference between these models on phase stability results is particularly drastic. The bond model reproduces the stability of the hep phase and displays a good agreement with experiments for the elastic constants.

A transferable orthogonal tight-binding model for molybdenum is developed which goes beyond the traditional two-center approximation. The elements of the Hamiltonian matrix as well as the repulsive potential are allowed to depend on the environment. Several bulk, atomic defect and surface properties are calculated and compared with ab-initio data and experimental results to check the accuracy of the model.

The semi-empirical tight-binding method is used to build up an interatomic potential in zinc. Using relaxed structures, the parameters are fitted to the lattice parameters, the elastic constants and the vacancy formation energy. The total energy calculation predicts the stability of the h.c.p. structure. The potential is used to calculate the energy of some extended defects: the basal stacking fault and two twin boundaries.

The recently developed Environment-Dependent Interatomic Potential (EDIP) holds the promise of a new degree of transferability in describing bulk phases and defects of elemental covalent solids with a simple theoretically motivated functional form. Here we explore to what extent the environment-dependence of the model can extrapolate successes of the fitted version for Si for bulk defects to disordered phases, which involve local configurations very different from those used in fitting. We find that EDIP-Si provides an improved description of the metallic bonding bond angles of the liquid and is the first empirical potential to predict a quench directly from the liquid to the amorphous phase. The resulting amorphous structure is in closer agreement with ab initio and experimental results than with any artificial prepration method. We also show that melting of the bulk crystal and premelting of the (100)2×1 surface are reasonably well described by EDIP-Si in spite of its not being fit to any such properties.

We construct transferable tight-binding parameters of silicon-hydrogen interactions, reproducing the electronic energy levels and vibrational frequencies of the silane(SiH4) molecule accurately. The potential function was rescaled with the exponential factor in order to ensure that the potential energy is smooth at an appropriate cut-off distance, which is very important in molecular-dynamics simulations. The parameters have been applied to other molecules and various surfaces such as hydrogenated Si(100) surfaces, for example, monohydride, dihydride, and (3×1) phase.

It is well-known that the Embedded Atom Method (EAM) predicts positive Cauchy pressures for cubic metals if physically-motivated embedding functions are used. Supris-ingly, even if the angular character of the covalent bonding is included within an orthorgonal or non-orthorgonal Tight-Binding (TB) description, the Cauchy pressure for most elemental and binary metallic systems remains positive. We describe the results of a detailed breakdown of the different contributions to the Cauchy pressure within the Harris-Foulkes approximation (HFA) to density functional theory. We show that negative values of the Cauchy pressure for both elemental transition metals such as Ir and binary intermetallics such as Ti3Al, TiAl and TiAl3 are well reproduced by the HFA. We argue that the negative Cauchy pressure (NCP) arises namely from the environment dependence of the local TB orbitals which leads to both environment-dependent bonding integrals and overlap repulsion. We discuss a particular functional form for overlap repulsion which leads to NCP and compare it with different fitting schemes proposed recently in TB theory.

Potential functions used in molecular dynamics simulations for metals are characterized through a calculation of the third-order elastic constants, the Gruneisen parameters, and the molecular dynamics simulation of point defects. The Lennard-Jones potential and the embedded atom method potentials for noble metals (Cu, Ag, Au) are characterized by using a common program code.

Semi-empirical tight-binding techniques have been extensively used during the last six decades to study local and extended defects as well as aperiodic systems. In this work we propose a tight-binding model capable of describing optical properties of disordered porous materials in a novel way. Besides discussing the details of this approach, we apply it to study porous silicon (p-Si). For this purpose, we use an sp3s* basis set and supercells, where empty columns are digged in the [001] direction in crystalline silicon (c-Si). The disorder of the pores is considered through a random perturbative potential, which relaxes the wave vector selection rule, resulting in a significant enlargement of the optically active k-zone. The dielectric function and the light absorption spectra are calculated. The results are compared with experimental data showing a good agreement.

A method is introduced for simulations of the coupled dynamics of electrons and ions in a molecule or material. It is applicable to general nonadiabatic processes, including interactions with an arbitrarily intense radiation field. The field is included in the electronic Hamiltonian through a time-dependent Peierls substitution. The time-dependent Schrödinger equation is solved with an algorithm that preserves orthogonality, and the atomic forces are obtained from a generalized Ehrenfest theorem. Calculations for GaAs and Si demonstrate that the method is reliable and quantitative.

Procedures for calculating the optical properties of periodic systems using the empirical tight-binding method are compared. Results of the linear and nonlinear susceptibilities are presented using a recently developed exact formalism [Lew Yan Voon and Ram-Mohan. Phys. Rev. B47, 15500 (1993)].

We propose an empirical tight-binding method for tetrahedrally coordinated cubic materials and apply it to group IV and III-V semiconductors, extending existing calculations by the inclusion of all five d-orbitals per atom in the basis set. The symmetry character of the conduction states at the surface of the Brillouin zone is considerably improved compared to calculations in smaller bases, and the corresponding band positions can be obtained within the experimental uncertainties. Because the distance dependence of the tight-binding parameters is derived from deformation potentials, the model is particularly suited for an investigation of strained superlattices where the states at direct or pseudo-direct conduction band minima are composed of wavefunctions of all the minima at Γ, X, and L of the constituents. Investigations of GaAs/AlAs and short-period superlattices indicate a strong mixing between the conduction band valleys in the miniband structure, and the results are in better agreement with experiments than state-of-the-art empirical pseudopotential calculations.