A scheme that reduces the calculations of ground-state properties of systems of interacting particles exactly to the solution of single-particle Hartree-type equations has obvious advantages. It is not surprising, then, that the density functional formalism, which provides a way of doing this, has received much attention in the past two decades. The quality of the energy surfaces calculated using a simple local-density approximation for exchange and correlation exceeds by far the original expectations. In this work, the authors survey the formalism and some of its applications (in particular to atoms and small molecules) and discuss the reasons for the successes and failures of the local-density approximation and some of its modifications.

The density functional formalism, its applications and prospects

Using the approach of Finnis and Sinclair, N-body potentials for copper, silver, gold and nickel have been constructed. The total energy is regarded as consisting of a pair-potential part and a many body cohesive part. Both these parts are functions of the atomic separations only and are represented by cubic splines, fitted to various bulk properties. For the noble metals, the pair-potentials were fitted at short range to pressure-volume relationships calculated by Christensen and Heine so that interactions at separations smaller than that of the first-nearest neighbours can be treated in this scheme. Using these potentials, point defects, surfaces (including the surface reconstructions) and grain boundaries have been studied and satisfactory agreement with available experimental data has been found.

Simple N-body potentials for the noble metals and nickel

The results of the study of symmetrical tilt boundaries, reported in the preceding part I, are generalized to asymmetrical tilt boundaries. A classification of tilt boundaries in cubic crystals is developed that reveals which boundaries to choose in order to study equilibrium faceting or intrinsic grain boundary dislocations (g.b.ds) accommodating a misorientation. Two series of atomistic studies of asymmetrical tilt boundary structures are presented based on this classification. The first is a study of long-period (27 ^ 97) [110] asymmetrical tilt boundaries in aluminium. The aims of this study are to investigate whether these boundaries are composed of fundamental structural elements, in the same way as was found in part I for symmetrical tilt boundaries, and to see if localized, distinct stress fields of edge g.b.ds exist throughout the misorientation range. With use of the results of this study, and the principle of continuity of boundary structure enunciated in part I, the boundary unit representation of a 27 — 1193 asymmetrical tilt boundary is derived as an example. It is generally found that the Burgers vectors of intrinsic secondary g.b.ds in tilt boundaries, based on favoured boundary reference structures, are non-primitive d.s.c. vectors. The reason for this is given and a simple formula is presented to derive the Burgers vectors of such dislocations for any favoured tilt boundary reference structure. It is pointed out that, in general, very low angle {0

On the Structure of Tilt Grain Boundaries in Cubic Metals I. Symmetrical Tilt Boundaries

The electric field gradient in noncubic metals

It is shown that the density can be used as the basic variable for calculating the properties of excited states. The correspondence is not between an eigenstate and its density, as is the case with the ground state, but between the subspace spanned by the number of lowest-energy eigenstates and the sum of their densities. An extension of the Hohenberg-Kohn-Sham theory (1964-5) for excited states has also been developed. The equations derived are similar in form to those for the ground-state density but the interpretation is different. The lowest-order approximation of the present theory coincides with Slater's 'transition-state' theory (1974).

http://iopscience.iop.org/article/10.1088/0022-3719/12/24/013/pdf

The energy density functional formalism for excited states

We present nonlinear self-consistent calculations of the charge density induced by isolated ${\mathrm{Li}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Mg}}^{++}$, ${\mathrm{Al}}^{+++}$, and ${\mathrm{Ca}}^{++}$ ions when placed in an electron gas of the appropriate metallic density. By comparison with linear-response theory we show that in the first four metals nonlinear effects in the response of the conduction electrons to the ionic perturbations play an important role in determining the charge density and the interionic potential. However as in the case of Na studied in the previous paper these nonlinear effects can be simulated by using a suitably adjusted model potential. The calculated phonon dispersion curves for Li, K, and Al agree very well with experiment. Nonlinear effects are also very likely to be important in Ca but further work is necessary before conclusions can be drawn.

Charge densities and interionic potentials in simple metals: Nonlinear effects. II

The density-functional formalism of Hohenberg, Kohn, and Sham is used to investigate the effects of nonlocal exchange and correlation on the Fermi surface of a simple-cubic metal. The "nonlocal" Fermi surface is obtained by solving the Dyson equation for the quasiparticle states on the Fermi surface with the nonlocal self-energy approximated according to the density-functional scheme in the presence of an external model pseudopotential. This was done by using the corresponding local theory to define a zeroth-order Hamiltonian which provides basis functions to solve the nonlocal eigenvalue problem. It was found that the maximum Fermi-surface distortions obtained from the nonlocal theory were substantially reduced from the local theory, as experiments suggest. The calculations were carried out in the random-phase approximation.

Mark Rasolt

Papers

Charge densities and interionic potentials in simple metals: Nonlinear effects. II

Investigations of nonlocal exchange and correlation effects in metals via the density-functional formalism