W. Kohn

Van der waals energies in density functional theory

In principle, density functional theory yields the correct ground-state densities and energies of electronic systems under the action of a static external potential. However, traditional approximations fail to include Van der Waals energies between separated systems. This paper proposes a practical procedure for remedying this difficulty. Our method allows seamless calculations between small and large inter-system distances. The asymptotic H-He and He--He interactions are calculated as a first illustration, with very accurate results.

Shallow Impurity States in Silicon and Germanium

Publisher Summary This chapter reviews current understanding of the shallow acceptor states in silicon and germanium. While these states are analogous to the donor states in a general way, one does not have nearly as detailed a picture of them. Secondly, spin resonance experiments, which have shed so much light on the nature of donor states, have not been successful in the case of acceptor states. Acceptor states are wave packets made up largely of Bloch waves chosen from near the top of the valence band. To understand them, one requires some information about the structure of this band. This information, which has, for the most part, been extracted from cyclotron resonance experiments, is summarized. In germanium spin resonance experiments have not been successful so that one does not have an experimental source for the g factor. The spin orbit interaction in germanium may be expected to be about an order of magnitude larger than in silicon because of the higher atomic number. To obtain the diamagnetic susceptibility, one must, as usual, calculate the energy of the donor state up the second order in the magnetic field H.

Indirect long-range oscillatory interaction between adsorbed atoms☆

The oscillatory part of the indirect interaction between two adatoms on a metal surface, separated by a large distance R, is examined for the jellium as well as for the tight-binding model. The asymptotic form of the interaction is derived from the singularity of its Fourier transform at wave number q = 2kF. For a substrate with a spherical Fermi surface, the interaction energy is proportional to cos(2kFR)R5. The fall-off is faster than the corresponding oscillatory interaction between two impurities in the bulk, which varies as cos(2kFR)R3. For substrates with a partially filled surface band, the interaction energy falls off much more slowly. Under simple assumptions, the interaction behaves as cos(2kFR)R2. Comparisons are made with the numerical calculations by Einstein and Schrieffer. The experimental results of Tsong on Re atoms adsorbed on W using field-ion microscopy is also discussed.

Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory.

The frequency-dependent exchange-correlation potential, which appears in the usual Kohn-Sham formulation of a time-dependent linear response problem, is a strongly nonlocal functional of the density, so that a consistent local density approximation generally does not exist. This problem can be avoided by choosing the current density as the basic variable in a generalized Kohn-Sham theory. This theory admits a local approximation which, for fixed frequency, is exact in the limit of slowly varying densities and perturbing potentials.

Elastic interaction of two atoms adsorbed on a solid surface

The long-range interaction of two adsorbed atoms mediated by the elastic distortion of the substrate is calculated classically for an elastically isotropic substrate. For identical atoms, the interaction is repulsive; for different atoms, it can be repulsive or attractive. It varies as ρ−3 with the distance ρ between the two adsorbed atoms. This is the same spatial dependence as for the dipole - dipole interaction between two adsorbed atoms. For two xenon atoms adsorbed on gold, the elastic interaction is somewhat smaller than the dipole-dipole interaction. The interaction energy is inversely proportional to the shear modulus of the substrate, so that it may become quite large near a distortive phase transition.

General Density Functional Theory

Over the course of the last 15 years density functional theory (DFT)* has evolved as a conceptually and practically useful method for studying the electronic properties of many-electron systems. In this chapter we present a critical review of the general theory together with some illustrative examples.† More complete discussions of several important areas of application may be found in other chapters of this book.

Adatom dipole moments on metals and their interactions

Abstract An expression is derived for the dipole moment μ, associated with an arbitrary adatom on an arbitrary metal surface, in terms of the differential work done in moving the adatom from the interior of the metal to its actual position in the presence and absence, respectively, of small, asymptotically uniform electric field on the exterior of the metal. With the aid of this expression it is shown that the non-oscillatory part of the interaction energy of two dipoles μ A and μ B , situated on the surface and separated by a large distance v , is given by U AB = 2 μ A μ B v −3 . This exceeds by a factor of 2 the interaction energy of two dipoles in the same relative configuration but in a vacuum.

EDGE ELECTRON GAS

The uniform electron gas, the traditional starting point for density-based many-body theories of inhomogeneous systems, is inappropriate near electronic edges. In its place we put forward the appropriate concept of the edge electron gas.

Density functional/Wannier function theory for systems of very many atoms

Conventional theoretical methods for calculating ground-state energies of multi-atom systems in general become impractical when the number of atoms, Na, exceeds ∼ 102, because the computing time rises with Nαa, where 2 < α < 3. Using so-called generalized Wannier functions in conjunction with density functional theory, we develop a procedure for the direct calculation of the GWFs (not requiring single particle eigenfunctions) whose computing time behaves as Na. The method allows the transfer of GWFs from one physical or chemical system to another.

An energy functional for surfaces

We propose a simple way of correcting general gradient and local density approximation surface energies for errors of these approximations intrinsic to surfaces by the appropriate use of reference systems with an exponential surface potential veff(z)∝e(z/a). A test of this approach applied to general gradient and local density approximation surface exchange energies for half jellium systems removes most of the surface-intrinsic errors and yields excellent results. We suggest that the same procedure would also be successful for surface correlation effects. We conclude with some general remarks about future directions of density functional theory.