DENSITY FUNCTIONAL THEORY AND ITS APPLICATION TO MATERIALS

Jacob’s ladder of density functional approximations for the exchangecorrelation energy
View Description Hide DescriptionThe groundstate energy and density of a manyelectron system are often calculated by KohnSham density functional theory. We describe a ladder of approximations for the exchangecorrelation energy as a functional of the electron density. At the lowest rung of this ladder, the contribution to the energy from a volume element of 3dimensional space is determined by the local density there. Higher rungs or levels incorporate increasingly complex ingredients constructed from the density or the KohnSham orbitals in or around this volume element. We identify which additional exact conditions can be satisfied at each level, and discuss the extent to which the functionals at each level may be constructed without empirical input. We also discuss the research that remains to be done at the exactexchange level, and present our “dreams of a final theory.” “Jacob left Beersheba and went toward Haran. He came to a certain place and stayed there for the night, because the sun had set. Taking one of the stones of the place, he put it under his head and lay down in that place. And he dreamed that there was a ladder set up on the earth, the top of it reaching to heaven; and the angels of God were ascending and descending on it.”

Model static structure factors and paircorrelation functions for the unpolarized homogeneous electron gas
View Description Hide DescriptionWe present a simple and accurate model for the electron static structure factors (and corresponding paircorrelation functions) for the 3D unpolarized homogeneous electron gas. This model stems from a combination of analytic constraints and fitting procedures to quantum Monte Carlo data. We also identify the correct longrange behavior of the paircorrelation function and of its spinresolved components. Finally, we use our fitting strategy for extracting other quantities from QMC simulations, namely the spinresolved contributions to the correlation energy and the static local fields (the latter ones according to the Singwi, Tosi, Land, and Sjölander scheme) which are given in this work as analytic functions of both the momentum transfer and the electronic density.

Basic timeindependent densityfunctional theorems for ground states and excited states
View Description Hide DescriptionSeveral basic timeindependent densityfunctional theorems are reviewed for ground states and excited states. In particular, the simple constrainedsearch formulation is utilized to prove the HohenbergKohn theorem for degenerate as well as for nondegenerate situations. Then, a timeindependent KohnSham theory is presented for an individual excited state, and firstorder adiabatic connection perturbation theory is compared with a common approximation within timedependent theory for excited states.

Electron confinement: Models of kinetic and exchange energy functionals
View Description Hide DescriptionTo gain insight into the basic variables to be utilized in constructing improved energy density functionals, various models of electron confinement will be discussed, in which analytic forms of either kinetic or exchange energy functionals can be derived. Among these models are (i) the Bardeen infinite barrier model of a surface (ii) the semiinfinite jellium model and (iii) an electron, confined by an infinite barrier but in a homogeneous electric field. In (i), an explicit nonlocal relation between kinetic and exchange energies can also be exhibited. Finally a relativistic generalization of what is essentially the Bardeen model relation between kinetic energy and density profile has been effected: this offers considerable simplification due to the fact that Dirac fourcomponent wave functions are thereby bypassed.

The role of first principles calculations in materials modelling
View Description Hide DescriptionFirst principles or ab initio calculations are now routinely applied to problems in physics, chemistry and minerals science. These calculations are now even being applied to biological systems. However, the number of applications of such calculations in materials science remains relatively low. This is somewhat surprising given the system sizes and complexities that are amenable to modern first principles calculations. In this paper I shall discuss some of the challenges of materials science in order to explain why first principles calculations alone will have very little impact on materials modeling. I shall also highlight some successful applications of first principles calculations to materials problems and outline possible developments that would significantly extend the range of successful applications in the future.

Densityfunctional simulations of carbon nanotubes
View Description Hide DescriptionA wealth of experimental and theoretical research over the previous decade has demonstrated the anomalous properties of carbon nanotubes, a novel material synthesized in the previous decade and having great potential application to nanotechnology. We review our localdensity functional approach for helical chain polymers that has been used extensively to study the electronic and structural properties of carbon nanotubes as well as other technologically important polymers. We provide detailed firstprinciples results for the density of states of carbon nanotubes supporting the validity of a simple Hückellevel picture of their Fermi level properties.

Many interacting electrons in a quantum dot
View Description Hide DescriptionThe propagator of N interacting identical particles in d spatial dimensions can be written as a FeynmanKac functional over a symmetrized process, i.e. as a Euclideantime path integral over the diffusion process of N identical free particles with superimposed potentialdependent exponential weights. Recently a manybody diffusion formalism [“MBDF”] was developed, which allows, for coordinatesymmetric potentials and for certain irreducible symmetry representations, to separate the total propagator into a sum of stochastically independent subpropagators. This method was applied to calculate “numerically exactly” the ground state energy for electrons in a parabolic confinement. In particular the example of a 2D closed shell system with six, twelve and twenty unpolarised interacting electrons in a quantum dot with parabolic confinement was treated. The results obtained by the MBDF method are compared with earlier theoretical approximations for this system.

Density functional theory approach to artificial molecules
View Description Hide DescriptionUsing the current spin density functional formalism we studied the ground state of two vertically coupled quantum dots as a function of the distance between both dots and the strength of an external perpendicular magnetic field. The tunneling between both dots is included. For zero magnetic field the results can be interpreted in terms of an effective single particle picture and we find that Hund’s rule breaks down for 11 and 12 electrons in the coupled dots. It is shown that the suppression of tunneling peaks can occur due to spin and/or isospin blockade. The spin blockade is much easier realized in coupled dots than in a single quantum dot. The application of an external magnetic field further increases these blockade regions.

Correlation corrected HartreeFock and density functional computations on nucleotide base stacks
View Description Hide DescriptionAb initio HartreeFock (HF) band structures and crystal orbital were calculated for periodic nucleotide base stacks. The HF results were connected for correlation using the inverse Dyson equation in its diagonal approximation. The self energy was computed in the MoellerPlesset 2 (MP2) level taking into account also relaxation. The quasi particle energies, giving the correlation corrected band structures, were iterated until selfconsistency. The band structures of the same base stacks were also computed using the density functional theory (DFT) in the form applied in Mintmire’s program for periodic polymers. The resulting physically most interesting features (widths and positions of the valence and conduction bands, respectively, ionization, potentials, the value of the fundamental gap) of the resulting band structures using the mentioned three different methods will be compared. Whenever experimental data are available they will be used for comparison.

Ab initio study of optical excitations: Role of electronhole interaction
View Description Hide DescriptionAn ab initio approach to calculating the optical absorption spectrum and exciton states in real materials is discussed. The approach is based on evaluating the oneparticle and the twoparticle Green’s function for the quasiparticle and optical excitations, including relevant electron selfenergy and electronhole interaction effects from first principles. The method has allowed the calculation of the continuum absorption spectrum, as well as, the discrete bound exciton states for a range of materials. Results are presented for bulk semiconductors and insulators, surfaces, conjugated polymers, and small clusters. In many of these systems, the electronhole interaction is shown to strongly alter the excitation energies and the optical spectra. The nature of bound and resonant exciton states are also discussed.

Monte Carlo simulations with firstprinciples energies
View Description Hide DescriptionWe present a method to perform efficiently Monte Carlo simulations for molecules with total energies calculated from first principles density functional theory using a gaussian basis set. It relies on the strong coupling between the Monte Carlo algorithm and the structure of the first principles code, which has been parallelized. The feasibility of the method is illustrated by carrying out extensive computer simulations for a cluster with 21 atoms. Possible generalizations and extensions of the method are briefly discussed.

Calculating the critical temperature of superconductors from first principles
View Description Hide DescriptionWe present a novel approach to the theory of superconductivity based on a formally exact density functional formulation. Within this framework, we perform firstprinciples calculations of the critical temperatures of conventional superconductors with strong and weak electronphonon coupling.

Properties of ZnO
View Description Hide DescriptionThe valence band structure of ZnO at has been determined by investigating the emission and reflection spectra. The data indicate that the is the top valence band and that the spinorbit splitting is positive. There appears to be very little exchange correction, thus the exciton spectra is hydrogenic for the and top The Zn dorbitals, which are approximately 8 eV below the top valence bands, have very little effect on the spinorbit splitting in contrast to CuCl where the Cu dorbitals cause a negative spinorbit splitting and a reversal of the top valence band structure. Various calculations using a variety of methods are reviewed and a discussion of the difficulty of obtaining very accurate theorical results is given. This includes firstprinciple, zero parameter calculations which approximate the exchangecorrelation operators, as well as effective mass approximations with a series of experimental adjusted parameters. These calculations have led to a longstanding controversy over the symmetry ordering of the valence bands in ZnO which has lasted for more than 30 years. The recent availability of ZnO crystals in which intrinsic exciton transitions are observed in emission and their splitting in a magnetic field have resolved this controversy.