摘要:

The ground-state energy and density of a many-electron system are often calculated by Kohn-Sham density functional theory. We describe a ladder of approximations for the exchange-correlation 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 3-dimensional space is determined by the local density there. Higher rungs or levels incorporate increasingly complex ingredients constructed from the density or the Kohn-Sham 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 exact-exchange level, and present our “dreams of a final theory.” “Jacob left Beer-sheba 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.” ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390175

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

We present a simple and accurate model for the electron static structure factors (and corresponding pair-correlation 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 long-range behavior of the pair-correlation function and of its spin-resolved components. Finally, we use our fitting strategy for extracting other quantities from QMC simulations, namely the spin-resolved contributions to the correlation energy and the static local fields (the latter ones according to the Singwi, Tosi, Land, and Sjo¨lander scheme) which are given in this work as analytic functions of both the momentum transfer and the electronic density. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390176

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Several basic time-independent density-functional theorems are reviewed for ground states and excited states. In particular, the simple constrained-search formulation is utilized to prove the Hohenberg-Kohn theorem for degenerate as well as for non-degenerate situations. Then, a time-independent Kohn-Sham theory is presented for an individual excited state, and first-order adiabatic connection perturbation theory is compared with a common approximation within time-dependent theory for excited states. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390177

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390178

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

To 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 semi-infinite jellium model and (iii) an electron, confined by an infinite barrier but in a homogeneous electric field. In (i), an explicit non-local 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 four-component wave functions are thereby by-passed. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390179

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

First principles orab initiocalculations 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. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390180

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

A 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 local-density 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 first-principles results for the density of states of carbon nanotubes supporting the validity of a simple Hu¨ckel-level picture of their Fermi level properties. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390181

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

The propagator ofNinteracting identical particles indspatial dimensions can be written as a Feynman-Kac functional over a symmetrized process, i.e. as a Euclidean-time path integral over the diffusion process ofNidentical free particles with superimposed potential-dependent exponential weights. Recently a many-body diffusion formalism [“MBDF”] was developed, which allows, for coordinate-symmetric potentials and for certain irreducible symmetry representations, to separate the total propagator into a sum of stochastically independent sub-propagators. 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. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390182

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Using 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. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390183

出版商:AIP    

年代:1901

数据来源: AIP

摘要:

Ab initioHartree-Fock (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 Moeller-Plesset 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. ©2001 American Institute of Physics.

ISSN:0094-243X    

DOI:10.1063/1.1390184

出版商:AIP    

年代:1901

数据来源: AIP