Kohn-Sham calculations combined with an average pair-density functional theory

A recently developed formalism in which Kohn-Sham calculations are combined with an ``average pair density functional theory'' is reviewed, and some new properties of the effective electron-electron interaction entering in this formalism are derived. A preliminary construction of a fully self-consitent scheme is also presented in this framework.Comment: submitted to Int. J. Mod. Phys. B (proceedings of the 30th International Workshop on Condensed Matter Theories

London dispersion forces without density distortion: a path to first principles inclusion in density functional theory

We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a constrained search formalism for a supramolecular wavefunction that is forced to leave the diagonal of the many-body density matrix of each fragment unchanged, and is exact for the interaction between one-electron densities. We discuss several aspects: the needed features a density functional approximation for the exchange-correlation holes of the monomers should have, the optimal choice of the one-electron basis needed (named "dispersals"), and the functional derivative with respect to monomer density variations.Comment: 12 pages, 4 figure

Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry

Improving the accuracy and thus broadening the applicability of electronic density functional theory (DFT) is crucial to many research areas, from material science, to theoretical chemistry, biophysics and biochemistry. In the last three years, the mathematical structure of the strong-interaction limit of density functional theory has been uncovered, and exact information on this limit has started to become available. The aim of this paper is to give a perspective on how this new piece of exact information can be used to treat situations that are problematic for standard Kohn-Sham DFT. One way to use the strong-interaction limit, more relevant for solid-state physical devices, is to define a new framework to do practical, non-conventional, DFT calculations in which a strong-interacting reference system is used instead of the traditional non-interacting one of Kohn and Sham. Another way to proceed, more related to chemical applications, is to include the exact treatment of the strong-interaction limit into approximate exchange-correlation energy density functionals in order to describe difficult situations such as the breaking of the chemical bond. © 2010 the Owner Societies

Strong Correlation in Kohn-Sham Density Functional Theory

We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe

The interaction-strength interpolation method for main-group chemistry: benchmarking, limitations, and perspectives

We have tested the original interaction-strength-interpolation (ISI) exchange-correlation functional for main group chemistry. The ISI functional is based on an interpolation between the weak and strong coupling limits and includes exact-exchange as well as the G\"orling-Levy second-order energy. We have analyzed in detail the basis-set dependence of the ISI functional, its dependence on the ground-state orbitals, and the influence of the size-consistency problem. We show and explain some of the expected limitations of the ISI functional (i.e. for atomization energies), but also unexpected results, such as the good performance for the interaction energy of dispersion-bonded complexes when the ISI correlation is used as a correction to Hartree-Fock.Comment: 20 pages, 20 figure

A variational approach to London dispersion interactions without density distortion

We introduce a class of variational wavefunctions that capture the long-range interaction between neutral systems (atoms and molecules) without changing the diagonal of the density matrix of each monomer. The corresponding energy optimization yields explicit expressions for the dispersion coefficients in terms of the ground-state pair densities of the isolated systems, providing a clean theoretical framework to build new approximations in several contexts. As the individual monomer densities are kept fixed, we can also unambiguously assess the effect of the density distortion on van der Waals interactions: for example, we obtain virtually exact dispersion coefficients between two hydrogen atoms up to $C_{10}$, and relative errors below $0.2\%$ in other simple cases.Comment: 5 pages, plus 6 pages of supplemental materia

Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution

The negative correlation energy per particle of a uniform electron gas of density parameter $r_s$ and spin polarization $\zeta$ is well known, but its spin resolution into up-down, up-up, and down-down contributions is not. Widely-used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available Quantum Monte Carlo data. In the low-density limit for $\zeta = 0$, we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the up and down contributions to the kinetic energy of correlation.Comment: new version, to appear in PRB Rapid Communicatio

Adiabatic connection at negative coupling strengths

The adiabatic connection of density functional theory (DFT) for electronic systems is generalized here to negative values of the coupling strength $\alpha$ (with {\em attractive} electrons). In the extreme limit $\alpha\to-\infty$ a simple physical solution is presented and its implications for DFT (as well as its limitations) are discussed. For two-electron systems (a case in which the present solution can be calculated exactly), we find that an interpolation between the limit $\alpha\to-\infty$ and the opposite limit of infinitely strong repulsion ($\alpha\to+\infty$) yields a rather accurate estimate of the second-order correlation energy E\cor\glt[\rho] for several different densities $\rho$, without using virtual orbitals. The same procedure is also applied to the Be isoelectronic series, analyzing the effects of near-degeneracy.Comment: 9 pages, submitted to PR