Exchange-correlation Potential Of Density Functional Theory Research Articles

Multilayer relaxation and search for ferromagnetic order at the (100) surface of bulk paramagnetic vanadium

Low-energy-electron-diffraction (LEED) intensity measurements and multiple-scattering analysis for V(100), supported by accurate characterization of surface impurity concentrations based on Auger-electron spectroscopy, are used to obtain a meaningful extrapolation of the first-layer relaxation to the clean surface value: ${d}_{12}=1.36\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, corresponding to ${\ensuremath{\Delta}}_{12}=\ensuremath{-}10%\ifmmode\pm\else\textpm\fi{}3%$ relative to the bulk value ${d}_{0}=1.514\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. A high-sensitivity probe for surface magnetism based on magneto-optic Kerr effect polarimetry using the cleanest surfaces achieved in the LEED experiment $(\ensuremath{\sim}5%\phantom{\rule{0.3em}{0ex}}\mathrm{C})$ yields a (sensitivity limited) null result with an estimated upper limit of $0.05\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}$/surface atom. These results are discussed within the framework of related experiments and in relation to the predictive accuracy of ab initio calculations that explore the surface structure and magnetism of V(100) both of which are sensitive to different approximations for the exchange-correlation potential in density-functional theory.

Time-Dependent Density-Functional Theory beyond the Local-Density Approximation

Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.

Exact Time-Dependent Exchange-Correlation Potentials for Strong-Field Electron Dynamics

By solving the time-dependent Schrödinger equation and inverting the time-dependent Kohn-Sham scheme we obtain the exact time-dependent exchange-correlation potential of density-functional theory for the strong-field dynamics of a correlated system. We demonstrate that essential features of the exact exchange-correlation potential can be related to derivative discontinuities in stationary density-functional theory. Incorporating the discontinuity in a time-dependent density-functional calculation greatly improves the description of the ionization process.

Density-functional theory calculations with correct long-range potentials

A variational method for forcing the exchange-correlation potential in density-functional theory (DFT) to have the correct asymptotic decay is developed. The resulting exchange-correlation potentials are much improved while the total energies remain essentially the same, compared with conventional density-functional theory calculations. The highest occupied orbital energies from the asymptotically corrected exchange-correlation potentials are found to provide significantly more accurate approximations to the ionization potential (for a neutral molecule) and the electron affinity (for an anion) than those from conventional calculations, although the results are usually inferior to direct methods by computing energy differences. Extending recent results from exchange-only DFT, we show that exact exchange-correlation potential is nonuniform asymptotically. Correcting the asymptotic decay of approximate exchange-correlation potentials towards the exact functional form binds the highest occupied orbitals for atomic and molecular anions, which supports the use of DFT calculations for negatively charged molecular species. With this technique, even hybrid functionals have local exchange-correlation potentials, effectively removing the largest objection to including these functionals in the panoply of Kohn–Sham DFT methods.

Exchange-only optimized effective potential for molecules from resolution-of-the-identity techniques: Comparison with the local density approximation, with and without asymptotic correction

The optimized effective potential (OEP) is (within a certain linear response approximation) the exact exchange-correlation potential of density-functional theory (DFT). In the program DEMON-DYNARHO, we have implemented the OEP at the exchange-only level without the evaluation of four-center integrals using resolution-of-the-identity techniques. We point out that great care must be taken in treating the asymptotic behavior of the OEP in finite basis set methods. Our results are compared with previous work using OEP-like potentials. Our OEP orbital energies are compared with experimental ionization potentials, Hartree–Fock (HF) orbital energies, and with orbital energies from the local density approximation (LDA) potential, with and without asymptotic correction (AC). We find that OEP orbital energies are a much better approximation to experimental ionization potentials than are HF orbital energies. LDA orbital energies also correlate well with OEP orbital energies, except for a molecule-dependent rigid shift, due to the well-known fact that the LDA potential falls off too rapidly at large distances. The resultant underbinding is largely corrected by the AC-LDA potential whose orbital energies correlate well with OEP orbital energies, with typical differences on the order of 0.5 eV. However larger differences between AC-LDA and OEP orbital energies are also observed, particularly for unoccupied orbitals and the reason for this is discussed. As an illustration of how the OEP might be used in practical calculations, we give an example from time-dependent DFT where use of the OEP instead of the AC-LDA potential leads to significant improvement in a key σ→π* excitation energy of ethylene.

Investigating exact density-functional theory of a model semiconductor.

Using the diffusion quantum Monte Carlo method, we calculte the ground-state density and energy, and the quasiparticle band gap, of a model semiconductor. The exchange-correlation potential of density-functional theory (DFT), ${\mathit{V}}_{\mathrm{xc}}$(r), is obtained using optimization techniques. From this we calculate the DFT functionals ${\mathit{E}}_{\mathrm{sc}}$ and ${\mathit{T}}_{\mathit{s}}$ and the DFT band gap for various external potentials and compare the results with the local-density approximation (LDA). Whereas energies are found to be very accurate in the LDA, and the density reasonably good, we find large differences in the shape of ${\mathit{V}}_{\mathrm{xc}}$(r).

Hartree-Fock theory of the inhomogeneous electron gas at metallic surfaces

In this paper we derive fundamental properties of the interacting inhomogeneous electron gas at jellium metal surfaces within the Hartree-Fock approximation. We also discuss the question of what constitutes quantum-mechanically the image charge at a metal surface, and provide a physical interpretation for the quantum-mechanical origin of the image potential. The self-consistent solution of the Hartree-Fock equations is in general formidable due to the integral exchange operator. We show that from a more fundamental physical viewpoint, the difficulty for the metal surface physics problem manifests itself in the complex structure of the orbital-dependent exchange charge densities that give rise to the orbital-dependent potentials. However, it is possible to solve the problem of the Pauli-correlated electron gas within the exchange-only formalism of density-functional theory. By employing the variational principle for the energy with the exchange energy component treated in its non-local form, and the variationally accurate “displaced-profile-change-in-self-consistent-field” expression for the work function, we derive rigorous upper bounds to the surface energy and accurate work functions. In order to understand what constitutes quantum-mechanically the image charge at a metal surface we study the structure of the average exchange charge density or Fermi hole as an electron is removed from within a metal to infinity outside. The study shows that the Fermi hole is localized to the surface region and is part of the image charge only for electron positions close to the surface. As the electron is removed further into the vacuum region, the width of the hole increases. In the asymptotic limit when the electron is removed to infinity, the hole is completely delocalized and spread throughout the crystal, its center of mass being singular. As a consequence it appears that it is the Coulomb hole charge distribution localized at the surface that is the image charge, but this has yet to be shown. Finally, we provide insights into the quantum-mechanical origin of the image potential. These ideas are based on our interpretation of the local exchange-correlation potential of density-functional theory as being the work done to remove an electron against the electric field of its Fermi-Coulomb hole charge density. Since the Coulomb hole charge is zero, the image potential in the asymptotic region far from the surface is the work done against the electric field of its Fermi hole. The results of preliminary calculations confirm this conclusion. Whether the Coulomb hole contributes to making the total effective potential the image potential for electron positions closer to the surface is yet unanswered. The above physical interpretation is based on the fact that the Fermi-Coulomb hole charge distribution is dynamic as a function of electron position. This explains why the exchange potential as calculated by the Slater method is incorrect. As such we also present the complete structure of the Slater potential at a metal surface and show that it leads to an erroneous value in the interior of the metal and that its asymptotic structure though image-potential-like has a coefficient approximately twice as large as that of the image potential.