Electron Correlation In Systems Research Articles

Effect of on-site Coulomb repulsion termUon the band-gap states of the reduced rutile (110)TiO2surface

We present a study concerning the effect of the on site $d\text{\ensuremath{-}}d$ Coulomb interaction energy $U$ on the band-gap states of nonstoichiometric rutile (110) $\mathrm{Ti}{\mathrm{O}}_{2}$ surface. As well known, the excess electrons resulting from the formation of oxygen vacancies localize on the $\mathrm{Ti}\phantom{\rule{0.2em}{0ex}}3d$ orbitals forming band-gap states. Local density approximation (LDA) does not give a correct description of these band-gap states, either with or without gradient corrections. The failure of LDA is often attributed to an inadequate treatment of electron correlation in systems with localized orbitals and is commonly corrected with an empirical local Coulomb repulsion term, i.e., the $\mathrm{LDA}+U$ method. This study provides a completely general strategy to estimate the $U$ value in this kind of systems, illustrated here for reduced (110) $\mathrm{Ti}{\mathrm{O}}_{2}$ surface, well characterized from experiments. From ab initio embedded cluster configuration interaction calculations, combined with the effective Hamiltonian theory, a value of $U$ of $5.5\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ is obtained, in good agreement with those reported for this system from x-ray photoemission spectroscopy experiments $(U=4.5\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$. It is observed that when the ab initio estimate of $U$ is injected into the periodic $\mathrm{LDA}+U$ calculations, a correct description of the gap states is obtained from the periodic $\mathrm{LDA}+U$ calculations. Additionally, the results indicate that the position of these states on the band gap strongly depends on the level at which lattice relaxation is taken into account, with significant differences between the density of states curves at the $\mathrm{LDA}+U$ level obtained using the optimal generalized gradient approximation or $\mathrm{LDA}+U$ geometries. These results suggest that this combined strategy could be a useful tool for those systems where electron correlation plays a key role, and no experimental data are available for the on-site Coulomb repulsion.

Electron correlations in systems with orbital degeneracies: The dual nature of 5f electrons, heavy fermions and spectral functions in U-compounds

The present paper focuses on the dual nature of 5f electrons in U compounds and the concept of partial localization. The latter can arise due to intra-atomic correlations described by Hund's rules. To derive a microscopic picture, the electronic correlations in orbitally degenerate systems are studied by exact diagonalizations for finite clusters. Results for excitation spectra are presented. The cluster calculations form the basis for an approximate treatment of extended systems. The excitation spectra of U-based compounds are calculated for models which account for the local atomic correlations and realistic band structures. We discuss how high-energy shoulders observed in photoemission can be understood and how heavy fermions can emerge.

Pairing representation in the complex molecular-orbital method

Numerical analysis revealed that the closed-shell complex molecular-orbital (CMO) wavefunction, which describes a significant part of the electron correlation in molecules, may be transformed into a very simple pairing form. This feature of the CMO method is essential for developing an efficient complex configuration mixing scheme, analogous to the configuration -interaction method. It should allow a reliable description of electron correlation in systems beyond the reach of present-day theories.

Spin projected extended Hartree–Fock calculations by direct minimization of the energy functional

A practicable SEHF scheme for the treatment of electron correlation in systems for which large scale configuration interaction calculations are prohibitive is presented. A study is made of the electronic structures to which the SEHF method may be most profitably applied. In order to illustrate this study and to provide a numerical demonstration of the minimization techniques ab initio SEHF calculations on a number of ten electron systems are reported. These calculations were performed for the singlet ground states of Ne, HF, H2O, NH3, CH4, and cyclic H10.