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

Abstract

We present a study concerning the effect of the on site d-d Coulomb interaction energy U on the band-gap states of nonstoichiometric rutile ͑110͒ TiO 2 surface. As well known, the excess electrons resulting from the formation of oxygen vacancies localize on the Ti 3d orbitals forming band-gap states. Local density approximation ͑LDA͒ 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 LDA+ U method. This study provides a completely general strategy to estimate the U value in this kind of systems, illustrated here for reduced ͑110͒ TiO 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± 0.5 eV is obtained, in good agreement with those reported for this system from x-ray photoemission spectroscopy experiments ͑U = 4.5± 0.5 eV͒. It is observed that when the ab initio estimate of U is injected into the periodic LDA+ U calculations, a correct description of the gap states is obtained from the periodic 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 LDA+ U level obtained using the optimal generalized gradient approximation or 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.

Synergistic Effects on Band Gap-Narrowing in Titania by Codoping from First-Principles Calculations

“…Here, we include the on-site Coulomb correction for the Ti 3d states, the so called GGA + U method [19], which can partially improve the prediction of the band gap. Here, U = 5.3 eV for Ti, which is in agreement with the optimal value (5.5±0.5eV) [20,21]; using this, the calculated band gap of pure anatase was 3.11 eV, which agrees well with the experimental value of 3.20 eV. A variety of U values (1.0, 2.0, 3.0, and 4.0 eV) were applied to the dopants.…”

Modifying the electronic structure of semiconducting single-walled carbon nanotubes byAr+ion irradiation

“…It is a generally accepted fact that DFT with localdensity approximation ͑LDA͒ or GGA exchange and correlation functionals frequently underestimates the absolute values of the band gap and may give wrong positions of the defect-induced states in the gap. [52][53][54] Physically, this is because DFT is inherently a ground-state theory, so that information about excited-state properties ͑that is the lowest unoccupied state͒ cannot be rigorously deduced in the absence of any explicit link between ground-state densities and excited-state quantities ͑the ground-state density uniquely determines the many-body Hamiltonian; that is, information about excited states is, in principle, encoded within the ground-state density͒. In fact, exchange and correlation effects are not rigorously included in the functionals.…”

Reactivity of sub 1 nm supported clusters: (TiO2)n clusters supported on rutile TiO2 (110)

“…To describe oxygen vacancy 95 formation in the cluster-support system, we apply the DFT+U approach 48,49 , which adds a Hubbard U correction to describe the reduced Ti states that result from vacancy formation. The need for an approach like DFT+U or hybrid DFT (which is too costly in a plane wave basis set for the present calculations 100 with up to 300 atoms) to describe localised reduced cation states is defective systems is well known and has been the subject of a number of papers 40,41,[50][51][52][53] . We have tested DFT and DFT+U with U = 3 eV 47 and U = 4.5 eV 27 on a number of oxygen vacancy structures and find that, of the two values of …”