Christopher Castleton

Tuning LDA+U for electron localization and structure at oxygen vacancies in ceria.

We examine the real space structure and the electronic structure (particularly Ce4f electron localization) of oxygen vacancies in CeO(2) (ceria) as a function of U in density functional theory studies with the rotationally invariant forms of the LDA+U and GGA+U functionals. The four nearest neighbor Ce ions always relax outwards, with those not carrying localized Ce4f charge moving furthest. Several quantification schemes show that the charge starts to become localized at U approximately 3 eV and that the degree of localization reaches a maximum at approximately 6 eV for LDA+U or at approximately 5.5 eV for GGA+U. For higher U it decreases rapidly as charge is transferred onto second neighbor O ions and beyond. The localization is never into atomic corelike states; at maximum localization about 80-90% of the Ce4f charge is located on the two nearest neighboring Ce ions. However, if we look at the total atomic charge we find that the two ions only make a net gain of (0.2-0.4)e each, so localization is actually very incomplete, with localization of Ce4f electrons coming at the expense of moving other electrons off the Ce ions. We have also revisited some properties of defect-free ceria and find that with LDA+U the crystal structure is actually best described with U=3-4 eV, while the experimental band structure is obtained with U=7-8 eV. (For GGA+U the lattice parameters worsen for U>0 eV, but the band structure is similar to LDA+U.) The best overall choice is U approximately 6 eV with LDA+U and approximately 5.5 eV for GGA+U, since the localization is most important, but a consistent choice for both CeO(2) and Ce(2)O(3), with and without vacancies, is hard to find.

Managing the supercell approximation for charged defects in semiconductors: Finite-size scaling, charge correction factors, the band-gap problem, and the ab initio dielectric constant

C. W. M. Castleton,1,2,* A. Höglund,3 and S. Mirbt3 1Material Physics, Materials and Semiconductor Physics Laboratory, Royal Institute of Technology (KTH), Electrum 229, SE-16440 Kista, Sweden 2Department of Physical Electronics/Photonics, ITM, Mid Sweden University, SE-85170 Sundsvall, Sweden 3Theory of Condensed Matter, Department of Physics, Uppsala University, Box 530, SE-75121 Uppsala, Sweden Received 2 November 2005; published 25 January 2006

Density functional theory calculations of defect energies using supercells

Reliable calculations of defect properties may be obtained with density functional theory (DFT) using the supercell approximation. We systematically review the known sources of error and suggest ho ...

B3LYP calculations of cerium oxides

In this paper we evaluate the performance of density functional theory with the B3LYP functional for calculations on ceria (CeO(2)) and cerium sesquioxide (Ce(2)O(3)). We demonstrate that B3LYP is able to describe CeO(2) and Ce(2)O(3) reasonably well. When compared to other functionals, B3LYP performs slightly better than the hybrid functional PBE0 for the electronic properties but slightly worse for the structural properties, although neither performs as well as LDA+U(U=6 eV) or PBE+U(U=5 eV). We also make an extensive comparison of atomic basis sets suitable for periodic calculations of these cerium oxides. Here we conclude that there is currently only one type of cerium basis set available in the literature that is able to give a reasonable description of the electronic structure of both CeO(2) and Ce(2)O(3). These basis sets are based on a 28 electron effective core potential (ECP) and 30 electrons are attributed to the valence space of cerium. Basis sets based on 46 electron ECPs fail for these materials.

Orbital ordering in the manganites: Resonant x-ray scattering predictions at the manganese L-II and L-III edges

It is proposed that the observation of orbital ordering in manganite materials should be possible at the L II and L III edges of manganese using x-ray resonant scattering. If performed, dipole selection rules would make the measurements much more direct than the disputed observations at the manganese K edge. They would yield specific information about the type and mechanism of the ordering not available at the K edge, as well as permitting the effects of orbital ordering and Jahn-Teller ordering to be detected and distinguished from one another. Predictions are presented based on atomic multiplet calculations, indicating distinctive dependence on energy, as well as on polarization and on the azimuthal angle around the scattering vector.

Finite-size scaling as a cure for supercell approximation errors in calculations of neutral native defects in InP

The relaxed and unrelaxed formation energies of neutral antisites and interstitial defects in InP are calculated using ab initio density functional theory and simple cubic supercells of up to 512 atoms. The finite-size errors in the formation energies of all the neutral defects arising from the supercell approximation are examined and corrected for using finite-size scaling methods, which are shown to be a very promising approach to the problem. Elastic errors scale linearly, while the errors arising from charge multipole interactions between the defect and its images in the periodic boundary conditions have a linear plus a higher order term, for which a cubic provides the best fit. These latter errors are shown to be significant even for neutral defects. Instances are also presented where even the 512 atom supercell is not sufficiently converged. Instead, physically relevant results can be obtained only by finite-size scaling the results of calculations in several supercells, up to and including the 512 atom cell and in extreme cases possibly even including the 1000 atom supercell.

Resonant Soft X-Ray Scattering Investigation of Orbital and Magnetic Ordering in La0.5Sr1.5MnO4.

We report resonant x-ray scattering data of the orbital and magnetic ordering at low temperatures at the Mn L-2,L-3 edges in La0.5Sr1.5MnO4. The orderings display complex energy features close to t ...

Screening and the quantitative π-model description of the optical spectra and polarizations of phenyl based oligomers

The long standing problem of the inability of many semiempirical models to correctly predict the polarization of the higher dipole allowed optical transitions of phenyl based π-conjugated polymers and molecules is examined and related to the issue of internal and external screening of π–π electron Coulomb interactions within the molecules. Following a review of previous theoretical and experimental work, π electron only the Complete Neglect of Differential Overlap (CNDO) model is presented which, for the first time, is able to predict accurately the energies and symmetries of all the observed optical transitions of benzene, biphenyl and trans-stilbene, up to ∼8–10 eV. In so doing, it is demonstrated that the problem with previous calculations was the noninclusion of screening from outside the π electron system itself. By fitting separately the spectra in hydrocarbon based condensed phases, in the gas phase and in solid rare gas matrices, and comparing the resulting model parameters, we show that, while th...

Optimal parametrisation of the Pariser–Parr–Pople Model for benzene and biphenyl

We obtain a parametrisation of the Pariser–Parr–Pople model of the π-conjugated systems which is optimal for benzene, biphenyl and poly(para-phenylene). We first optimise agreement with experiment for a number of low-lying excitations of benzene, leading to a phenyl transfer integral of 2.539 eV, an on-site Coulomb energy of 10.06 eV and a relative error of 2.8%, compared with 7.4% using the standard values. We next optimise agreement for the long axis polarised optical transitions of biphenyl with absorption data, leading to a bridging bond transfer integral of 2.22 eV.

Several different charge transfer and Ce3+ localization scenarios for Rh–CeO2(111)

We present DFT+U based electronic structure calculations in a p(3 × 3) slab supercell, for low coverages of atomically dispersed Rh interacting with the CeO2(111) surface, comparing Rh as an adatom, and as a dopant substituted into the surface layer. We find that, energetically, a Rh atom approaching a ceria(111) surface with both sparse O and Ce vacancies present strongly prefers to heal the Ce vacancies, but next it prefers to adsorb on a stoichiometric region rather than healing an O vacancy. In the adatom system, Rh is oxidized by electron transfer to a 4f orbital on one Ce ion in the surface layer, which is then nominally converted from Ce4+ → Ce3+ (i.e. Rh adatoms are single donors). We show that there are a number of different local minima, with Ce3+ localization at 1st, 2nd or 3rd nearest neighbour Ce sites. The second neighbour is the most stable, but all are close in energy. In the Rh-doped system (Rh replaces Ce), Rh is oxidized by charge transfer to neighbouring O atoms, and Rh doping leads to deep acceptor and donor states. Rh is not stable in the O sublattice. Moreover, based on vacancy formation energies, we find that oxygen vacancy formation is strongly enhanced in the vicinity of Rh dopants, but slightly suppressed in the vicinity of Rh adatoms.