Extrapolation theory for the real interpolation method

We develop an abstract extrapolation theory for the real interpolation method that covers and improves the most recent versions of the celebrated theorems of Yano and Zygmund. As a consequence of our method, we give new endpoint estimates of the embedding Sobolev theorem for an arbitrary domain Omega

X-ray photoelectron spectroscopy of oxygen adsorbates on Al(111): Theory experiment

We present the result of polar angle resolved x¿ray photoemission spectroscopy on Al(111)/O and cluster calculations of the O(1s) binding energy (BE) for various model situations. In the experimental data two O(1s) peaks are observed, separated by 1.3 eV. The angular behavior (depth¿resolution) could indicate that the lower BE peak is associated with an O atom under the surface, and the higher BE peak with an O atom above the surface. Equally, it could indicate oxygen islands on the surface where the perimeter atoms have a higher O(1s) BE than the interior atoms. The cluster calculations show that the former interpretation cannot be correct, since an O ads below the surface has a higher calculated O(1s) BE than one above. Cluster calculations simulating oxygen islands are, however, consistent with the experimental data.

Evidence for oxygen-island formation on Al(111): Cluster-model theory and x-ray photoelectron spectroscopy

The O 1s x-ray photoelectron spectroscopy spectrum for Al(111)/O at 300 K shows two components whose behavior as a function of time and variation of detection angle are consistent with either (a) a surface species represented by the higher binding-energy (BE) component and a subsurface species represented by the lower BE component, or (b) small close-packed oxygen islands with the interior atoms represented by the lower BE component and the perimeter atoms by the higher BE component. We have modeled both situations using ab initio Hartree-Fock wave functions for clusters of Al and O atoms. For an O atom in a threefold site, it was found that a below-surface position gave a higher O 1s BE than an above-surface position, incompatible with interpretation (a). This change in the O 1s BE could arise because the bond for O to Al may have a more covalent character when the O is below the surface than when it is above the surface. We present evidence consistent with this view. An O adatom island with all the O atoms in threefold sites gives calculated O 1s BE's which are significantly higher for the perimeter O atoms. Further, the results for an isolated O island without the Al substrate present also give higher BE¿s for the perimeter atoms. Both these results are consistent with interpretation (b). Published scanning-tunneling-microscopy data supports the suggestion that the chemisorbed state consists of small, close-packed islands, whereas the presence of two vibrational modes in high-resolution electron-energy-loss spectroscopy data has been interpreted as representing surface and subsurface oxygen atoms. In light of the present results, we suggest that a vibrational interpretation in terms of interior and perimeter adatoms should be considered.

Extent and limitations of density functional theory in describing magnetic systems

The performance of density-functional theory to solve the exact, nonrelativistic, many-electron problem for magnetic systems has been explored in a new implementation imposing space and spin symmetry constraints, as in ab initio wave function theory. Calculations on selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids carried out with and without these constraints lead to contradictory results, which provide numerical illustration on this usually obviated problem. It is concluded that the present exchange-correlation functionals provide reasonable numerical results although for the wrong physical reasons, thus evidencing the need for continued search for more accurate expressions.

Neutral atoms in ionic lattices: Excited states of KCl:Ag(0)

The optical-absorption spectrum of a cationic Ag0 atom in a KCl crystal has been studied theoretically by means of a series of cluster models of increasing size. Excitation energies have been determined by means of a multiconfigurational self-consistent field procedure followed by a second-order perturbation correlation treatment. Moreover results obtained within the density-functional framework are also reported. The calculations confirm the assignment of bands I and IV to transitions of the Ag-5s electron into delocalized states with mainly K-4s,4p character. Bands II and III have been assigned to internal transitions on the Ag atom, which correspond to the atomic Ag-4d to Ag-5s transition. We also determine the lowest charge transfer (CT) excitation energy and confirm the assignment of band VI to such a transition. The study of the variation of the CT excitation energy with the Ag-Cl distance R gives additional support to a large displacement of the Cl ions due to the presence of the Ag0 impurity. Moreover, from the present results, it is predicted that on passing to NaCl:Ag0 the CT onset would be out of the optical range while the 5s-5p transition would undergo a redshift of 0.3 eV. These conclusions, which underline the different character of involved orbitals, are consistent with experimental findings. The existence of a CT transition in the optical range for an atom inside an ionic host is explained by a simple model, which also accounts for the differences with the more common 3d systems. The present study sheds also some light on the R dependence of the s2-sp transitions due to s2 ions like Tl+.

Ground- and excited-state properties of M-center oxygen vacancy aggregates in the bulk and the surface of MgO

Aggregates of oxygen vacancies (F centers) represent a particular form of point defects in ionic crystals. In this study we have considered the combination of two oxygen vacancies, the M center, in the bulk and on the surface of MgO by means of cluster model calculations. Both neutral and charged forms of the defect M and M+ have been taken into account. The ground state of the M center is characterized by the presence of two doubly occupied impurity levels in the gap of the material; in M+ centers the highest level is singly occupied. For the ground-state properties we used a gradient corrected density functional theory approach. The dipole-allowed singlet-to-singlet and doublet-to-doublet electronic transitions have been determined by means of explicitly correlated multireference second-order perturbation theory calculations. These have been compared with optical transitions determined with the time-dependent density functional theory formalism. The results show that bulk M and M+ centers give rise to intense absorptions at about 4.4 and 4.0 eV, respectively. Another less intense transition at 1.3 eV has also been found for the M+ center. On the surface the transitions occur at 1.6 eV (M+) and 2 eV (M). The results are compared with recently reported electron energy loss spectroscopy spectra on MgO thin films.

Electronic and magnetic structure of LaMnO3 from hybrid periodic density-functional theory

The electronic and magnetic structures of the LaMnO3 compound have been studied by means of periodic calculations within the framework of spin polarized hybrid density-functional theory. In order to quantify the role of approximations to electronic exchange and correlation three different hybrid functionals have been used which mix nonlocal Fock and local Dirac-Slater exchange. Periodic Hartree-Fock results are also reported for comparative purposes. The A-antiferromagnetic ground state is properly predicted by all methods including Hartree-Fock exchange. In general, the different hybrid methods provide a rather accurate description of the band gap and of the two magnetic coupling constants, strongly suggesting that the corresponding description of the electronic structure is also accurate. An important conclusion emerging from this study is that the nature of the occupied states near the Fermi level is intermediate between the Hartree-Fock and local density approximation descriptions with a comparable participation of both Mn and O states.

Antiferromagnetic exchange interactions from hybrid density functional theory

A hybrid theory which combines the full nonlocal ¿exact¿ exchange interaction with the local spin-density approximation of density-functional theory is shown to lead to marked improvement in the description of antiferromagnetically coupled systems. Semiquantitative agreement with experiment is found for the magnitude of the coupling constant in La2CuO4, KNiF3, and K2NiF4. The magnitude of the unpaired spin population on the metal site is in excellent agreement with experiment for La2CuO4.

Extent and limitations of density functional theory in describing magnetic systems

The performance of density-functional theory to solve the exact, nonrelativistic, many-electron problem for magnetic systems has been explored in a new implementation imposing space and spin symmetry constraints, as in ab initio wave function theory. Calculations on selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids carried out with and without these constraints lead to contradictory results, which provide numerical illustration on this usually obviated problem. It is concluded that the present exchange-correlation functionals provide reasonable numerical results although for the wrong physical reasons, thus evidencing the need for continued search for more accurate expressions.

Conditional manipulation of sex ratios by ant workers: A test of kin selection theory

Variable queen mating frequencies provide a unique opportunity to study the resolution of worker-queen conflict over sex ratio in social Hymenoptera, because the conflict is maximal in colonies headed by a singly mated queen and is weak or nonexistent in colonies headed by a multiply mated queen. In the wood ant Formica exsecta, workers in colonies with a singly mated queen, but not those in colonies with a multiply mated queen, altered the sex ratio of queen-laid eggs by eliminating males to preferentially raise queens. By this conditional response to queen mating frequency, workers enhance their inclusive fitness.

New Genetic and Linguistic Analyses Show Ancient Human Influence on Baobab Evolution and Distribution in Australia

This study investigates the role of human agency in the gene flow and geographical distribution of the Australian baobab, Adansonia gregorii. The genus Adansonia is a charismatic tree endemic to Africa, Madagascar, and northwest Australia that has long been valued by humans for its multiple uses. The distribution of genetic variation in baobabs in Africa has been partially attributed to human-mediated dispersal over millennia, but this relationship has never been investigated for the Australian species. We combined genetic and linguistic data to analyse geographic patterns of gene flow and movement of word-forms for A. gregorii in the Aboriginal languages of northwest Australia. Comprehensive assessment of genetic diversity showed weak geographic structure and high gene flow. Of potential dispersal vectors, humans were identified as most likely to have enabled gene flow across biogeographic barriers in northwest Australia. Genetic-linguistic analysis demonstrated congruence of gene flow patterns and directional movement of Aboriginal loanwords for A. gregorii. These findings, along with previous archaeobotanical evidence from the Late Pleistocene and Holocene, suggest that ancient humans significantly influenced the geographic distribution of Adansonia in northwest Australia.