Acidic properties of [Al], [Ga] and [Fe] isomorphously substituted zeolites. Density functional model cluster study of the complexes with a probe CO molecule

The Brønsted acid strength and related characteristics of bridging hydroxyl groups in [Al]-, [Ga]- and [Fe]-framework-substituted zeolites have been studied using a model cluster density functional approach based on a gradient-corrected exchange-correlation energy functional. The acidity is found to decrease in the order Al(OH)Si > Ga(OH)Si > Fe(OH)Si in agreement with existing experimental and theoretical results. The present quantification is based on the calculated deprotonation energy of H₃Si(OH)TH₃, on the adsorption energy of a CO probe molecule as well as on the changes of the vibrational frequencies and absolute IR intensities of the O---H and of the C---O modes induced by CO adsorption. The vibrational parameters of the carbonyl adsorption complex in [Fe]-zeolites are predicted.     

Anab initio investigation of the inner shell excited states of the molecule Cl2

Restricted Hartree-Fock calculations of the Cl₂ molecule have been carried out to investigate the X-ray excited states below Cl 2p-electron ionization potential. Some inner shell excited states are shown to have a valence or a valence-Rydberg nature that results in a considerable intensity of the appropriate transitions in the X-ray absorption spectrum. A significant interaction among some electron configurations with a 2p vacancy is predicted.     

An SCF XαSW study of the electronic structure and X-ray and photoelectron spectra of Fe(II) and Fe(III) hexacyano complexes in a cluster approach

The electronic structure of the hexacyano complexes [Fe(CN)₆]^4– and [Fe(CN)₆]^3– as clusters of the cyanide complex salts has been calculated by the SCF XSW method. Theoretical photoelectron, X-ray emission and absorption spectra have been constructed. The contribution of the resonance emission to the X-ray emission spectra has been estimated. On the basis of detailed comparison of the theoretical and experimental spectra an assignment of the fine structure of the spectra has been proposed.     

Density functional studies of model cerium oxide nanoparticles

Density functional plane-wave calculations have been performed to investigate a series of ceria nanoparticles (CeO2-x)(n), n Ce3+ reduction have been accounted for through the use of an effective on-site Coulomb repulsive interaction within the so-called DFT+U approach. Twelve nanoparticles of up to 2 nm in diameter and of both cuboctahedral and octahedral forms are chosen as representative model systems. Energetic and structural effects of oxygen vacancy formation in these nanoparticles are discussed with respect to those in the bulk and on extended surfaces. We show that the average interatomic distances of the nanoparticles are most significantly affected by the creation of oxygen vacancies. The formation energies of non-stoichiometric nanoparticles (CeO2-x)(n) are found to scale linearly with the average coordination number of Ce atoms; where x < 0 species, containing partially reduced O atoms, are less stable. The stability of octahedral ceria particles at small sizes, and the predicted strong propensity of Ce cations to acquire a reduced state at lower coordinated sites, is supported by interatomic potential-based global optimisations probing the low energy isomers of the Ce19O32 nanoparticle.     

The value of two-person zero-sum repeated games with incomplete information and uncertain duration

Fix a zero-sum repeated game Γ with incomplete information on both sides. It is known that the value of the infinitely repeated game Γ_∞ need not exist (Aumann and Maschler 1995). It is proved that any number between the minmax and the maxmin of Γ_∞ is the value of a long finitely repeated game Γ _n where players’ information about the uncertain number of repetitions n is asymmetric.