The treatment of the spin coupling in the bonding of NO to the Ni-doped MgO (100) surface

The results are reported of density functional theory (DFT) and explicitly correlated wave-function (CASSCF and CASPT2) calculations on the bonding of NO with the Ni-doped MgO(100) surface. The surface is represented by means of a cluster of ions embedded in point charges. A comparison is made between unrestricted (spin polarized) and spin restricted approaches. While the geometry of the surface complex is described in quite an accurate way by a spin unrestricted DFT approach, e.g., using the B3LYP functional, the spin distribution does not correspond to that of the real physical situation. In fact, the spin polarized DFT treatment shows three unpaired electrons, two with spin up and one with spin down, while EPR experiments show clearly the existence of a single spin localized on an Ni 3d shell. A spin restricted B3LYP treatment, on the other hand, gives a correct spin distribution and geometry but fails in reproducing the adsorption energy. Other exchange-correlation functionals behave in a similar or even worse way. The CASPT2 results, by contrast, are in substantial agreement with the experiment, showing the importance of treating on the same footing the spin and electron correlation as well as the multi-configuration character of the wavefunction.     

On the evaluation of selected eigenpairs of large matrices based on function optimization algorithms

Large scale matrix diagonalization is reviewed and analysed in the context of normal function optimization techniques. The problem of obtaining high roots is discussed at length. The rational function optimization procedure and Taylor techniques are presented. It is demonstrated that these algorithms make it possible to obtain any desired eigenpair in an efficient way. Finally, the possibility of using a fixed subspace dimension during the diagonalization iterative process is discussed. To this end a short review is presented of the use of update Hessian matrices to diagonalize large matrices.     

POLYMER BOUND PYRROLE COMPOUNDS–VI. PHOTOPHYSICAL PROPERTIES OF MONOMERIC MODELS FOR POLYSTYRENE-BOUND PORPHYRINS

Abstract— Several porphyrin esters used as models for polystyrene-bound porphyrins have been prepared and their excited states have been studied by laser flash photolysis, IR phosphorescence of singlet molecular oxygen, O₂(¹Δ_g), and steady-state fluorescence. The photophysical properties of the porphyrin esters in solution are affected by the presence of nitro group(s) in the chain. In this case, an important decrease in φ_f, φ_T and φ_δ (to ca 0.7–0.4 of the value for the parent dimethyl ester) is observed. This is mainly due to intramolecular electron-transfer quenching [by the nitro group(s)] of the first excited singlet state of the porphyrin. The thermodynamic feasibility of this deactivation pathway has been confirmed polarographically. Quenching of the porphyrin triplet state and of O₂(¹Δ_g) by the nitro groups is negligible. The present conclusions explain also the results obtained previously for the photooxidation of bilirubin sensitized by the parent insoluble polystyrene-bound porphyrins. In that case the photooxidation rates were correlated directly with the quantum yield of O₂(¹Δ_g) production by the sensitizer. The consequences of these results for the use of polystyrene-bound porphyrins in sensitized photooxidation processes are discussed.     

Interpolation for a subclass of H ∞

We introduce and characterize two types of interpolating sequences in the unit disc \(\mathbb {D}\) of the complex plane for the class of all functions being the product of two analytic functions in \(\mathbb {D}\) , one bounded and another regular up to the boundary of \(\mathbb {D}\) , concretely in the Lipschitz class, and at least one of them vanishing at some point of \(\overline {\mathbb {D}}\) .