On a generalization of Kantor's likeable planes

Generalizing an idea of Kantor [7], Johnson and Wilke [5] introduced elusive sets of functions over GF(q) to represent translation planes of order q ² that admit a collineation group of order q ² in the linear translation complement and whose kern contains GF(q). In this paper we determine explicitly all elusive sets for q even. We obtain another translation plane of order 8².Deicated to Professors Adriano Barlotti and Luigi Antonio Rosati on the occasion of their 60th birthdayThis research was supported in part by a grant from the M.P.I. (40% funds).     

Synergism of porphyrin-core saddling and twisting of meso-aryl substituents

The structural chemistry of meso-aryl-substituted porhyrins has uncovered a bewildering variety of macrocycle distortions. Saddling angles range up to 40 degrees , while the plane of the phenyl groups at the meso positions may be anywhere between perpendicular to the porphyrin plane (theta = 90 degrees) and tilted to quite acute angles (theta = 30 degrees or even less). These two distortions appear to be correlated. This has naturally been explained by steric hindrance: when the phenyls rotate toward the porphyrin plane, for instance, coerced by packing forces, the pyrrole rings can alleviate the steric hindrance by tilting away to a saddled conformation. We demonstrate, however, that the two motions are intrinsically coupled by electronic factors and are correlated even in the absence of external forces. A saddling motion makes it sterically possible for the phenyl rings to rotate toward the porphyrin plane, which will always happen because of increasingly favorable pi-conjugation interaction with smaller angles theta. The considerable energy lowering due to pi conjugation counteracts the energy cost of the saddling, making the concerted saddling/rotation motion very soft. Unsubstituted meso-aryl porphyrins just do not distort, but an additional driving force may tip the balance in favor of the combined distortion motion. Internal forces having this effect are repulsion of the four hydrogens that occupy the central hole of the ring in porphyrin diacids but also steric repulsion in peripherally crowded porphyrins. These findings lead to a clarification and systematization of the observed structural variety, which indeed shows a remarkable correlation between saddling and phenyl ring tilting.     

Photochemistry of 1,2,4-oxadiazoles. A DFT study on photoinduced competitive rearrangements of 3-amino- and 3-n-methylamino-5-perfluoroalkyl-1,2,4-oxadiazoles

The photoinduced competitive rearrangements of 5-perfluoroalkyl-3-amino(N-alkylamino)-1,2,4-oxadiazoles have been investigated by DFT calculations and UV-vis spectroscopy. The observed product selectivity depends on the number of hydrogen atoms present in the amino moiety and involves two or three possible routes: (i) ring contraction-ring expansion (RCRE), (ii) internal-cyclization isomerization (ICI), or (iii) C3-N2 migration-nucleophilic attack-cyclization (MNAC). UV absorption and fluorescence spectra of the reactants, and vertical excitation energy values, calculated by time dependent DFT, support the involvement of a neutral singlet excited state in the photoexcitation process. The values of the standard free energy of the most stable prototropic tautomers of reactant, products, proposed reaction intermediates, and deprotonated anionic transition states allowed us to rationalize the competition among the three rearrangements, in agreement with chemical trapping experiments, in terms of: (i) the evolution of the excited state toward three stable ground-state intermediates, (ii) tautomeric and deprotonation equilibria occurring in methanol solution for each intermediate, and (iii) relative stabilization of intermediates and transition states in the thermally driven section of the reaction.     

A partition-based global optimization algorithm

This paper is devoted to the study of partition-based deterministic algorithms for global optimization of Lipschitz-continuous functions without requiring knowledge of the Lipschitz constant. First we introduce a general scheme of a partition-based algorithm. Then, we focus on the selection strategy in such a way to exploit the information on the objective function. We propose two strategies. The first one is based on the knowledge of the global optimum value of the objective function. In this case the selection strategy is able to guarantee convergence of every infinite sequence of trial points to global minimum points. The second one does not require any a priori knowledge on the objective function and tries to exploit information on the objective function gathered during progress of the algorithm. In this case, from a theoretical point of view, we can guarantee the so-called every-where dense convergence of the algorithm.     

Platinum(II) complexes bearing 1,1'-bis(diphenylphosphino)ferrocene as building blocks for functionalized redox active porphyrins

Reactions of the cationic complex ions [PtMe(Me2SO)(PP)]+ (PP = dppf (1,1'-bis(diphenylphosphino)ferrocene) and dppe (1,2-bis(diphenylphosphino)ethane)) with 5,10,15,20-tetrakis(4-pyridyl)-21H,23H-porphyrin (TpyP) led to the formation of the symmetrical tetraplatinated porphyrin complexes, [PtMe(PP)]4TpyP.X4 (PP = dppf, X = CF3SO3-, 3, and PP = dppe, X = BF4-, 5) containing the organometallic fragment [PtMe(PP)]. The precursor sulfoxide platinum complexes [PtMe(Me2SO)(dppf)]CF3SO3, 2 and [PtMe(Me2SO)(dppe)]BF4, 4, were prepared by halide abstraction from [PtMeCl(dppf)], 1, and by controlled protonolysis of [PtMe2(dppe)] respectively, in the presence of a small amount of dimethyl sulfoxide. All these starting platinum(II) compounds, as well as the porphyrin derivatives 3 and 5, were fully characterized through elemental analysis, 1H NMR mono- and bidimensional, 31P[1H], 31P-1H HMBC, UV/Vis absorption and photophysical measurements. The X-ray crystal structure of complex 1 has been determined. In order to ascertain the electronic influence of ferrocene, the spectroscopic and redox properties of 3 were compared with those of TPyP and of the analogous 5. Cyclic voltammetry (CV), differential pulse voltammetry (DPV), 1H and 31P NMR data, and UV/Vis data, all suggest a certain degree of communication between the central porphyrin and the peripheral hetero-bimetallic fragments. In contrast, no detectable interaction among these peripheral groups seem to come into play. Unlikely from the porphyrin derivative 5, formation of well defined fluorescent mesoscopic ring structures was easily achieved by simple evaporation from diluted dichloromethane solutions of 3.     

A Truncated Newton Method for the Solution of Large-Scale Inequality Constrained Minimization Problems

A new active set Newton-type algorithm for the solution of inequality constrained minimization problems is proposed. The algorithm possesses the following favorable characteristics: (i) global convergence under mild assumptions; (ii) superlinear convergence of primal variables without strict complementarity; (iii) a Newton-type direction computed by means of a truncated conjugate gradient method. Preliminary computational results are reported to show viability of the approach in large scale problems having only a limited number of constraints.     

Cellulose beads: a new versatile solid support for microwave- assisted synthesis. Preparation of pyrazole and isoxazole libraries

The synthesis of libraries of substituted pyrazoles and isoxazoles has been developed via in situ generation of polymer-bound enaminones. The synthetic protocol makes use of commercially available aniline cellulose, a low-cost and versatile biopolymer, under very mild conditions. This new support allowed us to carry out reactions in polar solvents under both conventional heating and MW irradiation without degradation of the polymer. The reaction between cellulose-bound enaminone and hydroxylamine or hydrazines to afford the target heterocycles in high yields directly in solution is the key step. The support can be conveniently recycled.     

Synthesis and molecular modelling studies of resorcin[4]arene-capped porphyrins

Three new resorcin[4]arene-capped porphyrins (3, 5 and 7) different in the porphyrin skeleton, in the linking arms and in the cavity dimensions, have been synthesised. Molecular modelling calculations explored the conformations and the cavity size of the three compounds and showed that their hydrophobic pockets can accommodate one molecule of water or methane (3 and 5), or benzene (7) without any distortion. Notably, the capped porphyrin 5 was able to inhibit the oxidation of Co(II) to Co(III), whereas compound 7 did it only partially.