Scattering Theory for Radial Nonlinear Schrödinger Equations on Hyperbolic Space

We study the long-time behavior of radial solutions to nonlinear Schr?dinger equations on hyperbolic space. We show that the usual distinction between short-range and long-range nonlinearity is modified: the geometry of the hyperbolic space makes every power-like nonlinearity short range. The proofs rely on weighted Strichartz estimates, which imply Strichartz estimates for a broader family of admissible pairs, and on Morawetz-type inequalities. The latter are established without symmetry assumptions. Received: July 2006, Revision: April 2007, Accepted: April 2007     

A Poisson Formula for the Schrödinger Operator

We prove a Poisson type formula for the Schrödinger group. Such a formula had been derived in a previous article by the authors, as a consequence of the study of the asymptotic behavior of nonlinear wave operators for small data. In this note, we propose a direct proof, and extend the range allowed for the power of the nonlinearity to the set of all short range nonlinearities. Moreover, H ¹-critical nonlinearities are allowed.     

Rhodium/tris-binaphthyl chiral monophosphite complexes: Efficient catalysts for the hydroformylation of disubstituted aryl olefins

A family of threefold symmetry phosphite ligands, P(O–BIN–OR)₃ (BIN = 2,2′-binaphthyl; R = Me, Bn, CHPh₂, 1-adamantyl), derived from enantiomerically pure (R)-BINOL, was developed. Cone angles within the range 240–270° were calculated for the phosphite ligands, using the computational PM6 Hamiltonian. Their rhodium complexes formed in situ showed remarkable catalytic activity in the hydroformylation of hindered phenylpropenes, under relatively mild reaction conditions, with full chemoselectivity for aldehydes, high regioselectivity, however with low enantioselectivity. The ether substituents at the ligand affected considerably the catalytic activity on the hydroformylation of 1,1- and 1,2-disubstituted aryl olefins. The kinetics of the hydroformylation of trans-1-phenyl-1-propene, using tris[(R)-2′-benzyloxy-1,1′-binaphthyl-2-yl]phosphite as model ligand, was investigated. A first order dependence in the hydroformylation initial rate with respect to substrate and catalyst concentrations was found, as well as a positive order with respect to the partial pressure of H₂, and a slightly negative order with respect to phosphite concentration and CO partial pressure.     

Influence of the solvent and metal center on supramolecular chirality induction with bisporphyrin tweezer receptors. Strong metal modulation of effective molarity values

We describe the synthesis of a bisporphyrin tweezer receptor 1·H(4) and its metalation with Zn(II) and Rh(III) cations. We report the thermodynamic characterization of the supramolecular chirality induction process that takes place when the metalated bisporphyrin receptors coordinate to enantiopure 1,2-diaminocyclohexane in two different solvents, toluene and dichloromethane. We also performed a thorough study of several simpler systems that were used as models for the thermodynamic characterization of the more complex bisporphyrin systems. The initial complexation of the chiral diamine with the bisporphyrins produces a 1:1 sandwich complex that opens up to yield a simple 1:2 complex in the presence of excess diamine. The CD spectra associated with the 1:1 and 1:2 complexes of both metalloporphyrins, 1·Zn(2) and 1·Rh(2), display bisignate Cotton effects when the chirogenesis process is studied in toluene solutions. On the contrary, in dichloromethane solutions, only 1·Zn(2) yields CD-active 1:1 and 1:2 complexes, while the 1:2 complex of 1·Rh(2) is CD-silent. In both solvents, porphyrin 1·Zn(2) features a stoichiometrically controlled chirality inversion process, which is the sign of the Cotton effect of the 1:1 complex is opposite to that of the 1:2 complex. In contrast, porphyrin 1·Rh(2) affords 1:1 and 1:2 complexes in toluene solutions with the same sign for their CD couplets. Interestingly, in both solvents, the signs of the CD couplets associated with the 1:1 sandwich complexes of 1·Zn(2) and 1·Rh(2) are opposite. The amplitudes of the CD couplets are higher for 1·Zn(2) than for 1·Rh(2). This observation is in agreement with 1·Rh(2) having a smaller extinction coefficient than 1·Zn(2). We performed DFT-based calculations and assigned molecular structures to the 1:1 and 1:2 complexes that explain the observed signs for their CD couplets. Unexpectedly, the quantification of the thermodynamic stability of the two metallobisporphyrin/diamine 1:1 sandwich complexes revealed the existence of interplay between effective molarity values (EM) and the strength of the intermolecular interaction (K(m); N···Zn or N···Rh) used in their assembly. The EM for the N···Rh(III) intramolecular interaction is 3 orders of magnitude smaller than that for the N···Zn(II) interaction, both of which are embedded in the same scaffold of the 1·M(2) bisporphyrin receptor.     

Quantum-mechanical study on the mechanism of peptide bond formation in the ribosome

Ribosomes transform the genetic information encoded within genes into proteins. In recent years, there has been much progress in the study of this complex molecular machine, but the mechanism of peptide bond formation and the origin of the catalytic power of this ancient enzymatic system are still an unsolved puzzle. A quantum-mechanical study of different possible mechanisms of peptide synthesis in the ribosome has been carried out using the M06-2X density functional. The uncatalyzed processes in solution have been treated with the SMD solvation model. Concerted and two-step mechanisms have been explored. Three main points suggested in this work deserve to be deeply analyzed. First, no zwitterionic intermediates are found when the process takes place in the ribosome. Second, the proton shuttle mechanism is suggested to be efficient only through the participation of the A2451 2'-OH and two crystallographic water molecules. Finally, the mechanisms in solution and in the ribosome are very different, and this difference may help us to understand the origin of the efficient catalytic role played by the ribosome.     

Self-consistent quantum mechanical model for the description of excitation energy transfers in molecules at interfaces

In this paper we present a quantum mechanical model to study excitation energy transfers in molecular systems located in the vicinity of an interface. The model is based on an approximate solution of the time-dependent density functional theory equations and solvent effects are introduced in terms of the integral equation formalism version of the polarizable continuum model. A unique characteristic of this model is that environment induced polarizing effects on the interacting molecules and screening effects on their interaction are included in a coherent and self-consistent way. The model is applied to different situations of the ethylene dimer in the vicinity of an air/water interface and compared with an alternative quantum electrodynamics approach.     

Ideal secret sharing schemes whose minimal qualified subsets have at most three participants

One of the main open problems in secret sharing is the characterization of the access structures of ideal secret sharing schemes. Brickell and Davenport proved that every one of these ideal access structures is related in a certain way to a unique matroid. Specifically, they are matroid ports. In addition to the search of general results, this difficult open problem has been studied in previous works for several families of access structures. In this paper we do the same for access structures with rank 3, that is, structures whose minimal qualified subsets have at most three participants. We completely characterize and classify the rank-3 access structures that are matroid ports. We prove that all access structures with rank three that are ports of matroids greater than 3 are ideal. After the results in this paper, the only open problem in the characterization of the ideal access structures with rank three is to characterize the rank-3 matroids that can be represented by an ideal secret sharing scheme. A previous version of this paper appeared in Fifth Conference on Security and Cryptography for Networks, SCN 2006, Lecture Notes in Computer Science 4116 (2006) 201–215.     

Density functional methods in the study of oxygen transfer reactions

The oxygen transfer reactions from heterocyclic compounds such as oxaziridine, methyldioxirane and ethylene oxide to ethylene and phosphine have been studied using different computational methods, and the results have been compared to those obtained with CASPT2 and CBS-QB3 methods. The results show that the generalized gradient approximation (GGA) functionals BLYP and PBEPBE, highly underestimate the barriers. On the other hand, the hybrid meta-GGA functionals (BB1K, M05 and M05-2X) and BHandHLYP tend to overestimate the barriers. Finally, the B3LYP and OPBE functionals provide reasonable barriers. Nevertheless, none of the tested functionals describes all the studied reactions with the same accuracy.