Generalizing the breakdown of the maximum hardness and minimum polarizabilities principles for nontotally symmetric vibrations to non-pi-conjugated organic molecules

In previous works we have shown that certain pi-conjugated organic molecules possess nontotally symmetric vibrations that break the maximum hardness (MHP) and minimum polarizability principles (MPP). We have also derived a set of simple rules to determine a priori without calculations whether a particular pi-conjugated organic molecule violates these two principles. In the present work, we generalize these results, and we show that not only pi-conjugated organic molecules but also other molecules without pi-conjugated structure or even pi-bonds can exhibit nontotally symmetric molecular distortions that do not follow these two principles. We have also found that the breakdowns of the MHP and the MPP are not necessarily connected, since the polarizability is not always proportional to the softness. Finally, we also introduced a methodology based on the diagonalization of the hardness Hessian matrix with respect to the vibrational normal coordinates to determine the nontotally symmetric molecular displacements that do not follow the MHP.     

Electron localization and delocalization in open-shell molecules

Localization and delocalization indices derived in the framework of the quantum Atoms in Molecules theory have recently been used to analyze the electron-pair structure of closed-shell molecules. Here we report calculations of localization and delocalization indices for open-shell molecules at the Hartree-Fock (HF) level. Several simple doublet and triplet radical molecules are studied. In general, interatomic delocalization between bonded atoms is heavily dependent on the order and polarity of the bond. Unpaired electrons also have a significant effect on the interatomic delocalization indices. Indeed, for many radicals, the analysis of the spin components reveals that the interatomic delocalization is very different for alpha and beta spin electrons in many cases. In general, at the HF level, the results can be rationalized in terms of orbital contributions. However, the definition of localization and delocalization indices is completely general, and they could be calculated at any level of theory, provided that the one- and two-electron densities are available.     

Peptide dendrimers based on polyproline helices

We present a new family of peptide dendrimers based on polyproline helices and cis-4-amino-L-proline as a branching unit. Dendrimers were synthesized by a convergent solid-phase peptide synthesis approach. The conformational transition between polyproline type I helix and polyproline type II helix was observed by circular dichroism in branched polyproline building blocks with more than 14 proline residues and in the resulting dendrimers. Both linear and dendritic polyprolines were found to be actively internalized by rat kidney cells. Preliminary results show that the antibiotic ciprofloxacin form complexes with branched polyproline chains in 99.5% propanol.     

High conversion of olefins to cis-diols by non-heme iron catalysts and H2O2

Efficient and highly stereoselective oxidation of olefins to cis-diols as the major product is obtained by using biomimetic non-heme FeII catalysts in combination with H2O2.     

Double beta decay andSU(4) symmetry

The amplitude for ββ decay with 2ν emission is shown to be related to (p,n) and (n,p) reactions on the initial and final states, respectively. The suppression of both ββ and (n,p) reaction is connected, and its origin is discussed by referring to theSU(4) symmetry. From present data on the first ones, we estimate the forward (n, p) strength of relevance for the ββ problem. The interest of the experimental determination of this strength is emphasized. Assuming a perturbative breaking of theSU(4) symmetry, results are given for⁷⁶Ge,⁸²Se,¹²⁸Te and¹³⁰Te.     

On the Volume of a Domain Obtained by a Holomorphic Motion Along a Complex Curve

Let D be a domain obtained by a holomorphic motion of a domain D _p M _p ^n–1 along a complex curve P in a complex space form M ⁿ . We prove that, if n= 2, the volume of D depends only on the geometry of D _p and the intrinsic geometry of P, but not on the extrinsic geometry of P. When M is closed (compact without boundary), then the dependence on P is only through its topology. When n > 2, and for arbitrary domains D _p, a similar result holds only for Frenet motions, but when D _p has certain integral symmetries (and only in this case) this result is still true for any motion .     

Interaction of water with self-assembled monolayers of alkylsilanes on mica

The interaction of water with self-assembled alkylsilane monolayers on mica substrates has been studied using an atomic force microscope operated in contact, noncontact, and electrical polarization modes. Complete monolayer films were found to be effective in blocking water adsorption. On partially covered surfaces water was found to produce large changes in the conductivity and surface potential of the exposed mica regions. It was also found that water could penetrate films near defects and at island edges.     

The role of intermolecular and molecule-substrate interactions in the stability of alkanethiol nonsaturated phases on Au(111)

The structure and stability of alkanethiols self-assembled on Au(111) have been studied as a function of the molecular chain length by means of atomic force microscopy (AFM) and grazing incidence X-ray diffraction (GIXD). Below saturation, phases consisting of molecules with different tilt angles and periodicities are formed. Differences in the mechanical stability of these phases are revealed by AFM experiments and discussed in terms of the competition between intermolecular and molecule-substrate interactions as a function of chain length. For long molecules, intermolecular interactions play a dominant role which stabilizes the formation of closed packed 30 degrees tilted ( radical 3x radical 3)R30 degrees structures. For short molecules, the van der Waals interaction with the gold substrate favors the formation of a 50 degrees tilted phase in which the molecules are arranged in a rectangular configuration.     

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

Using three typical pi-conjugated molecules (1,3,5-hexatriene, 1-formyl-6-hydroxyhexa-1,3,5- triene, and 1,1-diamino-6,6-dinitrohexa-1,3,5-triene) we investigate the level of ab initio theory necessary to produce reliable values for linear and nonlinear optical properties, with emphasis on the vibrational contributions that are known to be important or potentially important. These calculations are made feasible by employing field-induced coordinates in combination with a finite field procedure. For many, but not all, purposes the MP2/6-31+G(d) level is adequate. Based on our results the convergence of the usual perturbation treatment for vibrational anharmonicity was examined. Although this treatment is initially convergent in most circumstances, a problematic situation has been identified.     

Iterative method generated by inverse interpolation with additional evaluations

An improvement of the iterative methods based on one point iteration function, with or without memory, using n points with the same amount of information in each point and generated by the inverse polynomial interpolation is given. The adaptation of the strategy presented here gives a new iteration function with a new evaluation of the function which increases the local order of convergence dramatically. This method is generalized to r evaluations of the function. This method for the computation of solutions of nonlinear equations is interesting when it is necessary to get high precision because it provides a lower cost when we use adaptive multi-precision arithmetics. AMS subject classification 65H05