Novel numerical method for calculating the pressure tensor in spherical coordinates for molecular systems

We propose a novel method for computing the pressure tensor along the radial axis of a molecular system with spherical symmetry. The proposed method uses the slice averaged pressure to improve the numerical stability and precision significantly. Simplified expressions of the local pressure are derived for a conventional molecular force field including non-bond, bond stretching, angle bending, and torsion interactions; these expressions are advantageous in terms of the computational cost. We also discuss an algorithm to avoid numerical singularity. Finally, the method is successfully applied to three different molecular systems, i.e., a water droplet in oil, a spherical micelle, and a liposome.     

Electronic and topological chirality indexes for dissymmetric molecular systems

A new quantitative measure of molecular dissymmetry is proposed that is based on quantum-mechanical counterparts of notions extracted from differential geometry. Starting with the so-called torsion of a curve, we arrive at a chirality operator and appropriate average as the chirality index æ. The essential properties of æ are its additivity and also its ability to vanish for the racemic mixture of chiral structures. Some quantum-chemical approaches to calculating æ are presented, e.g., a typical one using only the adjacency matrix and the coordinates of atoms. Quasi-continuous and continuous systems, such as helices and Möbius-like structures, are studied.     

Peptidic molecular brushes with enhanced chirality

Tethering oligopeptides through one end densely packed onto a linear polymer main chain will greatly reduce freedom of the peptide chains, which affords an easy access to investigate the secondary structure of peptides under constrained condition. Herein, molecular brushes with densely grafted monodispersed Cbz‐protected oligolysine were efficiently synthesized via free radical polymerization of the macromonomer‐bearing lysine octamer, and the secondary structures of the oligopeptide side chains in solutions were investigated. To examine the architecture effects on helical conformation, circular dichroism spectra from the polymer were compared with that from the corresponding macromonomer. To check the chemical structural effects on conformation of the oligopeptide, Cbz groups from the molecular brushes were deprotected, and the secondary structures of the polymers were compared before and after the deprotection. Conformation of the deprotected polymer was further explored by varying solution pH values. Complexation of the positively charged, deprotected polymer with anionic surfactant provides an alternative route to mediate the secondary structures of the short peptides in the constrained environment. It has been found that oligolysine side chains within the molecular brushes can adopt enhanced α‐helical conformation through the crowding structures or can form β‐sheet by hydrophobic interactions between the complexed surfactants. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Coherent third-order spectroscopic probes of molecular chirality

The third-order optical response of a system of coupled localized anharmonic vibrations is studied using a Green's function solution of the nonlinear exciton equations for bosonized excitons, which are treated as interacting quasiparticles. The explicit calculation of two-exciton states is avoided and the scattering of quasiparticles provides the mechanism of optical nonlinearities. To first-order in the optical wave vector we find several rotationally invariant tensor components for isotropic ensembles which are induced by chirality. The nonlocal nonlinear susceptibility tensor is calculated for infinitely large periodic structures in momentum space, where the problem size reduces to the exciton interaction radius. Applications are made to alpha and 3(10) helical infinite peptides.     

Local symmetry and chirality of molecular faces

The concept of local symmetry has been applied to faces of planar sites such as carbon–carbon double bonds and aromatic rings with the principal results being as follows. The two faces of a planar site must have the same local symmetry group. This local symmetry group is limited to the polar point groups. For cyclic compounds, directed cycles must have chirotopic faces although the reverse is not necessarily true: chirotopic faces are possible for both directed and undirected cycles. A number of examples are provided to illustrate these results. Received: 30 June 1999 / Accepted: 4 October 1999 / Published online: 19 April 2000     

A geometrical approach to the degree of chirality and asymmetry

A new measure of the degree of chirality and asymmetry of a finite number of particles is proposed. To this end a space of configurations of identical particles is defined as the orbit space of the group of all permutations of particles embedded in an Euclidean space. This space is shown to be a metric space and the action of the translation and orthogonal groups is also defined. The results are applied to the study of an algebra of polynomials on the configuration space and its equivalence to the algebra of symmetric Cartesian tensors is demonstrated. An illustrative example is presented. Some general features of chirality are also briefly discussed.     

Analysis of molecular chirality using the lattice model of spatial structure

A lattice model of the spatial structure of a molecule is suggested. A broken line is constructed to characterize atoms and molecular fragments. The line is a spiral (left or right) embracing the whole lattice containing the molecule. The mutual arrangement of molecular fragments along the broken line is described by a molecular code. The code contains all the necessary information about molecular conformation and configuration in compressed form. Comparing the codes makes it possible to evaluate the structural similarity and dissimilarity of molecules. For example, one can easily estimate the chirality level for enantiomers. Using this approach is demonstrated on various model structures. A. V. Bogatskii Physicochemical Institute, Ukrainian Academy of Sciences. Odessa State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 541–546, May–June, 1998. This work was supported by INTAS grant INTAS-UA 95-0060.     

Cyclohexane-based low molecular weight hydrogelators: a chirality investigation

Seven new 1,3,5-cyclohexyltricarboxamide-phenylalanine derivatives were synthesized in order to investigate the effect of the amino acid chirality on the gelating properties of these small molecules in water. Gelation tests have shown that enantiomerically pure homochiral 1,3,5-cyclohexyltricarboxamide-L-phenylalanine is a non-hydrogelator as it crystallizes from water, whereas the heterochiral derivatives with either two L-phenylalanine moieties and one D-phenylalanine (LLD), or vice versa (DDL), are very good hydrogelators. Concentration-dependent gel-to-sol transition-temperature (T(gs)) curves for LLD or DDL gels show a sigmoidal behaviour, which is in contrast to the logarithmic curves generally observed for gels derived from low molecular weight gelators (LMWGs). Such sigmoidal behaviour can be related to interactions between fibre bundles, which give rise to intertwined bundles of fibres. Transmission electron microscopy (TEM) images of LLD and DDL gels show a network of thin, unbranched, fibre bundles with diameters of 20 nm. Right-handed twisted fibre bundles are present in the LLD gel, whereas left-handed structures can be found in the DDL gel. Each bundle of fibres consists of a finite number of primary fibres. Gels consisting of mixtures of gelators, LLD and DDL, and nongelators (LLL or DDD) were investigated by means of T(gs) measurements, CD spectroscopy and TEM. Results show that the incorporation of nongelator molecules into gel fibres occurs; this leads to higher T(gs) values and to changes in the helicity of the fibre bundles. Furthermore, it was found that peripheral functionalization of the homochiral derivatives LLL or DDD by means of a second amino acid or a hydrophilic moiety can overcome the effect of chirality; this process in turn leads to good hydrogelators.     

A memory of chirality approach to the stereoselective synthesis of 4-hydroxy-alpha-methylprolines

To extend the memory of chirality (MOC) methodology to structurally more diverse compounds, the synthesis of 4-hydroxy-alpha-methylprolines was undertaken. Yield and selectivity were very good, with an unexpected reversal in selectivity observed for the cyclization of one adduct with an unprotected hydroxyl.     

The effect of molecular chirality on the incidence of twisted smectic A phases

Four chiral chloro-esters were synthesized in order to examine systematically the effect that molecular chirality has on the temperature range and incidence of the twisted smectic A phase or the twist grain boundary phase as it has become known. We find that when the motion of the chiral centre is restricted by rotational hindrance, thereby increasing the chirality of the system, the twisted S_A phase range is increased. At low chirality the twisted S_A phase disappears altogether. Furthermore, it is shown that the transition temperatures of the chiral compounds are lower than their racemic analogues.     

Novel shape descriptors for molecular graphs.

We report on novel graph theoretical indices which are sensitive to the shapes of molecular graphs. In contrast to the Kier's kappa shape indices which were based on a comparison of a molecular graph with graphs representing the extreme shapes, the linear graph and the "star" graph, the new shape indices are obtained by considering for all atoms the number of paths and the number of walks within a graph and then making the quotients of the number of paths and the number of walks the same length. The new shape indices show much higher discrimination among isomers when compared to the kappa shape indices. We report the new shape indices for smaller alkanes and several cyclic structures and illustrate their use in structure-property correlations. The new indices offer regressions of high quality for diverse physicochemical properties of octanes. They also have lead to a novel classification of physicochemical properties of alkanes.     

DNA cholesteric phases: the role of DNA molecular chirality and DNA-DNA electrostatic interactions

DNA molecules form dense liquid-crystalline twisted phases both in vivo and in vitro. How the microscopic DNA chirality is transferred into intermolecular twist in these mesophases and what is the role of chiral DNA-DNA electrostatic interactions is still not completely clear. In this paper, we first give an extended overview of experimental observations on DNA cholesteric phases and discuss the factors affecting their stability. Then, we consider the effects of steric and electrostatic interactions of grooved helical molecules on the sign of cholesteric twist. We present some theoretical results on the strength of DNA-DNA chiral electrostatic interactions, on DNA-DNA azimuthal correlations in cholesteric phases, on the value of DNA cholesteric pitch, and on the regions of existence of DNA chiral phases stabilized by electrostatic interactions. We suggest for instance that 146 bp long DNA fragments with stronger affinities for the nucleosome formation can form less chiral cholesteric phases, with a larger left-handed cholesteric pitch. Also, the value of left-handed pitch formed in assemblies of homologous DNA fragments is predicted to be smaller than that of randomly sequenced DNAs. We expect also the cholesteric assemblies of several-kbp-long DNAs to require higher external osmotic pressures for their stability than twisted phases of short nucleosomal DNA fragments at the same DNA lattice density.