Noham Weinberg

A unification of chirality measures

A general classification of chirality measures is suggested, based on a new unifying scheme. Two classes of measures - congruity and resolution type — are defined All chirality measures so far reported in the literature are found to belong to one of these two classes. At a higher level of unification, a more general construction is suggested that includes congruity and resolution measures as limiting cases. It is shown that congruity measures are nested in clusters of eight, generated by 23 combinations of their possible choice of a reference object (chiral vs. achiral), representation form (optimized vs. factorized) and type of chiral object under consideration (discrete vs. continuous). Each of the eight cases can have an infinite number of variations depending on the choice of averaging scheme. The problem of dimensionality is discussed for congruity measures and is shown to be unresolvable only for the case of chirality measures based on the discrete metric (e.g. overlap measures).

Reaction Profiles and Energy Surfaces of Compressed Species

Both experiment and first principles calculations unequivocally indicate that properties of elements and their compounds undergo a tremendous transformation at ultrahigh pressures exceeding 1 Mbar due to the fact that the difference between intra- and intermolecular interactions disappears under such conditions. Yet, even at much milder pressures of 50-300 kbar, when molecules still retain their individual identity, their chemical properties and reactivity change dramatically. Since kinetics and mechanisms of condensed-phase reactions are described in terms of their potential energy (PES) or Gibbs energy (GES) surfaces, chemical effects of high pressure can be assessed through analysis of pressure-induced deformations of GES of solvated reaction systems. We use quantum mechanical and molecular dynamics simulations to construct GES and reaction profiles of compressed species, and analyze how topography of GES changes in response to compression. We also discuss the important role of volume profiles in assessing pressure-induced deformations and show that the high-pressure GES are well described in terms of these volume profiles and the reference zero-pressure GES.

Importance sampling as an efficient strategy for the conformational analysis of flexible molecules.

We propose an importance sampling technique for the conformational analysis of flexible molecules that bridges the gap between currently used uniform random search and random walk methods, and compare performances of these methods in their application to selected open-chain and closed-ring hydrocarbons. It is suggested that, if no information on conformational properties of a molecule is available, the optimum strategy of its conformational analysis should include a uniform random search followed by an importance sampling biased as prescribed by the uniform search and concluded by a random-walk or genetic algorithm routine to rectify the properties of the most important parts of the conformational space.