Continuous symmetry measures: Finding the closest C2-symmetric object or closest reflection-symmetric object using unit quaternions

A closed-form solution is provided for the problem of finding the closest reflection-symmetric object, and its relation to the problems of finding the closest achiral object, the closest inversion-symmetric object, and the closest projection plane is discussed. The key to the solution is reducing this problem to the problem of finding the best (least squares) c₂ rotation between two sets of points, in addition to solving the problem of finding the closest C₂-symmetric object. The solution is derived using the quaternion representation of rotation. It is shown that calculation of the best c₂ rotation can be reduced to the diagonalization of the outer product matrix of the pair (between the two sets). ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 772–780, 1999     

Quantitative chirality/enantioselectivity relations in large random supramolecular structures

We study the relationship between shape and enantioselectivity, employing quantitative geometric chirality measurements. The model we use comprises of the boundary surfaces of two-dimensional (2D) chiral, large, random selectors (diffusion limited aggregates), interacting with homologous series of small 2D-chiral S-shaped probes (the selectands). We show how the enantioselectivity of the selectors depends on the chirality of the selectands and report the following findings: I) The enantioselectivity of a chiral selector can switch preference from the "right" to the "left" enantiomer within a homologous series of selectands. II) At this switch point the chiral selector is functionally achiral. III) Within a homologous series of chiral selectands, there is a "resonance of recognition", namely, the classical key-lock concept is replaced by a picture of various degrees of recognition. IV) The degree of enantioselectivity and the switch in handedness preference are the outcome of a complex interplay between the details of the specific geometry of the selector and the selectand, and the global shape parameter of chirality measure. V) It is shown that isochiral selectands, namely selectands of the same chirality value, may be recognized differently by a chiral selector. VI) It is proposed that a more realistic way to treat the issue of minimal points needed for chiral interaction is resolution based. VII) It is shown how to attach handedness to purely random objects.     

On the abundance of chiral crystals

A common perception of many chemists is that non-biological chiral crystals comprise a small fraction of all crystals, as is the case of chiral non-biological molecules (~10%). We show that the proportion of non-biological chiral crystals is as high as 23%; and only ~6% of these are labelled as chiral.     

Continuous symmetry numbers and entropy

Traditionally, entropy changes are corrected for rotational permutability only if the molecule is perfectly rotationally symmetric. By this approach, only a small fraction of all known molecules must be evaluated in terms of symmetry numbers, while all other molecules are totally exempt of these considerations. A general approach which encompasses all molecules, symmetric or not, is proposed here. It is based on introducing the notion of continuity to symmetry numbers and on allowing noninteger values. In the first part of the account, we provide arguments as to why continuity is needed and what difficulties one may encounter by adopting the "black-or-white" approach to symmetry. In the second part, we provide a working methodology of how to evaluate the symmetry number content of any molecule, symmetric or not. Finally, in the third part, we demonstrate the implications of this approach on entropy issues involving melting points, Jahn-Teller distortions (of fullerene) upon ionization, molecular distortion due to overcrowdedness, permutability of isotopes, and the structure of proton sponges. It is shown that continuous symmetry numbers provide entropy values, which better agree with experimental observations, and that they are capable of identifying correlations between symmetry and physical/chemical measurables.     

Three-phase microemulsion/sol-gel system for aqueous catalysis with hydrophobic chemicals

A facile three-phase transport process is described that allows to carry out catalytic reactions in water, whereby all components are hydrophobic. According to this process a hydrophobic substrate is microemulsified in water and subjected to an organometallic catalyst, which is entrapped within a partially hydrophobized sol-gel matrix. The surfactant molecules, which carry the hydrophobic substrate, adsorb/desorb reversibly on the surface of the sol-gel matrix breaking the micellar structure, spilling their substrate load into the porous medium that contains the catalyst. A catalytic reaction then takes place within the ceramic material to form the desired products that are extracted by the desorbing surfactant, carrying the emulsified product back into the solution. The method is general and versatile and has been demonstrated with the catalytic hydrogenations of alkenes, alkynes, aromatic C=C bonds, and nitro and cyano groups.     

Minimal distortion pathways in polyhedral rearrangements

A definition of minimum distortion paths between two polyhedra in terms of continuous shape measures (CShM) is presented. A general analytical expression deduced for such pathways makes use of one parameter, the minimum distortion constant, that can be easily obtained through the CShM methodology and is herein tabulated for pairs of polyhedra having four to eight vertexes. The work presented here also allows us to obtain representative model molecular structures along the interconversion pathways. Several commonly used polytopal rearrangement pathways are shown to be in fact minimum distortion pathways: the spread path leading from the tetrahedron to the square, the Berry pseudorotation that interconverts a square pyramid and a trigonal bipyramid, and the Bailar twist for the interconversion of the octahedron and the trigonal prism. Examples of applications to the analysis of the stereochemistries of several families of metal complexes are presented.     

Heck vinylation of aryl iodides by a silica sol-gel entrapped Pd(II) catalyst and its combination with a photocyclization process

[reaction: see text] Silica sol-gel encaged PdCl(2)(PPh(3))(2) is a recyclable catalyst for the Heck vinylation of aryl iodides. It is possible to couple the Heck reaction with photocyclization in a one-pot process.     

Effect of temperature on the conformation of dibenzotropone adsorbed on montmorillonites

The nature of the adsorption complex formed between dibenzotropone (DBT) and montmorillonite at elevated temperatures is strongly dependent on the interlayer cations. This was shown by electronic and IR spectra, by X-ray diffraction, and by study of the effects of gradual heating of the samples on these analyses. All samples exhibited significant red shifts of the electronic spectra of DBT into the visible range. These red shifts are attributed to two factors, both contributing to the enhancement of the tropylium planar character of DBT: hydrogen-bonding of acidic interlayer water to the carbonyl group, imparting positive charge to the tropone ring; and π interactions between the aromatic moiety and the oxygen planes. The position of the maximum was temperature-dependent for Cu-, Ni-, Al- and Fe-montmorillonites, for which heating (100°) under vacuum increased the red shift. The organic molecule assumes a planar conformation and is oriented parallel to the clay layers. IR spectra confirming this conformational orientation of DBT are discussed. The basal spacings of the DBT montmorillonite associations depend on the number of water and DBT sheets present in the interlayers. Layers with one or two sheets of DBT and with up to two sheets of water could be distinguished, leading to a maximum spacing of 20.4 Å.