Kurt Mislow

On Borromean links

Abstractn-Borromean links are nontrivial links in whichn rings,n ≥ 3, are combined in such a way that any two component rings form a trivial link. The symmetry of links withn = 3 is discussed, and it is shown that such links form a variety of series whose members are different isotopy types. Examples are adduced of 3-Borromean links that are topologically chiral: Novel constructions are described ofn-Borromean links with and without at least one nontrivial sublink.

Conformational analysis of polysilanes by the empirical force field method

Abstract Empirical force field (EFF) parameters have been developed for molecules containing Si-Si bonds. These parameters have been adjoined to those of a standard EFF and the extended force field has been used to calculate structures and relative conformational energies for a variety of acyclic and cyclic catenated polysilanes.

Distance functions as generators of chirality measures

A non-numerical analysis is presented of chirality measures associated with a set of topologically equivalent distance functions. A chirality measure is defined as the minimum distance that separates a chiral and an achiral object (first kind) or two enantiomorphs (second kind). On the basis of this analysis, as applied to triangles in the Euclidean plane, results of an earlier computational study of the Hausdorff chirality measure are now fully understood. Analytical proof has been provided for an earlier conjecture, based on a numerical analysis, that the union of enantiomorphous triangles is achiral under conditions of maximal overlap. Geometric parameters for the most chiral triangle, as determined by a family of three measures of the first kind, are found to differ substantially from those determined by the corresponding measures of the second kind; none of these extremal triangles is degenerate.

Desymmetrization and degree of chirality

Chiral objects, viewed as distorted derivatives of achiral ones, may be represented by points in a configuration space that is spanned by a set of symmetry coordinates derived for the symmetry group of the achiral object of highest symmetry. We propose a measure (d) that quantifies the displacement of the representative point for a chiral object away from thenearest point representing an achiral object in such a multi-dimensional configuration space. If the symmetry coordinates are chosen so as to yield a similarity invariant measure, then the valuesd; obtained for a series ofi chiral objects can serve as a basis for comparing the degrees of chirality of these objects. The chirality of triangles inE2 is studied by this method, and it is shown that the most chiral triangle in terms of this measure corresponds to one that is infinitely flat, and that may be approached but is never attained. This result is compared to others obtained previously for the same system by the use of different measures of chirality.

An ab initio investigation into the SN2 reaction: Frontside attack versus backside attack in the reaction of F− with CH3F

The energy hypersurface for the attack of fluoride ion on methyl fluoride has been explored with ab initio LCAO-SCF calculations at a split-valence basis set level. Transition states for frontside and backside attack have been located. In addition to transition states, two possible F−-CH3F clusters have been identified. The transition state for the substitution of fluoride with retention of configuration is found to be 56 kcal/mol higher than the transition state for inversion of configuration. The transition state for hydride displacement with inversion is 62 kcal/mol above the transition state for fluoride substitution with inversion.

Shape space of achiral simplexes

We examine the general dimensional relation between the shape space of then-simplexes and the subspace of their achiral sets. It is found that the only simplexes that can be partitioned into “left-handed” and “right-handed” classes are the triangles in Euclidean 2-space.

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).

A left-right classification of topologically chiral knots

A method for partitioning topologically chiral knots into mutually heterochiral classes has been developed, based on the principle that for such knots there exist no diagrams whose vertex-bicolored graphs are composed of equivalent black and white subgraphs. The method, which introduces the concept ofwrithe profiles, is successfully applied to alternating as well as non-alternating prime and composite knots, and works in cases where the Jones and Kauffman polynomials fail to recognize the knots chirality. It is shown that writhe profiles are sensitive indicators of diagram similarity.

Conformational analysis of 1,1,2,2-tetraaryl-disilanes

Abstract A study of the static stereochemistry of 1,1,2,2-tetraphenyldisilane ( 1 ) and 1,1,2,2-tetramesityldisilane ( 2 ) by empirical force field calculations, X-ray diffraction, and 1 H NMR reveals that the preference for the anti conformation, exhibited by the unclamped 1,1,2,2-tetraarylethanes, is sustained in the analogous disilanes, although in somewhat attenuated form. This anti preference stands in contrast to the gauche preference of 1,1,2,2-tetraalkyldisilanes. Examination of 3 J HH coupling constants for R 2 HSiSiHR 2 ; (R = phenyl, mesityl, 2,6-dimethyl-phenyl, t -butyl, cyclohexyl) suggests the existence of a Karplus relation for H-Si-Si-H systems.

Meteorites: Optical Activity in Organic Matter

A low- amplitude, positive, Cotton effect, centered at about 340 millimicrons, has been observed in organic extracts of samples from ordinary (noncarbonaceous) chondrites. Ancillary evidence renders it likely that this optical activity derived from contamination by biologic materials on Earth.