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     

Point chirality functions,symmetry rules for chiral representations in one-centre molecular and field models

There are many problems (e.g. intermolecular forces, molecule-radiation field interactions) in which the separate entities (molecules, photons, or sources of static fields) many be represented by point moments (electric and magnetic. permanent or transition). Such point models lead to expressions containing moment products, which reduce on averaging to orientation-independent product functions that are characteristic of the species and its moment representation. Those functions that change sign when the chirality of the system is changed may be referred to as point chirality functions. In this paper, the point chirality functions generated from a given set of moments are defined, and in turn yield the conditions under which a given moment set is chiral; i.e. gives a chiral representation of the species it represents. They are shown to constitute a set of transferable parameters that lead to a unified approach to orientationally averaged chiral interactions of various kinds. By determining the point chirality functions of isolated chiral systems, the results are applied to interactions between various combinations of molecular, static field and radiation field systems without the need of considering the forms of each interaction in detail.     

Lifting the mirror symmetry of metal surfaces: decoupling the electronic and physical manifestations of surface chirality

Naturally occurring metal surfaces possess planes of mirror symmetry on the nanometer-length scale. This mirror symmetry can be lifted and chirality "physically" conveyed onto a surface by adsorbing a chiral molecule. Until now, it has not been known whether the conveying of chirality is limited to just the physical structure or whether it goes deeper and permeates the electronic structure of the underlying surface. By using optically active second harmonic generation (OA-SHG), it is demonstrated that the adsorption of some, but not all, chiral molecules can reversibly, and without significant structural rearrangement, measurably lift the mirror symmetry of the surface electronic structure of a metal. It is proposed that the ability of a chiral molecule to place a significant "chiral perturbation" on the electronic structure of a surface is correlated to its adsorption geometry. The microscopic origins of the observed optical activity are also discussed in terms of classical models of chirality. The results of the study challenge current models of how chiral adsorbates induce enantioselectivity in the chemical/physical behavior of heterogeneous systems, which are based on geometric/stereochemical arguments, by suggesting that chiral electronic perturbations could play a role.     

Communication: Experimental proof of symmetry breaking in tilted smectics composed of molecules with axial chirality

For the first time, domains with twisted structures have been established in planar samples of achiral compounds in tilted smectic C phase. This evidences separation of molecular conformers differing in the sense of axial chirality and confirms polar C(2) symmetry of these domains. A simple model considering polar surface anchoring energy and bulk energy of the twist can account for this finding. Conditions for coexistence of twisted and homogeneous domains are discussed.     

Controlling the position of functional groups at the liquid/solid interface: impact of molecular symmetry and chirality

With the aim of controlling the position of functional groups in a substrate-supported monolayer, a new family of functionalized linear alkyl chains was designed and synthesized, aided by molecular mechanics and dynamics simulations of its two-dimensional self-assembly on graphite. The self-assembly of these amino functionalized diamides at the liquid/solid interface was investigated with scanning tunneling microscopy. Intermolecular hydrogen-bonding interactions involving amides, combined with the effect of molecular symmetry and chirality, were found to guide the self-assembly. Control of the relative position and orientation of the amine groups was achieved, in the case of enantiopure compounds. Interestingly, racemates led to both racemic conglomerate and solid solution formation, with a concomitant loss of positional and orientational control of the amino groups as a result.     

Gauge symmetry, chirality and parity effects in four-particle systems: Coulomb's law as a universal function for diatomic molecules

Following recent work in search for a universal function (Van Hooydonk, Eur. J. Inorg. Chem., (1999), 1617), we test four symmetric +/- a(n)Rn potentials for reproducing molecular potential energy curves (PECs). Classical gauge symmetry for 1/R-potentials results in generic left right asymmetric PECs. A pair of symmetric perturbed Coulomb potentials is quantitatively in accordance with observed PECs. For a bond, a four-particle system, charge inversion (a parity effect, atom chirality) is the key to explain this shape generically. A parity adapted Hamiltonian reduces from ten to two terms and to a soluble Bohr-like formula, a Kratzer (1 - Re/R)2 potential. The result is similar to the combined action of spin and wave function symmetry upon the Hamiltonian in Heitler-London theory. Analytical perturbed Coulomb functions varying with (1 - Re/R) scale attractive and repulsive branches of PECs for 13 bonds H2, HF, LiH, KH, AuH, Li2, LiF, KLi, NaCs, Rb2, RbCs, Cs2 and I2 in a single straight line. The 400 turning points for 13 bonds are reproduced with a deviation of 0.007 A at both branches. For 230 points at the repulsive side, the deviation is 0.003 A. The perturbed electrostatic Coulomb law is a universal molecular function. Ab initio zero molecular parameter functions give PECs of acceptable quality, just using atomic ionisation energies. The function can be used as a model potential for inverting levels and gives a first principle's comparison of short- and long-range interactions, important for the study of cold atoms. Wave-packet dynamics, femto-chemistry applied to the crossing of covalent and ionic curves, can provide evidence for this theory. We anticipate this scale/shape invariant scheme applies to smaller scales in nuclear and high-energy particle physics. For larger gravitational scales (Newton 1/R potentials), problems with super-unification are discussed. Reactions between hydrogen and antihydrogen, feasible in the near future, will probably produce normal H2.     

Dynamic chirality, chirality transfer and aggregation behaviour of dithienylethene switches

The synthesis and characterisation of a series of chiral and achiral low molecular weight organogelators (LMWGs) based on bis-amide substituted dithienylethene photochromic switches is reported. The LMWGs gelate a range of solvents depending on the specific functionalisation of the hydrogen bonding amide groups. In mixtures of chiral and achiral LMWGs the stereochemical outcome of the chiral aggregation is determined by the chiral LMWG molecules in most cases. However, for the first time we demonstrate that the stereochemical outcome of the aggregation can be influenced by the achiral LWMG molecules in some cases. Furthermore specific π-π (and/or van der Waals) interactions of chiral LMWGs 1-3o with the solvent allow the solvent to influence the control of chirality of aggregation. This influence of the solvent has a dramatic effect on whether four- or two-gel states are available.     

Generalized selection rules: An augmentation procedure for the determination of symmetry invariants

A group Augmentation procedure is presented for the analytic determination of tensional invariants of arbitrary order for all point groups. The results are an ideal pratical adjunct to the generalized selection rule approach, which focuses predominantly on the concept of symmetry invariant operator products, and reduces in the non-quantum limit to the definition of classical tensorial invariants. The relationship to rotational averages is discussed, and some applications to spectroscopic processes are considered.     

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 inE ² 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.On leave from the Department of Chemistry, University of the Western Cape, Bellville 7530, South Africa.     

Geometric chirality products

Developed from Guye's produit d'asymétrie and formally similar to Ruch's chirality products, geometric chirality products are functions purely of molecular shape, without reference to chemical characteristics. In their normalized versions, geometric chirality products have all the attributes' of a chirality measure, i.e. they are similarity invariant and dimensionless in the interval [–1, 1]. An application to Boys' model of the tetrahedron is presented, and a detailed study of the results for triangular domains in E² is reported. According to this measure, the most chiral triangle is infinitely flat and infinitely skewed. The analysis leads to the paradoxical conclusion that the most chiral triangle is infinitesimally close to an achiral one, The results are compared with those obtained for an overlap measure of chirality, and the relationship between molecular models and measures of chirality is briefly discussed.On leave from the Department of Chemistry, University of the Western Cape, Bellville 7530, South Africa.     

Dipeptide-induced chirality organization

This review describes an outline of dipeptide-induced chirality organization by using molecular scaffolds. A variety of ferrocene-dipeptide conjugates as bioorganometallics are designed to induce chirality-organized structures of peptides. The ferrocene serves as a reliable organometallic scaffold with a central reverse-turn unit for the construction of protein secondary structures via intramolecular hydrogen bondings, wherein the attached dipeptide strands are constrained within the appropriate dimensions. Another interesting feature of ferrocene-dipeptide conjugates is their strong tendency to self-assemble through contribution of available hydrogen bonding sites for helical architectures in solid states. Symmetrical introduction of two dipeptide chains into a urea molecular scaffold is performed to induce the formation of the chiral hydrogen-bonded duplex, wherein each hydrogen-bonded duplex is connected by continuous intermolecular hydrogen bonds to form a double helix-like arrangement.     

Memory of chirality generated by spontaneous crystallization and asymmetric synthesis using the frozen chirality

Asymmetric synthesis using frozen chirality generated by spontaneous crystallization was performed. Achiral asymmetrically substituted imide with a tetrahydronaphthyl group on the nitrogen atom crystallized in a chiral fashion, with space group P2(1)2(1)2(1). The molecular chirality generated by spontaneous crystallization was retained in cold THF. The half-life determined on the basis of decreasing optical activity followed by CD spectrometer was 7.8, 33.1, and 150.0 min at -20, -30, -40 degrees C, respectively. The energy barrier (DeltaG()) of racemization was calculated with the temperature dependence of the kinetic constant to be 18.24-18.36 kcal mol(-)(1) at 233-253 K. The memorized frozen chirality was transferred to permanent optically active alcohols by nucleophilic addition with n-buthyllithium.     

Thermal and photochemical transformation of conformational chirality into configurational chirality in the crystalline state

Because they crystallize in chiral conformations in which abstraction of only one of two diastereotopic gamma-hydrogen atoms is possible, salts formed between achiral keto-acids possessing the tricyclo[4.4.1.0]undecane ring system and optically pure amines undergo Norrish type II cleavage in the solid state in enantiomeric excesses as high as 95% at 98% conversion, following removal of the ionic chiral auxiliaries. Thermal enolene rearrangement of the same salts results in optical yields approximately half those observed for the photochemical reaction.     

Topological chirality and achirality of links

Empirical and analytical methods employed in the detection of topological chirality and achirality (amphicheirality) in oriented and non-oriented links are critically examined.U-polynomials of non-oriented links are modified for use in the detection of topological chirality. By use of this method, all but eight (listed below) non-oriented links with up to four components and nine crossings are proven to be topologically chiral, including 4 ₁ ² , the abstract model of the only topologically chiral, non-oriented catenane (chemical link) synthesized so far. The topological chirality of certain 3-Borromean links is similarly proven. The amphicheirality of 2 ₁ ² 6 ₂ ² 8 ₈ ² 9 ₆₁ ² 6 ₃ ² 8 ₄ ³ 8 ₆ ³ and 8 ₄ ³ is proven by the demonstration that all eight non-oriented links can attain rigidly achiral presentations. Furthermore, we conjecture that 9 ₆₁ ² and a two-component, oriented link with an 11-crossing diagram are the first members of, respectively, a class of non-oriented and a class of oriented amphicheiral, non-alternating, prime links with odd crossing numbers. Amphicheirality combined with an odd crossing number is unprece dented among knots or links.     

Entropy in dissimilarity and chirality measures

Within the prospect of quantifying the geometrical dissimilarity of molecular models on the basis of a thermodynamical formalism, the algebra of stereogenic pairing equilibria is reviewed and applied to molecular geometry: developing Rassat's proposition, an interaction energy of two figures F and F is taken as proportional tod _H ^Emphasis>/2 (F, F), whered _H denotes the Hausdorff distance. IfG is a group of rotations in E _n the geometrical version of the general equation (E) of the chemical algebra defines a distance extensionD _p(F,F) ofd _H(F,F), which is independent of the orientations of F and F, and where the coefficientp is interpreted as the reciprocal of a temperature-like parameter:p 1/T. At K (p = ), no formal entropy contributes to the definition of the uniform distanceD . At K (p = 0), the discrimination between homo- and hetero-pairing of figures by the harmonic distance Do is averaged over orientation states. Temperature-dependent chirality measuresc _p are derived fromD _p, andc is analogous to Mislow's chirality measure. If T and oT are normalized enantiomorphic triangles with coincident centroids inE ₂,c _p(T) =D _p (T, T) is calculated forp = 0 andp = , and discussed for 0 <p < . Finally, the Hausdorff interaction model is putatively related to energy profiles versus dihedral angle inmeso- anddl-molecules.