Threaded Rings that Swim in Excitable Media.

Cardiac tissue and the Belousov-Zhabotinsky reaction provide two notable examples of excitable media that support scroll waves, in which a filament core is the source of spiral waves of excitation. Here we consider a novel topological configuration in which a closed filament loop, known as a scroll ring, is threaded by a pair of counterrotating filaments that are perpendicular to the plane of the ring and end on the boundary of a thin medium. We simulate the dynamics of this threaded ring (thring) in the photosensitive Belousov-Zhabotinsky excitable medium, using the modified Oregonator reaction-diffusion equations. These computations reveal that the threading topology induces an exotic motion in which the thring swims in the plane of the ring. We propose a light templating protocol to create a thring in the photosensitive Belousov-Zhabotinsky medium and provide experimental confirmation that this protocol indeed yields a thring.

Knot theory in modern chemistry.

Knot theory is a branch of pure mathematics, but it is increasingly being applied in a variety of sciences. Knots appear in chemistry, not only in synthetic molecular design, but also in an array of materials and media, including some not traditionally associated with knots. Mathematics and chemistry can now be used synergistically to identify, characterise and create knots, as well as to understand and predict their physical properties. This tutorial review provides a brief introduction to the mathematics of knots and related topological concepts in the context of the chemical sciences. We then survey the broad range of applications of the theory to contemporary research in the field.

Magnetic Shielding, Aromaticity, Antiaromaticity, and Bonding in the Low-Lying Electronic States of Benzene and Cyclobutadiene.

Aromaticity, antiaromaticity, and their effects on chemical bonding in the ground states (S0), lowest triplet states (T1), and the first and second singlet excited states (S1 and S2) of benzene (C6H6) and square cyclobutadiene (C4H4) are investigated by analyzing the variations in isotropic magnetic shielding around these molecules in each electronic state. All shieldings are calculated using state-optimized π-space complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs), in the 6-311++G(2d,2p) basis. It is shown that the profoundly different shielding distributions in the S0 states of C6H6 and C4H4 represent aromaticity and antiaromaticity "fingerprints" which are reproduced in other electronic states of the two molecules and allow classification of these states as aromatic (S0 and S2 for C6H6, T1 and S1 for C4H4) or antiaromatic (S0 and S2 for C4H4, T1 and S1 for C6H6). S2 C6H6 is predicted to be even more aromatic than S0 C6H6. As isotropic shielding isosurfaces and contour plots show very clearly the effects of aromaticity and antiaromaticity on chemical bonding, these can be viewed, arguably, as the most succinct visual definitions of the two phenomena currently available.

Shielding in and around Oxazole, Imidazole, and Thiazole: How Does the Second Heteroatom Affect Aromaticity and Bonding?

Isotropic magnetic shielding distributions in the regions of space surrounding oxazole, imidazole, and thiazole are used to investigate aromaticity and bonding in these five-membered heterocycles with two heteroatoms. This is achieved by constructing HF-GIAO and MP2-GIAO (Hartree-Fock and second-order Møller-Plesset perturbation theory with gauge-including atomic orbitals) isotropic shielding plots, within the 6-311++G(d,p) basis, using regular two-dimensional 0.05 Å grids in the molecular plane and in planes 0.5 and 1 Å above it. The extent of isotropic shielding delocalization in the contour plots in planes 1 Å above the molecular plane, which is a new sensitive two-dimensional aromaticity criterion, indicates that aromaticity decreases in the order thiazole > imidazole > oxazole; in combination with previous results on furan, pyrrole, and thiophene ( J. Org. Chem. 2013 , 78 , 8037 - 9043 ), the aromaticity ordering in the six five-membered heterocycles becomes thiophene > thiazole > pyrrole > imidazole > furan > oxazole. The results suggest that the inclusion of a second heteroatom in a five-membered heterocycle has a detrimental effect on its aromaticity, which is very minor in oxazole, when compared to furan, and small but noticeable in imidazole and pyrrole and in thiazole and thiophene.

Chemical bonding and aromaticity in furan, pyrrole, and thiophene: a magnetic shielding study.

Aromaticity and bonding in furan, pyrrole, and thiophene are investigated through the behavior of the isotropic shielding σiso(r) within the regions of space surrounding these molecules. HF-GIAO/6-311++G(d,p) and MP2-GIAO/6-311++G(d,p) (Hartree-Fock and second-order Møller-Plesset perturbation theory utilizing gauge-including atomic orbitals) σiso(r) contour plots are constructed using regular two-dimensional 0.05 Å grids in the molecular plane, in horizontal planes 0.5 and 1 Å above it, and in a vertical plane through the heteroatom. The nucleus-independent chemical shifts (NICS) calculated at the ring centers and at 0.5 Å and 1 Å above these centers, NICS(0), NICS(0.5), and NICS(1), respectively, support the widely accepted order of aromaticities thiophene > pyrrole > furan. The results suggest that accurate NICS calculations benefit more from the use of an extended basis set than from the inclusion of dynamical electron correlation effects. The different extents of σiso(r) delocalization observed in the horizontal contour plots and other features of σiso(r) are also consistent with an aromaticity reduction of the order thiophene > pyrrole > furan. It is suggested that the extent of σiso(r) delocalization in σiso(r) contour plots in planes 1 Å above the molecular plane could be used for comparing the relative aromaticities of a wide range of aromatic systems.

Magnetic shielding in and around benzene and cyclobutadiene: a source of information about aromaticity, antiaromaticity, and chemical bonding.

A detailed picture of the variations in the isotropic shielding σ(iso)(r) in and around the classical examples of aromatic and antiaromatic systems, benzene and square cyclobutadiene, in terms of isosurfaces and contour plots, is obtained by calculating σ(iso)(r) values at fine regular three-dimensional 7 × 7 × 7 Å grids of points with a spacing of 0.05 Å, using π space complete-active-space self-consistent field (CASSCF) wave functions constructed from gauge-including atomic orbitals (GIAOs). The results demonstrate that the σ(iso)(r) values can be used not only to distinguish between aromatic and antiaromatic systems but also to characterize chemical bonds and investigate the extents to which these bonds are affected by the aromatic or antiaromatic nature of the molecule in which they reside. The strong bonding interactions within the benzene ring are highlighted by the fact that the carbon-carbon and carbon-hydrogen bonds are wrapped up within a doughnut-shaped region of increased shielding, which is especially high along the carbon-carbon bonds, with protrusions marking the carbon-hydrogen bonds. The antiaromatic destabilization in square cyclobutadiene is seen as the consequence of the presence of a markedly deshielded dumbbell-shaped region in the center of the molecule, which disrupts the connections between the shielded regions outlining individual carbon-carbon bonds, decreases the shielding within these regions, and displaces them to off-bond locations outside the ring. The well-known deshielding of aromatic protons and increased shielding of antiaromatic protons are shown to be accompanied by analogous shielding differences along the whole lengths of the carbon-hydrogen bonds, as a result of which the carbon-hydrogen bonds should become slightly weaker in aromatic systems as opposed to the corresponding bonds in antiaromatic systems.

Braiding, branching and chiral amplification of nanofibres in supramolecular gels.

Helical nanofibres play key roles in many biological processes. Entanglements between helices can aid gelation by producing thick, interconnected fibres, but the details of this process are poorly understood. Here, we describe the assembly of an achiral oligo(urea) peptidomimetic compound into supramolecular helices. Aggregation of adjacent helices leads to the formation of fibrils, which further intertwine to produce high-fidelity braids with periodic crossing patterns. A braid theory analysis suggests that braiding is governed by rigid topological constraints, and that branching occurs due to crossing defects in the developing braids. Mixed-chirality helices assemble into relatively complex, odd-stranded braids, but can also form helical bundles by undergoing inversions of chirality. The oligo(urea) assemblies are also highly sensitive to chiral amplification, proposed to occur through a majority-rules mechanism, whereby trace chiral materials can promote the formation of gels containing only homochiral helices.

Exploring Chemical Bonds through Variations in Magnetic Shielding.

Differences in nuclear isotropic magnetic shieldings give rise to the chemical shifts measured in NMR experiments. In contrast to existing NMR experimental techniques, quantum chemical methods are capable of calculating isotropic magnetic shieldings not just at nuclei, but also at any point in the space surrounding a molecule. Using s-trans-1,3-butadiene, ethane, ethene, and ethyne as examples, we show that the variations in isotropic magnetic shielding around a molecule, represented as isosurfaces and contour plots, provide an unexpectedly clear picture of chemical bonding, which is much more detailed than the traditional description in terms of the total electron density.