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.

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.

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.

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 (S), lowest triplet states (T), and the first and second singlet excited states (S and S) of benzene (CH) and square cyclobutadiene (CH) 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 S states of CH and CH represent aromaticity and antiaromaticity "fingerprints" which are reproduced in other electronic states of the two molecules and allow classification of these states as aromatic (S and S for CH, T and S for CH) or antiaromatic (S and S for CH, T and S for CH).

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.

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.

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.

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.