Symmetry, Volume 2, Issue 1

Through-space isotropic NMR shielding values of a perpendicular diatomic hydrogen probe moved in a 0.5 Å grid 2.5 Å above several polycyclic aromatic/antiaromatic ring and aromatic/aromatic hydrocarbons were computed with Gaussian 03 at the GIAO HF/6...

This work expands the results and derivations presented in a recent letter. It is argued that symmetry breaking Hartree-Fock (HF) solutions of a simple model of the Cu-O planes in La₂CuO₄, are able to describe the insulator and antiferromagnetic char...

Generating functions play important roles in theory of orthogonal polynomials. In particular, it is important to consider generating functions that have symmetry. This paper is a survey on generating functions that define unitary operators. First, cl...

In this paper, we study the influence of hard supersymmetry breaking terms in a N = 1, d = 4 supersymmetric model, in S¹ × R³ spacetime topology. It is shown that when the radius of the compact dimension is large supersymmetry is unbroken, and dynami...

The NICS_zz-scan curves of aromatic organic, inorganic and “all-metal” molecules in conjunction with symmetry-based selection rules provide efficient diagnostic tools of the σ-, π- and/or double (σ + π)-aromaticity. The NICS_zz-scan curves of σ-aromati...

When liquid molecules are confined in a narrow gap between smooth surfaces, their dynamic properties are completely different from those of the bulk. The molecular motions are highly restricted and the system exhibits solid-like responses when sheare...

I report, emphasizing some key open issues and some aspects that are particularly relevant for phenomenology, on the status of the development of “doubly-special” relativistic (“DSR”) theories with both an observer-independent high-velocity scale and...

Despite the widely-held premise that initial boundary conditions (BCs) corresponding to measurements/interactions can fully specify a physical subsystem, a literal reading of Hamilton’s principle would imply that both initial and final BCs are requir...

A mechanistic study of the bimolecular nucleophilic substitution (S_N2) reaction for halomethane CH₃X (X = Cl, Br, or I) is approached by using symmetry principles and molecular orbital theory. The electrophilicity of the functionalized sp³–carbon is...

Several situations of general interest, in which the symmetry groups usually applied to spectroscopy problems need to be extended, are reviewed. It is emphasized that any symmetry group of geometrical operations to be used in Molecular Spectroscopy s...

The emphasis in the published literature has mostly been on symmetry as the critical source for beauty judgment. In fact, both symmetry and asymmetry serve as highly aesthetic sources of beauty, whether the context is perceptual or conceptual. The hu...

Information optimization is a centerpiece phenomenon in the universe. It develops from simplicity, then continuously breaks symmetry and cycles through instability to progress to increasingly dense nodes of complexity and diversity. Intelligence has...

This feature article gives a general introduction to the phenomenon of supramolecular chirogenesis using the most representative examples of different chirogenic assemblies on the basis of ethane-bridged bis-porphyrinoids. Supramolecular chirogenesis...

We report the mechanism and scope of “preferential enrichment”, which is an unusual symmetry-breaking enantiomeric resolution phenomenon that is initiated by the solvent-assisted solid-to-solid transformation of a metastable polymorphic form into a t...

Cyclooctatetraene (COT), the first 4nπ-electron system to be studied, adopts an inherently nonplanar tub-shaped geometry of D_2d symmetry with alternating single and double bonds, and hence behaves as a nonaromatic polyene rather than an antiaromatic...

Significant cases of time-evolution equations, the linear Schr¨odinger and the Fokker–Planck equation are considered. It is known that equations of this type can be transformed, in some cases, into a highly simplified form. The properties of these eq...

We compute the number of symmetric r-colorings and the number of equivalence classes of symmetric r-colorings of the quaternion group.

We extend the Landau theory of bent-core mesophases and d-wave high-Tc superconductors by considering additional secondary pseudo-proper order parameters. These systems exhibit a remarkable analogy relating their symmetry groups, lists of phases, and...

Statistical systems, in which spontaneous symmetry breaking can be accompanied by spontaneous local symmetry restoration, are considered. A general approach to describing such systems is formulated, based on the notion of weighted Hilbert spaces and...

Recent results on the optical absorption and symmetry of the Np(V) complexes with dicarboxylate and diamide ligands are reviewed. The importance of recognizing the “silent” feature of centrosymmetric Np(V) species in analyzing the absorption spectra...