Symmetry breaking in homo-oligomers: the curious case of mega-hemocyanin

Unsymmetrical bending occurs when the bending moment applied to a structural member does not align with its principal axis. This misalignment leads to complex stress distributions and deflection patterns that differ from those in symmetrical bending, and are essential for designing structures to withstand different loading conditions. In unsymmetrical bending, the neutral axis—where stress is zero—does not necessarily align with the geometric axes of the cross-section. The...

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...

A bond is formed between two atoms by sharing two electrons. When this bond is broken by supplying sufficient energy, either two electrons can be taken up by one atom forming ions by the cleavage called heterolysis, or the two electrons are shared by two atoms, with one each creating radicals by the cleavage called homolysis.

Unsymmetrical bending occurs when a structural member is subjected to bending moments in a plane that does not align with the member's principal axes. This scenario typically arises in beams and other structural components when loads are applied at non-ideal angles, introducing complexities in stress analysis.
When a bending moment is applied at an angle θ concerning the vertical axis of a symmetrical member, it can be resolved into components along the member's principal...

Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula. Structural isomerism of coordination compounds can be divided into two subcategories, the linkage isomers and coordination-sphere isomers.
Linkage isomers occur when the coordination compound contains a ligand that can bind to the transition metal center through two different atoms. For example, the CN− ligand can bind through the carbon atom or through the nitrogen atom. Similarly,...

In this lesson, we delve into the role of ring conformation and its stability, which determines the spatial arrangement and, consequently, the molecular symmetry and stereoisomerism of cyclic compounds. 1,2-Dimethylcyclohexane is used as a case study to evaluate the possible number of stereoisomers. Here, given the multiple (n = 2) chiral centers, there are 2n = 4 possible configurations that lack a plane of symmetry, as the ring skeleton exists in a non-planar chair conformation. In addition,...