Many covalent molecules have central atoms that do not have eight electrons in their Lewis structures. These molecules fall into three categories:

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...

Biological membranes show uneven distribution of different types of lipids in the inner and outer layers, resulting in transverse asymmetric membranes. The treatment of the erythrocyte membrane with the enzyme phospholipase confirmed the asymmetric nature of the lipid bilayer. The enzyme hydrolyzes lipids into fatty acids and hydrophilic groups. The phospholipase acts only on the outer layer of the membrane, while the inner layer remains intact. The phospholipase treatment resulted in 80%...

If a set of reactants can yield multiple constitutional isomers, but one of the isomers is obtained as the major product, the reaction is said to be regioselective. In such reactions, bond formation or breaking is favored at one reaction site over others.
The hydrohalogenation of an unsymmetrical alkene can yield two haloalkane products, depending on which vinylic carbon takes up the halogen. However, one product usually predominates, where hydrogen adds to the vinylic carbon bearing the...

Molecular Orbital Energy Diagrams

An even signal, whether in continuous-time or discrete-time, is defined by its symmetry with its time-reversed version. Mathematically, this is represented as