ABSTRACT
We introduce the topic of renormalization in chemistry by considering calculation of ring currents in polycyclic conjugated hydrocarbons based on the conjugated circuit model.
The discussion of conjugated circuits in previous chapters of this book have focused attention on resonance energies and aromaticity in general. In this section, we focus on use of conjugated circuits for calculations of ring currents. Ring currents have been at the center of attention of a number of theoretical chemists, starting with Linus Pauling’s work in 1936 on the diamagnetic anisotropy of aromatic molecules [1] through the most recent ab initio calculations of induced current densities by Patrick Fowler and others covering a span of some 60 years. Those interested in the long history of ring current calculations may consult two recent reviews on this subject, the paper by Lazzereti on ring currents [2], and the paper by Mallion and coworkers on topological ring currents [3-8]. We focus in this section on the latest, conceptually and structurally different, approach to ring currents in cyclic and polycyclic conjugated hydrocarbons. It is so different and unique because it is based on enumerations as a method of calculation rather than calculus as a tool for computation of ring currents. In view of this dramatic distinction in the character of the calculations, it is worth digressing and recalling some thoughts of G. N. Lewis, the father of the pre-quantum chemistry octet rule of covalent bonding. The octet rule was mostly applied to first row atoms: carbon, oxygen, and nitrogen. The octet rule states that atoms of main-group elements tend to combine in a molecule in such a way that each atom involves eight electrons in its valence shell.
