Topological orbitals, graph theory, and ionization potentials of saturated hydrocarbons

Clar's Aromatic Sextet Theory Revisited via Molecular Electrostatic Potential Topography

“…Moyano and Panigua 22 concluded from a study of polycyclic hydrocarbons, within the Hückel theoretical framework, that the preferred resonance structures are those that maximize the number of isolated aromatic sextets. Very recently, Li and Jiang 25 have used the Lanczos method for solving the VB model exactly for PBHs with up to 20 carbon atoms and discussed their local aromaticities based on the relative local hexagon energy (RLHE) as defined by Herndon and Ellzey . According to them, the benzene molecule is endowed with maximum aromaticity (RLHE = 1000) and other systems agree with Clar's intutive ideas such as the “dilution of aromatic sextet” and “empty ring”.…”

“…The concept of aromaticity has existed in the chemical literature for a long time. There have been a number of studies, both experimental and theoretical, using different approaches and methods to arrive at a unified definition of it. − These theoretical works can be classified into methods based on valence bond (VB) and molecular orbital (MO) approaches, as well as graph theoretical studies. Such studies, though partially successful, have helped in the identification and creation of newer molecular systems and the unearthing of structure−activity relations.…”

The arithmetic of aromaticity

“…When bicyclic systems consist of two fused rings, which have one carbon-carbon bond common to both rings, there are two different types possible, depending upon whether or not both rings have an even number of ring atoms. When both rings consist of an even number of atoms it is possible to draw a structure made up of alternate single and double bonds in such a way that the bond common to both rings is either a single or double bond, as, for example, in the case of naphthalene or biphenylene (2). For compounds with odd numbers of atoms in the rings, e.g., azulene (1), it is not possible to draw structures with alternate single and double bonds unless the bond common to both rings is a single bond.…”

“…In this case we may write 2+4 => 6, o 8 Continuing the bicyclic series from butalene are the compounds 9 and 10. For azulene, alternative structures could be contemplated, wherein, in similar fashion to biphenylene (2), which is best represented as two 6tt electron systems connected by two bonds of very low order (10), separate 4w and 6?r systems are found, viz. la and lb.…”

Local behavior of hückel parameters

“…One cannot restrict oneself to functions having a functional matrix in Po with maximal rank. For instance, case I1 [in scheme (6)] is an example, where the functional determinant vanishes and the local properties of the mapping are not sufficiently described by the linearization of the mapping.…”