Reducible and irreducible odd alternant hydrocarbon anions

Alternant hydrocarbons (AH) are defined as conjugated systems in which the atoms can be divided into two sets, starred and unstarred, in such a way that no atoms of like parity are directly linked. Benzene is typical. 

Since only atoms of opposite parity are covalently bonded, it follows that double bonds in these species must necessarily link starred and unstarred atoms. This fundamental feature of double bonding in alternant systems is an important factor governing the representation of mesomeric betaines. The relationship between mesomeric betaines and AHs will be developed later in the section. 

This review is primarily concerned with heterocyclic betaines that are isoelectronic with odd AH anions. For the purpose of recognizing and classifying these species, it is convenient to make a further subdivision by distinguishing between two types of odd AH anion. 

Many odd AHs contain even AH fragments on which the NBMO completely vanishes, i.e., the coefficients are zero on both the starred and unstarred sets of atoms. These regions to which the NBMO does not extend are referred to as inactive segments. For the purpose of this review we will describe those odd AHs that contain one or more inactive segments as reducible odd alternant hydrocarbons (ROAH). Examples of ROAH anions are the 3-phenylbenzyl anion (10), which contains an inactive phenyl group 

We shall refer to odd AHs which do not contain inactive segments as irreducible odd alternant hydrocarbons (lOAH). Thus the allyl anion (14), the benzyl anion (16), and the perinaphthenyl anion (18) are examples of lOAH anions. Within the framework of HMO theory, the NBMO of an lOAH 

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