Enumeration of the constitutional isomers of environmentally relevant substituted polycyclic aromatic compounds

Polycyclic aromatic compounds (PACs) are a diverse group of environmentally relevant compounds which can be persistent, bioaccumulative and toxic. The cyclic backbone of PACs can be substituted with halogens or hydrocarbon chains. The amount and positions of these substituents influence their toxicity. For many classes of PACs, substitution creates mixtures containing large numbers of isomers. For example, 209 theoretical isomers of chlorinated biphenyls are possible. Many other classes of environmentally relevant PACs exist where the number of theoretical isomers are unknown. Here, a mathematical approach using molecular symmetry and the binomial coefficient is presented that determines the number of theoretical isomers of PACs. The approach was validated on PACs with known isomer numbers and then applied to PACs with unknown isomer numbers. When the approach was applied to alkylated polycyclic aromatic hydrocarbons, the possible theoretical isomers ranged from 2 for C₁ naphthalene up to 19 502 for C₆ dibenzo(ah)anthracene. Heterocyclic PACs had similar numbers ranging from 4 isomers for C₁ dibenzothiophene to 13 938 for C₆ dibenzo[a,i]carbazole. The work presented will aide analytical chemists and ecotoxicologists in their efforts to develop methods to measure these compounds, and in attempting to assess the toxicity and environmental fate of individual isomers.