Number and Novelty in Approaches to the Calculation of Strainless Group Increments

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Abstract
In this paper we show that the large number of approaches using apparently unrelated strainless increments for unsubstituted alicyclic hydrocarbons in the literature are neither mathematically nor conceptually unique. We additionally demonstrate that if the strain energy assigned to a compound by any three sets of increments is known, the strain energy any other approach would assign can automatically be determined without considering any further details of the structure of the compound. Equivalently, there are but three mathematically distinct, i.e. linearly independent, strainless incremental approaches for these compounds. Thus the choice of which method to employ in one's own reasoning relative to a chemical problem must be based on personal, rather than strictly chemical or mathematical criteria. We proceed by presenting our criteria and their molecular realization, the concept of diagonal reference states. Diagonal reference states are defined from hydrocarbons composed solely of the group of interest. In particular, >C<, >CH–, –CH2– and –CH3 are derived from diamond, cubane, cyclohexane and ethane with the accompanying enthalpies of formation, +1.9, –9.7, –20.6. and –42.0kJ mol−1. The virtues and debits of this method are presented in support of our conclusion that this approach is preferable because it is diagonal.

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