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

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.

The strain energy of perchlorocyclopropane is small: It might even be negative. A density functional theory study of perhalocycloalkanes

“…The final approach discussed here makes use of diagonal 17 and ultradiagonal 18 reference species, 1/6(C 6 X 12 ) and 1/2(C 6 X 12 ), with which the SE is defined as and, in this case, numerically identical to For the parent, perfluorinated, and perchlorinated cyclopropanes within this model, the calculated SEs are 25.2, 45.6, and −12.1 kcal/mol, respectively. Using experimentally measured enthalpies of formation, the SE of cyclopropane is 27.5 kcal/mol.…”

Evaluation of strain in heterosiliranes: Systematics, surprises, and problems

“…It is to be recalled that cyclohexane was recommended as a reference species for cycloalkanes because it is composed of only one type of group, has a common local geometry for all six of the identical groups, and also minimizes the heat of formation per group. An extension of this "diagonal" philosophy, introduced by Van Vechten and Liebman [6], may be represented by the simple model…”

Interrelations in the Thermochemistry of Cyclopropanes

“…To date, cubane stands alone of these three species 108 for which a measured enthalpy of combustion, and hence of formation, is available for both the solid and gaseous states 109 . Indeed, cubane has been used as a paradigm for the group and concomitant understanding of strain energy 107 . Yet recently, through analysis of its 1,4-dicarbomethoxy derivative 110 , new derived values for the enthalpy of formation of solid and gaseous cubane have been suggested which differ from the earlier measured quantities by ca 45 kJ mol −1 .…”