ISOMERIC VARIATIONS IN ALKANES - BOILING POINTS OF NONANES

We present a detailed study of the variations of the boiling points am ong 35 nonane isomers as an illustration of structure-property studies . By restricting the attention to the molecules of a same size we have effectively eliminated the dominant role of the molecular size in the structure-property relationship which obscures the minor but importan t variations in the properties with molecular branching. In this way w e can better see the role of the molecular shape, that is, the variati ons in the molecular branching, plays in governing the relative magnit udes of molecular properties. We use the multiple regression analysis as the method for the analysis of experimental data. We consider three alternative ways of use of the regression analysis. As molecular desc riptors we have adopted the connectivity indices 1chi-6chi and 0chi. H owever, the approach outlined equally applies to other molecular descr iptors, i.e., topological indices, quantum chemical parameters, as wel l as to molecular properties as variables representing a molecule. We start by considering the descriptors 0chi-6chi as a basis, i.e., we us e the set of the descriptors in an in advance prescribed order. Becaus e of interdependence of the descriptors (and often strong interdepende nce of some descriptors) the so selected basis is nonorthogonal. Using the connectivity indices 0chi6-chi we get the regression with R (the coefficient of correlation) = 0.969 and S (the standard error) = 1.72. A consequence of nonorthogonality is that inclusion or exclusion of a single descriptor may dramatically alter the relative role that other descriptors play. Hence, as our second alternative we outline the pro cedure in which orthogonalized descriptors are used in structure-prope rty regression. As a result the coefficients of the regression equatio ns show stability, i.e., the coefficients do not change if regression equation is truncated or a descriptor is added to the regression. The standard error S and the coefficient of correlation R for the correlat ion have not changed with the orthogonalization, i.e., are not affecte d by the orthogonalization process. Finally, as the last alternative, we illustrate use of a ''greedy'' algorithm approach, in which one sel ects descriptor in a stepwise fashion. At each step interactively one selects the descriptor that produces the smallest standard error in th e structure-property regression. In this way we arrived at a regressio n with the correlation coefficients of R = 0.968 and the standard erro r of S = 1.69.