Oligomers. Relations between their computed free energies

Free energies G(X)_n of 12 1,ω-dihydrooligomers (X)_n (n, number of the monomeric units) have been determined by quantum calculations. We note that these values are correlated by (a) an excellent linear relationship: G(X)_n = An – 761.86 ± 10 (kcal mol^–1) (TPSS-TPSS/6.311 + + G(dp)); (b) for two oligomers (X)_n and (Y)_n, the difference of weighted free energies—G(X)_n/n – G(Y)_n/n—is a constant irrespective of n which results from the difference of free energies of the substituent. Consequently, from the G_n values of 1,ω-dihydrooligoethenes (in fact n-alkanes), a determination of the free energies of a 1,ω-dihydrooligomers (X)_n is obtained with a good accuracy by the calculation of the G value of its substituent; (c) the corresponding increments G(X)_n/n – G(X)_(n–1)/(n–1) are equaled and led to a single power law: [G_n/n – G_(n–1)/(n–1) = 1282/n^2.156 (kcal mol^–1), R = 0.9992] or a linear relationship: [G_n/n – G_(n–1)/(n–1) = 756.73/n(n–1) + 0.0211 (kcal mol^–1), R = 1]. Syndiotactic and isotactic 1,ω-dihydrooligomers (X) are illustrated in the Electronic Supporting Information.