Power Law Distribution Concerning Absolute Free Energies of Linear Sulfur Chains, Polythiazyls, Polyisoprenes, Linear trans-Polyenes, and Polyynes

After quantum calculations of absolute free energies of polyatomic sulfur derivatives or hydrocarbon oligomer compounds, we have studied the variations of Gn as a function of the number of repeating units n (sulfur atoms or hydrocarbon units, n = 2 to about 60), and observed that these values can be correlated by (a) a nearly perfect linear relationship, Gn = An + B (A and B, constants), with a high accuracy which enables an extrapolation for higher values of n, and (b) a power law:, δG = Gn/n – G(n–1) /(n – 1) = C/nd (C and d, constants). From comparison of variations of the C–C bond lengths, we show that the conjugation of trans-polyenes (up to C60H62) is more important than for polyynes (up to C60H2).