The vibrational frequencies of selected alkylcyclohexanes and related polycyclic molecules consisting of chair and boat six-membered rings were calculated using conventional Hartree-Fock theory with a 6-31G(d) basis and a hybrid density functional procedure (B3LYP) with a standard 6-311 G(d,p) basis. Appropriate scale factors were determined. The sums of zero-point (ZPE) and heat-content (H-T - H-0) energies thus obtained are well reproduced by an empirical formula featuring only the total number of carbon atoms, the number of tertiary carbons, the number of carbons in the cycle(s) and the number of cycles, while the presence of boat rings or the occurrence of butane-gauche interactions play no role in the description of ZPE + H-T - H-0. gauche interactions are revealed by the atomization energy, DeltaE(a)(*) = Sigma(k<l) epsilon(ki) - E-nb + F, of the molecule at its potential minimum. The intrinsic bond energies, epsilon(kl), account by far for the largest part of DeltaE(a)(*), Enb is a small interaction between nonbonded atoms, and F stands for what is due to variations of internuclear distances and to changes of electronic centers of charge. Of primary concern are the CH bonds overhanging cyclohexyl rings and their interaction with axial CH bonds of the latter. F = 0 if no such gauche interactions exist. Otherwise, the lowering of bond-energy terms, Delta Sigma(k<l) SO, is about twice the expected value, yet F restores the correct result. For each participating CH bond, F is tentatively interpreted as being due to repulsions between the electron clouds of the hydrogens and the ensuing deformations which shift their centroids by similar to 0.001 Angstrom closer to carbon, for a correction of 0.822 kcal/mol for one gauche interaction. The total F is proportional to the number of these interactions. Enthalpies of formation calculated on this basis, and with our approximation for ZPE + H-T - H-0, agree within 0.24 kcal/mol (root-mean-square deviation) with their experimental counterparts. (C) 2004 Elsevier B.V. All rights reserved.
