Intramolecular and Intermolecular Contributions to the Barriers for Rotation of Methyl Groups in Crystalline Solids: Electronic Structure Calculations and Solid-State NMR Relaxation Measurements

The rotation barriers for 10 different methyl groups in five methyl-substituted phenanthrenes and three methyl-substituted naphthalenes were determined by ab initio electronic structure calculations, both for the isolated molecules and for the central molecules in clusters containing 8–13 molecules. These clusters were constructed computationally using the carbon positions obtained from the crystal structures of the eight compounds and the hydrogen positions obtained from electronic structure calculations. The calculated methyl rotation barriers in the clusters (E clust) range from 0.6 to 3.4 kcal/mol. Solid-state 1H NMR spin–lattice relaxation rate measurements on the polycrystalline solids gave experimental activation energies (E NMR) for methyl rotation in the range from 0.4 to 3.2 kcal/mol. The energy differences E clust – E NMR for each of the ten methyl groups range from −0.2 kcal/mol to +0.7 kcal/mol, with a mean value of +0.2 kcal/mol and a standard deviation of 0.3 kcal/mol. The differences between each of the computed barriers in the clusters (E clust) and the corresponding computed barriers in the isolated molecules (E isol) provide an estimate of the intermolecular contributions to the rotation barriers in the clusters. The values of E clust – E isol range from 0.0 to 1.0 kcal/mol.