NMR Determinations of Barriers to Internal Rotation in Halogen-Substituted Ethanes

Abstract

The theory of Kaplan and Alexander for exchange in nuclear magnetic resonance (NMR) systems has been applied to exchange between three species with any number of nuclei of spin ½, in which all the nuclei in each species are exchanged by the interconversion. A set of explicit equations for the density matrix elements in this case is written down. Computer programs have been written to solve the equations in the two and three spin cases. The results enable the calculation of NMR spectra of highly coupled nuclei undergoing exchange. Absolute reaction rate theory has been used to express the rates of exchange in terms of activation energies. This has been combined with the Kaplan—Alexander theory to determine the free energies of activation for internal rotation in several halogenated ethanes, CFCl2–CFCl2, CF2Br–CCl2Br, CF2Br–CFBr2, CF2Br–CFBrCl, CFClBr–CFClBr, and CF2Br–CHBrCl. Spectra were calculated assuming limiting values for the transmission coefficient, k≪1, k=1. The first case implies free rotation occurs when a molecule is excited to sufficient energy to exceed the barriers. Alternatively, the second case implies that deactivation of the rotational mode occurs in a time comparable with the rotational frequency. The experimental results on CF2Br–CCl2Br can only be explained by the second possibility. The barriers are discussed in terms of the distortion necessary to form the activated complex in which the substituents are eclipsed. The low-temperature spectrum of the three rotamers of CF2Br–CHBrCl shows two large vicinal HF coupling constants (18 cps) and four small ones (less than 3 cps). The assignment of the rotamers made assuming that the low barrier observed between two of the rotamers does not involve eclipsing two large halogens indicates that the large coupling constants are trans and the four others are gauche coupling constants.