Vibrational analysis of a rate-slowing conformational kinetic isotope effect

An enthalpy-entropy approach to analyzing a rate-slowing conformational kinetic isotope effect (CKIE) in a deuterated doubly-bridged biaryl system is described. The computed isotope effect (kH/kD = 1.075, 368 K) agrees well with the measured value (kH/kD = 1.06, 368 K). The rate-slowing (normal isotope effect) nature of the computed CKIE is shown to originate from a vibrational entropy contribution defined by the twenty lowest frequency normal modes in the ground state and transition state structures. This normal entropy contribution is offset by an inverse vibrational enthalpy contribution, which also arises from the twenty lowest frequency normal modes. Zero point vibrational energy contributions are found to be relatively small when all normal modes are considered. Analysis of the HZPE, Hvib, and Svib energy terms arising from the low frequency vibrational modes reveals their signs and magnitudes are determined by larger vibrational energy differences in the labeled and unlabeled ground state structures.