where the prefactor comprises the spin-orbit coupling, ∆, measured at the hopping point and the instanton partition function Z ‡ , which like the reactant partition function Z e , can be split up into contributions from translations, rotations and vibrations. The vibrational component of Z ‡ requires the evaluation of second derivatives of the action with respect to the bead configurations and τ . The difference in point-group symmetry between the reactant minimum (C s ) and the MECP, MEPs and instanton paths (C 1 ) implies that the number of equivalent reaction mechanisms is σ = 2.