The secondary deuterium equilibrium isotope effect (EIE) for the reversible binding of C2H4 to (mu-eta(1),eta(1)-C2H4)O-s2(CO)(8) (1) and C2D4 to (mu-eta(1)-eta(1),-C2D4)O-s2(CO)(8)(1-d(4)) has been measured in dodecane solvent. The measured EIE is "inverse" (C2D4 binds better than C2H4) and has a value of K-H/K-D = 0.7(L) at 313 K (40 degrees C) where K-H/K-D [C2D4](s)[1]/[C2H4]((s))[1-d(4)]. Previously published vibrational assignments for 1 and 1-d(4) and literature values for C2H4 and C2D4 allowed the calculation of the same EIE using 16 isotopically sensitive vibrational modes for both 1 and 1-d(4) and all 12 vibrational modes for both C2H4 and C2D4. The calculated EIE is also "inverse" and has a value of 0.7110 at 313 K (40 degrees C). The EIE calculated from vibrational frequencies may be resolved into a mass and moment of inertia factor (MMI = 2.272), a vibrational excitation factor (EXC = 0.8820), and a zero-point energy factor (ZPE = 0.3548), where EIE = MMI x EXC x ZPE. Using symmetry correlation rules, contributions to the EXC and ZPE factors from changes in ethylene vibrational modes for individual modes may be determined. The MMI component may be further resolved into translation and rotational contributions with the help of moments of inertia calculated from a previously determined single-crystal neutron diffraction structure of 1. The analysis reveals that, contrary to expectation, most of the EIE is not due to changes in vibrational frequencies common to free and complexed ethylene upon coordination but is instead primarily due to a zero-point energy factor from a vibrational mode (a b(2)-symmetry twist) for 1 and 1-d(4) which is not present in free ethylene. This interpretation of the observed "inverse" EIE appears to be general for alkene complexation and may underlie other recently observed "inverse" secondary deuterium equilibrium isotope effects for the coordination of small molecules (including alkanes and dihydrogen) to transition-metal complexes.