Non-local density functional theory has been used to study acetylene metathesis catalysed by high oxidation state molybdenum alkylidyne complexes. The first part of this study discusses a dissociative mechanism in which a metallacyclobutadiene acts as an intermediate in the metathesis. In particular, the formation and decomposition of the metallacyclobutadiene, Cl3MoC3H3, was examined with the geometries, bonding and energetics of the whole process given. The formation of the metallacyclobutadiene was found to be a formally symmetry allowed process with a calculated energy barrier of only 10 kJ mol-1. The mechanism by which this process affords such a small reaction barrier was also examined in detail and found to be due to the ability of p and p* type orbitals to interact throughout the course of the reaction. The metallacyclobutadiene was determined to be 71 kJ mol-1 more stable than the acetylene and molybdenum carbyne reactants. In the second part of this study, the formation of the metallatetrahedrane was examined. The direct formation of the metallatetrahedrane from the acetylene and molybdenum carbyne fragments was determined to be a formally symmetry forbidden process and posses a barrier of 40 kJ mol-1 . The formation of the metallatetrahedrane by the tautomerization of the metallacyclobutadiene was also examined in detail The metallatetrahedrane was determined to be 52 kJ mol-1 more stable than the corresponding metallacyclobutadiene, and 122 kJ mol-1 more stable than the free acetylene and molybdenum carbyne.