Calculations employing density functional theory (Gaussian 98, B3LYP, LANL2DZ, 6-31G) have been undertaken to interrogate the factors influencing the metathesis reaction involving M-M, C-C, and M-C triple bonds for the model compounds M(2)(EH)(6), M(2)(EH)(6)(mu-C(2)H(2)), and [(HE)(3)M(tbd1;CH)](2), where M = Mo, W and E = O, S. Whereas in all cases the ethyne adducts are predicted to be enthalpically favored in the reactions between M(2)(EH)(6) compounds and ethyne, only when M = W and E = O is the alkylidyne product [(HO)(3)W(tbd1;CH)](2) predicted to be more stable than the alkyne adduct. For the reaction M(2)(EH)(6)(mu-C(2)H(2)) --> [(HE)(3)M(tbd1;CH)](2), the deltaG degrees values (kcal mol(-)(1)) are -6 (M = W, E = O), +5 (M = Mo, E = O), +18 (M = W, E = S), and +21 (M = Mo, E = S) and the free energies of activation are calculated to be deltaG() = +19 kcal mol(-)(1) (M = W, E = O) and +34 kcal mol(-)(1) (M = Mo, E = O), where the transition state involves an asymmetric bridged structure M(2)(OH)(4)(mu-OH)(2)(CH)(mu-CH) in which the C-C bond has broken; C.C = 1.89 and 1.98 A for W and Mo, respectively. These results are discussed in terms of the experimental observations of the reactions involving ethyne and the symmetrically substituted alkynes (RCCR, where R = Me, Et) with M(2)(O(t)()Bu)(6) and M(2)(O(t)()Bu)(2)(S(t)()Bu)(4) compounds, where M = Mo, W.