A computational model for the dimerization of allene.

Computations at the CCSD(T)/6-311+G(d,p)//B3LYP/6-311+G(d,p) level of theory support long-held beliefs that allene dimerization to 1,2-dimethylenecyclobutane proceeds through diradical intermediates rather than a concerted (π)2(s) + (π)2(a) mechanism. Two diastereomeric transition states with orthogonal and skew geometries have been located for C2-C2 dimerization of allene, with predicted barriers of 34.5 and 40.3 kcal/mol, respectively. In dimerization, the outward-facing ligands rotate in a sense opposite to the forming C-C bond. Both transition states lead to nearly orthogonal (D(2)) singlet bisallyl (or tetramethyleneethane) diradical. This diradical has a barrier to planarization of 3.2 kcal/mol through a planar D(2h) geometry and a barrier to methylene rotation of 14.3 kcal/mol. Bisallyl diradical closes through one of four degenerate paths by a conrotatory motion of the methylene groups with a predicted barrier of 15.7 kcal/mol. The low barrier to planarization of bisallyl, and similar barriers for methylene rotation and conrotatory closure are consistent with a stepwise dimerization process which can still maintain stereochemical elements of reactants. These computations support the observation that racemic 1,3-disubstituted allenes, with access to an orthogonal transition state which minimizes steric strain, will dimerize more readily than enantiopure materials and by a mechanism that preferentially bonds M and P enantiomers.