Ab initio calculations on the 5-exo versus 6-endo cyclization of 1,3-hexadiene-5-yn-1-yl radical: Formation of the first aromatic ring in hydrocarboncombustion

Two possible reaction pathways between 1,3-hexadien-5-yn-1-yl radical (1) a nd phenyl radical (2), a key reaction in soot formation during fuel combust ion processes, have been investigated using ab initio quantum mechanical el ectronic structure calculations. The complete active space (CAS) SCF method was used for geometry optimization of the equilibrium and transition-state structures relevant to the two competing mechanisms and computing their ha rmonic vibrational frequencies. Final energies were evaluated by single-poi nt calculations using essentially the G2M(RCC,MP2) method and corrected for zero-point and temperature effects. According to all calculated barrier he ights (DeltaU(double dagger), DeltaE(double dagger), DeltaH(double dagger), and DeltaG(double dagger)) the 5-exo cyclization of 1 to (2,4-cyclopentadi enyl)vinyl radical (3) is favored over the 6-endo cyclization to 2. As in t he case of the prototypical hex-5-enyl radical, the predicted highly regios elective 5-exo cyclization of 1 is due to favorable enthalpic and entropic factors associated with the formation of the smaller ring. Contrary to comm on belief, the lowest-energy pathway of the reaction 1 --> 2 is the 5-exo c yclization of 1 to 3 followed by cyclization of 3 to bicyclo[3.1.0]hex-3,5- dien-2-yl radical (4) and subsequent opening of the three-membered ring of 4 to yield 2. The simple (one-step) 6-endo cyclization of 1 affording 2 req uires a higher free energy of activation (Delta DeltaG(double dagger) = 1.5 kcal/mol at 298 K) than such a stepwise cyclization. In light of these res ults, the stepwise reaction pathway found between 1 and 2 should be include d in the set of reactions used in detailed kinetic modeling of soot formati on in shock-tube studies of acetylene pyrolysis.