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 Hydrocarbon Combustion

Two possible reaction pathways between 1,3-hexadien-5-yn-1-yl radical ( 1 ) and phenyl radical ( 2 ), a key reaction in soot formation during fuel combustion processes, have been investigated using ab initio quantum mechanical electronic 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 harmonic vibrational frequencies. Final energies were evaluated by single-point calculations using essentially the G2M(RCC,MP2) method and corrected for zero-point and temperature effects. According to all calculated barrier heights ( Δ U ⧧, Δ E ⧧, Δ H ⧧, and Δ G ⧧ ) the 5- exo cyclization of 1 to (2,4-cyclopentadienyl)vinyl radical ( 3 ) is favored over the 6- endo cyclization to 2 . As in the case of the prototypical hex-5-enyl radical, the predicted highly regioselective 5- exo cyclization of 1 is due to favorable enthalpic and entropic factors associated with the formation of the smaller ring. Contrary to common belief, the lowest-energy pathway of the reaction 1 → 2 is the 5- exo cyclization 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 requires a higher free energy of activation ( ΔΔ G ⧧ = 1.5 kcal/mol at 298 K) than such a stepwise cyclization. In light of these results, the stepwise reaction pathway found between 1 and 2 should be included in the set of reactions used in detailed kinetic modeling of soot formation in shock-tube studies of acetylene pyrolysis.