The regions of the C13H11 potential energy
surface (PES) related to the unimolecular isomerization and decomposition
of the 1-methylbiphenylyl radical and accessed by the 1-/2-methylnaphthyl
+ C2H2 reactions have been explored by ab initio
G3(MP2,CC)//B3LYP/6-311G(d,p) calculations. The kinetics of these
reactions relevant to the growth of polycyclic aromatic hydrocarbons
(PAH) under high-temperature conditions in circumstellar envelopes
and in combustion flames has been studied employing the RRKM-Master
Equation approach. The unimolecular reaction of 1-methylbiphenylyl
proceeding via a five-membered ring closure followed by H elimination
is predicted to be very fast, on a submicrosecond scale above 1000
K and to result in the formation of an embedded five-membered ring
in the 9H-fluorene product. The 1-/2-methylnaphthyl
+ C2H2 reaction mechanism involves acetylene
addition to the radical on the methylene group followed by a six-
or five-membered ring closure and aromatization via an H atom loss.
Despite of the complexity of the C13H11 PES,
these straightforward pathways are dominant in the high-temperature
regime (above ∼1000 K), with the prevailing products being
phenalene, with a significant contribution of 1H-cyclopenta(a)naphthalene,
for 1-methylnaphthyl + C2H2, and 1H-cyclopenta(b)naphthalene and 3H-cyclopenta(a)naphthalene,
for 2-methylnaphthyl + C2H2. The methylnaphthyl
reactions with acetylene represent a clean source of the three-ring
PAHs, but they are relatively slow owing to the high entrance barriers
of ∼10 kcal/mol, with the rate constants of about an order
of magnitude lower as compared to those for naphthyl + allene and
σ-aryl + C2H2. The 1-methylnaphthyl +
C2H2 and 2-methylnaphthyl + C2H2 reactions represent prototypes for PAH growth by an extra
six- and five-membered ring on a zigzag edge or a corner of PAH and
the generated modified Arrhenius expressions are recommended for kinetic
modeling of PAH expansion by the mechanism of acetylene addition to
methylaryl radicals.