Ab initio MO and density functional calculations indicate that the ring opening of the cyclobutene
radical cation (CB
•+) follows two competitive pathways, whose energy barriers differ by less than 1 kcal/mol
at the highest level of theory employed, RCCSD(T)/cc-pVTZ//UQCISD/6-31G*. The first corresponds to a
conrotatory rearrangement to the cis-butadiene radical cation (cis-BD
•+). The second one leads to trans-BD
•+
via a very flat potential energy plateau which comprises cyclopropylcarbinyl-type structures of the type proposed
some time ago by Bauld, but the controtatory stereochemistry is preserved also along this process. State
correlation diagrams indicate that the rearrangement leading to trans-BD
•+ may occur adiabatically along a C
2
reaction coordinate. Despite this, the transition state has no symmetry. This seemingly “unnecessary” loss of
symmetry is traced back to the proximity of the 2A and 2B surfaces in the vicinity of the C
2 stationary points,
where the two states encounter a strong vibronic interaction which leads to breaking of the C
2 symmetry.
These vibronic interactions are also responsible for the general flattening of the potential energy surface in
this area.
The reaction of acetylene (Ac) with its radical cation
(Ac•+) is studied at the
CCSD(T)/cc-pVTZ//QCISD/6-31G* level of theory and by the B3LYP/6-31G* density functional
method. Contrary to earlier claims, we
find that vertical ionization of the neutral acetylene dimer leads to a
bound state which relaxes to a T-shaped
ion−molecule complex 8.3 kcal/mol below the separated fragments.
Once Ac and Ac•+ have approached to
less than an ≈3 Å center to center distance, spin and charge begin
to delocalize and the complex collapses
smoothly to the cyclobutadiene radical cation (CB) via a linear
complex (LC1) and/or a cyclopropenylcarbene
cation (CC). Rearrangements to other stable
C4H4
•+ isomers require H shifts
which are promoted by localization
of the positive charge on one C atom. From LC1 this leads directly to
the transition state LC2 for formation
of a pivotal intermediate, H2CCCHCH•+
(methyleneallene, MA), which in turn collapses with
E
a ≈ 3
kcal/mol to the methylenecyclopropene radical cation (MCP), the most
stable C4H4
•+ isomer.
Additional
[1,2] H shifts which require higher activation energies lead to the
radical cations of butatriene (BT, E
a
≈17
kcal/mol from MA) or vinylacetylene (VA, E
a ≈
20 kcal/mol from MA) which are of stability similar to
that
of CB. These findings are in accord with condensed phase
experiments on alkylated acetylenes, where the
corresponding CB derivatives were the only products observed.
However, in gas phase studies other
C4H4
•+
isomers were observed in Ac + Ac•+ reactions.
Perhaps these arise through bifurcations leading to
structures
with localized charge without passing through the stationary points
located in this study. B3LYP/6-31G*
results were found to be in close agreement with the reference coupled
cluster calculations for most parts of
the C4H4
•+ potential energy
surface probed in this study. However, it should be noted that
density functional
methods may give a wrong dissociation behavior for radicals because
they fail to localize the spin (and the
charge in the present case) when this is required and therefore cannot
be used in the loosely bound region for
ion−molecule complexes.
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