4434 J. Am. Chem. Soc., Vol. 120, No. 18, 1998
Ford et al.
Azine (A) was formed on photolysis of DMD in all solvents.
Azine can be formed by several mechanisms including the
reaction of a carbene with its diazirine precursor. This reaction
is very fast and complicates analysis of the kinetics of
benzylchlorocarbene.23
It seems unlikely that azine is formed by reaction of DMD
with DMC because the lifetime of DMC is very short and does
not change upon doubling the concentration of precursor. We
believe that DMC rearranges to its isomeric diazo compound
and that this species forms azine by a non-carbenic mechanism.
Figure 9. Calculated structures of the reactants, transition states, and
products of the reactions dimethylcarbene f propene (A), (cyano-
methyl)methylcarbene f 1-cyanopropene (B), and ethylmethylcarbene
f 2-butene (C).
the nonbonded electrons localized at the carbenoid center. For
propene the active space includes the valence π space.
All multireference calculations have been performed using
the MOLCAS-3 program systems.33 Gaussian 9434 was used
to optimize the geometries, and the CCSD(T) calculations were
performed with MOLPRO96.35
III. Theory
III.1. Results. III.1.1. Geometries. Recently, some of us
(S.M., M.F.) have reported the singlet-triplet energy separation
of methylated carbenes.10a This was the starting point of the
present investigation. As the rearrangement reaction begins,
one hydrogen atom moves in a plane that is almost perpendicular
to the plane formed by the three carbon atoms, while the
remaining two hydrogen atoms on the same methyl group swing
very rapidly into a nearly planar position. Moreover, as the
π-bond is formed, we observe a contraction of the C-C bond
distance. In contrast, the “spectator” methyl group behaves
almost perfectly like a rigid body. It rotates and bends by
approximately 16° and 7°, respectively, such that the methyl
group is placed in a conformation close to that in propene. At
the transition state, the lengths of the breaking and forming C-H
bonds are 125.1 and 132.6 pm, respectively. The length of the
preformed C-C double bond is 140.2 pm. Focusing on the
second half of the reaction, the moving hydrogen atom rotates
into the plane of the carbon atoms to form the new C-H bond.
This movement is followed by a further shortening of the
forming C-C double bond and additional, rather small adjust-
ments of the positions of the other atoms. The structures of
the reactants, transitions states, and products are shown in Figure
9.
To complement the experimental work we studied the 1,2-
H-shift reaction of dimethylcarbene, as well as the cyano- and
methyl-substituted analogues, by ab initio quantum chemical
methods. To optimize the geometries of the reactants, products,
and transition states, we used the second-order Møller-Plesset
(MP2) method24 in combination with analytic derivative methods
and 6-31G(2p,d) basis sets.25,26 Barrier heights and exother-
micities were then determined by single-point calculations using
the CCSD(T) method27,28 and atomic natural orbital (ANO) type
basis sets29 contracted to (4s3p2d) and (3s2p) functions for
carbon, nitrogen, and hydrogen, respectively.
To validate our approach, we performed calculations using
the complete active space (CAS)SCF method30 followed by
second-order multireference configuration interaction (SD-
MRCI),31 including Davidson’s correction,32 and multireference
second-order perturbation calculations, the so-called CASPT2
approach.33 Due to the strong mixing of the orbitals describing
the C-H and C-C bonds, the choice of an active space for the
CASSCF method was particularly difficult, and it was necessary
to use the smallest meaningful active space, two electrons in
two orbitals. Thus, the CASSCF wave function of singlet
dimethylcarbene as well as that of the transition state structure
included the ...(σ)2(π)0 and ...(σ)0(π)2 configurations correlating
To optimize the geometries of the substituted systems, i.e.,
(cyanomethyl)methylcarbene and methylethylcarbene, the struc-
tures of dimethylcarbene, the transition state, and propene were
used as templates to which the methyl or cyano group was
attached. These structures were then used as starting points
for geometry optimizations. The structures of all possible
rotamers were optimized, but only the structures of lowest
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(26) Dill, J. D.; Pople, J. A. J. Chem. Phys. 1975, 62, 2921.
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Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng,
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