reaction exactly equal the net rate r 2 along the grey–green dinuclear {M–M}
sequence.
The monometallic CBER mechanism [M ¼ M
f g, M À M
f
g] CBER in Fig. 7 has
two limiting kinetic scenarios, and these can arise for a number of reasons.
Limit of Linear Rates
a. Can occur if a rate limiting step exists in the light blue sequence {M}
b. Can occur if a rate limiting step exists in the medium blue sequence {M}
c. Can occur if a rate limiting step exists in the grey–green sequence {M–M} and
the equilibria favour the formation of dinuclear species
Limit of Quadratic Rates
d. Can occur if step α is rate limiting step
e. Can occur if step β is rate limiting step and the equilibria do not favour the
formation of dinuclear species
f. Can occur if a rate limiting step exists in the grey–green sequence {M–M} and
the equilibria do not favour the formation of dinuclear species
Much of the conditional phasing used above arises from the complication
associated with whether the equilibria favour the mononuclear or dinuclear species.
From an encounter probability viewpoint alone, at typical loadings of 1–100 ppm
metal, the bimolecular α step may frequently become rate determining.
Jacobsen’s group has shown two interesting systems which have strictly quadratic rate kinetics. In the one case, a chromium–salen complex is used to catalyse
the asymmetric ring opening of epoxides by trimethylsilyl (TMS) azide [33], and in
the other case, a (pybox)YbCl 3 complex is used to catalyse the ring opening of
epoxides with TMSCN [34]. In both cases the authors propose mechanisms in
which there is bimolecular reaction between mononuclear complexes and where
each mononuclear species brings with it a moiety which is eventually incorporated
in the final organic product. In the first mechanism, a dinuclear complex is explicitly proposed as is a step for fragmentation. In situ spectroscopic data is not
reported. However formally, there does not seem to be α and β steps per
se. Therefore, although there are quite a few similarities between these two systems
and the bicyclic structure in Fig. 7, the final reaction network may or may not be
somewhat different to a monometallic CBER definition.
A special case of the monometallic CBER mechanism [M] CBER arises when the
light blue sequence {M} and the medium blue sequence {M} are forced to be
disjoint. This could occur if the two pools of intermediates are not permitted to
interchange. Therefore, as one example, assume that all ligands in the light blue
sequence {M} are labile and can dissociate, and assume further that at least one
ligand in the medium blue sequence cannot dissociate. If, for example, a carbene
or tridentate ligand is attached to {M
# }, then the moles {M} + {M – M
# } and
{M
# } + {M – M
# } can be varied independently, and a different experimental
situation arises. There are a few reasons to suspect that a quadratic limiting case
200
M. Garland
sequence.
The monometallic CBER mechanism [M ¼ M
f g, M À M
f
g] CBER in Fig. 7 has
two limiting kinetic scenarios, and these can arise for a number of reasons.
Limit of Linear Rates
a. Can occur if a rate limiting step exists in the light blue sequence {M}
b. Can occur if a rate limiting step exists in the medium blue sequence {M}
c. Can occur if a rate limiting step exists in the grey–green sequence {M–M} and
the equilibria favour the formation of dinuclear species
Limit of Quadratic Rates
d. Can occur if step α is rate limiting step
e. Can occur if step β is rate limiting step and the equilibria do not favour the
formation of dinuclear species
f. Can occur if a rate limiting step exists in the grey–green sequence {M–M} and
the equilibria do not favour the formation of dinuclear species
Much of the conditional phasing used above arises from the complication
associated with whether the equilibria favour the mononuclear or dinuclear species.
From an encounter probability viewpoint alone, at typical loadings of 1–100 ppm
metal, the bimolecular α step may frequently become rate determining.
Jacobsen’s group has shown two interesting systems which have strictly quadratic rate kinetics. In the one case, a chromium–salen complex is used to catalyse
the asymmetric ring opening of epoxides by trimethylsilyl (TMS) azide [33], and in
the other case, a (pybox)YbCl 3 complex is used to catalyse the ring opening of
epoxides with TMSCN [34]. In both cases the authors propose mechanisms in
which there is bimolecular reaction between mononuclear complexes and where
each mononuclear species brings with it a moiety which is eventually incorporated
in the final organic product. In the first mechanism, a dinuclear complex is explicitly proposed as is a step for fragmentation. In situ spectroscopic data is not
reported. However formally, there does not seem to be α and β steps per
se. Therefore, although there are quite a few similarities between these two systems
and the bicyclic structure in Fig. 7, the final reaction network may or may not be
somewhat different to a monometallic CBER definition.
A special case of the monometallic CBER mechanism [M] CBER arises when the
light blue sequence {M} and the medium blue sequence {M} are forced to be
disjoint. This could occur if the two pools of intermediates are not permitted to
interchange. Therefore, as one example, assume that all ligands in the light blue
sequence {M} are labile and can dissociate, and assume further that at least one
ligand in the medium blue sequence cannot dissociate. If, for example, a carbene
or tridentate ligand is attached to {M
# }, then the moles {M} + {M – M
# } and
{M
# } + {M – M
# } can be varied independently, and a different experimental
situation arises. There are a few reasons to suspect that a quadratic limiting case
200
M. Garland