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Sigmatropic rearrangements are identified by their order,
[i,j], and the easiest way to think about this
is by looking at a couple of examples
and recognizing that this [i,j] notation
comes by identifying how far the σ bond migrates.
So in order to identify how far the σ bond migrates,
we first need to identify which σ bond is it
that's undergoing a migration.
So let's first look at this Claisen rearrangement.
The Claisen rearrangement involves a vinyl ether,
that's this part, connected to an allylic ether,
that would be the bottom part, the allylic ether.
Now, if we notice in the reactant,
there's a bond present between oxygen and CH2,
but that bond has gone in the product,
and so that must be the bond that breaks.
Where does that σ bond migrate to?
Well, if we look,
these CH2 groups initially were unconnected in the reactant,
but now they're connected in the product,
so the migration must go toward
the positions that are labeled 3 and 3'.
Where do those labels come from?
What we do in assigning the order [i,j]
is to begin by putting 1's
at the position of the bond that breaks.
And then we number the top half and the bottom half
away from the σ bond that breaks.
So a 1 is positioned on oxygen,
2 and 3 until we get to the atom
where the σ bond migrates to.
Then on the bottom side,
we go from 1' to 2' until we get to this position, 3'.
The connection is between the 3 and the 3' position,
meaning that the σ bond moved over by two atoms.
We call this a [3,3] sigmatropic rearrangement
and this particular one with this vinyl ether-allylic ether
is known as the Claisen rearrangement.
The Cope rearrangement is a hydrocarbon analog
of the Claisen rearrangement.
It involves a pair of vinyl bonds
that undergo the [3,3] sigmatropic rearrangement.
The migration is that bond,
and so again, we number 1, 2, 3 across the top,
1', 2', and 3' down along the bottom
because we get to the terminal position
where the new σ bond forms.
This is a [3,3] sigmatropic rearrangement
just like the Claisen rearrangement.
If we look at the case on the bottom,
we'll see that it's a [2,3] rearrangement.
How do we come to that conclusion?
Well, the bond that breaks is this one.
We recognize that there's a CH2 oxygen bond in the reactant
that doesn't exist in the product.
That bond breaks, where does it migrate to?
We can see that there's a new bond that's formed
between this atom, this CH connected to R,
and the position that is a CH2.
The new bond is formed there.
So now we number on opposite sides of the bond that breaks,
1
and 1'
and we continue to number
until we get to the terminal positions.
The 1' goes to 2', and that's the end of the line.
And then 1, 2, 3 is the end of the line for the other half.
The connection is between positions 2 and 3
if we put the smaller number first
and so we have the [2,3] sigmatropic rearrangement.
In the next webcast, we'll examine
the [1,5] sigmatropic rearrangement
doing a frontier molecular orbital analysis
on that reaction.