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Let's finish up this series of web casts
by working through an FMO analysis
for the hypothetical reaction
between allyl cation and allyl anion.
These are two species that we previously encountered
when we talked about LCAO construction
of 3 atom π systems.
I've reproduced the π energy levels shown here
and LCAO representations of their molecular orbitals.
To get the FMO analysis started
what we need to do is to consider
the two possible frontier orbital interactions.
We could for example consider *** cation/LUMO anion
or we could consider the *** anion/LUMO cation interaction.
This second one looks much better because
the much smaller energy gap
between the *** of the anion and the LUMO of the cation,
and that makes perfect sense
because we expect the negative charge on the anion
to give a very high level ***
and we expect the positive charge on the cation
to give a low-lying LUMO.
So let's focus on that
as the major frontier orbital interaction
and the next thing we need to do is identify the way
in which they'll come together in order to form a reaction.
So we focus on these two LCAO representations
of their molecular orbitals
and we try to match coefficients both in terms of sign
and in terms of the size of the coefficients.
Well, in this case because the molecules are symmetrical,
the two coefficients happen to be identical in size
and so we don't need to worry about size.
All we need to do is to make sure that the lobes
come together with the same sign
so that when we multiple those two coefficients
we get a positive term
in that equation that describes the energy of interaction.
That's the way they should come together.
What it says is the two terminal carbons
should come together
and if we look at the bonds and atoms that are drawn on the-
at the bottom we could imagine that the curved arrows
would indeed reproduce that same picture.
So that would be the curved arrow
between the non-bonding lone pair
and the empty orbital on the cation
and that would produce a new bonding interaction
that would form the σ bond between those two.
Now what about the alternative ***/LUMO interactions?
What if that had been considered?
What would have been the result?
Well, first of all, it's not considered
because it's such a large energy difference between those two,
but had it been considered
we would have gone through the same process
of trying to match phases,
largest lobes being the most important,
and on this case you can see that for the *** cation
the largest lobe is in the center
and so if we match phase to the largest lobe on the anion
we would end up trying to bring those two species together.
And then when we attempted to draw it out,
well, it's a little bit strange
but we would expect a new bond to be formed there
and in order to do so we end up with this very
funny charged system that looks like that,
maybe we would try and combine positive and negative charges
to make the structure that's shown here.
This is a simple hypothetical example.
We didn't have to go through the FMO analysis to predict
that this isn't the observed pathway,
but the observed pathway is just what you would expect.
Nonetheless, I think from this example you can see
how the FMO analysis is going to work
for cases that... not like this one,
but where we wouldn't be able to predict
which reaction pathway would be more favorable.
And we'll see plenty of examples throughout the semester
of this sort of analysis.