Let's do a quick review of multiplicity in proton NMR. We have 4 different types of neighbors,
multiplicity is going to be equal to N+1, but we have four different types of neighbors,
homotopic, enantiotopic, both of these are going to split identically to one another
for their neighbor, and then diastereotopic and heterotopic are going to split differently
ok so let's look at a simple example and then put these to work and lets label our spectrum
with abc and d for four observable signals. Methyl protons that are next door to an allylic
position will shift to this position so 3H integration of 3 and these guys are going
to be a singlet. A singlet means zero neighbors because 1-1=0 for the singlet, these 3 are
also homotopic, and then we have another allylic position, the protons we've labeled d, the
d protons here are enantiotopic to one another and their neighbors are enantiotopic, so these
neighbors for our signal d here are enantiotopic and they will split d equivalently so what
we have here is a triplet which means we have 2 neighbors so we integrate to 2 because we
are a CH2 and we have 2 equivalent neighbors as far as splitting is concerned so we get
a triplet. And then on the other end of the spectrum or molecule we have "a" here the
other methyl protons shift to just under one, and they have two neighbors, here's "a", here's
the neighbors of "a", so 2 enantiotopic neighbors , you change one you change the other to a
deuterium for example vs. a hydrogen you get R and S so you have enantiotopic protons,
no existing chiral center, they split the same again 2 neighbors splitting the same
way, we integrate to 3, a triplet means we have 3 neighbors. But then we have the protons
that we will label "b" and so b has a couple of different types of neighbors. If we are
just looking at the protons at b, they don't split each other because they are enantiotopic,
they give the same signal, but they have 2 neighbors of one type and 3 neighbors of another,
they've got multiple neighbors, we've got an integration of 2 here and this is a multiplet,
because it's got two different types, heterotopic, 'a' and 'd' are heterotopic to one another,
they are going to give different splitting. To explain complex splitting, how it works,
we have more than one type of neighbor so either heterotopic or diastereotopic relationship
of one neighbor to another. For example we have 6 neighbors of one type here because
we have the same homotopic relationship of both of these methyl groups by rotation of
180 degrees about the molecule, these are 6 true neighbors of one type, a is homotopic
these are homotopic neighbors, they all split the same. We would expect to see123456 7 so
7 a septet for these, and that's a normal splitting pattern, the heights of those peaks
are not perfect by Pascal's triangle but it's a septet for homotopic neighbors of that type.
A heterotopic neighbor such as we have here, we'll label these a and b, these are different
than one another we have 3 neighbors of one type and we have two neighbors of the other
type. These are heterotopic to one another because if we change of them to a deuterium
for example we get constitutional isomers, we get a different name for the compound,
they are different so here we would get complex splitting for a multiplet. The other way is
to have diastereotopic neighbors so if we consider the hydrogen I've highlighted yellow
here, it has one neighbor of one type, one neighbor of another and then a diastereotopic
neighbor. So these two are diastereotopic to one another, they split differently they
split their neighbor differently and this red proton here is diastereotopic to the original
hydrogen marked in yellow, and so it actually gives a different splitting. You end up with
a multiplet as well for these. Now the effect of the splitting depends the coupling constant
which is abbreviated J. For a simple triplet for example the coupling constant is the difference
here, measured in hertz which are related to ppm, just the difference in the distance
between these two so you've got the coupling constant that's the same for both of these
peaks. So if we've got a multispin system such as above. Let's redraw what we've got
so we've got 2 neighbors of this type which we labeled d and "a", and 3 neighbors of this
type. So let's suppose that the coupling constant between a and b is greater than the coupling
constant between b and d. These are going to split into a quartet, because N+1, 3 neighbors
plus 1 is four. These are going to split the signal from b into a triplet. Neighbors 2
+ 1. Well if the coupling constant to a is bigger than the coupling constant to b and
d. Then we are going to end up with a, excuse me, a quartet of triplets. So if it's much
much greater we will resolve all of these into a quartet of triplet. So what we've got
are triplets individually and overall a quartet of those. We've got a quartet and a triplet
blended together. If we reverse this situation and say well the coupling constant between
ab is less than the coupling constant between b and d so b and d is greater, we are going
to have a triplet of quartets. So in the first example the quartet J looked like this, here's
Jab. and little bitty J between bd. In the next example here the triplet of quartets
we are going to see 1,2,3,4 / 1,2,3,4 /1,2,3,4 we are going to see that the coupling constant
of b and d to make the triplet so here's the triplet 1,2,3 vs. the four smaller, the complex
spin results in a big coupling constant between b and d and a small between a and b. AND if
those coupling constants are equal, then the old N+1 rule works and so we have a total
of 5N+1 = 6, we get our true sextet as we normally would . And again the heights are not perfect, but we would get
our N+1splitting as normal. It all depends on those coupling constants as to what it
looks like for the complex spin system. AND if the value of the coupling constants are
unknown, the values are unknown, then we would just call it a multiplet and be done with
it. Rather than a quartet of triplets or a triplet of quartets. If we don't know just
call it a multiplet and be done with it.