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- More complex splitting
occurs when a proton has two different kinds of neighbors. And a good example of
this is the blue proton that I circled in Cinnamaldehyde. So the blue proton has a
signal with a chemical shift about 6.7 parts per million. So down here is a zoomed in view of the signal for the blue proton. Let's look at neighboring protons. So the blue proton is on this carbon, and we have a carbon next door
right here with one proton, so there's one neighboring proton. Here's another carbon
next door with one proton, so we have two neighboring protons. So let's try to apply
the n plus one rule here. So if n is equal to two, we
have two neighboring protons, we would expect n plus one peaks. So two plus one is equal to three, so a signal with three peaks or a triplet. But that's not what we see for the signal for the blue proton. We see one, two, three, four lines here. So the n plus one rule
doesn't work in this case. And that's because the n
plus one rule works when the neighboring protons
are equivalent and here the two neighboring
protons are not equivalent. So we need a new way to explain the signal for the blue proton. And we're going to use what's
called a splitting tree. So we're going to start with
the signal for the blue proton, so here's the signal for the blue proton. It's going to be split
by the proton next to it, this proton in red. And the coupling constant between the red and the blue proton is 12 hertz. So let's go ahead and show,
let's show this signal is split into a doublet,
so let me go ahead and draw in the blue lines here. So we get the signals
split into a doublet, the coupling constant is 12
hertz, so this distance here represents 12 hertz. So why can we think about it
being split into a doublet? Well you can think about a variation of the n plus one rule here, right? So we're talking about
one neighboring proton, so n is equal to one, so one
plus one is equal to two, so we split the signal into
a doublet with two lines. Alright, now let's
think about what happens with the other protons, so this one. Ok well that's going to take
each line of the doublet that we just drew and split
it into another doublet. So this line gets split into a doublet, and this line gets split into a doublet. The coupling constant
this time is six hertz. So this distance here
represents six hertz, and this distance represents six hertz. So why was each line split into two? Well once again we can use a modification of the n plus one rule here. We're talking about one neighbor
here, so n is equal to one, so one plus one is equal to two, so each line is split into two. So each line is split into a doublet. For this line and for this line. This line is split into a doublet, too. So we get four lines for the
signal of the blue proton. If we go over here we
see those four lines, one, two, three and four. And we call this a doublet of
doublets, or a double doublet. What would happen if the
coupling constants were the same? So let's just pretend like
they're both 12 hertz, so let's go ahead and draw what
we would see for the signal. So we have our blue proton's signal, is split into a doublet
by the red protons, so let's go ahead and
draw in our doublet here. And let's say this distance
represents 12 hertz, so 12 hertz here, and let's
say the coupling constant over here was also 12 hertz,
so instead of six hertz. So each line of the doublet
we just drew is split into another doublet
from our other neighbor. And this time I'm going to show a coupling constant of 12 hertz. So each line of the doublet in blue is split into another doublet. So the line in blue on the
left is split into a doublet, and the line in blue on the
right is split into a doublet, because of our one neighboring proton. Well I changed the coupling
constant so now I just have to pretend like now we're
dealing with 12 here, so the coupling constants are the same. And notice what this gives us, this gives us a triplet, right? So here is one line and then
we're going to get this peak, and then we're going
to get this peak here. So if the coupling constants are the same, you get a triplet, you get what the n plus one rule predicted. So that's just something
to think about with the origin of the n plus one rule. Let's do another example. So let's go down here and
let's look at this molecule. So we're going to focus in
on this proton here in blue. And we have neighboring protons right? So this neighboring proton,
the coupling constant between those two is 12
hertz, and then over here, we have two neighboring protons,
and the coupling constant between the magenta protons
and the blue is seven hertz. So let's think about the signal
for the blue proton here, so here we have the signal
for the blue proton, which isn't split, let's think
about what the red proton is going to do. We have one neighbor, so one
plus one is equal to two. So we're going to split the
signal for the blue proton in two, so we get a doublet here, so let me go ahead and
draw in the doublet. The coupling constant was
twelve hertz, so this distance right here is 12 hertz. Now you have a situation
where we're thinking about the magenta protons, we have two of them. So n is equal to two, so two
plus one is equal to three. So the magenta protons are
going to split each line of the doublet that we just drew into a triplet. So we're going to get a triplet here, let me go ahead and draw that in. So for a triplet, and our
coupling constant is seven hertz, so let me see if I can draw that here. So that distance is supposed
to represent seven hertz, So let me draw that in. So this distance is seven
hertz, this distance corresponds to seven hertz, and one line
of our doublet is split into a triplet now. Same thing happens for
the other line, right? Same thing happens for
this line right here, we need to split that into a triplet because of these magenta protons. So we're going to split that
into a triplet, once again, we need to think about a
distance of seven here, seven hertz. So we have on both sides,
we have seven hertz, let me go ahead and draw that
in, so this is talking about seven hertz, and this is
talking about seven hertz. So that one line is split into a triplet, so let's draw that in
here, one, two and three. So finally, how many peaks
would we expect for the signal for this blue proton? So one, two, three, four, five, six. So we would expect six
peaks for this signal, for this blue proton,
because of the neighboring protons which are on different
types of environments. So this is complex splitting.