Todays Lecture

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Todays Lecture
8) Monday, Oct 16 Introduction to 2D NMR a. Two
pulse exchange experiment (aka NOESY) b. COSY for
homework
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1D NMR
For a single spin and no coupling, a 1D NMR
experiment can be described as follows. Recall
that the drawing of the FID signifies that the
receiver is turned on to record the signal.
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The next step
What happens to the spins if the receiver is not
turned on?
Just the same thing (they dont care if you
record their signal or not).
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Time to add another pulse
What happens here?
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Lets look in more detail
Here is the real part (cosine) of a signal
following a 90 degree x-axis pulse. Thus, this
is the signal along the y-axis. The frequency
is 128 Hz with and the line width is 2 Hz. The
data have a spectral width of 200 Hz (time
between points 0.001s) and 256 total points.
Below is an expansion of the first 10 points.
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What will happen with a second 90x pulse at these
different points?
Remember that these points started from a 90x
pulse, so they start out along the y axis.
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The first 90x pulse is filled black. The second
is unfilled and placed at different points. The
second pulse is trying to rotate the
magnetization to the z axis (like a 180 degree
pulse). It does that for the first point, but
the second point is already pointing along the y
axis, so it will be rotated up toward the z
axis. However, it is not as long as the first
point. The 3rd point is almost zero, but will
still be rotated up.
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Next Step Add a 3rd 90x pulse some fixed time
after the 2nd pulse
Right now, nothing happens along the z-axis
except relaxation.
(Dont worry about Ix term during ?, because we
will eventually eliminate it.)
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Thought Experiment Chemical Exchange
The ring above contains the only 2 protons in a
NMR sample. The red environment on the left
causes H1 to have a frequency of 128 Hz, and the
blue environment causes H2 to have a frequency of
30 Hz.
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Indulge me for a minute for a thought experiment
After the ring flips, the red environment on the
left now causes H2 to have a frequency of 128 Hz,
and the blue environment causes H1 to have a
frequency of 30 Hz. This is called chemical
exchange.
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Chemical Exchange also gives rise to very
interesting spectra
kex1 s-1
If two NMR peaks are in chemical exchange, the
spectrum depends significantly on the exchange
rate. The simulations on the left are two peaks
separated by 80 Hz and with different exchange
rates. Note that when the exchange rate is close
to the difference in frequencies, the peaks
almost disappear.
kex80 s-1
kex180 s-1
kex250 s-1
kex1000 s-1
kex5000 s-1
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Indulge me for a minute for a thought experiment
For now, the rule is that the ring flips 1 time
during a time t and only when the magnetization
is pointing along the z-axis. Lets see what
happens to H1 during our 3 pulse experiment.
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Chemical exchange thought experiment
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2D Exchange NMR
t1
t2
FT in t1 will give 2D frequency spectrum
f2
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2D FT
f2
f1
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2D NMR
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Homework due next week COSY
Using product operators, evaluate the COSY
(Correlated Spectroscopy) sequence above for a
two-spin coupled system. Dont worry about terms
for relaxation.
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Next Lecture
8) Introduction to biological solid state NMR
(Dr. Long) a. Time scales of molecular motion b.
Spin vs. space c. Revisit spin interactions from
solids perspective