Principles and Applications of NMR Spectroscopy

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Principles and Applications of NMR
Spectroscopy Instructor Tai-huang Huang
(bmthh_at_ibms.sinica.edu.tw), [phone]
http//www.nmr.sinica.edu.tw/thh/lect
ure.html Time  Tuesday and/or Friday 2-5
PM (9/21, 10/5, 10/8, 10/12, 10/15, 10/22,
10/26, 10/29, 11/2, 11/9, 11/12, 11/16, 11/19,
11/30, 12/7) Place Rm. N617, IBMS, Academia
Sinica Textbooks 1. Lecture by James Keeler
on Understanding NMR spectroscopy
(http//www-keeler.ch.cam.ac.uk/lecture
s/) 2. Rules, G.S. and Hitchens, T.K.
Fundamentals of Protein NMR spectroscopy 3.
Cavanagh, Fairbrother, Palmer, and Skelton
Protein NMR spectroscopy Principles
and practice Academic press, 1996. 4.
Selected review articles.
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• Curse Content
• This will be a comprehensive lecture
  course, focusing on modern high field
• NMR spectroscopy in solution, with applications
  to protein structure, dynamics
• and functional studies. Topics to be covered
  include
• Basic NMR theory, including quantum mechanical
  and vectorial descriptions 
• of NMR spectroscopy.
• 2. Basic experimental aspects of NMR NMR data
  acquisition and processing.
• 3. Product operator formalism analysis of pulse
  programs.
• 3. Spin dynamics Coherent selection, phase
  cycling, gradient enhanced
• spectroscopy.
• 4. Heteronuclear multidimensional NMR
  spectroscopy.
• 5. Relaxation and protein dynamics.
• 6. Special topics TROSY, RDC, PRE and reduced
  dimensionality etc.
• 7. Applications to protein NMR in solution.

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• Course Outline
• Lect Date Topics
• 1 9/21 NMR and Energy level
• 2 10/5 Vector Model
• 3 10/8 Fourier Transform and
  Data processing
• 4 10/12 How the spectrometer works
• 5 10/15 Product Operator
• 6 10/22
• 7 10/26 Two dimensional NMR
• 8 10/29
• 9 11/2 Coherence selection and phase
  cycling
• 10 11/5
• 11 11/9 Relaxation
• 12 11/12 Selective topics
• 13 11/16 Selective topics
• 14 11/19 Selective topics
• 15 11/30 Selective topics
• 16 12/7 Selective topics

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NMR Historic Review
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2002 Nobel prize in Chemistry was awarded to
Kurt Wuthrich
NMR is a versatile tool and it has applications
in wide varieties of subjects in addition to its
chemical and biomedical applications, including
material and quantum computing.
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Felix Bloch 1952, Physics
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Dominant interactions H HZ HD HS
HQ.HZ Zeeman Interaction HD
Dipolar Interactions HS Chemical Shielding
Interaction. HQ Quadrupolar Interaction

• Basic Nuclear Spin Interactions

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Electrons
3
3
Nuclear Spin j
Ho
Nuclear Spin i
Ho
1
1
2
5
4
4
Phonons
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Lecture 2 Vector Model
Bulk Magnetization The sum of all magnetic
moments (1020 spins)
Larmor frequency ?o ?Bo (radS-1)
or ? ?Bo /2? (Hz)
Pulse
Detection
90 deg pulse
a deg pulse
Z
Mo
?
Signal
Y
?ot
X
Mosin?
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Effect of external magnetic field
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• ? Collecting NMR signals
• The detection of NMR signal is on the xy plane.
  The oscillation of Mxy generate a current in a
  coil , which is the NMR signal.
• Due to the relaxation process, the time
  dependent spectrum of nuclei can be obtained.
  This time dependent spectrum is called free
  induction decay (FID)

Mxy
time
(if theres no relaxation )
(the real case with T1 T2)
time
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Rotating frame A reference frame which rotate
with respect to the Z-axis
of the laboratory frame at frequency ?rot
Z
Mo

• Lamor frequency in the rotating frame ? ?o -
  ?Rot
• ? ??B then ?B ? / ? Bo -
  ?Rot/ ?
• For ?Rot ?o ?B 0

?
Bo
Y
?ot
X
Mosin?
?Rot/ ?
In the rotating frame with ?rot ?o the signal
one observe is Mosin? (No oscilation) and ?B 0
Effective field In the presence of RF-field
(Radio frequency) B1 the total field Static
frame B Bo B1 Rotating frame Beff ?B B1
Tilt angle
M will rotate about Beff at a rate of ?eef ?Beff
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Effective field in frequency unit
Z
Mo

• On resonance pulse ?rot ?o and ? 0
• ?eff ?1 (The magnetization will rotate
• w.r.t. the B1 axis by an angle,
• (the flipping angle) ? ?1?
• ? ?o ? ?o pulse (90o, 180o pulse)
• 180o pulse is also called the inversion pulse

?
Bo
Y
B1
?ot
X
Mosin?
?Rot/ ?
For arbitrary angle ?
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Hard pulse If B1 gtgt ?B the effectiv field lies
along B1 and all
resonances appeared to be on resonance. Example
Is P(90o) 12 us pulse a hard pulse for ?B
10 ppm in 500 MHz spectrometer
? ? 90o ?/2 ?B1 x12X10-6 ? ?1 ?B1
?/24x106 ??1 ?/2? 20.8 kHz ?B 10 ppm/2
5x500 2.5 kHz ltlt ??1 Ans Yes, it is a hard
pulse.
Detection in the rotating frame
mHz
?rot
Probe
Transmitter
?o
mHz
?rot
?rot - ?rot
Digitizer Computer
Receiver
mHz
kHz
Basic pulse acquiring scheme
More than one resonance
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Pulse calibration
Spin Echo
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Z
Pulses of different phases
Y
X
Y-pulse (90y)
X-pulse (90X or 90)
Relaxation (Inversion recovery expt)
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• NMR Relaxation

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? ?o - ?rot the offset frequency
90
1.6

• To record a 200 ppm 13C spectrum at 600 MHz
  spectrometer
• 200 ppm x 150 3o kHz ?1 ?/1.6 30000/1.6
  18,750 Hz ? Gauss ?
• ? P(90) ? Us for 13C ?

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Selective excitation of a range of resonances
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Selective inversion (Soft pulse)
Shaped pulses are designed to affect only the
resonances of interest
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