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6. Special topics: TROSY, RDC, PRE and reduced dimensionality etc.
7. Applications to protein NMR in solution.
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
NMR Historic Review
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.
Felix Bloch 1952, Physics
Edward M. Purcell 1952, Physics
Kurt Wuthrich 2002, Chemistry
Richard R. Ernst 1992, Chemistry
Isador I. Rabi1944, Physics
Paul Lauterbur 2003, Medicine
Peter Mansfield 2003, Medicine
CW NMR 40MHz(1960)
Basic Nuclear Spin Interactions
Nuclear Spin i Nuclear Spin j
Electrons
Phonons
3
1
Dominant interactions: H = HZ + HD + HS + HQ.
HZ = Zeeman Interaction HD = Dipolar Interactions HS = Chemical Shielding Interaction. HQ = Quadrupolar Interaction
6
HoHo
4
5
4
3
1 2
4
Lecture 2: Vector Model
Bulk Magnetization: The sum of all magnetic moments (1020 spins)
Larmor frequency:
o = Bo (rad·S-1);
or = Bo /2 (Hz)
Detection:
Mo
z
xB1
yo
x
Mxyy
90 deg pulse
a deg pulse
Signal:
Pulse
ot
Mo
MosinX
Y
Z
b. Effect of external RF field B1: 0BM
dt
dM
Effect of external magnetic field:
1
BMdt
dM
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 there’s no relaxation ) (the real case with T1 &T2)
Rotating frame: A reference frame which rotate with respect to the Z-axis of the laboratory frame at frequency rot
ot
Mo
MosinX
Y
Z
Lamor frequency in the rotating frame: = o - Rot
= B then B = / = Bo - Rot/
For Rot = o B = 0
Bo
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 + B1Rotating frame: Beff = B + B1
Tilt angle:
M will rotate about Beff at a rate of eef = Beff
Effective field in frequency unit:
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”
ot
Mo
MosinX
Y
Z
Bo
Rot/
B1
For arbitrary angle :
Hard pulse: If B1 >> 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 kHzB = 10 ppm/2 = 5x500 = 2.5 kHz << 1 Ans: Yes, it is a hard pulse.
Detection in the rotating frame :
ProbeTransmitter
ReceiverDigitizer
Computer
rot
roto
rot - rotkHzmHz
mHz
mHz
Basic pulse acquiring scheme :
More than one resonance:
Pulse calibration:Spin Echo :
Pulses of different phases:
X Y
Z
Y-pulse (90y) X-pulse (90X or 90)
1
BMdt
dM
Relaxation (Inversion recovery expt):
NMR RelaxationNMR Relaxation
= 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 ?
Selective excitation of a range of resonances:
Selective inversion (Soft pulse):
Shaped pulses are designed to affect only the resonances of interest