nmr.sinica.tw/~thh/nmr_core_facility_training_cours.html
DESCRIPTION
Course web page:. http://www.nmr.sinica.edu.tw/~thh/nmr_core_facility_training_cours.html. Designing of pulse program: Design the pulse program to excite desired coherence. Get ride of unwanted coherence. Optimize pulse program design. Coherence transfer pathway. Phase cycling. - PowerPoint PPT PresentationTRANSCRIPT
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http://www.nmr.sinica.edu.tw/~thh/nmr_core_facility_training_cours.html
Course web page:
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CTP of DOF-COSY:
CTP of NOESY (pathway 1):
Designing of pulse program:
1. Design the pulse program to excite desired coherence.2. Get ride of unwanted coherence.3. Optimize pulse program design.
Coherence transfer pathway. Phase cycling. Gradient selection
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Coherence order:
(Rotate 2, double quantum. P = 2)
(Order : p = ± 1)
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Coherence order: Only single quantum coherences are observables Single quantum coherences (p = ± 1): Ix, Iy, 2I1zI2y, T1yI2z …. etc Zero quantum coherence: Iz, I1z2z
Raising and lowering operators: I+ = ½(Ix + iIy); I- = 1/2 (Ix –i-Iy) Coherence order of I+ is p = +1 and that of I- is p = -1
Ix = ½(I+ + I-); Iy = 1/2i (I+ - I-) are both mixed states contain order p = +1 and p = -1For the operator: 2I1xI2x we have:2I1xI2x = 2x ½(I1+ + I1-) x ½(I2+ + I2-) = ½(I1+I2+ + I1-I2-) + ½(I1+I2- + I1-I2+)
The double quantum part, ½(I1+I2+ + I1-I2-) can be rewritten as:
Similar the zero quantum part can be rewritten as:
½(I1+I2- + I1-I2+) = ½ (2I1xI2x – 2I1yI2y)
P = +2
P = -2 P = 0
P = 0
(Pure double quantum state)
(Pure zero quantum state)
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Evolution under offsets:
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Phase-shifted pulses: Let the initial state of order p as (p) and the final state of order p’ after a pulse as (p’). The effect of the radio frequency pulse can be written as:
where Uo is the unitary transformation. If the rf pulse is applied along an axis having a phase angle w.r.t. the X-axis the effect is to rotate the unitary matrix by:
Thus,
But
Thus,
where and
Therefore if the rf pulse is phase shifted by the coherence will acquire a phase of
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Review on product operator formalism:
1. At thermal equilibrium: I = Iz
2. Effect of a pulse (Rotation): exp(-iIa)(old operator)exp(iIa) = cos (Old operator) + sin (new operator)
3. Evolution during t1 : (free precession) (rotation w.r.t. Z-axis):
= - Iy for 1tp = 90o
Product operator for two spins: Cannot be treated by vector model
Two pure spin states: I1x, I1y, I1z and I2x, I2y, I2z
I1x and I2x are two absorption mode signals and
I1y and I2y are two dispersion mode signals.
These are all observables (Classical vectors)
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Coupled two spins: Each spin splits into two spins
Anti-phase magnetization: 2I1xI2z, 2I1yI2z, 2I1zI2x, 2I1zI2y
(Single quantum coherence) (Not observable)
Double quantum coherence: 2I1xI2x, 2I1xI2y, 2I1yI2x, 2I1yI2y (Not observable)
Zero quantum coherence: I1zI2z (Not directly observable)
Including an unit vector, E, there are a total of 16 product operators in a weakly-coupled two-spin system. Understand the operation of these 16 operators is essential to understand multi-dimensional NMR expts.
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Evolution under coupling:
Hamiltonian: HJ = 2J12I1zI2z
Causes inter-conversion of in-phase and anti-phase magnetization according to the Diagram, i.e. in-phase anti-phase and anti-phase in-phase according to the rules:
Must have only one component in the X-Y plane !!!
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2D-NOESY of two spins w/ no J-coupling:
Consider two non-J-coupled spin system:1. Before pulse:: Itotal =
Let us focus on spin 1 first:2. 90o pulse (Rotation):
3. t1 evolution:
4. Second 90o pulse:
5. Mixing time: Only term with Iz can transfer energy thru chemical exchange. Other terms will be ignored. This term is frequency labelled (Dep. on 1 and t1). Assume a fraction of f is lost due to exchange. Then after mixing time (No relaxation):
6. Second 90o pulse:
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7. Detection during t2:
The y-magnetization =Let A1
(2) = FT[cos1t2] is the absorption signal at 1 in F2 and A2(2) = FT[os2t2] as the absor
ption mode signal at 2 in F2. Thus, the y-magnetization becomes:
Thus, FT w.r.t. t2 give two peaks at 1 and 2 and the amplitudes of these two peaks are modulated by (1-f)cos1t1 and fcos1t1, respectively.
FT w.r.t. t1 gives:
where A11 = FT[cost] is the absorption mode signal at 1 in F1.
Starting from spin 1 we observe two peaks at (F1, F2) = (1, 1) and (F1, F2) = (1, 2)
Similarly, if we start at spin 2 we will get another two peaks at: (F1, F2) = (2, 2) and (F1, F2) = (2, 1)
Thus, the final spectrum will contain four peaks at (F1, F2) = (1, 1), (F1, F2) = (1, 2), (F1, F2) = (2, 1), and (F1, F2) = (2, 2)
The diagonal peaks will have intensity (1-f) and the off-diagonal peaks will have intensities f, where f is the fraction magnetization transferred, which is usually < 5%.
(Diagonal) (Cross peak)
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7.4. 2D experiments using coherence transfer through J-coupling
7.4.1. COSY:
After 1st 90o pulse:
t1 evolution:
J-coupling:
Effect of the second pulse:
(p=0, unobservable)
(p=0 or ±2)(unobservable)
(In-phase, dispersive)
(Anti-phase)(Single quantum coh.)
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The third term can be rewritten as:
Thus, it gives rise to two dispersive peaks at 1 ± J12 in F1 dimension
Similar behavior will be observed in the F2 dimension, Thus it give a double dispersive line shape as shown below.
The 4th term can be rewritten as:
Two absorption peaks of opposite signs (anti-phase) at 1 ± J12 in F1 dimension will be observed.
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Similar anti-phase behavior will be observed in F2 dimension, thus multiplying F1 and F2 dimensions together we will observe the characteristic anti-phase square array.
Use double-quantum filtered COSY (DQF-COSY)
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Double-quantum filtered-COSY (DQF-COSY):
Using phase cycling to select only the double quantum term (2) can be converted to single quantum for observation. (Thus, double quantum-filtered)
P = 2 P = -2 P = 0 P = 0
Rewrite the double quantum term as:
The effect of the last 90o pulse:
Anti-phase absorption diagonal peak
Anti-phase absorption cross peak
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- NOESY
Pathway 1: At t1:
After the second X-pulse only the IY term contributeand it becomes cost1IX, which is also the only observable after the third X-pulse. Thus, the signal detected at t2 = 0 is: =
During detection only the I- term is observable. Thus, the final signal is a amplitude modulated signal of the form:
If, instead we choose the CTP shown on the right then at t1 = 0
Iy =
If we keep only the I- term of IY: During t1 the magnetization evolve asFollowing thru the rest of the pulse sequence gives the following phase modulated observable signal:
If we choose the p=+1 CTP we will again observe phase modulated signal:
Note: if we choose p = -1 or +1 the signal strength is only half that of the amplitude modulated CTP.
Pathway 2:
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Pathway selection by phase cycling :Select only coherence transferred from p = +2 to -1, or p = - 3. Phase shift caused by the pulse sequence will - p = - (-3). For = 90o p = - 270o.
If we wish to select p = - 3 CTP the receiver need to phase shifted accordingly, i.e. set the receiver phase as 0o, 270o, 1800 and -90o at each cycle. The same pulse sequence will cause p = 2 coherent to shift - p = - (-2) = 180o, shown on the following table.
With the receiver set at 0, 270, 180 and 90 the - p = - 2 CTP will cancel each other.
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- p = - 1 coherence: Phase change = -(-1) = 90o :
Same as - p = - 3 Both - p = - 3 and +1 coherences are preserved but - p = - 2 coherence is not observed. It can be shown that this four step phase cycling scheme will select any pathway with - p = - 3 + 4n where n = ±1, ±2, ±3 ….
General rules: For a phase cycling scheme with
To select a change in coherence order, p, the receiver phase is set to -pxk for each step and the resulting signals are summed. The cycle will also select changes in coherence order p ± nN where n = ±1, ±2, …
The highest coherence order that can be generated for a system with m coupled spins one-half nuclei is m
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Refocusing pulses:
A 180o pulse simply change the sign of the coherence order, i.e. p = +1 p = -1, or p = -2. Likewise, for p = -1 p = +1 CTP p = +2.
Two step EXORCYCLE: 180o pulse: 0o, 180o; Receiver: 0o, 0o select all even p.Selection of double quantum (p = +2 p = -2): pulse: 450 (8 steps); Receiver: ?
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Combined phase cycles: To select the CTP shown on the left the first pulse select p = +1 and the second pulse select p = +2. then we need to consider each pulse separately and combine them together. If we use is a 4 step cycle for each pulse the combined phase cycle will take 16 steps, as shown below.
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Tricks: 1. The first pulse: The first pulse usually generate coherence order p = ± 1. If
retaining both of these coherence orders is acceptable one needs not to cycle the first
pulse.2. Grouping pulse together: Devise a phase cycling scheme to select for double quantum coherence, p = ± 2.Method 1: Focus only on the last step to select for p = +1 p = ± 2 and/or p = -1 p = ± 2.
Method 2: Consider the sequence as a whole and select for CTP p = 0 p = ± 2 or p = ± 2.
3. The last pulse: Since only p = -1 is observable one needs not to worry about other coherence orders that may be generated by the last pulse even though they may be generated.
Example: DQF-COSY:
1. Grouping: Group the first two pulses to achieve CTP 0 ±2, i.e. p = ±2. This has been discussed above the result is; pulse: 0o, 90o, 180o, 270o; receiver: 0o, 180o, 0o, 180o.
2. Focus on the last pulse and select p = +1 and p = - 3 since only p = -1 is observable. Luckily, the following scheme select both CTP: pulse: 0o, 900, 180o, 270o; Receiver: 0o, 270o, 180o and 90o.
Axial peaks (F1 = 0, F2):
Causes: 1. Recovery due to T1 relaxation (T1 noise); 2. Imperfect 90o pulse
Remedy: Two-step phase cycling: pulse, 0o, 180o and receiver: 00, 180o to select p = ±1.
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Shifting the whole sequence – CYCLOPS.The overall CTP is 0 -1, or p = -1. Thus, any pulse sequence can be cycled as a group toselect p = -1 with the CYCLOPS sequence with both pulse and receiver cycle through0o, 90o, 180o and 270o.
Equivalent cycles: For a given pulse there are several alternative phase cycling schemes to achieve the same results. For example, the DQF-COSY sequence:
If, instead, we wish to keep the receiver at fixed phase we can the alter the third pulse as follow two cycles to achieve the same consequence.
Denote:
0 = 0o
1 = 90o2 = 180o
3 = 270o
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P 0 1 2 3R 0 2 0 2
P 0 1 2 3R 0 0 0 0
P1 0 1 2 3 2 3 0 1 p2: 0 1 2 3 0 1 2 3 R 0 0 0 0 2 2 2 2
(HMQC)
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P-type (+1, +2):
N-type (-1, +2):
To generate pure P- or N-type magnetization one can combine as follow: