# Continuum of Frequency Excite all Resonances at the same time F

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Continuum of Frequency Excite all Resonances at the same time F
How to observe NMR? Time Domain Frequency Domain t Continuum of Frequency Excite all Resonances at the same time υ F FT Short and high power pulse irradiation at Fo MHz The short pulse will be able to excite all NMR spins, which are at different resonance frequencies at the same time in one go. Therefore one can no longer detecting the absorption of energy as in the CW NMR experiment by sweeping the frequency or magnet strength. One just need to detect the radiation signal emitted by the all excited NMR spins at the same time. How ? Net Magnetization flipped to xy plane Bo Excited Spin

Receiver at position x picked up a varying electromagnetic signal
How to observe NMR? Precessing Spin In order to detect all the radiation signals from all spins at the same time, we can use the same trick of detecting the variation of magnitudes of radiation at different time using a receiver coil at position x. 1D NMR Experiment Receiver at position x picked up a varying electromagnetic signal

Intensity decreases with time. Why?
How to observe NMR? Intensity decreases with time. Why? Free Induction Decay (FID) FT Time Domain The resulting time domain data (so called Free Induction Decay) can be FT to regenerate the frequency domain normal NMR spectrum. Why the FID has diminishing intensity with time? It is because of relaxation so that there will be less excited spins with time. In case of more than one spins at two different frequencies. Instead of a decaying sine wave of one frequency. You can see a mixture of more than one frequency in the FID. Frequency Domain

Modern NMR Experiments
Multi-pulses: 90 degree , 180 degree or shaped pulses Multi-channels : 1H, 15N, 13C (one channel one freq) with gradient z Multi-dimensional: t1, t2, t3 (one dimension one t)

What is Multi-pulsed NMR
Experiments? t Short Pulse Quantum States Bulk Magnetization (not quantized) Mz Bo Modern High field NMR spectrometers are designed to carry out NMR experiment in pulse mode. Considering the shining of a very short but high power radiation pulse on the NMR sample. FT transformation of the time domain short pulse into frequency domain in fact corresponding to a continuum of radiation frequency. In other words the short pulse will be able to excite all NMR spins, which are at different resonance freq at the same time in one go. Therefore there is no need to sweep the freq and to excite the NMR spins one by one. (question) Therefore one can instead of detecting the absorption of energy as in the CW NMR experiment. One just need to detect the radiation signal emitted by the excited NMR spins. In order to detect all the radiation signals from all spins at the same time, we can use the same trick of detecting the magnitudes of radiation at different time. Excited Spin

Models for the description of NMR experiments:
1. Quantum Model: Density Matrix Analysis, Product operator formalism, very powerful but difficult to use. 2. Vector Model: Classical formalism, too simple but easy to visualize. Bo Net Magnetization flipped to xy plane x y x y inverted Mz Mz 180y Mz My 90-x Spin Gymnastics! By varying the power, time length (angle) or phase (direction) of the pulse

(thumb position of your right hand)
Spin Gymnastics Interconversion rules between different M directions by applying 90 degree pulses Phase of pulse (thumb position of your right hand) Starting M direction Mz Mx 90y Use Right Hand Rule Mz 90z Mx 90x My 90y Mz Mx My

C—H N—H HB HA What is Multi-pulsed NMR Experiments?
Magnetization can be transferred between nuclei through cross-talking by: bonding: J coupling (H-H, H-C, H-N, etc…) Close in space: dipolar coupling Therefore information related to the other nuclei (e.g. chemical shifts δ, bonding, J-couplings, distances dAB) can be encoded in the NMR signals as well. C—H N—H dAB HB HA

Raw NMR data FID = F(t1, t2) (n1 x n2 points)
Mulit-Dimenstional NMR? t1 Single pulse 1D NMR Experiment 1. Preparation: Recycle delay for relaxation 2. Applying pulse 3. Acquisition of FID Raw NMR data FID = F(t1) n1 points 2D NMR Experiment relaxation Raw NMR data FID = F(t1, t2) (n1 x n2 points) Exchange info get FID J or δ coding in t The short pulse will be able to excite all NMR spins, which are at different resonance frequencies at the same time in one go. Therefore one can no longer detecting the absorption of energy as in the CW NMR experiment by sweeping the frequency or magnet strength. One just need to detect the radiation signal emitted by the all excited NMR spins at the same time. How ? One dimension One t

Mulit-Dimenstional NMR?
F(t1) FT F(t1,t2) FT F(t1,t2,t3) FT F(w1) F(w1,w2) F(w1,w2,w3) Today my lecture topic is Introduction to NMR Spectroscopy It will discuss about two questions: What is Multi-pulsed NMR Experiments? What is Multi-dimensional NMR Spectroscopy? 1D 2D 3D

COSY: Correlation Spectroscopy
N2 points COSY: Correlation Spectroscopy F(t1,t2) FT(t2) N1 Sine wave in t2 F(t1,w2) FT(t1) F(w1,w2) δa δb Ha J-coupled to Hb

Homonuclear Experiment: Single channel, single resonance
2D COSY (directly J-coupled) TOCSY or HOHAHA (Total Correlation Spectroscopy) (directly or indirectly J-coupled) 2D NOESY (thru space dAB) (NOE Spectroscopy) 2D ROESY (Rotating frame NOESY) (thru space dAB)

Heteronuclear Experiment: Double resonance (e.g H, C)
H,C-Hetero-COSY (directly H-C J-coupled) DEPT (Distortionless Enhancement via Polarization Transfer) Detecting C Inverse experiment: magnetization is transferred back to the more sensitive H HSQC (Heteronuclear Single Quantum Correlation) (directly H-C J-coupled) HMQC (Heteronuclear Multi-Quantum Correlation) (directly H-C J-coupled)

Heteronuclear Experiment: Triple resonance
Triple resonance: H, C, N

Why NMR? So informative, so many applications and so much FUN!
2nd advantage of pulsed FT NMR: allow multi-dimensional NMR

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