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Nuclei With Spin Align in Magnetic Fields HoHo anti-parallel parallel Alignment Energy E = h H o Efficiency factor- nucleus ConstantsStrength of magnet Resonance: energy match causes transitions

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Resonance: Perturb Equilibrium HoHo h E H1H1 2. pump in energy E = h H o Efficiency factor- nucleus ConstantsStrength of magnet p ap 1. equilibrium EE p ap 3. non-equilibrium

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Return to Equilibrium (Relax): Read Out Signals p ap 5. equilibrium h E 4. release energy (detect) p ap EE 3. Non-equilibrium

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Magnetic Resonance Sensitivity E is small At room temp., N ~ 1:10 5 Intrinsically low sensitivity! E = h H o Efficiency factor- nucleus ConstantsStrength of magnet N p N ap = e - E/kT Sensitivity f (population difference) S ~ N = Increase sensitivity by increasing magnetic field strength

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Intrinsic Sensitivity Nucleus Natural Relative Abundance Sensitivity 1 H2.7 x 10 8 99.98 1.0 13 C6.7 x 10 7 1.11 0.004 15 N -2.7 x 10 7 0.36 0.0004 31 P1.1 x 10 8 100. 0.5 e - 1.8 x 10 11 100. >600

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The Classical Treatment: Nuclear Spin Angular Momentum HoHo anti-parallel parallel Torque + int. motion = precession Precession around Z axis Larmor frequency: = H 0 Two spins All spins Sum Bulk Magnetization excess facing down

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Effect Of An RF Pulse Only the excess spins RF y phase coherence = RF y t = H 0 f Fourier Transform NMR frequency Variation of signal at X axis vs. time t AxAx

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The Power of Fourier Transform 90º x RF pulse t 11 1 = H 0 2 = H 0 f Fourier Transform + 22 NMR frequency domain Spectrum of frequencies NMR time domain Variation in amplitude vs time t A

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Relaxation- Return to Equilibrium t z axisx,y plane 0 1 2 t 0 1 2 8 8 E -t/T 2 t 1-e -t/T 1 t Longitudinal Transverse Transverse always faster!

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Longitudinal (T 1 ) Relaxation MECHANISM Molecular motions cause the nuclear magnets to fluctuate relative to a fixed point in space Fluctuating magnetic fields promote spins to flip between states Over time, spin flips cause a return to equilibrium t dM z /dt = M eq – M z /T 1 M z (t) = M eq (1-e -t/T 1 ) M z (t) M eq

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Transverse (T 2 ) Relaxation t MECHANISM Magnetic field is not homogenous to an infinite degree Each spin comprising the bulk magnetization will feel a slightly different field Over time, the spin fan out (lose coherence) dM x,y /dt = M x,y /T 2 Linewidth time

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The Pulse FT NMR Experiment equilibration 90º pulse detection of signals Experiment (t) Data Analysis Fourier Transform Time domain (t)

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NMR Spectrum Chemical Shift & Linewidth Chemical shift: intrinsic frequency Linewidth: relaxation (MW)

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Preparation of Magnetization Building Towards 2D NMR E 90º pulse t1t1 Equilib.Detect E- 90º pulse t1t1 Detect If E is sufficiently long, full peak intensity If E is too short, intensity is reduced What if we caused the peak intensity to vary at a rate equal to the precession freqeuncy?

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Frequency Labeling Systematically Alter The Equilibrium 0t1t1 t1t1 t1t1 22 t1t1 33 t I 0 FT FT the variation in intensity and get Larmor frequency!

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Indirect Detection 2D NMR t1t1 t2t2 1) Add pulse to frequency label during t 1 2) Introduce mixing period before t 2 t1t1 t2t2 mix F1F1 F2F2

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The Mixing Process- Uses Coupling Through Bonds Through Space

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2D NMR: Coupling is the Key 2D detect signals twice (before/after coupling) Same as 1D experiment 90º pulse t1t1 t2t2 t1t1 t2t2 Mixing causes an exchange between spins that are coupled 2D NMR Pulse Sequence

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The 2D NMR Spectrum Pulse Sequence Spectrum Coupled spins give rise to crosspeaks Before mixing After mixing t2t2 t1t1

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Multi-Dimensional NMR: Built on the 2D Principle 3D- detect signals 3 times Same as 1D experiment 90º pulse t2t2 t1t1 t3t3 3D NMR Pulse Sequence (t3)(t3) Experiments are composites

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