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

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 EE p ap 3. non-equilibrium

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

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

Intrinsic Sensitivity Nucleus  Natural Relative Abundance Sensitivity 1 H2.7 x C6.7 x N -2.7 x P1.1 x e x >600

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

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

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

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

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

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

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

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

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?

Frequency Labeling Systematically Alter The Equilibrium 0t1t1 t1t1  t1t1 22 t1t1 33 t I 0   FT FT the variation in intensity and get Larmor frequency!

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

The Mixing Process- Uses Coupling Through Bonds Through Space

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

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

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