CHEM / BCMB 4190/6190/8189. Introductory NMR. Lecture 10

Transcription

1 CHEM / BCMB 490/690/889 Introductory NMR Lecture 0 - -

2 CHEM 490/690 Spin-Echo The spin-echo pulse sequence: 90 - τ τ(echo) Spins echoes are widely used as part of larger pulse sequence to refocus the effects of: ) unwanted chemical shift precession 2) magnet inhomogeneity 3) heteronuclear J coupling The spin-echo does not refocus homonuclear J coupling The spin-echo pulse sequence can be used to measure the relaxation parametert 2 ; it does not refocus the effect of T 2 relaxation a τ a 80 or 90 τ 80 AT H RD Typical delays and pulse lengths: RD τa AT = Recycling delay ~ sec. = Spin-echo delay ~ 50 ms = Acquisition time ~ 0.2 sec. ~ 0 µs ~ 20 µs - 2 -

3 The spin-echo in vector diagram A) Lets consider the non-coupled single spin case. Example: H in CHCl 3 (carbon not 3 C-labeled) with ν H = ν rf + 00 H H: 90 x- τa - 80 y - τa (echo) M 90 τ a M 80 τ a Detected Signal after FT: Chemical shift (H) - 3 -

4 H: 90 x- τa - 80 x - τa (echo) M 90 τ a M 80 τ a Detected Signal after FT: Chemical shift (H) Note that the intensity is ploted relatively to the positive signal on the previous page. In practice, this signal would be drawn as a positive signal by adjusting the ero order phase correction by

5 Conclusions: ) Chemical shift evolution (precession) is refocused by the spin-echo 2) Similarly the spin-echo refocuses magnet inhomogeneity ( B o ): The magnetic field B o is not perfectly homogeneous throughout the volume of the sample, therefore not all nuclei experience the same magnetic field. The small differences in magnetic field ( B o ) across the sample volume causes nuclei that are chemically equivalent to precess at different rate

6 B) Lets consider a simple case of heteronuclear coupling, i.e. a two-spin AX system with A = H and X = 3 C Example: 3 C in CHCl 3 (carbon is 3 C-labeled) with ν rf = ν H J AX = 209 H 3 C: 90 x- τa - 80 x - τa (echo)- Acquisition time M 90 τ a ν = νh - /2J 80 τ a M ν = νh +/2J Detected Signal after FT: 209 H Chemical shift (H) - 6 -

7 More on the two-spin AX system with A= H and X= 3 C (e.g. 3 CHCl3): ) Energy level diagram H transition 3 with C in β state ββ N 3 C transition with H in β state βα N + C 3 αβ C transition with H in α state N + H αα H transition 3 with C in α state N + C + H 2) Essentially equal population differences for the 3 C transitions for 3 CHαCl3 and 3 CHβCl3 Population diferences: αα to αβ transition: (N + H + C) - (N + H) = C βα to ββ transition: (N + C) - (N ) = C αα to βα transition: (N + H + C) - (N + C) = H αβ to ββ transition: (N + H) - (N ) = H 3) Two different Larmor frequencies as a result of C-H coupling ν ( 3 CHαCl3) = νc - /2*JCH ν ( 3 CHβCl3) = νc + /2*JCH with JCH = 209 H and δ = 77.7 ppm (center of the doublet) 4) In the first delay τ of the spin-echo experiment, a phase angle Θ is created between these two vectors Θ = 2πJCH* τ Examples: If τ = 0 than Θ = 0, if τ = /(4J) than Θ = π/2 = 90, etc

8 Pulse sequence of the J-modulated spin-echo experiment: Vector diagrams for the J-modulated spin-echo experiment: - 8 -

9 Chemical-shift refocusing in the J-modulated spin-echo experiment: Example: J-modulated spin-echo experiment for three different CH groups (I, II, and III) whose Larmor frequencies ν and C-H coupling constants J increase in the order: ν < ν2 < ν3 and J < J3 < J2 A) Pulse sequence B) Vector diagrams and spectra for 90 -τ (BB)-acquisition C) Vector diagrams and spectra for the full experiment - 9 -

10 Attached proton test (APT) with the J-modulated experiment: Lets consider various types of carbons and their precession frequencies: - quaternary carbon (Cq): νc - CH group: νc ± /2*JCH - CH2 group: νc, νc ± JCH - CH3 group: νc ± /2*JCH, νc ± 3/2*JCH Pulse sequence and vector diagram: - 0 -

11 The effect of pulse field gradients on transverse magnetiation: In high-resolution NMR, the magnetic field Bo should be as homogenous as possible because small field variations Bo causes undesirable peak broadening (e.g. bad shimming). However, introducing field inhomogeneity by linear pulse field gradients can be very useful for removing remaining magnetiation in the x-y plane: - between FIDs - within a pulse sequence for phase cycling - within a pulse sequence for water suppression - within a pulse sequence to measure diffusion constants A) Nuclei within different volume slices experience different effective field strengths: B) A single gradient dephases magnetiation in the x-y plane: - -

12 C) Phase coherence is regained by a second gradient applied in opposite direction The pulsed field gradient spin-echo experiment: - 2 -

13 As for the standard spin-echo experiment, it refocuses - chemical shift - Heteronuclear J coupling - magnetic field inhomogeneity For simplification, lets consider a single H on resonance, in the absence of heteronuclear J coupling, and no magnetic field inhomogeneity: Axial diffusion means that the value of gn, and therefore the precession frequency νn changes between the first and the second pulse field gradients. In this case, refocusing is incomplete and the intensity of the signal is reduced. This effect can be used to measure diffusion coefficients and for water suppression in macromolecular NMR