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6. 1-D Multipulse Experiments:

6. 1-D Multipulse Experiments:. 1. Spin-echo sequence 2. Attached proton test 3. Spin energy levels 4. Spin population inversion (SPI) ‏ 5. Polarization transfer 6. INEPT 7. DEPT 8. Summary. The NMR challenge.

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6. 1-D Multipulse Experiments:

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  1. 6. 1-D Multipulse Experiments: 1. Spin-echo sequence 2. Attached proton test 3. Spin energy levels 4. Spin population inversion (SPI)‏ 5. Polarization transfer 6. INEPT 7. DEPT 8. Summary

  2. 06-1D Multipulse Experiments (Dayrit) The NMR challenge • Nuclear properties are determined by the spin quantum number, I, and the magnetogyric constant, . The proton, 1H, is the most sensitive nucleus; other nuclei, in particular 13C, are insensitive. • The energy differences between the spin energy levels are small. As a result, the population difference between spin energy levels is small, and the intensity of the NMR signal is low. • Many NMR-active isotopes have less than 100% natural abundance. How can one improve the sensitivity of NMR?

  3. 06-1D Multipulse Experiments (Dayrit) The Single-pulse NMR experiment • Imperfect pulse • Imperfect magnetic field homogeneity

  4. 06-1D Multipulse Experiments (Dayrit) The NMR solutions • Develop better NMR hardware: higher field magnets, (higher Bo), better probes, more powerful computers and improved electronics. • Develop ingenious NMR experiments • Manipulate spin populations using ingeniously designed multipulse sequenceswhich vary the pulse angle, excitation of specific nuclei, timing, phase, and others. • Multi-pulse sequences as building blocks. • Two of the most serious NMR challenges are: loss of phase coherence and insensitive nuclei . The corresponding NMR solutions arespin echo  and polarization transfer .

  5. 06-1D Multipulse Experiments (Dayrit) Problem: Loss of phase coherence • Nature of problem: The individual spins experience different local magnetic fields due to imperfections of the hardware, sample conditions, etc. This leads to a “spreading out” of the spins = loss of phase coherence  loss of transverse magnetization, Mx and My. • NMR solution: spin-echo: allow the spins to spread out in one direction during time , apply a 180°-pulse and allow the spins to refocus for time Repeat as needed. • Coupled nuclei are split with varying energies, J (Hz = s-1). The spin-echo sequence can differentiate nuclei according to their J values by selecting the appropriate time constant, t.

  6. 06-1D Multipulse Experiments (Dayrit) Spin-echo 90x' - ( - 180x' - ) - ( - 180x' - ) - ( - 180x' - )... 1st echo 2nd echo 3rd echo

  7. 06-1D Multipulse Experiments (Dayrit) 1st echo 2nd echo 3rd echo Spin-echo 90x' - ( - 180x' - ) - ( - 180x' - ) ( - 180x' - )... • At the top of the 1st echo, we achieve a refocusing of the spin vectors which spread out during time  as a result of inhomogeneities and other effects. • The spin echo sequence can be used for both 1H and 13C. • It is most useful in the manipulation of vectors of coupled heteronuclear spin systems. Let us consider the spin-echo experiment on the four types of substituted carbon: Cq, CH, CH2, and CH3.

  8. 06-1D Multipulse Experiments (Dayrit) 13C Vectors in a 13C1H system (no 1H decoupling): after a 90x’ pulse assuming on-resonance, 0: The slow vector is due to 13C1H while the fast vector is due to 13C1H. The frequencies of the two vectors will be: (13C 1H) = 0 - ½ 1J(C,H) = 0 -  (13C 1H) = 0 + ½ 1J(C,H) = 0 + where 2  = 1J(C,H)‏ (AQT)‏ For 13C1HCl3 (no 1H decoupling): 1J(C,H) = 209 Hz. At 100 MHz, 0 = 77.7 or 7770 Hz. Therefore, (13C 1H) = 7666 Hz and (13C 1H) = 7875 Hz.

  9. 06-1D Multipulse Experiments (Dayrit) If we allow the two J-coupled 13C vectors to spread out further (i.e., no acquisition yet), after time , each vector will travel: {2[½ J(C,H)]} or (2) and {2[-½ J(C,H) ]} or [2 (-) ]. The phase angle between the two 13C vectors, , of a 13C1H system can be calculated as:  = 2 (J(C,H) )  or  = 2 2

  10. 06-1D Multipulse Experiments (Dayrit)  = 2 (J(C,H) )  or  = 2 2 Let J = 1 Hz ( = 0.5 Hz): after  = 1 s, the fast vector will advance by , while the slow vector will regress by ; the phase angle will be 2 (=0), and they will refocus along the -y’ axis. For 13C1HCl3 where J = 209 Hz, the vectors will refocus along the -y’ axis at  = 4.8 ms.

  11. 06-1D Multipulse Experiments (Dayrit) • Consider two CH groups, with J1=125 and J2=200 Hz, and let both vectors be on-resonance. • Each pair of vectors will spread out according to J:  = 2 (JC,H) . Therefore, each pair of vectors will refocus along the -y’ axis at : 8 and 5 ms, respectively. • By selecting appropriate values for , we can do the following: • We can select the coupling which we wish to be refocused; and • We can select the sign (or phase) of refocusing to be along either y’ axis.

  12. 06-1D Multipulse Experiments (Dayrit) Effect of broadband 1H decoupling during 13C acquisition: • For a CH coupled system, broadband 1H decoupling collapses the 13C doublet into a singlet. • The magnitude and phase (sign) of the singlet depends on the position of the 13C doublet during 1H decoupling. This is the basis for the 13C spin-echo pulse sequence.

  13. a  c d b e Spin-echo sequence for a CH group, on-resonance: There are two 13C vectors corresponding to the attached 1H with the 1H and 1H spins. (a) 90x pulse on 13C. (b) The vectors fan out at different  depending on the interval . (c) The 180x°-pulse flips the vectors across x’ axis (-radians). (d,e) Broadband 1H decoupling collapses the 13C multiplet into a singlet vector. (continued…)

  14. a  c d b e Spin-echo sequence for a CH group, on-resonance: (d,e) Since the vector is now a singlet and is on-resonance, it does not spread out during the second -interval. Acquisition of the echo gives peaks whose phaseand magnitude depend on : an interval of 1/J sec allows the vectors to move by  radians. (from: Friebolin, Basic One- and Two-Dimensional NMR.)‏

  15. Spin-echo sequence for three CH groups with off-resonance signals: The sign and magnitude of each of the CH groups depends on both their J(CH) values and the off-resonance position. B: Truncated sequence: 13C: 90x'--{BB 1H}-AQT Phase (sign) and magnitude of the CH groups differ. (continued)‏

  16. Spin-echo sequence for three CH groups with off-resonance signals: C: Complete sequence: 13C: 90x'--180x'-{BB 1H}-AQT BB decoupling collapses the doublets into singlets, which refocus in the -y’-axis during the second -interval. With spin echo (and refocusing), CH groups give a negative singlet. (from: Friebolin, Basic One- and Two-Dimensional NMR.)‏

  17. The attached proton test (APT): Spin-echo for 13C-{1H} for Cq, CH, CH2, and CH3, on-resonance,  =1/J sec. CH and CH3 groups are (+) while the Cq and CH2 groups are (-).(from: Friebolin, Basic One- and Two-Dimensional NMR.)‏

  18. 06-1D Multipulse Experiments (Dayrit) • Attached Proton Test • If the vectors are on-resonance: • Cq: No coupling (the 13C signal is a singlet). The effect of the spin echo sequence is to remove inhomogeneities. • CH: (13C signal is a doublet) The two vectors move away at a rate of J Hz from each other and centered around the y’-axis. • CH2: (13C signal is a triplet) The middle vector is stationary along the y’-axis while the two flanking vectors fan out at a rate of J Hz. • CH3: (13C signal is a quartet) Each of the four vectors is separated by J Hz and centered on the y’-axis.

  19. 06-1D Multipulse Experiments (Dayrit) The attached proton test (APT) spectrum of a neuraminic acid derivative. Note that the sign of the CH and CH3 groups are (+) while the Cq and CH2 groups are (-).(from: Friebolin, Basic One- and Two-Dimensional NMR.)‏

  20. 06-1D Multipulse Experiments (Dayrit) Spin-echo sequence: summary The spin echo sequence - (  - 180x' -  ) - is a building block used in many NMR pulse sequences. It can be used for the following: 1. Refocusing of vectors to correct for inhomogeneities. 2. For heteronuclear coupling, e.g. C-Hn: By setting  =J-1, it is possible to distinguish different multiplies of C using the attached proton test (APT) (J-modulation). • The intensity of the spin-echo peak is sensitive to the value of J and . Some signals will appear weak if at  the y’-component of the vector is small. That is, the various spin-echo signals peak at different values of .

  21. 06-1D Multipulse Experiments (Dayrit) APT: anatomy of a multipulse sequence One-dimensional multiple-pulse experiments generally have three stages: preparation, evolution / mixing, and detection. APT: ... -PD-90x'--180x'-{BB 1H}-AQT-PD - ... • The preparation stage has two functions: to make sure that the starting conditions are at steady state equilibrium and to set-up the spins so that they are in the proper condition for the transfer of spin information. • Evolution / mixing is implemented with a fixed waiting period,  or , where the transfer of information can take place among the spins; one common feature is a spin-echo sequence: (--180x’/ y’--). • Detection refers to the acquisition of the FID.

  22. 06-1D Multipulse Experiments (Dayrit) Problem: insensitive nuclei • Nature of problem: The two elements of most interest in organic chemistry are H and C. 1H is the most sensitive NMR nucleus; however, 13C is insensitive because of its low  and % isotopic abundance. • NMR solution: polarization transfer: develop a pulse sequence that is able to transfer energy from 1H to 13C. The transfer of energy results in the increase in the spin population of the upper spin energy level of 13C, which results in higher sensitivity.

  23. 06-1D Multipulse Experiments (Dayrit) Polarization transfer: Using spin energy levels • The single spin system • The spin energy levels for a single spin system are populated following the Boltzmann law: • N / N = exp (-E/kBT)‏ • For a single spin system, there are two spin energy levels corresponding to  and  spin orientations. • The energy separation between the  and  spins depends on Bo.   Bo 

  24. 06-1D Multipulse Experiments (Dayrit) • Spin energy levels for a coupled spin system, AX • Spin-spin coupling is a localized interaction due to the proximity of nuclei possessing spin quantum number > 0. • For a coupled two spin system, AX, four spin energy levels are generated, AX, AX, AX, and AX, where the first spin refers to the orientation of the A nucleus, and the second spin refers to the X nucleus. AX AX AX  AX

  25. 06-1D Multipulse Experiments (Dayrit) Spin population for a coupled spin system, AX Assume that the ground state population of the  and  spins of both nuclei A and X are: A = X = 51% and A = X = 49% The populations of the four AX spin energy levels become: AX = (.51)2 = .26 AX = (.51)(.49) = .25 AX = (.49)(.51) = .25 AX = (.49)2 = .24 AX (24%)‏ AX AX  (25%)‏ (25%)‏ AX (26%)‏

  26. 06-1D Multipulse Experiments (Dayrit) Spin population for a coupled spin system, AX • The energy difference between the spin energy levels, J Hz, is determined by the energy of interaction of the spins, and not by the external magnetic field, Bo. Thus, J is independent of Bo. • This means that J will have the same value regardless of the strength of the magnetic field. • The relative energies and spin population differences among the spin levels remain the same. AX (24%)‏ AX AX  (25%)‏ (25%)‏ AX (26%)‏

  27. 06-1D Multipulse Experiments (Dayrit) Spin population for a coupled spin system, AX • The spin population will be distributed according to the Boltzmann distribution, with the relative populations: AX >  ~  > . (The thickness of the bars represent the relative spin populations.) • The magnitude of the energy differences depends on the strength of the coupling.

  28. 06-1D Multipulse Experiments (Dayrit) 1H: 13C: Spin population for a coupled spin system, AX In a spin system, the population is distributed among spin energy levels according to the Boltzmann distribution. For a heteronuclear AX (1H-13C) system, the relative equilibrium populations are: (1H 13C)‏ (1H13C)‏ (1H13C)‏ (1H13C)‏

  29. 06-1D Multipulse Experiments (Dayrit) Spin population for a coupled spin system, AX Consider a AX system such as CHCl3. There will be 6 isotope combinations. Polarization transfer will take place only between appropriate pairs. (1H12C) and (1H12C): The carbons are not NMR active; the protons are singlets. Although this group comprises the majority of natural abundance CHCl3 (~99%), they do not contribute to this experiment.  (1H13C), (1H13C), (1H13C), and (1H 13C): There are two types of 1Hspins and 1H spins which are determined by the attached 13C. Similarly, there are two types of 13Cspins and 13C spins which are determined by the attached 1H.

  30. 06-1D Multipulse Experiments (Dayrit) invert 1,2 3,4 1,3 2,4   X A E • Selective Population Inversion (SPI)‏ • 1H, the “sensitive” nucleus, has the larger . By inverting the populations of the energy levels connected by the A transitions, the intensities of the X (13C) transitions are enhanced. This achieves polarization transferfrom the more sensitive nucleus (1H) to the less sensitive nucleus (13C). SPI is the general mechanism of polarization transfer. 1H: 13C:

  31. 06-1D Multipulse Experiments (Dayrit) • Signal Enhancement by SPI • The new intensities obtained by SPI are a function of the ratios of the magnetogyric constants, : • 1 + (A/X) and 1 - (A/X) • Since (1H/13C)  4, the intensities of the positive and negative peaks are increased by about +5x and -3x, respectively. However, SPI is cumbersome since it requires that the 1H irradiation be selective. • The differences in the populations of the spin energy levels are reflected in the intensity and sign of the Mz vector: at equilibrium, Mz is positive; if the populations are equal, Mz = 0; if the spin populations are inverted, Mz is negative.

  32. 06-1D Multipulse Experiments (Dayrit) • Polarization transfer • The magnetogyric ratio gives the magnitude of the separation between spin energy levels: E = hBo / 2 • which determines the relative spin populations (Boltzmann distribution): • N / N = exp (-E / kBT )‏ • Among the nuclei in organic compounds, 1H has the highest magnetogyric ratio, , and therefore is the most sensitive.

  33. 06-1D Multipulse Experiments (Dayrit) Polarization transfer Polarization transfer is a technique by which we can take advantage of the presence of 1H by transferring spin population levels from 1H to nuclei of lower . Polarization transfer takes place through the intervening bonds. • This phenomenon has given rise to a family of polarization transfer (PT) experiments, most notably INEPT (Insensitive Nuclei Enhancement by Polarization Transfer) and DEPT (Distortionless Enhancement by Polarization Transfer). The polarization transfer technique was developed from the J-modulated spin-echo sequence. Recall the spin energy level diagram for an AX system ...

  34. 06-1D Multipulse Experiments (Dayrit) Basic polarization transfer sequence: The simplest pulse sequence for polarization transfer is a 90x’ -  - 90x’ building block: 1H: 90x’ -  - 90x’ . . . . . . . 13C: . . . . . . . . . . . . .90x’ - AQT Assume a CH system. Let us set  =(2JCH)-1. For a series of sequences where the waiting time is varied as follows - 0, , 2, etc., the 1H vector will alternate between y’(i.e.: +y, -y, +y, etc). The second 1H 90x’-pulse, converts this to alternating z’. Next, we implement a 13C 90x’-pulse. When the waiting times are 0, 2, 4, etc, the 13C peak is enhanced by polarization transfer because the 1H vector shall be along the -z’ direction (i.e., population inversion).

  35. Basic polarization transfer sequence: 1H: 90x’ -  - 90x’ . . . . . . . 13C: . . . . . . . . . . . .90x’ - AQT The behavior of the 1H vector for  = (2J)-1, and waiting time of 0, , and 2. For these values, the 1H will point at either z’. At intermediate waiting times, it is the y’ component only that will contribute to polarization transfer. (from: Sanders and Hunter, Modern NMR Spectroscopy)

  36. 06-1D Multipulse Experiments (Dayrit) Basic polarization transfer sequence: 1H: 90x’ -  - 90x’ . . . . . . . 13C: . . . . . . . . . . . . .90x’ - AQT For CHCl3, JCH=210 Hz. Let  =(2J)-1 = 2 ms. If we set  in increments of 250 s, the amplitude of the 13C signal will be modulated as shown: (from: Sanders and Hunter, Modern NMR Spectroscopy)‏

  37. 06-1D Multipulse Experiments (Dayrit) INEPT pulse sequence: As in SPI, the main objective of INEPT is the inversion of the spin energy levels associated with the 1H transitions and the transfer of this spin polarization to 13C. INEPT was developed to overcome the limitation of SPI of requiring a selective pulse. The INEPT pulse sequence combined spin echo and polarization transfer: a 180 pulse was placed in the middle of the delay period in order to remove any effects from the 1H shifts. 1H: 90x’ -  - 180x’ -  - 90y’ . . . . . 13C: . . . . . . . . 180x’ -  - 90x’ - . . . . AQT [ spin echo ] [ polarization transfer ]

  38. INEPT Pulse Sequence. (a-f) 1H 90°-pulse and spin-echo sequence. The MHC(slow vector, ccw) and MHC (fast vector, cw) fan out during waiting time,  = (4 1JCH)-1. (e) A simultaneous 180° pulse on 13C flips the 13C vectors by 180° and reverses the direction of the attached 1H vectors. (f) After an interval of  = (4 1JCH)-1, the 1H vectors are antiparallel along the ±x-axis. (continued)‏

  39. INEPT Pulse Sequence. (g) The 1H-90°y’-pulse flips the antiparallel 1H vectors to the ±z-axis. This represents the spin population of 1H. (g’) The spin population of 1H is transferred to the attached 13C yielding antiparallel 13C vectors along the ±z-axis.

  40. INEPT Pulse Sequence. (h) The 13C-90°x’-pulse flips the antiparallel 13C vectors to the ±y-axis for acquisition. The frequencies and heteronuclear J-couplings evolve during acquisition time. This yields positive and negative 13C peaks separated by 1JCH Hz centered on the resonance frequency.

  41. 06-1D Multipulse Experiments (Dayrit) INEPT Pulse Sequence. At the end of the INEPT pulse sequence, the MCH and MCH vectors with the appropriate value of 1JCH (=(4JCH)-1) are antiparallel (=180°) along the ±y’ axis after the 13C 90°x’-pulse. The vectors will relax back to the +z axis. The INEPT 13C signal for CHCl3 will have (+) and (-) peaks, separated by J Hz. The frequency position depends on whether it is on-resonance (=0) or off-resonance.

  42. 06-1D Multipulse Experiments (Dayrit) Relative frequency of attached protons (J-modulation)‏ CHnMCH Relative frequency • CH MCH0 - ½ J(C,H)‏ • MCH0 + ½ J(C,H)‏ • CH2MCH0 - J(C,H)‏ • MCH+ MCH0 • MCH0 + J(C,H)‏ • CH3MCH0 - 1½ J(C,H)‏ • MCH+ MCH+ MCH0 - ½ J(C,H)‏ • MCH+ MCH+ MCH0 + ½ J(C,H)‏ • MCH0 + 1½ J(C,H)‏

  43. 06-1D Multipulse Experiments (Dayrit) • INEPT for CH, CH2 and CH3 groups • The 13C peaks are enhanced by SPI. • CH group: Doublet with (+) and (-) peaks. • CH2 group: Triplet: (+), (0), (-). The middle peak is not detected . • CH3 group: Quartet: (+1), (+3), (-3), (-1). • Cq: Singlet vector simply relaxes according to T1. The amplification of the 13C signals depends on the magnitude of the MH vectors during the instant at which polarization transfer takes place and this differs for the various carbon groups and 1JCH. Assuming an average (compromise) 1JCH value of 145 Hz:  = (4 1JCH)-1 = 1.7 ms.

  44. 06-1D Multipulse Experiments (Dayrit) Multiplets observed in the 13C NMR spectra for CH, CH2, and CH3 groups. Left: 13C NMR spectrum without 1H decoupling. Right. 13C INEPT without 1H decoupling. (from: Friebolin, Basic One- and Two-Dimensional NMR Spectroscopy.)

  45. 06-1D Multipulse Experiments (Dayrit) Improving INEPT • It is difficult to interpret an INEPT spectrum because of overlaps of (+/-) multiplet peaks and the absence of a central peak for CH2. Two improvements can be made: the peaks corresponding to each group can be in the same phase, and multiplets can be collapsed to singlets. • The pulse sequences that have been developed for this purpose are the refocused INEPT and the refocused INEPT with broadband proton decoupling, {BB 1H}.

  46. 06-1D Multipulse Experiments (Dayrit) Refocused INEPT 1H: 90x’ -  - 180x’ -  - 90y’ -  - 180x’ -  - BB 13C: . . . . . . . . . 180 -  - 90y’ -  - 180x’ -  - AQT [ INEPT ] [ spin-echo ] 1. The refocused INEPT is a combination of INEPT + spin-echo. 2. There is no 13C 90 read pulse. It is the spin-echo that is acquired. 3. {BB 1H} collapses the 13C multiplets into singlets. The 13C vectors evolve only according to their frequencies during AQT. 4. Quaternary 13C nuclei are not affected by polarization transfer, and refocused INEPT does not bring the Cq vectors into the y’ axis during acquisition. Therefore, Cq groups are not detected.

  47. 06-1D Multipulse Experiments (Dayrit) Refocused INEPT 1H: 90x’ -  - 180x’ -  - 90y’ -  - 180x’ -  - BB 13C: . . . . . . . . . 180 -  - 90y’ -  - 180x’ -  - AQT [ INEPT ] [ spin-echo ] 5. The spin-echo is the refocusing step. The second fixed delay time, , is set in the same way as the spin-echo sequence. However, this involves some compromise as the different CHn groups will refocus differently. A compromise value is  = 3/(81JC,H) ~ 2.6 ms. 6. The second pair of simultaneous 180-pulses during the spin-echo portion has a similar effect on the MC vectors: the vectors are flipped across the y’ axis and their directions are reversed.

  48. 06-1D Multipulse Experiments (Dayrit) Refocused INEPT 1H: 90x’ -  - 180x’ -  - 90y’ -  - 180x’ -  - BB 13C: . . . . . . . . . 180 -  - 90y’ -  - 180x’ -  - AQT [ INEPT ] [ spin-echo ] 7. The CH and CH3 groups appear as positive peaks, while the CH2 groups appear as negative peaks. Cq nuclei are not detected. 8. Because the polarization transfer process depends on the magnitude of the MH vectors, INEPT sequence should not be longer than either the T1 or T2 value of 1H.

  49. INEPT spectra of a neuraminic acid derivative. A: 13C NMR with {BB 1H}; B: Gated decoupling (with multiplets but no NOE enhancement); C: INEPT spectrum; D. Refocused INEPT; and E. Refocused INEPT spectrum with {BB 1H}. Cq nuclei are not detected by this sequence. (from: Friebolin, Basic One- and Two-Dimensional NMR Spectroscopy)

  50. 06-1D Multipulse Experiments (Dayrit) Selective Enhancement by Polarization Transfer: DEPT • One of the disadvantages of the refocused INEPT sequence is its inability to distinguish CH from CH3 unambiguously (peaks from both types are positive). • Distortionless Enhancement of Polarization Transfer (DEPT) was developed to overcome this shortcoming. It is today the most widely-used 13C experiment to determine carbon multiplicity.

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