Assume MAS on powders for all problems, unless stated otherwise (or obvious from the context). Calculation Exercise #1 (Wednesday)

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1 Exercises for Solid-State NMR Spectroscopy in Materials Chemistry Mattias Edén, Department of Materials and Environmental Chemistry, Stockholm University Assume MAS on powders for all problems, unless stated otherwise (or obvious from the context). Calculation Exercise #1 (Wednesday) 1. Assume you start with a spin-1/2 ensemble at thermal equilibrium, i.e. with the magnetization vector pointing along the z-axis. Assume you can apply an x-pulse of any flip angle. Which pulses (there are several options) could you apply if you want to leave the magnetization vector at the following positions after each pulse? z z z x -z y a) b) c) z 45 o x y x y d) x y 2. Assume a sample with an ensemble of one spin-1/2 site in a strong magnetic field. The net magnetization vector points along the y axis of the rotating frame. (a) Suggest one rf pulse (flip angle and phase) that would convert the spin magnetization vector at thermal equilibrium into the direction described above. It should be clear from your answer what the direction of the magnetization vector is at thermal equilibrium. (b) Depict graphically the magnetization vector before and after a consecutive application of each of two pulses: a 90 pulse followed by a ( /2) 180 pulse. Clearly indicate how each pulse change the direction of the magnetization vector within a coordinate system. Indicate clearly the rotation axis associated with each pulse. (c) After both pulses, could you acquire an NMR signal from your sample? 1

2 3. A certain phosphate has one 31 P site with aniso /2 =12.8 khz at B 0 =9.4 T ( 0 /2= MHz). Assume that the 31 P MAS spectrum is recorded at r /2 =6.50 khz. (a) Sketch how it may appear (units of Hz) with emphasis of the number and positions of the spinning sidebands. Assume /2 =-2.5 khz for the centerband. Make an estimate how many spinning sidebands that would be expected to be visible in the spectrum, based on the ratio ( aniso / r ), and previously given examples ( =1). (b) What is aniso? 4. The 31 P MAS NMR spectrum above was recorded from an inorganic phosphate salt at an external magnetic field of T. The phosphate comprises one crystallograhically unique P site. The centerband peak is marked by an asterisk and the maxima of two selected peaks are indicated. The spectrum includes all spinning sidebands of significant intensity. The spectrometer reference frequency is set on-resonance with respect to the primary standard for 31 P (i.e., the signal from 85% H 3 PO 4 ). (a) Determine the MAS frequency used to record the NMR spectrum. (b) Calculate (accurately) the isotropic chemical shift, expressed both in Hz and in shift units of ppm. (c) Determine the sign for each of aniso and aniso. As for the asymmetry parameter, one of the following possibilities is correct: 0.04, 0.64 or Make a selection. Motivate your answers, particularly your choice of. (d) Calculate (as accurately as you can) the values and aniso and aniso. (e) Using tabulated values of 31 P isotropic chemical shifts in phosphates, assign the 31 P NMR signal to a Q n group (i.e., specify what n is). Explain your reasoning and comment on whether you think that you can do this assignment unambiguously, or if several possibilities exist. (f) Regarding the Q n assignment: now assume that you exploit all information available to you from both isotropic and anisotropic chemical shifts. List all information you can use and comment on if (and then how) this modifies your answer in (e) 2

3 5. The structure of the mineral hillebrandite, Ca 2 SiO 3 (OH) 2 is built by Q 2 units. The 29 Si site is associated with iso =-86 ppm, aniso = ppm and =0.71. (a) Calculate the isotropic frequency separation in Hz between the 29 Si nuclei in hillebrandite and those of TMS at a magnetic field of 9.40 T (here 0 /2 =79.50 MHz), assuming that the spectrum from the mineral is recorded by using very fast MAS. (b) Determine aniso /2 at B 0 =9.40 T and B 0 =17.60 T. (c) Assume 29 Si NMR spectra are recorded at each magnetic field of (b), using r /2 =3.200 khz. By estimating the respective ratios aniso / r, which magnetic field would you prefer if your MAS spectra are to be used to determine aniso and? Motivate. (d) Which spinning frequency at B 0 =9.4 T would give you an essentially identical spinning sideband manifold (here we only consider the spinning sidebands amplitudes and not their exact frequency positions) as that recorded at T and khz MAS? Sketch how the recorded spectra could appear at each field. 3

4 Calculation Exercise #2 (Friday) 6. Which of the following underlined nuclei would you expect to cross-polarize (i) most rapidly and (ii) slowest from its surrounding 1 H spin(s)? Motivate carefully your answers. Only consider dipolar couplings and ignore potential relaxation effects, and ignore the minor differences between Si O and P O bond-lengths. a) b) c) d) H Si 7. You apply nutation frequencies of 1 /2 =72 khz and 1 /2 =60 khz in order to effect 1 H 29 Si CP in a mesoporous silica-based material. Which spinning frequencies could be used for successful CP? Motivate your reasoning by calculations. 8. (a) Consider the 31 P- 31 P through-space dipolar coupling at an internuclear distance r. What is the corresponding dipolar coupling if the internuclear distance is (A) 2r or (B) 3r? Draw a conclusion. Based on the result, explain why a 31 P 2QC experiment using a short interval for 2QC excitation may be used to distinguish 31 P present in the following two constellations: (i) (ii). It can be assumed that all neighbouring oxygens bridge to some other cation that is not 31 P. (b) Assume that all oxygens are non-bridging. Would there be another way to distinguish (i) from (ii) without an advanced experiment relying on 31 P 2Q excitation? % 13 C-enriched glycine has two inequivalent 13 C sites, 13 CH 2 and 13 COOH, associated with isotropic shifts of 43.5 ppm and ppm, respectively. The corresponding anisotropic chemical shifts are aniso [CH 2 ]= ppm and aniso [COOH]= ppm. Assume you record a 13 C MAS NMR spectrum at T using high-power CW decoupling during acquisition. (a) Which spinning frequency would you choose if you want to record your NMR spectrum at the n=2 rotational resonance condition? What are the two main qualitative differences in spectral features between the resulting 13 C spectrum and one recorded at 25 khz MAS? Motivate your answers and show all calculations required to reach them. (b) Which 13 C site would you think is most difficult to decouple from its surrounding protons? Motivate shortly. (c) Assume that you would like to record a 13 C NMR spectrum from glycine, showing only the peak from the CH 2 functional group. Would this be possible? If so, how would you do it? Motivate! 4

5 10. An organic molecule X has been 13 C-enriched at 3 out of 4 positions as follows: 13 C[1] 12 C[2] 13 C[3] 13 C[4] Each number within brackets [..] marks the spin label. Each 13 C has the following isotropic chemical shift: 1 =55 ppm, 3 =65 ppm, 4 =30 ppm. Note that internuclear distances among spins within different molecules of the crystal structure are long relative to those within each molecule. (a) Assume a 2QF experiment is carried out on a powder of X. The 2QC excitation interval ( exc ) is short, so that only 2QC involving directly bonded 13 C are created. Sketch and assign the resulting 2QF 13 C NMR spectrum. Ignore CSA and assume that all relevant NMR peaks are narrow. Motivate your reasoning. (b) Sketch the corresponding 2QC-1QC 2D correlation spectrum, assuming the same value of exc as in (a). The 2D spectrum should contain all peaks that are expected to be observed, with their correspondning coordinates (i.e., ppm-values ) clearly marked along both the horizontal (1QC) and vertical (2QC) spectral dimension. You also need to motivate your reasoning and show any relevant calculations. (c) How many 2D peaks would the correlation spectrum in (b) comprise if 13 C would occupy all four C positions in X, and 2 = 3? Motivate briefly. 5

6 Hand-in Exercises 1. Consider the two crystalline silicate minerals Ca 3 SiO 4 Cl 2 ( iso =-74.0 ppm) and Na 2 SiO 3 ( iso =-77.0 ppm). Each structure has one unique 29 Si site. (a) Based on the compositions alone, which Q n units are for each case expected to build the structure? (3p) (b) The following chemical shift anisotropies were determined: aniso = 73.5 ppm and aniso = 11.0 ppm. Pair each CSA with the corresponding mineral: motivate your reasoning. (2p) Assume a 29 Si NMR spectrum is recorded from a 50:50 (mol-%) mixture of the two silicates at B 0 =9.40 T. The spectrometer reference frequency is set at the isotropic chemical shift of the 29 Si site of Na 2 SiO 3. (c) Calculate the resonance offset frequencies (in Hz) for each site. (3p) (d) Sketch the MAS spectrum (on a frequency scale in Hz) that would be obtained at r /2 =3.00 khz. You may decide yourself which values of to use. You need to make an estimate of roughly how many spinning sidebands you are to draw for each site. Throughout the problem, motivate your reasoning both by text and by explicit calculations. Assume infinitely narrow peaks. Note that as for 29 Si, the scale runs with frequencies increasing to the left. (5p) 2. The 29 Si NMR spectrum shown above was recorded from a mesoporous silica material of composition SiO 2. 1 H 29 Si CPMAS was used with a (long) contact time interval of 10 ms at 10 khz MAS. The experimental NMR spectrum was deconvoluted into each of the three (grey) peaks from 29 Si in SiO 4, SiO 3 (OH) and SiO 2 (OH) 2 groups; note that these groups are usually labelled by the Q n nomenclature. The spectrometer reference frequency was MHz and the resonance frequency of the standard reference TMS was MHz. (a) Assign each 29 Si peak by its corresponding Q n unit. Motivate briefly your answer. (2p) (b) Calculate the resonance offset frequency (in khz) for each of the two 29 Si environments that give the most intense NMR peaks in the spectrum. Base you calculations on the peak maxima of the grey deconvoluted signals; you first need to estimate (as accurately as you can) their positions in ppm. (5p) (c) List the three Q n units according to which you think are most and least common in the mesoporous structure. Sketch how the corresponding 29 Si MAS spectrum acquired by singlepulses might look (use a ppm-scale), roughly reflecting the relative site populations. Explain 6

7 why the NMR peak intensities in this spectrum may be different from what is apparently suggested by the CPMAS spectrum. (4p) (d) Describe the 2D HETCOR experiment and its relation to CP. Sketch how a 2D HETCOR spectrum (contour plot) might look from the mesoporous silica material, if using a short (~2 ms) contact interval ( CP ). Motivate your answers and remember to clearly label the spectral axes and the peak(s) in the 2D spectrum. (5p) 3. A 2D spectrum is shown at the last page: This is to be handed in together with your solution, containing the requested information below. The spectrum was recorded using a 2QC-1QC 31 P correlation experiment applied to a glass from the PbO-P 2 O 5 system. A through-space dipolar recoupling pulse sequence was used under MAS conditions. The 1D spectra on top and to the left correspond to projections along the horizontal (1QC) and vertical (2QC) dimensions of the 2D spectrum, respectively. (a) Based on the glass composition, predict which 31 P Q n unit(s) that is(are) expected to dominate in the glass structure. (3p) (b) Using a chemical shift table, assign the two peaks A and B. Motivate your answer and also comment why it is reasonable by comparing with your answer in (a). (2p) (c) Assign the correlation peaks labelled X and Y (two peaks) in the 2D spectrum according to which Q n1 - Q n2 units are involved in each 2QC. Motivate briefly your answer. (2p) (d) The values of the vertical scale are not shown. Predict the positions of the peaks X and Y along the vertical dimension of the 2D spectrum. Motivate your reasoning (giving two values without any motivation result in 0p). (2p) (e) The average 31 P- 31 P through-space dipolar coupling constant in a P-O-P segment of a phosphate glass is roughly 700 Hz. Calculate its corresponding 31 P- 31 P internuclear distance; give the answer with 3 significant digits. (4p) (f) Assume that you have one homonuclear S-S spin-pair in a crystalline compound, and that the two S-spins may be recoupled selectively and their NMR signals do not overlap with any other S-spin signals. Explain qualitatively and shortly the principle behind measuring homonuclear distances using 2QF experiments: what is the idea behind such experiments and how are they carried out to give the desired information? You may base your discussion on a sketch of the pulse sequence protocol (and qualitatively explaining its segments), but it is sufficient to outline the key ideas. (4p) (g) Given that a phosphate glass only comprise one type of Q n unit, the same procedure of (f) may be used to obtain an average 31 P- 31 P internuclear distance representative of the glass. However, for the present lead phosphate glass, it is not possible to get a reasonably accurate distance measurement for each of the Q n1 - Q n2 pairs by only performing a series of 2QF 1D MAS spectra. Explain why. However, assuming you have the possibility to acquire a series of 2D 2QC-1QC correlation spectra, it is possible to get information about the average internuclear distance between 31 P in neighboring tetrahedra. Explain shortly what parameter(s) you would change between different 2D acquisitions, and how analyzing the results from a series of 2D spectra could be used to obtain average internuclear distances representative for each pair of correlated Q n1 - Q n2 units. (4p) 7

8 0.55PbO P 2 O 5 A B X Y 2QC dimension (ppm) 1QC dimension (ppm)