Spectrum slicing

D spin-echo MAS NMR experiments have been carried out on polycrystalline [2,3- C2]-L-alanine, so that two unusual resonance lines emerged along the Fi axis. To examine the spectral structure observed in the Fi direction more closely the 2D NMR experiment has been undertaken using a sufficiently small ti increment, yielding many more resonance lines on a spectrum sliced along the Fi axis. In addition, it has been shown that the intensities of resonance lines are largely dependent on the dipolar interaction. 

In order to partition the occupied states into slices, it is necessary to have a guess for the Fermi level. The guess does not need a high degree of accuracy. For this the Fermi level from the previous SCF iteration can be used. This means that the spectrum slicing method will need to be bootstrapped with a regular method similarly to Chebyshev-Davidson. 

In a spectrum slicing method, there is a danger that adjacent slices will compute approximations to the same eigenpair. Given an approximation, (A, ), to an... 

Two-dimensional NMR spectra are normally presented as contour plots (Fig. 3.11a), in which the peaks appear as contours. Although the peaks can be readily visualized by such an overhead view, the relative intensities of the signals and the structures of the multiplets are less readily perceived. Such information can be easily obtained by plotting slices (cross-sections) across rows or columns at different points along the Fi or axes. Stacked plots (Fig. 3.11b) are pleasing esthetically, since they provide a pseudo-3D representation of the spectrum. But except for providing information about noise and artifacts, they offer no advantage over contour plots. Finally, the projection spectra mentioned in the previous section may also be recorded. 

Another approach to obtain spatially selective chemical shift information is, instead of obtaining the entire image, to select only the voxel of interest of the sample and record a spectrum. This method called Volume Selective spectroscopY (VOSY) is a ID NMR method and is accordingly fast compared with a 3D sequence such as the CSI method displayed in Figure 1.25(a). In Figure 1.25(b), a VOSY sequence based on a stimulated echo sequence is displayed, where three slice selective pulses excite coherences only inside the voxel of interest. The offset frequency of the slice selective pulse defines the location of the voxel. Along the receiver axis (rx) all echoes created by a stimulated echo sequence are displayed. The echoes V2, VI, L2 and L3 can be utilized, where such multiple echoes can be employed for signal accumulation. 

There are many specific ways to generate equally spaced tags but they are all based on the same principle of manipulating the rf pulses to generate equally spaced bands of rf radiation in the frequency domain. It is well known that under ordinary conditions, meaning normal levels of nuclear spin excitation, the frequency spectrum of the rf excitation pulse(s) is approximately the Fourier transform of the pulses in the time domain. Thus, a single slice can be generated in the... 

Fig. 5.3.2 (A) NMR spectrum of hyperpolar- abundance of approximately 25% of the, 29Xe ized 129Xe from a sample that contains bulk gas isotope. (B) 2D slice of 3D chemical shift phase (0.3 ppm) and xenon occluded within selective MRI of the bulk gas phase. (C-E) 2D aerogel fragments (25 ppm). The gas mixture slices of 3D chemical shift selective MRI of the used for the experiment contained 100 kPa of 25 ppm region for various recycle times T.

Fig. 5.3.3 (A) NMR spectrum of hyperpolarized 129Xe in NaX zeolites. (B) 2D slice in the flow direction of a 3D chemical shift selective MRI of gas in the zeolite pellets. (C) 2D slice perpendicular to the flow direction of the same 3D chemical shift selective MRI as in (A). Adapted from Ref. [14].

Figure 5.5.8 shows the volume selective spectroscopy pulse sequence used. This pulse sequence combines elements of NMR spectroscopy and MRI pulse sequences three slice selective rf pulses are applied in three orthogonal directions to obtain 1H spectra from pre-determined local volumes within the sample [30]. In this particular application, spectra were recorded from local volumes of dimension 1.5 mm x 1.5 mm x 0.5 mm within the fixed bed the data acquisition time for each spectrum was 3 min. Figure 5.5.9(a) shows the local volumes selected within slice 3 of the bed, as identified in Figure 5.5.7. In Figure 5.5.9(b) the 1H spectra recorded from within these volumes are shown data are presented only for the range of... 

Fig. 20. A few examples of the Doppler-selected TOF data are exemplified. The TOF spectra have been converted into velocity space and weighted by a term. For each spectrum, the VUV laser frequency is selected to slice through the Newton sphere near the center-of-mass, i.e. wcm- The cap marked on the top corresponds to the (v, j ) state of the co-product F1F for Ec = 1.18kcal/mol. Note the slight tilt of the dashed lines which act as a visual guide for quantum state assignments.

Figure 8 F2 Slices through a series of 1,1-ADEQUATE spectra of retrorsine (2) at the F2 shift of the H17 resonance.51 The optimization is shown above the individual spectral segments. The correlation shown in the individual traces is that from the 07 sp2 resonance to the 05 sp2 resonance. The absence of this response in the 60 Hz optimized spectrum (see Figure 7) prompted the acquisition of the series of spectra shown.

The 5 Hz optimized l,n-ADEQUATE spectrum of strychnine (1) is shown in Figure 9.70 The high resolution 600 MHz proton spectrum is shown in Figure 10A and compared to slices extracted at the Fi frequency of the C15 methylene resonance in the 5 Hz optimized l,n-ADEQUATE spectrum (B) and the 60 Hz optimized 1,1-ADEQUATE spectrum (C). The adjacent carbons (via Vcc) show correlations in the 5 Hz optimized INADEQUATE spectrum that are unsuppressed but all possible three-bond... 

B) Slice taken through the 5 Hz optimized INADEQUATE spectrum of 1 at the F1 shift of the C15 methylene resonance. (C) Comparison slice taken through the 60 Hz optimized 1,1-ADEQUATE spectrum of 1 at the Fn shift of the C15 methylene resonance. 

Figure 3 2D 27Al-29Si RAPT-CP-CPMG HETCOR data for zeolite ZSM-4 recorded at 14.1 T with 10 kHz MAS. The 2D spectrum was acquired in 30 rows of hypercomplex data, with 64K scans per row, h increments of 100 ps, and acquisition time of 38 hours. In the right, ID slices taken through the centers of Ah and Al2 resonances are compared with ID 29Si MAS spectrum.

Note that this procedure is suitable also for the calculation of eigenmodes in circular ring and disk microresonators. The cross-sections of disk microresonators are usually simpler, without any mid-slices, which leads to shorter calculation times. However, good estimate of initial values of the propagation constants of the disk modes for their search in the complex plane is more difficult, and their mode spectrum is denser than for ring microresonators with similar radii of curvature. 

---