Two-dimensional frequency spectrum

Fig. 26. A schematic diagram of the normal two-dimensional VACSY experiment. FIDs (spin-1,) are collected for different sample spinning angles, / . After appropriate processing, a two-dimensional frequency spectrum is produced in which the chemical shift anisotropy powder patterns are separated according to the isotropic chemical shift.

Two-dimensional NMR methods that yield a two-dimensional frequency spectrum have not yet been attempted successfully to study metal interactions with HS, although instances of successful applications of these approaches can be found in the study of metalloproteins (Kingery et al., 2001). Mononuclear ( H) two-dimensional NMR experiments, such as total correlation spectroscopy (TOCSY), can show H- H coupling throughout the complete spin system, and exchange protons can provide information on sites to which metal attach. For example, N-containing units in HS that bind the metal can be identified since the amido protons from these structures will exchange and disappear from the spectrum. 

Fig. 1.4.6 Two-dimensional frequency spectrum for the eariy-stage spinodai decomposition of the...

Figure 3.24 The pulse sequence for two-dimensional nuclear Overhauser effect spectroscopy (NOESY), The pulse sequence is divided into the preparation (P), evolution or tx (E), mixing (M), and detection or t2 (D) periods. The data are recorded in the detection period for many equally spaced values of tx and double Fourier-transformed to give the two-dimensional frequency spectrum.

Two-dimensional NMR spectroscopy may be defined as a spectral method in which the data are collected in two different time domains acquisition of the FID tz), and a successively incremented delay (tj). The resulting FID (data matrix) is accordingly subjected to two successive sets of Fourier transformations to furnish a two-dimensional NMR spectrum in the two frequency axes. The time sequence of a typical 2D NMR experiment is given in Fig. 3.1. The major difference between one- and two-dimensional NMR methods is therefore the insertion of an evolution time, t, that is systematically incremented within a sequence of pulse cycles. Many experiments are generally performed with variable /], which is incremented by a constant Atj. The resulting signals (FIDs) from this experiment depend... 

Confirmation of structure 34 was obtained by examination of the two-dimensional COSY spectrum which showed no coupling between the 2 -H and 4 -H signals at 8 5.06 and 3.46 but coupling of both of them with the 3 -methylene signal at 8 2.21. NOE experiments showed enhancement of the 6-H signal at 8 6.28 when irradiated at the frequency of the 5-OH group. This confirms that the piperidine ring is attached at C-8. 

In Section 12.3 it was described how, with the help of a two-dimensional exchange spectrum, domain sizes in the iPP/EP blend are estimated. There an estimated value for the Xe diffusion coefficient was used. Now with experimental data from Table 12.2 the average EPDM domain size for the iPP/EPDM blend can be calculated. It was assumed that the structure of the EPDM in the blend is the same as in the pure material, (i.e., the Xe diffusion coefficient in the EPDM domains in the blend is equal to the measured D for pure EPDM and likewise for iPP), then for Xe in the EPDM domain during A = 1.2 seconds is 20 grn. In the same time for Xe in the iPP matrix is approximately 5 grn. These distances for a diffusion time of 1.3 milliseconds, the inverse of the frequency difference 770 Hz of the two lines in the Xe NMR spectrum of the blend, are 0.6 and 0.2 grn, respectively. The average size of the EPDM domains in the iPP/EPDM blend is... 

Experiments described in this section are suited to investigate ultraslow motion with correlation times in the millisecond-to-second range. Here, the NMR spectra are given by their rigid-lattice limit and one correlates the probability to find given NMR frequencies at two different times separated by the so-called mixing time tm [11,72]. A two-dimensional (2D) spectrum results, being a function of two NMR frequencies at t = 0 and t = tm, respectively. Since the NMR frequency reflects the orientation of the molecule, 2D spectra provide a visual representation of the reorientational process. Time- and frequency-domain... 

Frequencies and intensities of the iines in the two-dimensional 7-spectrum of an AB spin system when both spins experience the same 180 non-selective inverting pulse (45)... 

The two-dimensional COSY spectrum for ethanol is shown in Fig. 15.15, with the two frequency coordinates expressed in terms of chemical shifts 5] and 52-In Sections 15.3 and 15.4, we had considered in detail the NMR spectrum for this molecule. The one-dimensional spectrum, drawn at the top, consists of three chemical-shifted components for the CH3, OH and CH2 protons, with two of... 

Fig. 10 Two-dimensional /1//2 cross-sections from four-dimensional N.C-NOESY data for the DHl domain of Kalirin. One dimensional cross sections parallel to the/i axis at the f2 frequencies indicated by the colored lines are shown above each panel. Panel A is the real/real component of the two dimensional DPT spectrum using quadrature detection in all dimensions. Panel B is the DPT spectrum obtained using only the real/real/real component from the three indirect time dimensions of the time domain data. Panel C is the maximum entropy spectrum obtained using random phase detection. Panels B and C employ l/8th the number of samples used in panel A...

Chan Pang 2000) described the Fourier transform approach to detect the structural defect of fabrics. Since the three-dimensional frequency spectrum is very difficult to analyze and many defects occur along the horizontal and vertical axes, two significant spectral diagrams (called the central spatial frequency spectra) are introduced to increase the efficiency of the analysis process. Seven significant characteristic parameters were extracted from the central spatial frequency spectra to describe the defect type. 

Because of the two frequencies, Wj and Wg, that enter into the Raman spectrum, Raman spectroscopy may be thought of as a two-dimensional fomi of spectroscopy. Nomially, one fixes oij and looks at the intensity as a frmction of tOj, however, one may vary tOj and probe the intensity as a frmction of tOj - tOg. This is called a Raman excitation profile. 

Muns ENDOR mvolves observation of the stimulated echo intensity as a fimction of the frequency of an RE Ti-pulse applied between tlie second and third MW pulse. In contrast to the Davies ENDOR experiment, the Mims-ENDOR sequence does not require selective MW pulses. For a detailed description of the polarization transfer in a Mims-type experiment the reader is referred to the literature [43]. Just as with three-pulse ESEEM, blind spots can occur in ENDOR spectra measured using Muns method. To avoid the possibility of missing lines it is therefore essential to repeat the experiment with different values of the pulse spacing Detection of the echo intensity as a fimction of the RE frequency and x yields a real two-dimensional experiment. An FT of the x-domain will yield cross-peaks in the 2D-FT-ENDOR spectrum which correlate different ENDOR transitions belonging to the same nucleus. One advantage of Mims ENDOR over Davies ENDOR is its larger echo intensity because more spins due to the nonselective excitation are involved in the fomiation of the echo. 

There are actually two independent time periods involved, t and t. The time period ti after the application of the first pulse is incremented systematically, and separate FIDs are obtained at each value of t. The second time period, represents the detection period and it is kept constant. The first set of Fourier transformations (of rows) yields frequency-domain spectra, as in the ID experiment. When these frequency-domain spectra are stacked together (data transposition), a new data matrix, or pseudo-FID, is obtained, S(absorption-mode signals are modulated in amplitude as a function of t. It is therefore necessary to carry out second Fourier transformation to convert this pseudo FID to frequency domain spectra. The second set of Fourier transformations (across columns) on S (/j, F. produces a two-dimensional spectrum S F, F ). This represents a general procedure for obtaining 2D spectra. 

Two-dimensional NMR A strange concept, when we consider that all the spectra we have previously dealt with were of course plotted in two dimensions, the two axes (dimensions) being a frequency axis (horizontal, expressed in ppm rather than in Hz for reasons we have already discussed) and an intensity axis. To understand the basic idea of two-dimensional NMR (2D NMR) we should first remind ourselves that while the spectrum we see and use is plotted as a... 

Chapter 3 is devoted to dipole dispersion laws for collective excitations on various planar lattices. For several orientationally inequivalent molecules in the unit cell of a two-dimensional lattice, a corresponding number of colective excitation bands arise and hence Davydov-split spectral lines are observed. Constructing the theory for these phenomena, we exemplify it by simple chain-like orientational structures on planar lattices and by the system CO2/NaCl(100). The latter is characterized by Davydov-split asymmetric stretching vibrations and two bending modes. An analytical theoretical analysis of vibrational frequencies and integrated absorptions for six spectral lines observed in the spectrum of this system provides an excellent agreement between calculated and measured data. 

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