Quad-spectrum

We now introduce the quantities called cospectrum 4>s( u 2) quad-spectrum xPsiyi, V2) of cross correlation, which are given by... 

The cospectrum and quad-spectrum are well-known quantities in the field of time-series analysis [6,7]. They represent, respectively, the in-phase correlation and ji/2 out-of-phase (i.e., quadrature) correlation of individual Fourier components of signals at a specific Fourier frequency s. 

The synchronous and asynchronous spectrum, especially those expressed in terms of the amplitudes of cosine and sine function, clearly reveal the close resemblance of the functional forms to the ones given for the cospectrum and quad-spectrum in Equations (FIO) and (Fll). The amplitudes of cosine and sine component, respectively, of the dynamic spectrum with a single frequency 5 reflect the real and imaginary parts of the Fourier transform of the dynamic spectrum at the Fourier frequency of s = 5. Alternatively, the more general synchronous spectrum and asynchronous spectrum in Equation (F15) derived for the dynamic spectrum with arbitrary waveforms may be viewed as the collective sum totals of individual correlation spectra obtained for the corresponding Fourier components. 

In practice this may not be achieved perfectly, so weak quad images may be produced. They can be readily recognized as they show different phases than the rest of the spectrum. 

Lyotropic polymeric LC, formed by dissolving two aromatic polyamides in concentrated sulphuric acid, have been studied using variable-director 13C NMR experiments.324 The experimental line shapes at different angles w.r.t the external field were used to extract macromolecular order and dynamic in these ordered fluids. An interesting application of lyotropic LC is for the chiral discrimination of R- and S-enantiomers, and has recently been demonstrated by Courtieu and co-workers.325 The idea was to include a chiral compound 1-deutero-l-phenylethanol in a chiral cage (e.g., /1-cyclodextrin) which was dissolved and oriented by the nematic mean field in a cromolyn-water system. Proton-decoupled 2H NMR spectrum clearly showed the quad-rupolar splittings of the R- and S-enantiomers. The technique is applicable to water-soluble solutes. 

Try out the effect of several modes for DC correction available with 2D data. Load the raw data of the magnitude mode 2D COSY spectrum D NMRDATA GLUCOSE 2D HH GHHCO 001001.SER and choose no, quad and qpol as BC mod in F2. Note that usually for Fl no baseline correction is applied in the time-domain, i.e. BC mod (F1) = no. Fourier transform the data and store the individual spectra using ascending processing numbers. Compare corresponding rows to inspect the effect of different baseline corrections. 

Mossbauer spectroscopy of the 57Fe nucleus has been extensively used to investigate aspects of spin equilibria in the solid state and in frozen solutions. A rigid medium is of course required in order to achieve the Mossbauer effect. The dynamics of spin equilibria can be investigated by the Mossbauer experiment because the lifetime of the excited state of the 57Fe nucleus which is involved in the emission and absorption of the y radiation is 1 x 10 7 second. This is just of the order of the lifetimes of the spin states of iron complexes involved in spin equilibria. Furthermore, the Mossbauer spectra of high-spin and low-spin complexes are characterized by different isomer shifts and quad-rupole coupling constants. Consequently, the Mossbauer spectrum can be used to classify the dynamic properties of a spin-equilibrium iron complex. 

Figure 15.17 shows 2H spectra of powdered hexamethyl-benzene-D g. Since we are dealing with a powder, we expect powder patterns, and the back-to-back superimposition of a pair of asymmetric powder lineshapes is clearly seen. Quad-rupolar interactions can get quite large, and in most cases they will dominate the chemical shift spectrum. For deuterium, which has a rather tiny quadrupole moment, the quadrupolar interaction varies from about 25 kHz in hexamethylbenzene-D g to about 200 kHz in carboxylate deuterons. In the heavier nuclei, such as 127I, the quadrupolar interaction can reach 2000 MHz No one is ever likely to observe a spectrum that wide. 

Fig. 8 Schematic of a tandem quadrupole MS/MS instrument. A tandem quadrupole MS/MS instrument consists of two quad-rupole MS filters, MSI and MS2, separated by a collision cell. Each quadrupole MS filter consists of four cylindrical or hyperbolic shaped rods. A unique combination of direct current (dc) potential and radiofrequency (rf) potential is applied to each pair of rods (one pair 180° out of phase with the other). A mass spectrum results by varying the voltages at a constant rf/dc ratio. A variety of scan modes (e.g., full scan, product ion, precursor ion, neutral loss) provide unique capabilities for quantitative and qualitative structure analysis. (Courtesy of Micromass, Manchester, UK.)...

Since 14N has 1= 1 its relaxation is usually dominated by quad-rupolar interactions. These produce broad lines, both in the 14N NMR spectrum and in the spectra of nuclei spin-spin coupled to nitrogen, (la, 2a) The 13N nucleus has I =, thus in a diamagnetic, chemically stable molecule it is relaxed by one or more of several less efficient mechanisms. 

Scenario (a) transplants acquisition parameters from a typical ID proton spectrum into the second dimension leading to unacceptable time requirements, whereas (b) and (c) use parameters more appropriate to 2D acquisitions. All calculations use phase cycles for f quad-detection and axial peak suppression only and, for (b) and (c), a recovery delay of Is between scans. A single zero-filling in f] was also employed for (b) and (c). 

Fig. 7.7 The Mossbauer spectra at 1-6 K for (a) soluble Prussian blue, (b) insoluble Prussian blue, (c) Turnbull s blue. The ferric six-line spectrum shows a small quad-rupole splitting, Si — Sz= ie g(3 cos Q — 1). [Ref. 31, Fig. j]...

The Mossbauer spectra were obtained for crystallized Mo-Fe protein isolated from Azotobacter grown on Fe-enriched media (99). Between 20° and 200°K, the spectrum of the native protein is a doublet with an isomer shift of 0.39 mm/sec (relative to Fe metal) and a quad-rupole split of 0.84 mm/sec indicative of high-spin Fe A small shoulder on the high-field side may indicate high-spin Fe or Fe (107) and may represent the unique portion of the iron involved in N2 complexation. Reduction with hydrosulfite converts at least 25% of the iron to a form representative of high-spin Fe or Fe. ... 

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