Line broadening multiplication

Most simply this can be done by multiplying each data point in the FID by an exponential decay term that starts at unity but decays to a negligible value at its end. Such an exponential multiplication (EM) is a simple and effective way to increase the signal-to-noise ratio at the expense of added line broadening (LB). The LB term in this function can be altered... 

Figure 1.37 The effect of line broadening (LB) multiplication on the appearance of H-NMR spectra. (a IJB = 10) and (b LB = 5) H-NMR spectra recorded after multiplying the FIDs by positive LB values. (c LB = 0). The same H-NMR spectrum recorded without line broadening. (d LB = -2) Sharper signals are obtained when the FID is multiplied by negative LB values. 

Fig. 6a-e OCH2 signal of compound 1 (200 MHz) a Only Fourier transformation b Fourier transformation preceded by multiplication of FID by a negative line broadening function (-0.3 Hz) c Fourier transformation preceded by multiplication of FID by a shaped sine bell function (SSB = 1) d Fourier transformation preceded by multiplication of FID by a positive line broadening function (0.8 Hz) e Fourier transformation preceded by multiplication of FID by a positive line broadening function (1.9 Hz)... 

Other good news comes in the shape of the 13C nucleus having a spin quantum number of /2. This means that 13C signals are generally sharp as there are no line-broadening quadrupolar relaxation issues to worry about and we don t have to deal with any strange multiplicities. 

The kinetic information for NMR experiments is contained in the line broadening observed for a nucleus that resides in two different magnetic environments, and values for rate constants can be obtained using line-shape analysis.28,68,69 Line broadening experiments obtained using ID NMR is the method of choice when analyzing the kinetics of a molecule in two sites. 2D NMR techniques, such as 2D EXYS are employed when the kinetics are sequential, i.e. more than one step, or multiple sites are analyzed.69 For example in the case of supramolecular systems this technique was employed to measure the exchange kinetics in capsules.70... 

The exact nature of the epimerization is still not known. NMR studies are hampered by line broadening and multiplication due to frozen rotations in the Af,A-diisopropylcar-bamoyl group at the required low temperatures. Some indications were gained by a H NMR investigation of the temperature dependence of the kinetics in the epimerization of the (—)-sparteine and (—)-a-isosparteine complexes derived from 1-lithioinden-l-yl carbamates 295 and 296, carried out in cooperation with G. Fraenkel (equation 72, Table 7). These complexes are chemically stable above 0°C, and interpretable spectra were obtained. 

At intermediate exchange rates, the coupling manifests itself through line broadening or by actually giving multiple lines. If you look at the several spectra of ethanol in Figure 9-29, you will notice how the shape of the OH resonance varies from a broad singlet to a distinct triplet. 

In the definition of line broadening it is necessary to exercise some discrimination. On the one hand spectral linewidths of less them 0.17 cm-1 are observed for some of the vibronic bands of the lowest singlet system of benzene 1f 2 - -1diff in the vapor phase W, while on the other hand many electronic spectra have been encountered, in particular in higher excited singlet and triplet systems, for which few or no vibrational features are apparent. In crystal spectra at 4 K, linewidths as sharp as 0.5 cm-1 are often obtained for the lowest excited state of any multiplicity, despite coupling with the lattice modes, which may be expected to lead to considerable broadening. Nevertheless, these crystal linewidths are considerably more than the linewidths observed in the vapor phase and certainly more than the natural radiative widths. 

Answer Gaussian multiplication has been applied to the FID to improve the resolution. The line broadening (LB) was set to -1.0 Hz and the Gaussian maximum (GB) to 0.1. The resulting spectra have distorted lineshapes and intensities. If we attempt to enhance the resolution still further using a GB of 0.15 and an LB of -2.0 Hz, the spectrum becomes almost unrecognizable, as shown below. These parameters must be optimized for each spectrum, or even each signal. 

Processing Exponential multiplication with line broadening of 5-8 Hz gives acceptable line widths for lignin signals... 

Answer The data were Mated with an exponential multiplication [before Fourier transformation to improve the signal-to-noise ratio in the frequency spectrum ( 1.3.4). The line broadening parameter used was 1 Hz, forcing a rapid decay of the FID. This gives a greater. linewidth than is imposed by the field homogeneity and relaxation rates,... 

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