Spectroscopy time-domain experiments

It is important to note that the two electric fields that lead to a Raman transition can have different polarizations. Information about how the transition probability is affected by these polarizations is contained within the elements of the many-body polarizability tensor. Since all of the Raman spectroscopies considered here involve two Raman transitions, we must consider the effects of four polarizations overall. In time-domain experiments we are thus interested in the symmetry properties of the third-order response function, R (or equivalently in frequency-domain experiments... 

In the one-dimensional NMR experiments discussed earlier, the FID was recorded immediately after the pulse, and the only time domain involved (ij) was the one in which the FID was obtained. If, however, the signal is not recorded immediately after the pulse but a certain time interval (time interval (the evolution period) the nuclei can be made to interact with each other in various ways, depending on the pulse sequences applied. Introduction of this second dimension in NMR spectroscopy, triggered byjeener s original experiment, has resulted in tremendous advances in NMR spectroscopy and in the development of a multitude of powerful NMR techniques for structure elucidation of complex organic molecules. 

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... 

Since there are two time variables, i and h, to be incremented in a 3D experiment (in comparison to one time variable to increment in the 2D experiment), such experiments require a considerable data storage space in the computer and also consume much time. It is therefore practical to limit such experiments to certain limited frequency domains of interest. Some common pulse sequences used in 3D time-domain NMR spectroscopy are shown in Fig. 6.2. 

An important technical development of the PFG and STD experiments was introduced at the beginning of the 1990s the Diffusion Ordered Spectroscopy, that is DOSY.69 70 It provides a convenient way of displaying the molecular self-diffusion information in a bi-dimensional array, with the NMR spectrum in one dimension and the self-diffusion coefficient in the other. While the chemical-shift information is obtained by Fast Fourier Transformation (FFT) of the time domain data, the diffusion information is obtained by an Inverse Laplace Transformation (ILT) of the signal decay data. The goal of DOSY experiment is to separate species spectroscopically (not physically) present in a mixture of compounds for this reason, DOSY is also known as "NMR chromatography."... 

Scalar coupled experiments COSY and TOCSY The correlated spectroscopy (COSY) experiment is one of the most simple 2D-NMR pulse sequences in terms of the number of RF pulses it requires [32]. The basic sequence consists of a 90-C-90-acquire. The sequence starts with an excitation pulse followed by an evolution period and then an additional 90° pulse prior to acquisition. Once the time domain data are Fourier transformed, the data appear as a diagonal in... 

Every NMR experiment must have a preparation sequence (inducing the nuclei to resonate) and detection capability (finding out what happened). Two-dimensional NMR spectroscopy adds two more domains between preparation and detection. These are an indirect evolution time, q, and a mixing sequence (see Figure 3.15). The two dimensions of two-dimensional NMR spectroscopy are those of time. In one time domain, FIDs containing frequency and intensity information about the observed nuclei is collected. The second time dimension refers to the time that elapses between some perturbation of the system and the onset of data collection in the time domain. The second time period is varied, and a series of FID responses are collected for each of the variations. 

Ultrafast vibrational spectroscopy offers a variety of techniques for unraveling the microsopic dynamics of hydrogen bonds occurring in the femto- to picosecond time domain. In particular, different vibrational couplings can be separated in nonlinear experiments by measuring vibrational dynamics in real-time. Both coherent vibrational polarizations and processes of population and energy relaxation have been studied for a number of hydrogen bonded systems in liquids [1],... 

Fourier transform NMR spectroscopy, on the other hand, permits rapid scanning of the sample so that the NMR spectrum can be obtained within a few seconds. FT-NMR experiments are performed by subjecting the sample to a very intense, broad-band, Hl pulse that causes all of the examined nuclei to undergo transitions. As the excited nuclei relax to their equilibrium state, their relaxation-decay pattern is recorded. A Fourier transform is performed upon this relaxation-decay pattern to provide the NMR spectra. The relaxation-decay pattern, which is in the time domain, is transformed into the typical NMR spectrum, the frequency domain. The time required to apply the Hl pulse, allow the nuclei to return to equilibrium, and have the computer perform the Fourier transforms on the relaxation-decay pattern often is only a few seconds. Thus, compared to a CW NMR experiment, the time can be reduced by a factor of 1000-fold or more by using the FT-NMR technique. 

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