Time-domain spectroscopy defined

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... 

With so many fields using Fourier analysis, the notation is varied and sometimes conflicting (Table 3.2 lists some of the notation). Interestingly, the infrared spectroscopy and mathematics notation arc completely opposite. Be-cau.se of this ambiguity, wc will define column 3 in Table 3.2 a.s the apodization domain because this is where the apodization is alwa s applied. For lack of a better tenn. we will refer to column 2 as the time domain. 

The electronic absorption spectra of complex molecules at elevated temperatures in condensed matter are generally very broad and virtually featureless. In contrast, vibrational spectra of complex molecules, even in room-temperature liquids, can display sharp, well-defined peaks, many of which can be assigned to specific vibrational modes. The inverse of the line width sets a time scale for the dynamics associated with a transition. The relatively narrow line widths associated with many vibrational transitions make it possible to use pulse durations with correspondingly narrow bandwidths to extract information. For a vibration with sufficiently large anharmonicity or a sufficiently narrow absorption line, the system behaves as a two-level transition coupled to its environment. In this respect, time domain vibrational spectroscopy of internal molecular modes is more akin to NMR than to electronic spectroscopy. The potential has already been demonstrated, as described in some of the chapters in this book, to perform pulse sequences that are, in many respects, analogous to those used in NMR. Commercial equipment is available that can produce the necessary infrared (IR) pulses for such experiments, and the equipment is rapidly becoming less expensive, more compact, and more reliable. It is possible, even likely, that coherent IR pulse-sequence vibrational spectrometers will... 

Parent radical cations derived from alkanes and alkyl chlorides can be directly observed in the nanosecond time domain by time-resolved spectroscopy such as laser flash photolysis and electron pulse radiolysis. Especially the latter one enables the direct ionization of the solvents independently on the optical properties of the sample and a well-defined electron transfer regime according to Eq. (2) or (3). Representative examples of the radiolyfic generation of solvent radical cations are given in Eqs. (4) and (5a) for the cases of 1-chlorobutane and -decane. ... 

The basic idea behind the DOSY concept is similar to the one behind multidimensional NMR. In 2-D NMR, a modulation in the phase or signal intensity with respect to a known time increment is recovered by inverse FT. In a DOSY experiment, the diffusion coefficient is recovered from the signal decay as a function of a diffusion increment by an ILT. In fact, the approximate ILT of the signal amplitude with respect to q, where q is defined as ygSf (t), yields the second dimension of the spectrum which correlates the chemical shift with the diffusion coefficient. Therefore, it was termed diffusion ordered spectroscopy (DOSY). However, unlike the FT of the time domain signal that yields a unique solution, ILT does not yield a unique solution. Therefore, several software packages were developed to overcome this problem. Readers interested in more details concerning the DOSY techniques can consult a recent extensive review on the subject [17]. 

In picosecond time-resolved Raman spectroscopy, the sample is pumped and probed by energetically well-defined optical pulses, producing a full vibrational spectrum over a 1000 2000 cm 1 window.207 One would expect vibrational spectroscopy to be restricted to the picosecond time domain and above by the Heisenberg uncertainty principle (Equation 2.1), because a 1 ps transform-limited pulse has an energy width of... 

Relaxation experiments were among the earliest applications of time-domain high-resolution NMR spectroscopy, invented more than 30 years ago by Ernst and Anderson [23]. The progress of the experimental methodology has been enormous and only some basic ideas of the experiment design will be presented here. This section is divided into three subsections. The first one deals with Bloch equation-type experiments, measuring and Tj when such quantities can be defined, i.e. when the relaxation is monoexponential. As a slightly oversimplified rule of thumb, we can say that this happens in the case of isolated spins. The two subsections to follow cover multiple-spin effects. 

On the basis of this, two-dimensional (2D) NMR spectroscopy experiments can be defined as experiments that involve one time domain for signal evolution (fi) and an additional time domain for detection and signal acquisition (t2) together with appropriate radio-frequency... 

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