Multidimensional spectroscopy

Principles and Characteristics A new level of understanding is achieved when several analytical techniques are combined in a hyphenated approach. On the other hand, in a simple experiment in which spectroscopic analysis is performed as a function of time, concentration, or other additive properties, the output will be multidimensional, and a number of independent variables will determine its dimensions. If 

The separation of interactions by 2D spectroscopy can be compared with 2D chromatography. In a onedimensional thin layer or paper chromatogram, the separation of the constituents by elution with a given solvent is often incomplete. Elution with a second solvent in a perpendicular direction may then achieve full separation. In NMR spectroscopy, the choice of two solvents is replaced by the choice of two suitable (effective) Hamiltonians for the evolution and detection periods which allow unique characterisation of each line. 

Two-dimensional spectroscopy is a rather novel concept, and a powerful tool in analysing spectra. The advantages of generalised 2D correlation spectroscopy are  

Synchronous 2D correlation spectra represent coupled or related changes of spectral intensities, while asynchronous correlation spectra represent independent or separate variations [1007]. The 2D cross-correlation analysis enhances similarities and differences of the variations of individual spectral intensities, providing spectral information not readily accessible from ID spectra. 

Although the idea of generating 2D correlation spectra was introduced several decades ago in the field of NMR [1008], extension to other areas of spectroscopy has been slow. This is essentially on account of the time-scale. Characteristic times associated with typical molecular vibrations probed by IR are of the order of picoseconds, which is many orders of magnitude shorter than the relaxation times in NMR. Consequently, the standard approach used successfully in 2D NMR, i.e. multiple-pulse excitations of a system, followed by detection and subsequent double Fourier transformation of a series of free-induction decay signals [1009], is not readily applicable to conventional IR experiments. A very different experimental approach is therefore required. The approach for generation of 2D IR spectra defined by two independent wavenumbers is based on the detection of various relaxation processes, which are much slower than vibrational relaxations but are closely associated with molecular-scale phenomena. These slower relaxation processes can be studied with a conventional 

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W. W. Urban and T. Provder, eds.. Multidimensional Spectroscopy of Polymers Vibrational, NMR, and Tluorescence Techniques, American Chemical Society, Washington, D.C., 1995. 

The second development that has revolutionized the practice of NMR was the introduction of multidimensional spectroscopy. This was initialized by Jeener [2], who showed that, by introducing a second pulse and varying the time between them, a second time-axis could be constructed. A double Fourier transformation yields the familiar two-dimensional spectrum, nowadays known by everyone as the COSY spectrum. Ernst, already involved in the development of FT-NMR, showed that the concept was more generally applicable [3], and paved... 

The same logic can be applied in multidimensional spectroscopy, to decrease -noise in favourable cases -noise can be reduced by an order of magnitude, allowing weak cross-peaks to be detected [9]. The 2D experiments for which -noise poses the greatest problem are those which require strong signals to be nulled, either by phase cycling or by the use... 

JC Song, DC Neckers. In MW Urban, T Provder, eds. Multidimensional Spectroscopy of Polymers. ACS Symposium Series 598. Washington, DC American Chemical Society, 1995, p 472. 

Thus, using very sophisticated spectral resolving techniques, one can obtain important structural information on coal. Hence, multiple pulse/multidimensional spectroscopy offers an exciting new analytical tool for the study of complex materials such as coal and coal macerals. 

In resonant infrared multidimensional spectroscopies the excitation pulses couple directly to the transition dipoles. The lowest order possible technique in noncentrosymmetrical media involves three-pulses, and is, in general, three dimensional (Fig. 1A). Simulating the signal requires calculation of the third-order response function. In a small molecule this can be done by applying the sum-over-states expressions (see Appendix A), taking into account all possible Liouville space pathways described by the Feynman diagrams shown in Fig. IB. The third-order response of coupled anharmonic vibrations depends on the complete set of one- and two-exciton states coupled to thermal bath (18), and the sum-over-states approach rapidly becomes computationally more expensive as the molecule size is increased. 

In this chapter we surveyed the theoretical analysis of resonant multidimensional spectroscopies generated by the interaction of 3 fs pulses with a Frenkel exciton system. Closed expressions for the time-domain third-order response function derived by solving the NEE are given in terms of various exciton Green functions. Alternatively, the multidimensional time-domain signal can be calculated starting from the frequency domain the third-order... 

In the characterization of multidimensional spectroscopy by Ernst et al. (1987), the different classes may be termed separation, correlation and exchange respectively. The DOSY and MOSY experiments represent a type of separation spectroscopy in which the independent chemical shift and mobility information can be independently displayed. In the next section we describe an example involving exchange spectroscopy. 

In this section, we will consider the use of multidimensional spectrometers as chromatography detectors. In multidimensional spectroscopy, the spectral intensity is a function of more than one spectral parameter. For exaiaple, detection by means of fluorescence is inherently t% o dimensional because the observed intensity is a function of two variables, wavelength of emission and travelength of excitation (15). Other examples of two dimensional spectroscopy aret MS IS ( ) and the v u ious types of two dimensional NMR ei riments (36). Appellof and Davidson... 

While the main recent advance in NMR has been the development of multidimensional spectroscopy, novel catalytic applications include in situ studies and two-dimensional (2D) solid-state techniques such as correlation spectroscopy, spin diffusion, and quadrupole nutation. Completely new techniques have appeared, such as multiple-quantum spin counting, and old ones have developed in quite unexpected directions. For example, cross-polarization, a 20-year-old experiment, has recently been applied to quadmpolar nuclei to yield important new information on heterogeneous catalysts. Magic-angle spinning (MAS) of quadru-polar nuclei has been extended to methods in which the sample is spun about two different angles either simultaneously or sequentially (DOR and DAS). These experiments have been made possible by the significant advances in NMR instrumentation in the last decade. 

A distinct feature of NMR spectroscopy, the possibility to simultaneously observe hundreds of atoms in complex macromolecules, finds its foundation in the invention of multidimensional experiments almost 40 years ago [1,2]. The approach, however, has an important caveat the ultimate resolution obtained in multidimensional experiments comes at a very high price, the long data collection times needed to systematically sample the large multidimensional spectral space. The number of measured data points increases polynomially with the spectrometer field and the desired spectral resolution, and exponentially with the number of dimensions. The problem of lengthy sampling compromises or even prohibits many applications of multidimensional spectroscopy in chemistry and molecular biology. Fortunately, the advent of fast NMR spectroscopy offers a number of solutions. 

The initial idea of generating two-dimensional correlation spectra was introduced several decades ago in the field of NMR spectroscopy [13-16]. Since then, numerous successful applications of multidimensional resonance spectroscopy techniques have been reported, including many different types of studies of polymeric materials by 2D NMR [17 19]. Flowever, until now the propagation of this powerful concept of multidimensional spectroscopy in other areas of spectroscopy, especially vibrational spectroscopies such as IR and Raman, has been surprisingly slow. 

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