Coherence transfer description

For the description of correlation experiments throughout this review, the following conventions will be used The detected nucleus in a two- or three-dimensional experiment is written first and is followed by the other nuclei involved in any of the coherence transfer steps of an n-dimensional experiment separated by slashes. Notation in parentheses ( ) denotes an intermediate nucleus in a relayed correlation experiment this nucleus is actively involved in the coherence transfer sequence but its chemical shift is not sampled in a separate time domain. Notation in denotes additional nuclei that are not involved in the coherence transfer but decoupled during acquisition (usually ). 

The product operator approach comes into its own when coupled spin systems are considered such systems cannot be treated by the vector model. However, product operators provide a clean and simple description of the important phenomena of coherence transfer and multiple quantum coherence. 

In this chapter NMR-SIM is used to illustrate the theoretical principles of NMR spectroscopy instead of the more usual pure mathematical description. There are many textbooks, reviews and original papers in the literature dealing with the fundamentals of NMR spectroscopy and the reader is referred to them [2.1 - 2.7]. Alternatively the reader can use the list of references at the end of chapter 5 but these relate primarily to the pulse sequences discussed in that chapter. The design of any new experiment always starts with a formal analysis of the problem and an examination of the coherence transfer processes necessary to obtained the required information. The present chapter focuses on three items ... 

The detection of NMR signals is based on the perturbation of spin systems that obey the laws of quantum mechanics. The effect of a single hard pulse or a selective pulse on an individual spin or the basic understanding of relaxation can be illustrated using a classical approach based on the Bloch equations. However as soon as scalar coupling and coherence transfer processes become part of the pulse sequence this simple approach is invalid and fails. Consequently most pulse experiments and techniques cannot be described satisfactorily using a classical or even semi-classical description and it is necessary to use the density matrix approach to describe the quantum physics of nuclear spins. The density matrix is the basis of the more practicable product operator formalism. 

This condition follows directly from the energy-conserving delta function in (41) and from the prerequisite that F34, 2 =F 3, 2i- TTierefore in our description, up to second order in the perturbation expansion, only coherence transfer among near-resonant states is allowed. 

Finally, we consider the performance of the MFT method for nonadiabatic dynamics induced by avoided crossings of the respective potential energy surfaces. We start with the discussion of the one-mode model. Model IVa, describing ultrafast intramolecular electron transfer. The comparison of the MFT method (dashed line) with the quantum-mechanical results (full line) shown in Fig. 5 demonstrates that the MFT method gives a rather good description of the short-time dynamics (up to 50 fs) for this model. For longer times, however, the dynamics is reproduced only qualitatively. Also shown is the time evolution of the diabatic electronic coherence which, too, is... 

Let us begin with the one-mode electron-transfer system. Model IVa, which still exhibits relatively simple oscillatory population dynamics [205]. SimUar to what is found in Fig. 5 for the mean-field description, the SH results shown in Fig. 13 are seen to qualitatively reproduce both diabatic and adiabatic populations, at least for short times. A closer inspection shows that the SH results underestimate the back transfer of the adiabatic population at t 50 and 80 fs. This is because the back reaction would require energetically forbidden electronic transitions which are not possible in the SH algorithm. Figure 13 also shows the SH results for the electronic coherence which are found to... 

The transfer of spectral weight from low frequencies to high frequencies that accompanies the formation of pseudogap matter is the inverse of process in heavy electron materials by which at some onset temperature the itinerant coherent heavy electron state emerges out of the local moments that make up the Kondo lattice. It has recently proved possible to develop a two-fluid description that describes this emergent... 

Current transfer shifts both charge and momentum from donor to acceptor. We have reviewed time-dependent [38] and steady-state [39, 40] descriptions of current transfer through chiral bridges [36, 37]. In the tight-binding models, current transfer arises from coherent interferences between resonant or tunneling paths. This kind of interference has received attention in recent studies of molecular wires and nanodots [45-50]. 

With reference to the description of dipolar recoupling in the previous sections and our first presentation of these data in Ref. 70, we here demonstrate the applicability of optimal control theory for the design of dipolar recoupling experiments for transfer of coherence from N to which could involve typical and spin... 

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