Coherence Transfer Processes

Any pulse sequence that uses more than one excitation pulse make use of coherence evolution and coherence transfer. The coherence evolves due to chemical shift or scalar coupling while at the same time or in a different time period coherence transfer processes are generated or occur. The four normal coherence transfer processes are given in Table 

2 and according to [2.8 - 2.10] they must be categorized as either coherent and incoherent transfer processes. Coherent transfer processes rely on scalar (indirect) coupling interaction whereas incoherent processes are based on dipolar (indirect) coupling interaction or exchange among spins. The current version of NMR-SIM only permits calculations of coherent transfer processes. 

Coherent transfer processes induced by polarization transfer or cross polarization differ by the preparation pulse sequence as shown in Fig. 2.1 for a heteronuclear IS spin system. Using polarization transfer two RF pulses create antiphase coherence with the S spin retaining the antiphase coherence state whereas for cross polarization using two spinlock pulses, which obey the Hartmann-Hahn condition, in-phase coherence is generated for both the I and the S spins. 

Basic coherence transfer preparation sequence on a heteronuclear IS spin system (I = sensitive nucleus e.g. IH, S = insensitive nucleus e.g. l C) (a) by polarization transfer or (b) by cross polarization. 

The effect of the coherence transfer for an IS spin system can be summarized as follows  

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However, careful kinetic measurements on related systems showed the invalidity of wire-type behavior [41]. Furthermore, Sen and coworkers [42] recently showed that the appearance of rapid, long-distance charge transfer for metallointercalators may be an artifact caused by the formation of aggregates. Currently, there are no data that clearly support the existence of a coherent transfer process in DNA over a distance greater than one or two base pairs [43, 44]. 

A more general approach is required to interpret the current experiments, Jean and co-workers have developed multilevel Redfield theory into a versatile tool for describing ultrafast spectroscopic experiments [22-25], In this approach, terms neglected at the Bloch level play an important role for example, coherence transfer terms that transform a coherence between levels i and j into a coherence between levels j and k ( /t - = 2) or between levels k and l ( f - j - 2, k-j = 2) and couplings between populations and coherences. Coherence transfer processes can often compete effectively with vibrational relaxation and dephasing processes, as shown in Fig. 4 for a single harmonic well, initially prepared in a superposition of levels 6 and 7. The lower panel shows the population of levels 6 and 7 as a function of time, whereas the upper panels display off-diagonal density matrix ele-... 

It has been found that the short-range interaction model can be applied to study the vibrational relaxation of molecules in condensed phases. This model is applied to treat vibrational relaxation and pure dephasing in condensed phases. For this purpose, the secular approximation is employed to Eq. (129). This assumption allows one to focus on several important system-heat bath induced processes such as the vibrational population transition processes, the vibrational coherence transfer processes, and the vibronic processes. 

The rate constants of the vibrational coherence dynamics such as vibrational coherence transfer can be derived by using the same interaction model used in Eq. (130). For example, the rate constants of the vibrational coherence transfer processes from bv + 1 ->bv + 1 to bv -+bi/ and from bv —l 1 to bv ->bv are, respectively, given by... 

Figure Ila shows how an ideal cosine amplitude modulation of the RF carrier wave could be approximated by a rectangular RF pulse scheme, which is much easier to implement. Such a scheme comprises of pulses with alternating phases of 0° and 180° and is referred to as FAM. As was already mentioned, the modulation frequency should be tuned such that Vm matches tq, at least during part of the excitation. Due to the sample spinning, the quadrupolar splitting of many crystallites will pass through the v n value. It was shown that mismatches between and the powder i/qS do not create large phase distortions and simultaneous adiabatic and direct coherence transfer processes result in relatively pure MQ SQ transfers. By pure we mean that no significant phase dispersions are observed when looking at the transfer of each crystallite separately.

Figure 5.28. The coherence transfer process responsible for generating crosspeaks in correlation spectroscopy, illustrated for the Aj transition. Coherence of spin-A during ti of a 2D sequence becomes coherence of spin-X during t2, thus correlating the two spins in the resulting spectrum.

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 ... 

NMR-SIM is very powerful simulation tool based on a density matrix approach and is designed to make low demands on computer resources. The spin system parameters consist of a small basic set of spin parameters chemical shift, weak/strong scalar J coupling, dipolar coupling, quadrupolar coupling, longitudinal and transverse relaxation time. Currently the calculated coherence transfer processes are limited to polarization transfer and cross polarization. 

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. 

Two-dimensional Experiments. - Various modifications of the two-dimensional solid state NMR experiments have been proposed. Carravetta et al. have shown that in many cases, the commutation properties of the mixing Hamiltonian leads to selectivity in the allowed coherence transfer processes leading to enhanced resolution in the cross-peaks of 2D solid state NMR spectra. ... 

We performed an experiment to verify the atomic coherence transfer process with Rb. Fig. 22(b) shows a related level diagram of Rb. We choose the sublevels... 

These equations provide an introduction to the concept of coherence transfer, the process by which one coherence is transformed into another. In each case a component of -spin magnetization is transformed into /-spin magnetization. In the first equation the coherence transfer process, brought about by the second 90° pulse, is... 

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