Single-quantum approach

Kg. 58. Multiple-quantum spectra of a 36mer RNA with correlations from the sugar protons into the bases. The enhancement of signal to noise using the multiple quantum (blue) approach as opposed to the conventional single quantum approach (red) is clearly put into evidence in... 

The present chapter has no ambition to cover all these topics. We focus solely on the information content of the two-pathway coherent control approach, where the energy-domain, single quantum states approach to the control problem simplifies the phase information and allows analysis at the most fundamental level. We regret having to limit the scope of this chapter and thus exclude much of the relevant literature. We hope, however, that this contribution will entice the reader to explore related literature of relevance. 

A system of adsorbed particles is often treated as a two-dimensional gas covering the adsorbent surface. Such an approach is quite justified and fruitful, as long as we are dealing with physical adsorption when the influence of the adsorbent on the adsorbate can be regarded as a weak perturbation. In case of chemical adsorption (the most frequent in catalysis), the concept of a two-dimensional gas becomes untenable. In this case the adsorbed particles and the lattice of the adsorbent form a single quantum-mechanical system and must be regarded as a whole. In such a treatment the electrons of the crystal lattice are direct participants of the chemical processes on the surface of the crystal in some cases they even regulate these processes. 

We shall proceed from a concept which in a certain sense is contrary to that of the two-dimensional gas. We shall treat the chemisorbed particles as impurities of the crystal surface, in other words, as structural defects disturbing the strictly periodic structure of the surface. In such an approach, which we first developed in 1948 (I), the chemisorbed particles and the lattice of the adsorbent are treated as a single quantum-mechanical system, and the chemisorbed particles are automatically included in the electronic system of the lattice. We observe that this by no means denotes that the adsorbed particles are rigidly localized they retain to a greater or lesser degree the ability to move ( creep ) over the surface. 

K itself the quantum numbers, then in a single-configuration approach they may be treated as exact quantum numbers as well. 

For configurations with one electron or hole above closed shells the moments of the spectrum are conditioned in the single-configuration approach by only one-electron spin-orbit interaction, and then the dimensionless quantities skewness jci and excess K2 (formulas (32.7)) as well as orbital quantum number and, therefore, do not depend on the accuracy of radial orbitals, namely,... 

The change in the chemical environment of a nucleus at the binding interface of a ligand-protein complex upon binding is likely to induce a change in chemical shift. This effect is used for example as a readout in the SAR by NMR approach to detect binding and thus identify lead molecules (33). Heteronuclear chemical shifts (particularly 13C and 15N) are widely used in such experiments and are detected via HSQC-type (heteronuclear single quantum correlation) experiments. 

In this article we approach the topic of coherent control from the perspective of a chemist who wishes to maximize the yield of a particular product of a chemical reaction. The traditional approach to this problem is to utilize the principles of thermodynamics and kinetics to shift the equilibrium and increase the speed of a reaction, perhaps using a catalyst to increase the yield. Powerful as these methods are, however, they have inherent limitations. They are not useful, for example, if one wishes to produce molecules in a single quantum state or aligned along some spatial axis. Even for bulk samples averaged over many quantum states, conventional methods may be ineffective in maximizing the yield of a minor side product. 

Other strategies that show great promise in reducing NMR acquisition time utilise methods to obtain multiple sets of data from one experiment through a concept known as time-shared evolution. An example of this process that should find utility in natural products elucidation was demonstrated by a pulse sequence called CN-HMBC.93 Traditionally, a separate 13C-HMBC and 15N-HMBC were acquired independently. However, the CN-HMBC allows both 13C- and 15N-HMBC spectra to be obtained simultaneously. By acquiring both data sets simultaneously, an effective 50% time reduction can be achieved.93 This approach has also been demonstrated for a sensitivity-enhanced 2D HSQC-TOCSY (heteronuclear multiple bond correlation total correlation spectroscopy) and HSQMBC (heteronuclear single quantum... 

The excitation and detection of multiple quantum transitions in systems of coupled spins offers, among other advantages, an increase in resolution over single quantum n.m.r. since the number of lines decreases as the order of the transition increases. This paper reviews the motivation for detecting multiple quantum transitions by a Fourier transform experiment and describes an experimental approach to high resolution multiple quantum spectra in dipolar systems along with results on some protonated liquid crystal systems. A simple operator formalism for the essential features of the time development is presented and some applications in progress are discussed. 

However, the classical approach should not be used for a quantitative interpretation of the experimental results for single-quantum vibrational predissociation. The classical process, which should show the correspondence with the quantiun one, is the cleavage of a bond under a condition when the quantum of energy transferred to this bond from a diatomic fragment, hQ, is much smaller than the dissociation energy, Ej, of the bond, i.e. h l . This condition does not contradict the classical limit,... 

Available methods and problems Describing the liquid phase - especially of complicated liquids such as ILs - is still a nontrivial task [21], Whereas gas phase properties of such substances might be accessible by making use of quantum chemical (QC) methods (i.e., electronic structure methods, see [2, 22]), involving one single molecule or ion pair in an isolated and static picture, most properties of the liquid state are not effectively captured by single molecule approaches of this sort, simply because of the neglect of temperature and environment as well as of the dynamics. 

A rigorous examination of the various MQ MAS sequences has been carried out with reference to sensitivity enhancement in the isotropic dimension and the lineshapes of the corresponding MAS peaks in the anisotropic dimension. An echo efficiency parameter has been defined as an indicator of the performance aspects of the various sequences. A consequence of the systematic analysis has been the combination of a spin-lock pulse for excitation of MQ coherences and an amplitude-modulated pulse for their conversion into observable single-quantum coherences. This approach has resulted in an improved performance over other sequences with respect to both the anisotropic lineshapes and the isotropic intensities. 

A new approach to combining CP with MQ MAS in a 2D NMR experiment has been demonstrated, involving CP from H to the single-quantum coherences of a quadrupolar nucleus.In two separate methods, pure-absorption line shapes have been obtained using a z-filter and a reversed split-ti method. 

A similar logic to that above applies to gradient selection in the HSQC experiment, for which a variety of different approaches are also possible [7]. A suitable sequence employing the echo-antiecho approach is illustrated in Fig. 6.10, and requires only two gradients in proportion to the magnetogyric ratios of the X and H spins since each acts on single-quantum X and H magnetisation. Thus, for a correlation experiment, ratios of 4 1 and... 

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