Multiple quantum transitions

It has been pointed out that the central ( 2, transition does not experience any first-order quadrupole interaction. The absence of first-order broadening effects is a general property of symmetric (m, - m) transitions. There are cases where this can be a distinct advantage, the most direct instance being for integer spin nuclei (e.g. D and both 1=1) where there is no ( /2, — /2) transition. The main problem is to excite and detect such higher-order transitions, for which there are two separate approaches. The sample may either be irradiated and detected at the multiple quantum frequency (called overtone spectroscopy) or the MQ transition can be excited and a 2D sequence used to detect the effect on the observable magnetisation. 

Overtone spectroscopy developed for irradiates the sample at approximately twice the Larmor frequency (Tycko and Opella 1987). If the quadrupole interaction is sufficiently large that second-order quadrupole effects are significant, the (— 1 1) transition becomes weakly allowed. In powders the spectmm is still structured, allowing the interactions to be deduced, but is narrowed by a factor of 8vq/xq. 

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Multidimensional and heteronuclear NMR techniques have revolutionised the use of NMR spectroscopy for the structure determination of organic molecules from small to complex. Multidimensional NMR also allows observation of forbidden multiple-quantum transitions and probing of slow dynamic processes, such as chemical exchange, cross-relaxation, transient Over-hauser effects, and spin-diffusion in solids. 

Multiple quantum transitions (MQT) in ENDOR spectra may be observed for nuclei with I 1 if two or more (rf) photons of the same or of different frequencies combine to produce an ENDOR transition41,62,99"101). In a MQT the magnetic quantum number nij changes by An = n. The MQT should therefore be clearly distinguished from corresponding forbidden single quantum transitions (SQT) with Am] > 0 discussed in Sect. 3.3. 

During the last few years the versatility of ENDOR spectroscopy has been improved by a number of new techniques which make use either of special types of pumping fields (CP-ENDOR, PM-ENDOR), of more than one rf field (DOUBLE ENDOR, multiple quantum transitions, nuclear spin decoupling) or a different display of the spectrum (EI-EPR). In addition to these techniques, alternative methods have been developed (electron spin echo and electron spin echo ENDOR) which are able to supplement or to replace the ENDOR experiment under certain conditions. The utility of all these various advanced techniques, particularly in studies of transition metal compounds, has recently been demonstrated. 

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. 

Detection of multiple quantum transitions in c.w. experiments is well known. Extension to high order transitions is not promising, since the transitions observed are a sensitive function of r.f. field strength. This leads to difficult spectral simulations and experimental problems of saturation and sample heating. 

The alternative time domain experiment is the determination of multiple quantum transition frequencies by following the time development of multiple quantum coherences point by point.This work treats a class of such multidimensional... 

An important conclusion drawn from this equation is that the first-order quadrupolar interaction has no effect on symmetric transitions, namely on the single-quantum central transition (m=l/2 m =-l/2) and multiple-quantum transitions (m=3/2om =-3/2, (m=5/2 m =-5/2,...). The first-order quadrupolar interaction affects the satellite transitions, m= l/2 m = 3/2... 

Connectivity information and spectral editing may be performed by combining crosspolarization (CP) and MQMAS. These include direct CP from a spin-j to the quadrupolar spin and subsequently its detection with MQMAS scheme. CP can be performed by polarizing either the CT of the quadrupolar nucleus followed by an inverse split- MQMAS scheme, allowing the incorporation of FAM pulses,or by directly polarizing the multiple-quantum transitions during the CP contact time. ° °... 

A. Pines, D. J. Ruben, S. Vega, and M. Mehring, New approach to high-resolution proton NMR in solids deuterium spin decoupling by multiple-quantum transitions, Phys. Rev. Lett. 36, 110-113 (1976). 

In NMR spectroscopy we tend not to use this approach of thinking about energy levels and the transitions between them. Rather, we use different rules for working out the appearance of multiplets and so on. However, it is useful, especially for understanding more complex experiments, to think about how the familiar NMR spectra we see are related to energy levels. To start with we will look at the energy levels of just one spin and them move on quickly to look at two and three coupled spins. In such spin systems, as they are known, we will see that in principle there are other transitions, called multiple quantum transitions, which can take place. Such transitions are not observed in simple NMR spectra, but we can detect them indirectly using two-dimensional experiments there are, as we shall see, important applications of such multiple quantum transitions. 

There are three more transitions which we have not yet described. For these, M changes by 1 but all three spins flip they are called combination lines. Such lines are not seen in normal spectra but, like multiple quantum transitions, they can be detected indirectly using two-dimensional spectra. We will also see in section 2.6 that these lines may be observable in strongly coupled spectra. The table gives the frequencies of these three lines ... 

Some of the stable states are clearly regular. These include some extreme motion adiabatic states, discussed previously, that have no direct coupling to the doorway channel. In order to decay, such states must undergo multiple quantum transitions (often as many as 10), until they diffuse to the doorway channel. Figures 21 and 22 show that many of the adiabatic states are very resistant to diffusion and serve as bottlenecks for dissociation. 

Frequencies of several single- and multiple-quantum transitions ... 

We should, finally, mention also the possibility to Indirectly detect resonance l2X. 2H experiments. A 2D experiment invariably involves two variable time periods (i)(see Fig. 7). During the initial "evolution period" the w.j-information is acquired by the nuclear spins and "stored" in the form of phase or amplitude information which is read out and recorded during the detection period together with the (02-lnformatlon. The indirect detection of the U3. -information permits the study of otherwise inaccessible properties. This feature can be utilized to indirectly observe resonance of low sensitivity nuclei (2JJ and of forbidden transitions (2 3S 35j, i. . multiple quantum transitions and combination lines. In this respect 2D spectroscopy really provides novel information. In particular zero quantum transitions, l.e. transition between energy levels of equal magnetic quantum number had never been observed before (35J(see Fig. 8). 

As a last example of NMR of solids the recent work of Pines and co-workers must be mentioned. They have shown that use of multiple quantum transitions and cross-polarization, magic... 

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