Multi-quantum transitions

Fig. 2.2.12 Spectrum (a) and energy level diagram (b) of two coupled spins j, A and X. The arrows indicate the orientation of the magnetic moments in the magnetic field. The continuous lines connecting the energy levels correspond to observable single-quantum transitions. The broken lines indicate forbidden multi-quantum transitions. The splitting of the resonance lines gives the strength 7ax of the interaction.

Multi-quantum transitions can only be observed indirectly by a modulation of the detected signal with the phase of the multi-quantum coherence. This modulation is achieved in an experiment by variation of an evolution time prior to detection. Repetitive detection of the signal for different evolution times provides the information about the evolution of the multi-quantum coherence. The indirect detection of spectroscopic information based on phase or amplitude modulation of the detected signal is the principle of multi-dimensional NMR spectroscopy [Eml]. Thus multi-quantum NMR is a special form of 2D NMR. Also, NMR imaging can be viewed as a special form of multi-dimensional NMR spectroscopy, where the frequency axes have been coded by the use of magnetic field gradients to provide spatial information. 

Formation of Intermediate N20 ( E+) Complex in Electronically Non-Adiabatic Channel of NO Synthesis. Estimate the maximum gas temperature To, when the formation of the intermediate N20 ( E+) complex proceeds as a multi-quantum transition and is determined by the vibrational energy of N2 molecules. Use relations (6-25) and (6-26) and estimate the probability of the multi-quantum transition. Explain why this mechanism is a preferred one in cold plasma-chemical systems. 

The pulse Fourier transform approach to magnetic resonance spectroscopy has been extensively developed and successfully applied to systems of one-half spin and their mutual interactions. But resonance spectroscopy of spin systems with the higher half- and integer spin quantum numbers is commonplace, for example, in the case of alkali metal nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) of transition metal compounds involving multi-quantum transitions. Similarly, magnetic resonance at zero field entails the observation of multi-quantum transitions. 

D. Collison, M. Helliwell, V.M. Jones, F.E. Mabbs, E.J.L. Mclnnes, P.C. Riedi, G.M. Smith, R.G. Pritchard and W.I. Cross, Single and double quantum transitions in the multi-frequency continuous wave electron paramagnetic resonance (cwEPR) of three six-co-ordinate nickel(II) complexes ... 

Formally, multi-quantum coherences of order p are described by irreducible tensor operators Tqp (cf. Table 3.1.2 for coupled spins [Eml]. The coherence order is described by p = mf-mi (cf. Fig. 2.2.11), where m and /n, are the final and initial magnetic quantum numbers of a transition. For double-quantum coherence, for example, p = 2. The total spin coherence q corresponds to the maximum order possible. In this case, p = q so that maximum coherence order is described by T,. 

Multi-quantum spectroscopy is important in solid-state NMR because it has several valuable advantages (1) it can be used to simplify a crowded spectrum because the higher the order of the transitions, the fewer in number they are (2) it can directly reflect structural and dynamic information because the creation of a high-order quantum transition requires many spins to evolve cooperatively (3) in some cases, multi-quantum decoupling is less demanding (4) the efiiect of a gradient field on an n-quantum transition (in spin-1/2 systems) is n times that of a single quantum transition. 

Treatment of angular momentum in a multi-quantum regime natiually benefits fi-om this operation. We applied this theorem to quantum operator Af(aPy), defined as cosa + M cosP +cosy, in which cos a, cos P, and cosy are direction cosines of Euler angles a, p, and y. The resultant eigenvalues of the angular momentum are independent of direction, but the projection matrices are dependent. The matrix for an angular momentum can therefore be resolved as a product of the transformation matrix with a direction cosine and an eigenfunetion matrix that corresponds to the transition. The projection matrix, after removal of information on direction, is an intrinsic density matrix. The proeedure to obtain... 

Multi dimensional quantum mechanical calculations are needed for the quantitative description of the effects discussed above. Rigorously stated, such calculations are very laborious. In this connection, considerable attention has been paid during the last two decades to the development of simplified methods for resolving the multi-dimensional problems. We refer, for instance, to the method of classic S-matrix [60] and the quantum-mechanical method of the transition state [61]. The advantage of these methods is the use of realistic potential energy surfaces the shortcoming is the fact that only... 

In order to get more detailed information about, e.g., bond strengths and equilibrium geometries in transition metal systems it is necessary to include electron correlation. This can be done either by traditional ab initio quantum chemistry models, e.g., Cl-methods and coupled cluster methods, or by density functional theory (DFT) based methods. Correlated ab initio methods are often computationally very demanding, especially in cases where multi-reference based treatments are needed. Also, the computational cost of these methods increases dramatically with the size of the system. This implies that they can only be applied to rather small systems. 

Multinuclear (isocyanide)gold complexes, reactivity, 2, 287 Multi-phase organometallic catalysis, in ionic liquids, 1, 856 Multiple-quantum MAS, half-integer spin quadrupolar nuclei central transition NMR studies, 1, 466 Multistate magnetization transfer, in dynamic NMR magnetization, 1, 410 Multistep catalytic cycles... 

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