A2B system

In Section 3.5 we discussed the simple, first-order system AX. As the ratio Av/J decreases, the two doublets approach each other with a characteristic distortion of peak heights to give an AB system, but no additional peaks appear. However, as an A2X system—a triplet and a doublet—develops into an A2B system, additional peaks do appear, and the system presents a higher order spectrum the J values no longer coincide with the measured differences between peaks [see simulated spectra in Bovey (1988) and in Wiberg and Nist (1962)]. 

We know from Section 6.7 that the true wave function i/q,. . . , t/r4 are linear combinations of the basis functions. If we begin with symmetrized functions, such as and then each of the ip s can be formed exclusively from symmetric functions or exclusively from antisymmetric functions. Stated another way, functions of different symmetry do not mix. The result is that, like the situation with Fz, many off-diagonal elements of the secular equation must be zero, and the equation factors into several equations of lower order. We shall study an example of this factoring in Section 6.13, when we consider the A2B system. 

As in the ABC case, the basis functions divide into four sets according to fz with 1,3, 3, and 1 functions in each set. However, of the three functions in the set with fz = % or — V2 two are symmetric and one antisymmetric. Hence each of the two 3X3 blocks of the secular equation factors into a 2 X 2 block and 1X1 block. Algebraic solutions are thus possible. Furthermore, the presence of symmetry reduces the number of allowed transitions from 15 to 9, because no transitions are allowed between states of different symmetry. (One of the nine is of extremely low intensity and is not observed.) Thus the A2B system provides a good example of the importance of symmetry in determining the structure of NMR spectra. 

Like in the past, most of the data on the QEC effect involve this class of the metal hydrides. The NMR formalism used in the description of the coherent and stochastic dynamics in the trihydrides is a phenomenological generalization of that describing the two-particle case. In consistence with the spirit of the semiclassical AB theory, the dynamics in the two two-particle subsystems (of which either engages the nucleus in the centre) are assumed to be independent. In the trihydrides, the central hydride atom lies in the molecular symmetry plane such that the three hydride nuclei form an A2B system. Therefore, the pertinent line shape equation has the form... 

Adenosine is produced by many tissues, mainly as a byproduct of ATP breakdown. It is released from neurons, glia and other cells, possibly through the operation of the membrane transport system. Its rate of production varies with the functional state of the tissue and it may play a role as an autocrine or paracrine mediator (e.g. controlling blood flow). The uptake of adenosine is blocked by dipyridamole, which has vasodilatory effects. The effects of adenosine are mediated by a group of G protein-coupled receptors (the Gi/o-coupled Ai- and A3 receptors, and the Gs-coupled A2a-/A2B receptors). Ai receptors can mediate vasoconstriction, block of cardiac atrioventricular conduction and reduction of force of contraction, bronchoconstriction, and inhibition of neurotransmitter release. A2 receptors mediate vasodilatation and are involved in the stimulation of nociceptive afferent neurons. A3 receptors mediate the release of mediators from mast cells. Methylxanthines (e.g. caffeine) function as antagonists of Ai and A2 receptors. Adenosine itself is used to terminate supraventricular tachycardia by intravenous bolus injection. 

Extracellular adenosine acts through a class of G protein-coupled receptors (GPCRs), defined across mammalian species as Ab A2a, A2B, and A3ARs (adenosine receptors). Adenosine has a cytoprotective role in the body, both in the periphery and in the central nervous system. Following binding of adenosine, or another naturally occurring agonist, the receptor... 

Two AR subtypes, Ax and A3, couple through G to inhibit adenylate cyclase, while the other two subtypes, A2a and A2B, stimulate adenylate cyclase through Gs or G0if (for A2a). The A2BAR is also coupled to the activation of PLC through Gq. Furthermore, each of these receptors may couple through the (3,y subunits of the G proteins to other effector systems, including ion channels and phospholipases. Levels of intracellular... 

Figure 6. Bending potential curves for the X2A1, A2B electronic system of BH2 [33,34]. Full hotizontal lines K = 0 vibronic levels dashed lines K = 1 levels dash-dotted lines K = 2 levels dotted lines K = 3 levels. Vibronic levels of the lower electronic state are assigned in bent notation, those of the upper state in linear notation (see text). Zero on the energy scale corresponds to the energy of the lowest vibronic level.

A2a adenosine receptors are highly expressed in the basal ganglia 314 A2b adenosine receptors regulate vascular permeability 314 A3 adenosine receptors are few in the central nervous system 314... 

Figure 1.1 (a) Chemical potential diagrams for systems forming a complete range of solid solutions. The tangent shows at its terminal points, X, Y the chemical potentials of the elements x and y which are in equilibrium with the solid solution of composition M (b) Potentials for the system A-B, which forms the two stable compounds the stoichiometric A2B and the non-stoichiometric AB2. The graph shows that there are many pairs of potentials A, B in equilibrium with A2B and only one pair for a particular composition of AB2 AB is metastable with respect to decomposition to A2B and AB2... 

Since the time of Flory, only a few papers have appeared in the hterature in which the kinetics of A2B condensation reactions are treated. A purely theoretical paper was recently pubhshed by Moller et al. where Flory s theory of AjjB polycondensations was expanded to describe the distribution of molecules containing arbitrary numbers of branching units [43]. In another paper, Hult and Malmstrom studied the kinetics of a reacting system based on 2,2-bis(hy-droxymethyljpropionic acid [44]. 

It is obvious that the projection operators for the different species have different numbers of terms in them. The HON species have 12 terms (3 x 2 ) while the A2B-type species have four terms, and the HDT+ isotopomer has only two terms. This results in different sizes of the spin-projected basis sets, and for this reason the properties obtained in this work are not precisely comparable between the A3, A2B, and ABC systems, although a very good idea of the trends may be obtained from the data in Table XVI. While all of the above are given in terms of the original particles, it should be noted that the permutations used in the internal particle basis functions are pseudo -permutations induced by the permutations on real particles. 

From the foregoing discussion, it is evident that a variety of isomers are possible for unsymmetrically substituted cyclophosphines P NMR spectra are informative for distinguishing between these isomers. For example, two isomers of the cyclic trimers cyclo-(PR)2(PR ) are observed. The symmetrical isomer with identical substituents on the same side of the ring exhibits an A2B spin system, whereas the asymmetric isomer gives rise to an ABC spin system (Figure 11.5) (see Section 3.4.3). 

Salts of hexafluorovanadate can be obtained by high temperature techniques or from solutions containing hydrofluoric acid. For instance, X-ray patterns and DTA were used for the characterization of 17 double fluorides obtained by solid state reactions in the systems VF3 + MF (M = Li, Na, K, Rb, Cs, Tl) and seven double fluorides in the systems VF3 + MF2 (M = Ca, Sr, Ba, Pb),296 and the lattice constants297,29s and magnetic properties298 of A2B[VF6] (A, B = Cs, Rb, Tl, K, Na, Li) were also reported. The structure of the high temperature j0 phase of Li3VF6 has been determined and compared with the cryolite-type stable a form. The vanadium atoms have an octahedral coordination.299... 

Salvatore et al. 1993). While the existence of the A2B adenosine receptor was anticipated from pharmacological data much earlier (Bruns 1980), the A3 subtype turned out to be an entirely new adenosine receptor which was initially identified as an orphan receptor in rat testis (Meyerhof et al. 1991). Later it was cloned from various tissue and species (Zhou et al. 1992 Salvatore et al. 1993 Linden et al. 1993 Hill et al. 1997). Expression in cellular systems revealed the unique pharmacological characteristics and species differences of the A3 adenosine receptor. For details about adenosine receptor subtypes see Fredholm et al. 2001a. 

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