Q’-C coordination

Ir(C02)(Q)(dmpe)2 (dmpe = bis(dimethylphosphino)ethane), isostructural with 3, reacts with ESOsMe to afford the methoxycarbonyl-Ir complex Ir(C02CH3)(Cl) (dmpe)2 [24]. Such reactivity provides evidence that the oxygen atoms of CO2 q -C-coordinated to a metal center are characterized by a significant nucleophilic character and can interact with electrophiles. 

It is interesting to note that in q -C-coordinated CO2 complexes the frequency splitting between the two v(OCO) stretching modes is often less than 400 cm , and, in end-on (q -OCO) complexes, the out-of-plane bending mode y(C=0), absorbing in the 650-500 cm range, shows a pronounced 0 effect, different... 

Since so (trans) < 0.005], it is possible to rule out a photosensitized isomerization mechanism involving the establishment of thermal equilibrium between 11-cis and all-trans forms during the lifetime of the triplet state. Also excluded is the quantitative population of a common minimum along the C q-C 2 torsional coordinate. This conclusion is consistent with recent studies (169,175) which, in variance with the previous investigation (171), have reported different T-T spectra upon excitation of all-trans and 11-cis retinal. 

Pyridines in their transition metal complexes coordinate as )] (N), q (C,C), (N,C), or q ligands (Figured). By far the most common coordination mode is (N), in which the lone electron pair on the nitrogen donates to a Lewis acidic metal center (see Lewis Acids Bases). The M-N bond lies in the plane of the pyridine ring (Figure 6). Few reactivity studies of (N) pyridine ligands have been reported. One of potential interest for HDN is the base-catalyzed exchange of the pyridine protons for deuterium... 

Let us draw a sphere, Cji, with the center at the origin of the Cartesian coordinate system and of a radi is R, big enough that domain Q belongs completely to the ball Oil bounded by the sphere Cg Q C Og (Figure 8-1). Applying inequality (8.112) to the difference field inside this ball, Og, we have... 

The important feature of qc p is that when a chain possesses one thermodynamically stable fold (or global minimum conformation), q p = 1 for all a and P while for a homopolymerlike collapsed globule, qap —> 1/N (indicating no stable folds or conformers). A third possibility can exist as well which typifies the spin-glass phase. The chain has numerous stable folds (or many low energy conformers). In this case, there exists a set of thermodynamically definite folds with coordinates, r, and q c = 1 when = f and q 1/N when. ... 

Competitive isotherms such as the Langmuir isotherm (Eq. 4.5) are represented by surfaces in a suitable space. The single-component isotherm is represented by a curve in the q, C) plane (see Chapter 3). Binary competitive isotherms are represented by two surfaces, one in the three-dimensional space qi, Ci, C2), the other one in the space q2, C, C2). Figure 4.1 shows an example of these plots [11]. These surfaces intersect, as is easy to show. Consider a vertical cylinder centered on the vertical axis of coordinates (Ci = 0, C2 = 0). This cylinder intersects the plane (Ci, C2) along a circle of radius C. It intersects the surface q C, C2) along a curve that decreases from qi (C, 0) to 0 when we move from the axis Ci to the axis C2 on the cylinder. In the same time, the intersection of the isotherm surface qiiCi, C2) is a curve increasing from 0 (on axis Cx) to q2(C, 0). These two curves intersect in one point of coordinates (Ci, C2). In this point we have... 

In the prolate case, the ellipsoidal coordinates (f, //) are related to circular cylindrical coordinates (r, z) by the transformation z = c cosh cos y and r —c sinh sin q. The coordinate surface / = /o (constant) defines the surface of a prolate spheroid, with major and minor semiaxes ao and bo given by... 

Now, if xCQ-ufoO) X (Q-u(ai°)) = 8(Q-u(aj0)) (Dirac s delta distribution) one gets (q u(ai°)) = 0, (q c(°) as one would formally expect. The difference is now apparent. The frame oq0 is related to the classical arrangement of sources and can be used to define frames helping describe the motion of the nuclear masses. But Q0 is defined with the nuclear framework. To use the nuclear coordinates for that task leads to problems as shown by Woolley and Sutcliffe [1 4 7 17]. 

Figure 7 The four steps in the application of the kinetic energy operator by the Fourier method (A - B - C - D) (lower panel) coordinate space (upper panel) momentum space. A is the original wave function i i(g). B represents the wave function in momentum space 4>(p) obtained by Fourier transform of ty(q). C is the application of the kinetic energy operator in momentum space. (p) = p2/2M ij>(p) where T = p2/2M is also shown. D is (<7) = h is the final...

Table 4 Effects of OSSE on average C1 NQR frequency differences of coordinated and free ort/jochlorines 2,6-dichlorophenolato(Q,C complexes of late transition metals (as compared to zinc complexes)...

C-C bond formation initiated from the square planar bis-o-vinyl complexes (6, 7 and 8) also proceeds through the three-centered transition state (Fig. 5). Upon metal-carbon o-bond breakage and reductive ehmination, the coordination vacancy becomes available at the metal center and a n-complexof buta-l,3-di-ene is formed. Double bond coordination (q -C=C) to the metal atom is preferred in this case, while the structure with central C-C bond coordination has an imaginary frequency corresponding to q -C-C—>q -C=C rearrangement. 

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