Second-spheres

In the fir.st iteration proces.s, the class values of the atoms of the structure. show information already known (the degree of the nodes). Hence Morgan takes the neighboring atoms into account. He considers the environment of an atom by summing class values of all directly adjacent atoms. This process results in a new class value called the extended connectivity (EC) value of the atom. The new EC value expresses indirectly the neighborhood of the adjacent atoms in a second sphere (Figure 2-43). 

The next highest numbered atom compared with the current atom (in this second. Sphere, atom 2) bccomc.s the current one. All unnumbered atom.s attached to the current atom are numbered serially according to their decreasing EC values. As in step 2, atoms with equivalent EC values are numbered serially following the specific rules. 

Fifty minutes later, a second sphere exploded, and a third sphere emptied itself through broken pipework. Three other butane spheres ruptured without creating any flying missiles. The village of Feyzin, 400 m (0.25 mi) from the blast site suffered widespread but minor blast damage. 

In the relative coordinate system in which the first sphere is at rest, a collision can occur only if the center of the second sphere lies within the collision cylinder" as shown in figure 9.6. Now, the volume of the cylinder is equal to b d4> db u 5t. Prom figure 9.6 it should be clear that... 

Second-sphere photochemistry and photophysics of coordination compounds. V. Balzani, N. Sab-batini and F. Scandola, Chem. Rev., 1986, 86, 319 (173). 

Here MX, Y designates an outer sphere or second sphere complex. There is every reason to suppose that formation and dissociation of MX, Y occurs at rates approaching the diffusional-control limit so that the slow conversion to MY is a negligible perturbation on the equilibrium of the first step. There is a similarity here the Langmuir, the Michaelis-Menten and the Lindemann-Hinshelwood schemes. 

In the case of the Na+ and K+ complexes of N9-ethyladenine-aza-18-crown-6, the metal ions exhibit different types of interaction at the minor groove site N3 (Fig, 14) (52). The Na+ complex, 6, shows a second-sphere interaction involving the coordinated H20 hydrogen bonding to N3 [Na-OH2 2.327, H0 N3 2.836 A], In contrast, the K+ complex, 7,... 

Fig. 14. Structures of (6), illustrating the second-sphere interaction with A-N3, and (7), showing the K1 A N3 binding. Reproduced with permission from Ref. (52). Copyright 2001, Royal Society of Chemistry.

The specific structure of [(H20)5Ni(py)]2+ was observed in the complexes with the second-sphere coordination of calix[4]arene sulfonate.715 There are two different [(H20)5Ni(py)]2+ cations in the complex assembly. In one the hydrophobic pyridine ring is buried in the hydrophobic cavity of the calixarene with the depth of penetration into the calixarene cavity being 4.3 A (Figure 9). The second independent [(H20)5Ni(py)]2+ cation is intercalated into the calixarene bilayer. 

Figure 2 The molecular dynamics simulation picture of [Gd(DOTA)(H20)] in aqueous solution shows the inner sphere water, directly bound to the metal (its oxygen is dark) the second sphere water molecules, bound to the carboxylates of the ligand through hydrogen bridges (their oxygens are gray) and outer sphere or bulk water molecules without preferential orientation (in white).

Phosphonate or carboxylate groups of the ligand are capable of tightly binding water molecules that cannot be treated any more using only translational diffusion. For such cases, a second sphere contribution (r nd) has to be added to the overall proton... 

Measurement of pH-dependent equilibria can also be used to identify coordination isomerization reactions in addition to stepwise dissociation, such as in the case of the iron(III) complex of exochelin MN (59). Here, a combination of spectrophotometric and potentiometric titration characterized multiple equilibria involving second-sphere protonation, coordination isomerization, and stepwise dechelation, and is illustrated in Fig. 8. 

Siderophore-ionophore supramolecular assembly formation via host-guest complexation of the pendant protonated amine arm of ferrioxamine B has been confirmed by X-ray crystallography (Fig. 28) (203). The stability and selectivity of this interaction as a function of ionophore structure, metal ion identity, and counter anion identity were determined by liquid-liquid extraction, isothermal calorimetry, and MS (204 -211). Second-sphere host-guest complexation constants fall in the range 103— 106M-1 in CHC13 and methanol depending on ionophore structure. 

Imagine a sphere of dazzling white brilliance above your head. Then, with an exhalation of breath, see a beam of white light descend and form another sphere of white light at the throat area. On an out-breath, see a beam descend from the second sphere to establish a third in your chest region. Continue the same process to build a fourth sphere in your... 

Most network structures involving crown ethers are simple hydrogen bonded chains where the crown forms second sphere coordination interactions with a complex ion. These are known for [18]crown-6, [15]crown-5 and [12]crown-4 hosts with a variety of metal complexes [17-25]. For instance when combined with the small [12] crown-4, the perchlorate salts of Mn(II), Ni(II) and Zn(II) form polymeric chain structures with alternating crown ethers and [M(H20)6]2+ cations [19]. Similarly the larger [18]crown-6 forms simple linear chains with metal complexes and cations such as fra s-[Pt(NH3)2Cl2] [20], [Cu(NH3)4(H20)]2+ (Fig.2) [21],and [Mg(H20)5(N03)] + [22],... 

The picture is much more complicated in the presence of slow-exchanging protons with different lifetimes (see Section II.A.3). In the hypothesis that the closest protons are exchanging with a very low rate, for instance, and second sphere water protons are fast-exchanging, the latter will provide the largest contribution to relaxation (for an example see. Section II. C). 

The smaller contribution to solvent proton relaxation due to the slow exchanging regime also allows detection of second and outer sphere contributions (62). In fact outer-sphere and/or second sphere protons contribute less than 5% of proton relaxivity for the highest temperature profile, and to about 30% for the lowest temperature profile. The fact that they affect differently the profiles acquired at different temperature influences the best-fit values of all parameters with respect to the values obtained without including outer and second sphere contributions, and not only the value of the first sphere proton-metal ion distance (as it usually happens for the other metal aqua ions). A simultaneous fit of longitudinal and transverse relaxation rates provides the values of the distance of the 12 water protons from the metal ion (2.71 A), of the transient ZFS (0.11 cm ), of the correlation time for electron relaxation (about 2 x 10 s at room temperature), of the reorienta-tional time (about 70 x 10 s at room temperature), of the lifetime (about 7 x 10 s at room temperature), of the constant of contact interaction (2.1 MHz). A second coordination sphere was considered with 26 fast exchanging water protons at 4.5 A from the metal ion (99), and the distance of closest approach was fixed in the range between 5.5 and 6.5 A. 

Interestingly, the reorientational time is about 2-3 times larger than expected for a hexaaqua ion. Indeed, the second sphere water molecules... 

The presence of second-sphere water molecules could be considered also for other metal aqua ions, like iron(III) and oxovanadium(IV) aqua ions, where the reorientational time is found to be longer than expected. However, in the other cases increases much less than for the chromium(III) aqua ion, thus suggesting that second-sphere water molecules are more labile, their lifetime being of the order of the reorientational time. 

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