In-plane coordination

X andy axes represent the in-plane coordinates ( figure Bl.5.5). 

The stress-strain relations in arbitrary in-plane coordinates, namely Equation (4.5), are useful in the definition of the laminate stiffnesses because of the arbitrary orientation of the constituent laminae. Both Equations (4.4) and (4.5) can be thought of as stress-strain relations for the k layer of a multilayered laminate. Thus, Equation (4.5) can be written as... 

In fact, in addition to the usual strong N2CuS in-plane coordination [Cu-N(His46) Cu-N(Hisl 17) Cu-S(Cysl 12)], in axial positions there are either the usual weak fourth Cu-S bond [Cu-S(Metl21)], or an... 

There is another fundamental difference between solid and liquid surfaces. Crystals can respond differently in different directions when increasing the surface area. As a result the number of equations increases by a factor of two as we have to consider contributions for the two in-plane coordinates separately. 

Vlv in VO-NaY shows anisotropic and eight equally spaced hyperfine ESR splittings indicative of V,v in a square pyramidal configuration. Upon coordination with bpy the in-plane coordination becomes more covalent, while V=0 shows decreased covalency. All this is evidence for the existence of square pyramidal VO(bpy)2 complexes with tetragonal planar distortion. 

It is evident from all the experimental results that the cataljftic activity is closely associated with remarkable lability and regioselective reactivity of the in-plane coordination sites in the Pt4 clusters owing to a trans effect from the Pt—Pt bonds (see Section II,A-C). 

Some crystal structures of chelate complexes have been reported. An O-acryloyl-lactate-TiCU complex (Fig. 3) [26,27] has rare out-of-plane (Fig. 4) coordination of the acryloyl carbonyl group to the titanium a further study has been conducted [28]. Diethyl phthalate-TiCU [29], l,2-diketone-TiCl4 [25], and achiral [24] or chiral [30] acyloxazolidinone-TiCU complexes have been reported to involve in-plane coordination as shown in Fig. 5. The /S-alkoxyketone-TiCU complex shown in Fig. 6 [31] is characterized by a rare out-of-plane coordination geometry (dihedral bond angle of... 

Ti-0-C3-C4 = 57.6 °). This out-of-plane coordination was proved by NOE experiments to persist in solution. Treatment of the diastereomeric /8-alkoxyketone with TiCU generates the titanium chelate with in-plane coordination geometry (Eq. 1) [31]. NMR study of these out-of-plane and in-plane complexes of the j8-alk-oxyketones revealed that the titanium portion in the former complex acts as a stronger Lewis acid than that of the latter [31,32]-... 

If the alkenyl (aryl) residue and alkene ligand on palladium are in a cis orientation, rotation of the alkene can lead to its in-plane coordination, and subsequent syn insertion of... 

Another important issue for liquid/crystal interfaces is their roughness. It was shown in [8] that treatment of fluctuations in the interfacial width as a function of in-plane coordinates permits calculation of the stiffness for various interfaces, which can be used for calculations of the anisotropy of interfacial... 

Marchelli used RP-HPLC to separate D,L-amino acids and dansylated amino-acids by adding Cu11 terdentate complexes as shown to the mobile phase, forming the three in-plane-coordinated complex, dominant between pH 6 to 9.60... 

Figure 4 Maps of the average density of nitrogen adsorbed in three nanotube bundles. The contours are for constant density in the x, y planes i.e., for an observer looking in the z direction parallel to the pore axes. The pore diameters are (a) 1.37mn, (b) 1.43 nm, and (c) 0.69 nm. The in-plane coordinates x, y are defined so that unit x, y= 0.07, 0.14 run, respectively. The larger blobs show density contours inside the tubes and the smaller ones are for molecules adsorbed in the interstices between the hexagonally packed tubes. The interaction potential for the Nj is diatomic thus, the approximate molecular length is 0.1 run greater than the width which is 0.35 nm. The consequence is that the tube of (c) is too small to admit the N2 molecules so that the adsorption shown there is essential all interstitial. Also, in (a) and (b), the N2 appears to lie parallel to the tube axis and is adsorbed on the tube walls. The differences between the (a) and (b) contours are at least partly due to the differences in the numbers of molecules in these systems. These amount to 334 and 199 in (a) and (b).

Figure 4.34. A plot of the average walklength n) j versus the total number of lattice sites for a three-layer lattice subject to confining boundary conditions with the reaction center placed at the centrosymmetric site of the lowest (basal) layer. Displayed here are results for lattices of in-plane coordination v = 3 (circles) and v = 6 (triangles).

Reaction of the pentadentate bispidine-based systems with H2O2 in methanol at low-temperature yields a purple solution of the low-spin iron(III) end-on hydroperoxo complexes that of the isomer with an in-plane coordination of the hydroperoxide is, as expected, considerably more stable than that with an axially coordinated substrate. Deprotonation to the end-on high-spin peroxo complex (seven-coordinate) is reversible for the more stable isomer, with a p T value of... 

To proceed further, one can consider the displacements u = u x, y) and v = v(x, y), which are functions only of the in-plane coordinates x and y in two-dimensional problems. It can be readily shown that the displacements are related to the strains through the following relationships ... 

Planar coordination compounds with aromatic ligands (Fig. 42), especially those having extended 77 systems, show 77-77 interaction in solid states. In alkene or alkyne 77-bonded Cud) complexes, in-plane coordination ofaC = CorC = C bond to trigonal planar Cu(I) centers often leads to planar molecular conformations (167-171). The infinite 77-77 stacking columns are confirmed in the 2,2 -bipyridine (L55) com-... 

The development of stresses in the scale is caused by various mechanisms which are briefly considered in the following. The relation between the stress, elastic strain, 8el, within the alumina scale is given by the Hooke s law. The elastic properties of the polycrystalline scale are assumed to be isotropic with E0 as Young s modulus and i as Poisson s ratio. Because of the free surface of the scale, a plane stress state in the scale is supposed with = 0. z is the direction perpendicular to the film plane, and x,v are the in-plane coordinates. The x-component of the stress tensor is then given by... 

It is clear that, if available, monocations such as potassium and sodium will be incorporated into a quadruplex. The potassium and ammonium ions are too large to be coordinated by a single G-quartet in a coplanar fashion. As a result, coordination of these ions occurs between two G-quartets planes. Each quadruplex involving n quartets will then accommodate n — 1) of these specific ions. For example, quantitative determination of ammonium peak intensity revealed that three NH4 ions are placed between four quartets. In contrast, the smaller Na" ion (ionic radius of 1.18 A) allows for in-plane coordination. Multiple Na" ions are therefore not restricted to the spacing between G-quartets, and can move further away form each other to reduce electrostatic repulsions. In any case, empty sites between quartets are probably very rare. In fact, although vacant coordination sites are likely to exist (as ions move between sites, see below), their lifetime must be very short as demonstrated, for example, by Federiconi et who determined a site occupancy of 0.97 K " ions per tetramer in GMP quadruplexes prepared in 0.5 M KCl. 

Figure 1 The G-quartet. A is shown coordinated in the plane of the quartet by the 06 oxygen atoms. The dashed circle represents the ionic radius of a, which is too large for in-plane coordination...

In order to describe the second-order nonlinear response from the interface of two centrosymmetric media, the material system may be divided into three regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic stmcture or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Formally, we can describe this sheet by a nonlinear dipole moment per unit area, which is related to a second-order bulk polarization by hy P - fr, y, z, f) = P, (.r. v, f Here z is the surface normal direction, and the X and j axes represent the in-plane coordinates (figure Bl. 5.5). 

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