Overlap forces

The asymmetric induction that has been observed in this reaction can be explained in terms of the model shown in Scheme 9. In the most stable conformation the appropriately positioned phenyl group shields selectively the Re,Re face of the chromadiene by 7r,7r-orbital overlap forcing the nucleophile to attack preferentially on the opposite side. 

In fact, the origin of the (8-N) rule resides in the delicate balance between the repulsive overlap forces and the attractive covalent bond forces. The bond lengths are not invariant as drawn in Fig. 8.1, since the atoms do not behave as hard spheres with fixed nearest-neighbour distances. Assuming a repulsive pair potential... 

The discussion about the possible presence of a small contribution of d-n overlap forces at the surface of NiO is of interest because it may occur with Ni2+ interacting with adsorbates with r-acceptor characteristics, such as CO, NO (Section IV.I.2), and O2. IR spectra of O2 adsorbed at 77 K on progressively sintered NiO sampels (274) follow a trend similar to that observed for CO. In particular, on high-surface-area samples, O2 species formed at edge, step, and corner sites are predominant, whereas on progressively more sintered samples neutral species adsorbed in side-on configuration on Ni2+ of the (001) faces become the only species detectable by IR spectroscopy. 

The calculated frequencies are in satisfactory agreement with the experimental values for the (0112) and (1120) faces. This result again indicates that the Cr3+ CO bond is mainly electrostatic in nature (even if a minor contribution of chemical overlap forces is present). 

These results mean that the surface ions are located on the silica surface in at least three different local environments (in approximate agreement with the picture illustrated in Fig. 37). The frequencies of the D(CO) stretching modes (all higher than that of the CO gas) are similar to those observed for CO on ZnO thus, electrostatic and a-type overlap forces are mainly involved. Most likely, the electrostatic interaction prevails in the complexes absorbing at 2200 cnT1 (as expected for an ion carrying a charge of +3). 

When low-valent transition metal ions are involved (Ni2+, Co2+, and Cu+), d-n overlap forces become important, and the dynamic polarizability is greatly enhanced. In this case, the CO cannot be considered as a good probe of Lewis acid strength (the stretching frequency is close to or even less than that of CO gas). 

Body Overlap Forces to the Dynamical Matrix of Alkali Halides. 

For SFe, the measurements of Rosenberg and Bimbaum give a very small value of B, comparable to those obtained from atomic gas mixtures. By neglecting possible contributions from dipoles caused by overlap forces, and attributing all of to the effects of the hexadecapole moment, Rosenberg and Bimbaum calculate an upper limit of + 17 x 10 Cm for [Pg.52]

If valence is thought of as a measure of a bond s attractive force, it should, at equilibrium, be proportional to the repulsive overlap force between the atom cores. Not surprisingly, expressions that have been proposed for the repulsive component of interatomic forces are similar in form to Equations 10.1 and 10.2. Biirgi and Dunitz [16] have shown that Equation 10.1 can be derived from the Morse potential, and Brown and Shannon [8] have shown that the constant, W, in Equation 10.2 is related to the Born exponent [17]. 

A recently measured disjoining-pressure isotherm of an isolated lamella is shown in Figure 8 for the surfactant sodium dodecyl sulfate (SDS) at 10-3 kmol/m3 in aqueous 0.01 kmol/m3 sodium chloride brine (65). A solid line connects the data points for three independent experimental runs, shown by various symbols. The negative, attractive portion of the isotherm between thicknesses of about 4 and 5 nm is not sketched because equilibrium measurements are not possible there. The measured isotherm indeed obeys the classic S-shape. Film meta-stability demands that the slope of the isotherm be negative (2<5, 72). For positive slopes, even the slightest, infinitesimal disturbance ruptures the film. Thus, the lamella in Figure 8 can exist only along the two repulsive branches near 4 nm and above 7 nm. The thicker branch or common black film arises from electrostatic overlap forces, and the inner branch or Newton black... 

For the Li -H2 system, the Hartree-Fock interaction energy, which includes the effect of overlap forces, becomes comparable to that calculated from a perturbative treatment of the electrostatic (ion-quadrupole) and inductive (ion-induced-dipole) contributions when the interaction energy is O.l eV. In this case, however, the Langevin model may not even be used at thermal energies since the ion-quadrupole interaction energy is comparable to that due to the ion-induced-dipole interaction in the relevant range of separation ( SA). ... 

Carbonization is another PSM strategy. This approach fabricates porous carbon by thermal treatment of POFs with or without a template. In the carbonization process, chemical bond breaking accompanies the formation of a novel porous framework, as well as shrinking of the pore size. Generally, the carbonized porous material exhibits strong host-guest interactions due to the overlapped force field and the enhanced polarity. ... 

Confining ourselves to nearest-neighbour interactions for the overlap forces in the NaCl structure (Fig.4.4), we find from (4.22,23)... 

In the case shown in Figure 2a the chemical potential of the film, psxj, is the same as that in the 3D film phase under the same conditions. On the other hand, in the case where there are overlapping force fields originating from the two interfrices of the thin film (cf. Figure 2b), the chemical potential deviates from its value in the 3D phase. More precisely. 

The properties of the overlapping force fields may vary from one case to another depending on their origin. Consequently, the excess chemical potential, pex, can be influenced by forces underlying adsorption at the film surfaces, dispersion forces or electric forces acting between charged film surfaces. 

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