Non-bonding repulsion

As osmium forms a tetroxide, OsFg might possibly exist, especially in view of the existence of the osmium(VIII) oxyfluorides, but MO calculations indicate the Os—F bond would be weaker in the binary fluoride. It is also likely that non-bonding repulsions between eight fluorines would make an octafluoride unstable [23b],... 

Table 1. Block diagonalized G and F matrices for tetrahedral XY4 and octahedral XYn molecules, using the modified Urey-Bradley force field. Adapted from Nakmoto (1997). nix and nij are the masses of atoms ofX and Y, and r is the length of the X-Y bond. K, H, and are force constants for bond stretching, bond-angle bending, and non-bonded repulsion, respectively.

It can be rationalized both in terms of the electron-withdrawing effect caused by the pentavalent P s, and in addition, by the increased crowding of the P(III) site, resulting from non-bonding repulsions between the sulfur atoms and the methyl groups, with no means of apportioning these two effects. 

The argument is plausible when 1,2-diairyl substituents are present because of non-bonded repulsions between the aromatic systems. On the other hand, inspection of models of the l,2-dimethyl-2-norbomyl ion fails to reveal a similar barrier and it is doubtful if a steric argument permits a reasonable explanation of the data. Consequently, we believe that the data imply that a-participation is not only not strong enough to stabilize the symmetrically substituted ion relative to the classical tertiary species, but it would most probably be also too weak to stabilize the parent system. 

The third and by far the largest class is that of structures with more parameters than bond lengths. A calculation of the structure must now include a consideration of non-bonded distances, and in favourable cases might be expected to provide insight into the relative importance of the different kinds of non-bonded interactions in the crystal (mainly repulsions). Even here, caution must be exercised. In a number of cases it has been shown that non-bonded repulsions can be successfully simulated by the simple device of maximising the crystal volume subject to the constraint of fixed bond lengths . Only when this ploy fails will it be necessary to enquire more closely into the nature of interatomic forces. 

In the observed structure the two Zr-O distances are significantly different. The long bonds are in ZrOSiO rings allowing the short Zr... Si and O... O distances to increase, and it might be supposed that the occurrence of unequal Zr-O bonds arises from these non-bonded repulsions. 

These two structures have been described above (Sect. 2.6.3 and Sects. 2.8.1, 3.2) and are depicted in Figs. 16 and 29. We have already suggested (Sect. 4) that in forsterite (a-Mg2Si04, olivine type) the repulsive forces between O... O (d 2.6 A) are less than those between Mg... Mg (d = 3.0 A) which, in turn, are less than those between Mg... Si (d 2.7 A). One would therefore expect that in the phase transition a-Mg2Si04 (olivine) — y-Mg2Si04 (spinel) the principal result would be an increase in the last of these distances, in order to relieve the largest non-bonded repulsions . And this is indeed the case the mean non-bonded (next-nearest neighbour) distances are as shown... 

At the second level the question arises as to why such simple and well-known cation arrangements appear in oxides. It seems to us plausible that this is a consequence of important non-bonded repulsions between the cations. Om belief is that these are frequently greater than anion... anion repulsions. And certainly this is consistent with the observed regularity of the cation arrays - which is often greater than that of the anion arrays. (Good examples are provided by various olivines and humites, an extreme case being that of the chondrodite type 2Cd2Si04 Cd(OH)2 which is shown in Fig. 25.)... 

The boat-boat (417) and the twist-boat-boat (418) have low torsional strains but severe non-bonded repulsions, which, as usual, are transferred to internal angle strains. However, heteroatoms can modify these repulsions and certain transannular interactions can drastically reduce them. Even so, the boat-boat family is relatively unimportant as its energy is calculated to be quite high (12 kj mol-1) in cyclooctane. It probably serves as an intermediate for certain conformational interconversions of the boat-chair, especially when the twist-boat-chair pseudorotation itinerary is of high energy. In cyclooctane the boat-boat and its twisted partner have nearly the same energies and are not separated by a significant barrier. 

The effect of polar groups on the diimide reaction is sensitive to the configuration of the attached groups. For example, fumaric acid (trans) is ten times as reactive as maleic acid (els ) and the ratio of reactivities of the geometrical isomers of cinnamic acid, trans/cis. is 10 3 (ref. 21b). In comparison, cis- and trans-2-butene have almost identical reactivities. The difference may be explained by a change in the degree of advancement of the transition state towards the saturated product where the eclipsed conformation would result in a greater non-bonded repulsive interaction between the cis-substituents than the trans. 

Figure 5. Hydrogen-hydrogen non-bonded repulsion energies versus distance for MM2 (dotted line) and 6-12 (solid line) potential functions. The energies at 1.71 and 1.87 A are shown.

There are two types of solute-solvent interactions which affect absorption and emission spectra. These are universal interaction and specific interaction. The universal interaction is due to the collective influence of the solvent as a dielectric medium and depends on the dielectric constant D and the refractive index n of the solvent. Thus large environmental perturbations may be caused by van der Waals dipolar or ionic fields in solution, liquids and in solids. The van der Waals interactions include (i) London dispersion force, (ii) induced dipole interactions, and (iii) dipole-dipole interactions. These are attractive interactions. The repulsive interactions are primarily derived from exchange forces (non bonded repulsion) as the elctrons of one molecule approach the filled orbitals of the neighbour. If the solute molecule has a dipole moment, it is expected to differ in various electronic energy states because of the differences in charge distribution. In polar solvents dipole-dipole inrteractions are important. 

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