Bond Orbital Mode

Low-energy bonding orbital In one mode, the orbitals interact favorably (with low energy) and together occupy a bonding orbital. 

The key geometric features of the optimized Pd-Cl bridging structures were found to nicely match those determined experimentally, and the presence of rather strong Cl-B interactions was substantiated by Natural Bond Orbital (NBO) analyses. For both complexes, rotation around the P— Pd bond allowed the location of another minimum devoid of any Cl-B interaction (B-pendant form, coordination mode E) (Figure 27). The two forms lie very close in energy (AG298 = 3-5 kcal), in agreement with the coexistence of the two coordination modes in solution. 

In addition to a relatively small inductive effect, two modes of stabilization of positive charge by the P-R3M substituent have been suggested. The first involves the classical cation 7, where the positive charge is stabilized by hyperconjugation (G-p conjugation) between the C-M o bonding orbital and the vacant carbocation... 

The special points method depends upon retention of the translational periodicity of a lattice, which is lost if we consider defects, surfaces, or lattice vibrations. (Even the special vibrational mode with frequency listed in Table 8-1 entailed a halving of the translational symmetry.) It is therefore extremely desirable to seek an approximate description in terms of bond orbitals, so that the energy can be summed bond by bond as discussed in Chapter 3. We proceed to that now. 

The important accomplishment in this section has been the reduction of the problem to the point where the energy can be computed bond by bond, either approximately, by the Bond Orbital Approximation, or more accurately, by in-eluding the bonding antibonding matrix elements in perturbation theory. It is not so important for the understanding of the uniform shears, but will be important in other properties. Before we can examine these, however, we must consider another mode of shear in the lattice. 

It is possible in principle to calculate all of these modes from the theory of the electronic structure, which is equivalent to the calculation of all the force constants. Indeed we will see that this is possible in practice for the simple metals by using pseudopotential theory. In covalent solids, even within the Bond Orbital Approximation, this proves extremely difficult because of the need to rotate and to optimize the hybrids, and it has not been attempted. The other alternative is to make a model of the interactions, which reduces the number of parameters. The most direct approach of this kind is to reduce the force constants to as few as possible by symmetry, and then to include only interactions with as many sets of neighbors as one has data to fit- for example, interactions with nearest and next-nearest neighbors. This is the Born-von Karman expansion, and it has somewhat surprisingly proved to be very poorly convergent. This simply means that in all systems there arc rather long-ranged forces. 

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