Other Quantitative Descriptions of Molecular Structure

SECTION 1.8. OTHER QUANTITATIVE DESCRIPTIONS OF MOLECULAR STRUCTURE 

In acyclic structures, such effects are averaged by rotation, but in cyclic structures differences in C—H bond strengths based on the different alignments can be recognized. The C—H bonds that are in an anti orientation to the lone pair are weaker than the C—H bonds in other orientations. 

The examples that have been presented in this section illustrate the approach that is used to describe structure and reactivity effects within the framework of MO description of structure. In the chapters that follow, both valence bond theory and MO theory will be used in the discussion of structure and reactivity. Qualitative valence bond terminology is normally most straightforward for saturated systems. MO theory provides useful insights into conjugated systems and into effects that depend upon the symmetry of the molecules under discussion. 

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Polymer products synthesized in laboratories and in industry represent a set of individual chemical compounds whose number is practically infinite. Macro-molecules of such products can differ in their degree of polymerization, tactici-ty, number of branchings and the lengths that connect their polymer chains, as well as in other characteristics which describe the configuration of the macromolecule. In the case of copolymers their macromolecules are known to also vary in composition and the character of the alternation of monomeric units of different types. As a rule, it is impossible to provide an exhaustive quantitative description of such a polymer system, i.e. to indicate concentrations of all individual compounds with a particular chemical (primary) structure. However, for many practical purposes it is often enough to define a polymer specimen only in terms of partial distributions of molecules for some of their main characteristics (such as, for instance, molecular weight or composition) avoiding completely a... 

Even today, however, it is not a simple task to obtain chemical pictures at the transition state (TS) or along a reaction path. Discussion on the nature of TS is, for instance, often conducted using other features such as molecular structures and energy profiles rather than the wave functions themselves if the bond length at TS is closer to that of the product than reactant, it is called a late TS, or if the reaction is highly exothermic, this reaction is assumed to proceed via an early TS. These discussions are qualitative and ambiguous. A more quantitative and clear-cut chemical description is necessary. 

As with other schemes of partitioning the electron density in molecules, Mulliken population analysis is arbitrary and is strongly dependent on the particular basis set employed. However, the comparison of population analyses for a series of molecules is useful for a quantitative description of intramolecular interactions, chemical reactivity and structural information. In another approach, the Lowdin population analysis, the atomic orbitals are first transformed to an orthogonal set, as are the molecular orbital coefficients [Lowdin, 1970]. 

A quantitative treatment of the Jahn-Teller effect is more challenging (46). A major issue is that many theoretical models explicitly or implicitly assume the Bom—Oppenheimer approximation which, for octahedral Cu(II) systems in the vibronic coupling regime, cannot be correct (46,51). Hitchman and co-workers solved the vibronic Hamiltonian in order to model the temperature dependence of the molecular structure and the attendant spectroscopic properties, notably EPR spectra (52). Others, including us, take a more simphstic approach (53,54) but, in either case, a similar Mexican hat potential energy description of the principal features of the Jahn-Teller effect in homoleptic Cu(II) complexes emerges (Fig. 13). 

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