Extent Huckel Theory

Molecular mechanics and semiempirical calculations are all relativistic to the extent that they are parameterized from experimental data, which of course include relativistic effects. There have been some relativistic versions of PM3, CNDO, INDO, and extended Huckel theory. These relativistic semiempirical calculations are usually parameterized from relativistic ah initio results. 

Another policy in writing the book has been the attempt to base the deduction of all equations on first principles. What actually constitutes such principles is, to an extent, a matter of individual preference. Any attempt at definition would immediately lead one into the field of the professional philosopher. Such an intrusion the author is, above everything, anxious to avoid. Fie feels, however, that the attempt to build from the ground up has been accomplished in most of the subjects considered. Exceptions are, however, the extension of the Debye-Huckel theory, and the application of the interionic attraction theory to electrolytic conductance. In the latter case the fundamentals lie in the field of statistical mechanics, which cannot be adequately treated short of a book the size of this one, and which, in any case, would not be written by the author. 

Crystallographic measurements give sizes for unsolvated ions, and these vary considerably from ion to ion. But, in solution, most ions will be solvated and to differing extents. This is a problem which is not explicitly tackled by the simple Debye-Huckel theory. 

There have been attempts to modify Bjerrum s treatment to remove this arbitrariness, but none has been used universally to any great extent in the interpretation of experimental data. Nevertheless, despite this artificiality, the Bjerrum theory coupled with the Debye-Hiickel theory has proved a very useful and relatively successfiil tool in discussing electrolyte solutions. This success is especially noteworthy when the Bjerrum-Debye-Huckel theory is compared with the alternative approach of Guggenheim s numerical integration which gives similar results (see Section 10.13.1). Table 10.2 gives values of K ssoc for various charge types and for various values of a and q. 

It is found that in many cases experimental values of conductances do not agree with theoretical values predicted by the Onsager equation (see Equation (4.18)) and that mean ion activity coefficients cannot always be properly predicted by the Debye-Huckel theory. It was suggested by Bjerrum that, under certain conditions, oppositely charged ions of an electrolyte can associate to form ion pairs. In some circumstances, even association to the extent of forming triple or quadruple ions may occur. The most favourable situation for association is for smaller ions with high charges in solvents of low dielectric constant. Hence such phenomena occur to a usually small extent in water. 

Huckel s theory initiated a wealth of experimental work, all of which fitted with the prediction of enhanced stabilization in (4n + 2)7t-systems. The measure of variegated physical and chemical quantities (such as heats of combustion and hydrogenation, magnetic susceptibilities, electronic spectra and the proclivity to react in Diels-Alder reactions) was found to correlate with the extent of aromatic character, as estimated by the theoretical methods 86). 

The characteristic polynoxmal of the molecular graph and its zeros (i.e., the graph spectrum) are of considerable importance in theoretical chemistry. Their applications in Huckel molecular orbital theory are treated in detail in another chapter of this book. Attempts to use the coefficients of Cg(G) in chemical documentation [27,58] were unsuccessful [20] because of the existence of many Isospectrai graphs. The largest zero of Ch(G) has been proposed as a measure of the extent of branching in the corresponding molecule [59-61]. 

Clearly if Ya is unity then the solution is ideal. Otherwise the solution is nonideal and the extent to which ya deviates from unity is a measure of the solution s non-ideality. In any solution we usually know [A] but not either a a or Ya- However we shall see in this chapter that for the special case of dilute electrolytic solutions it is possible to calculate ya- This calculation involves the Debye-Hdckel theory to which we turn in Section 2.4. It provides a method by which activities may be quantified through a knowledge of the concentration combined with the Debye-Huckel calculation of ya- First, however, we consider some relevant results pertaining to ideal solutions and, second in Section 2.3, a general interpretation of Ya-... 

---