Beyond Huckel theory

Computational Chemistry Using the PC, Third Edition, by Donald W. Rogers ISBN 0-471-42800-0 Copyright 2003 John Wiley Sons, Inc. 

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Fisher M and Levin Y 1993 Criticality in ionic fluids Debye Huckel Theory, Bjerrum and beyond Phys. Rev. Lett. 71 3826... 

Because of its severe approximations, in using the Huckel method (1932) one ignores most of the real problems of molecular orbital theory. This is not because Huckel, a first-rate mathematician, did not see them clearly they were simply beyond the power of primitive mechanical calculators of his day. Huckel theory provided the foundation and stimulus for a generation s research, most notably in organic chemistry. Then, about 1960, digital computers became widely available to the scientific community. 

In the Debye-Huckel theory, an ion in solution is treated as a conducting sphere. The distance of closest approach of two ions is a.4 The solution beyond a... 

It will be a pity if economic pressures and industrial competition force the adoption of approximate theoretical strategies before they have been properly assessed by comparison with rigorous ab initio results. These pressures, at present, appear to be being resisted and the best semi-empirical work [29,95] keeps its eye on the underlying fundamental theory. Probably the near-future will contain many more such semi-empirical calculations and, thereby, a body of information which can be used to make predictions (one is reminded of the role, years ago, of Huckel theory). In the long run, the useful species will likely be so large as to be beyond ab initio calculations. As well, the near-future will almost certainly see improved measurements. 

Ionic solutions are elegantly described by the Debye-Huckel theory, which is beyond the scope of this text. 

In 1923, the Debye-Huckel limiting law was derived and it has served as an excellent model for simple salts at very low concentrations. The limiting form of this theory can be derived in several ways which should also give correct results at moderate concentrations. The mathematics involved in proceeding beyond the... 

Going beyond solutions of electrolytes in water, several other possibilities need consideration electrolytes in nonaqueous solvents, nonelectrolytic behavior in solutions, and nonelectrolytes in nonaqueous solvents. None of the theories proposed for the quantitative prediction of solution behavior has been as successful as that of Debye and Huckel for dilute ionic aqueous solutions. Nevertheless, general trends can be predicted. 

The simplest model that goes beyond the Dehye-Huckel and GC theories of point ions and takes into account the finite size of ions is the soolled primitive model. Here, ions are described as simple hard spheres and the solvent is approximated hy a dielectric continuum. An even more special case is the soolled restricted primitive model, in which both ions have the same size. 

The criterion used to choose the topics covered in this book was their usefulness in application to problems in chemistry and biochemistry. Thus cluster expansion methods for a real gas, although very useful for the development of the theory of real gases per se, was judged not useful except for the second virial coefficient. Similarly, the statistical mechanical extensions of the theory of ionic solutions beyond the Debye-Huckel limiting law were judged not useful in actual applications. Some important topics may have been missed either because of my lack of familiarity with them or because I failed to appreciate their potential usefulness. I would be grateful to receive comments or criticism from readers on this matter or on any other aspect of this book. 

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