Hilckel theory

Let us now consider a pair of ions in aqueous solution from such a crystal. In the Debye-Hilckel theory it is assumed that in pure solvent, the mutual potential energy is — e2/ r, where e is the macroscopic dielectric constant of the solvent,2 until the ions come into contact with each... 

The best functions to use in the extrapolation can be determined from the dependence of 7+ and on the ionic strength. Theoretically, httle is known about the dependence of on concentration (6), but from the Debye-Hilckel theory, we should expect log 7 + to depend on with the dependence approaching linearity with increasing dilution. 

A second example is provided by a semiempirical correlation for multi-component activity coefficients in aqueous electrolyte solutions shown in Fig. 2. This correlation, developed by Fritz Meissner at MIT [3], presents a method for scale-up activity-coefficient data for single-salt solutions, which are plentiful, are used to predict activity coefficients for multisalt solutions for which experimental data are rare. The scale-up is guided by an extended Debye-Hilckel theory, but essentially it is based on enlightened empiricism. Meissner s method provides useful estimates of thermodynamic properties needed for process design of multieffect evaporators to produce salts from multicomponent brines. It will be many years before sophisticated statistical mechanical techniques can perform a similar scale-up calculation. Until then, correlations such as Meissner s will be required in a conventional industry that produces vast amounts of inexpensive commodity chemicals. 

The regioselectivity in radical addition reactions to alkenes in general has successfully been interpreted by a combination of steric and electronic effectsIn the absence of steric effects, regiochemical preferences can readily be explained with FMO theory. The most relevant polyene orbital for the addition of nucleophilic radicals to polyenes will be the LUMO for the addition of electrophilic orbitals it will be the HOMO. Table lO lists the HOMO and LUMO coefficients (without the phase sign) for the first three members of the polyene family together with those for ethylene as calculated from Hilckel theory and with the AMl semiempirical method. ... 

According to the Debye-Hilckel theory (Chapter XVII), A should bo 0.375 for all uni-univalent strong electrolytes in aqueous solution at 0 C x should be exactly 0.5 for all strong electrolytes. 

Using a model like that in Section 2.1.2.3, the extra conjugation for this kind of Z-substituted allyl anion will mix v 3 of the pentadienyl anion with ip2 of butadiene (Fig. 4.5). This also suggests that the terminus, the y carbon, ought to be the more nucleophilic site. Clearly this is not borne out in practice, but measurements of the total electron population agree with this result. The excess n charge, calculated from the 13C-NMR chemical shifts of the lithium dienolate 4.75, show that the charge on C-2, the a carbon, is approximately twice that at C-4.328 The simple version of Hilckel theory is inadequate for this problem. 

More sophisticated procedures involve taking the start MO coefficients from a semi-empirical calculation, such as Extended Hilckel Theory (EHT) or Intermediate Neglect of Differential Overlap (INDO) (Sections 3.13 and 3.10). The EHT method has the advantage that it is readily parameterized for all elements, and it can provide start orbitals for systems involving elements from essentially the whole periodic table. An INDO calculation normally provides better start orbitals, but at a price. The INDO calculation itself is iterative, and it may suffer from convergence problems, just as the ab initio SCF itself. 

C. A. Coulson, R. B. Mallion, and B. O Leary, Hilckel Theory for Organic Chemists (Academic Press, London, 1978). 

The cyclopentadienyl cation (5) was generated in a matrix and observed by ESR spectroscopy. Simple Hilckel theory predicts this species will have a triplet ground state with a symmetrical Dzt, geometry 5a, and this is confirmed by recent ab initio calculations the ESR spectrum of 5 in a matrix is in agreement... 

In the case of 6T little efforts have been done towards a band like description of the excitonic or the charge carriers, because in most cases disorder dominated the experimental data [30] (see below) and hence a band like description did not seem applicable. However, Siegrist et al. [103] applied an extended Hilckel theory to... 

---