Hiickel theory generalities

The regioselectivity in radical addition reactions to alkenes in general has successfully been interpreted by a combination of steric and electronic effects1815,47. In 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 10 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 Hiickel theory and with the AMI semiempirical method48. 

The following plot compares the Debye-Hiickel theory (dashed) with experiment (solid) for HC1 (circles) and H2S04 (triangles), showing the generally satisfactory agreement at... 

Slater-type orbitals were introduced in Section 5.2 (Eq. (5.2)) as the basis functions used in extended Hiickel theory. As noted in that discussion, STOs have a number of attractive features primarily associated with the degree to which they closely resemble hydrogenic atomic orbitals. In ab initio HF theory, however, they suffer from a fairly significant limitation. There is no analytical solution available for the general four-index integral (Eq. (4.56)) when the basis functions are STOs. The requirement that such integrals be solved by numerical methods severely limits their utility in molecular systems of any significant size. 

The contribution of electrostatic interactions to fast association was analyzed by applying the classical Debye-Hiickel theory of electrostatic interactions between ions to mutants of bamase and barstar whose ionic side chains had been altered by protein engineering (Chapter 14).16 The association fits a two-step model that is probably general (equation 4.84). 

The self-consistent generalization of Hiickel theory. Molecular orbitals in Chemistry, Physics, and Biology, edited by P.-O. Lowdin and B. Pullman New York Academic Press, 1964. 

From the papers of Lipscomb, Lohr, Hoflmann, et al. (7, 8, 9,10,11, 12) we first learned of their work on an extended Hiickel theory for polyatomic molecules. We also benefited from a visit to Harvard to discuss this work before their computer program became generally available. Our computer program is based on what we learned from them at that time and on our experience since then in applying it to our particular types of molecules. 

The only closed-shell fullerenes predicted by simple Hiickel theory fall into two types the leapfrog fullerenes Ceo+en (n 1), and the cylinders 70+30 and 34+36 (m > 0) formed by stretching Dsh-Cio and Da-C 4 along then-respective 5 and 5 axes. The simplicity of the theory unfortunately prevents these rules having any general utility. Neither of the two IPR-isomers of 75 is predicted to be stable but Z>2- 76 has been isolated, whereas the expected fiillerene Ded-Cji has not, although its apparent low stability may be... 

E is a linear function of The equations may be connected with the Debye and Hiickel theory of electrolytes. In the case of non-electrolytes (e.g. sucrose, urea) 0 Ez) is a linear function of c, not of and this result would be expected from the general theory of solutions. Jones, Taylor, and Vogel, however, found different slopes against with different 1, 1-valent electrolytes the plots were never strictly linear and the slopes at 25° were all negative. The great influence of valency predicted was not found with Na2S04. 

Generalized Atomic Polar Tensor (GAPT), for Hiickel theory, 93, 94 atomic charges. 226... 

In multi-orbit molecular structures, the need can arise to identify several FCAO-MOs of the same symmetry, over the structure vertices and this requirement provides a second useful example of the general utility of the orbit by orbit approach to the formation of group orbitals. In this section, the calculation of the electronic structure of the moiety Cso as an exercise in Hiickel theory, illustrates the benefits, which arise, when the LCAO-MOs are constructed from group orbitals formed on the vertices of the two structure orbits O20 and Oeo. 

The electrostatic methods just discussed suitable for nonelectrolytic solvent. However, both the GB and Poisson approaches may be extended to salt solutions, the former by introducing a Debye-Huckel parameter and the latter by generalizing the Poisson equation to the Poisson-Boltzmann equation. The Debye-Huckel modification of the GB model is valid to much higher salt concentrations than the original Debye-Hiickel theory because the model includes the finite size of the solute molecules. 

For the RPM, the first term cancels, and the second is dominant. In principle, c (r ) defined in this way may also vary locally. Third, one may also calculate C2g by working backward from the Laplace transformation of the pair correlation function, as done by Lee and Fisher [94] for the pair correlation function of their generalized Debye-Hiickel theory (GDH). 

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