Extended Hiickel theory application

The pioneering calculations of Wolfsberg and Helmholtz on Mn04, Cr04 and CIO4 are usually cited as the first applications of extended Hiickel theory... 

The systematic application of extended Hiickel theory to organic molecules comes with the work of Hoffmann. 

After the finding of a sweet taste in L-Asp-L-Phe-OMe (aspartame) by Mazur et at. (6), a number of aspartyl dipeptide esters were synthesized by several groups in order to deduce structure-taste relationships, and to obtain potent sweet peptides. In the case of the peptides, the configuration and the conformation of the molecule are important in connection with the space-filling properties. The preferred conformations of amino acids can be shown by application of the extended Hiickel theory calculation. However, projection of reasonable conformations for di- and tripeptide molecules is not easily accomplished. 

By far, the theoretical approaches that experimental inorganic chemists are most familiar with and in fact nse to solve questions qnickly and qnalitatively are the simple Huckel method and Hoffinann s extended Hiickel theory. These approaches are nsed in concert with the application of symmetry principles in the bnUding of syimnetry adapted linear combinations (SALCs) or gronp orbitals. The ab initio and other SCF procednres ontlined above prodnce MOs that are treated by gronp theory as well, bnt that type of rigor is not usually necessary to achieve good qnahtative pictures of the character aud relative orderiugs of the molecular orbitals. 

Nowadays, the success of the methods proposed by Hoffmann 50> and by Pople and Segal 51> among the chemists tends to promote the use of pure atomic orbital bases for all-valence treatments. The first method is a straightforward application of the Wolfsberg-Helmholz treatment of complexes to organic compounds and is called the Extended Hiickel Theory (EHT), because its matrix elements are parametrized in the same way as the Hiickel method with overlap for n electrons. The other method, known under the abbreviation Complete Neglect of Differential Overlap (CNDO), includes electron repulsion terms by extending to a orbitals the successful approximation of zero-differential overlap postulated for n electrons. 

The extended Hiickel approach has proved to be rather successful for such a simple theory for example, the famous Woodward-Hoffmann rules (see Section 5.9.4) were based upon calculations using this model. Extended Hiickel theory has found particular application in those areas where alternative theories cannot be used. This is largely due to the fact that the basis set requires no more than experimentally determined ionisation potentials. It is particularly useful for studying systems containing metals these systems are problematic for many other methods due to the lack of suitable basis sets. 

Experience shows that solutions of other electrolytes behave in a manner similar to the examples we have used. The conclusion we reach is that the Debye-Hiickel equation, even in the extended form, can be applied only at very low concentrations, especially for multivalent electrolytes. However, the behavior of the Debye-Hiickel equation as we approach the limit of zero ionic strength appears to give the correct limiting law behavior. As we have said earlier, one of the most useful applications of Debye-Hiickel theory is to... 

Abstract A historical view demystifies the subject. The focus is strongly on chemistry. The application of quantum mechanics (QM) to computational chemistry is shown by explaining the Schrodinger equation and showing how this equation led to the simple Hiickel method, from which the extended Hiickel method followed. This sets the stage well for ab initio theory, in Chapter 5. 

The widespread application of MO theory to systems containing a bonds was sparked in large part by the development of extended Hiickel (EH) theory by Hoffmann (I) in 1963. At that time, 7r MO theory was practiced widely by chemists, but only a few treatments of a bonding had been undertaken. Hoffmann s theory changed this because of its conceptual simplicity and ease of applicability to almost any system. It has been criticized on various theoretical grounds but remains in widespread use today. A second approximate MO theory with which we are concerned was developed by Pople and co-workers (2) in 1965 who simplified the exact Hartree-Fock equations for a molecule. It has a variety of names, such as complete neglect of differential overlap (CNDO) or intermediate neglect of differential overlap (INDO). This theory is also widely used today. 

The Extended Debye-Hiickel Theory. The Debye-Hitckel theory is successful in accounting for the experimental results when its application is limited to solutions in which the ratio of the electrical to the thermal energy of the ions is very smalt, i.e.,... 

When applicable, the extended Debye-Hiickel theory of Gronwail, LaMer and Sandved,21r although rather laborious, furnishes a means for the determination of Eo values. Its use may be illustrated by the work of Cowperthwaite and LaMer 22 on zinc sulphate, using a cell of type (25). Their data are given in Table II. Due to the fact that this... 

Equation (26.41) predicts to within approximately 10% mean molal activity coefficients for salt concentrations up to 0.1 molal. The more accurate form of the activity coefficient equation [Equation (26.40)] allows the model to be extended to salt concentrations up to 0.5 molal. To expand the applicability of the Debye-Hiickel theory to higher concentrations, additional terms are added to Equation (26.40), such as [4]... 

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