Huckel molecular orbital method extended, applications

In recent years the fundamental ideas of Huckel molecular orbital theory, the Huckel rule, and other aspects of aromaticity have been extended to polyhedral three-dimensional inorganic structures regarded as aromatic like the two-dimensional aromatic hydrocarbons. Such an extension of Huckel molecular orbital theory requires recognition of its topological foundations so that they can be applied to three-dimensional structures as well as two-dimensional structures. In this connection graph theoretical methods can be used to demonstrate the close analogy between the delocalized bonding in two-dimensional planar aromatic systems such as benzene and that in three-dimensional deltahedral boranes, and carboranes. Related ideas can be shown to be applicable for metal carbonyl clusters, bare post-transition metal clusters, and polyoxometallates. ... 

Methods based on simulated Ab initio Molecular Orbital technique (SAMO) or cm the application of Linear Combination of Localized Orbitals have been proposed. The a priori advantages are a negligible cost (typically of the order of magnitude of an extended Huckel calculation) and the ab initio character of the approach. They suffer however from a rather tedious generation of a high number of matrix elements and it is still impossible to... 

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. 

Molecular-orbital theory has taken many forms and has been dealt with by many approximations. In 1963 Hoffmann S presented a formalism which he referred to as extended Hiickel (EH). In the 1930 s, however, this formalism would simply have been called molecular-orbital, since it is a straightforward application of molecular-orbital (MO) theory, using a one-electron Hamiltonian. Hoffmann referred to it as extended Hiickel because it did not limit itself to 7r-electron systems and was able to deal with saturated molecules by including all overlap integrals. In these respects it did extend the usual, or simple Huckel, method, which was customarily applied to 7T-electrons, and assumed complete tt — a separability. 

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