Simple Huckel Theory

Bond energies relative to energy levels other than x = 0 are invariant. The reference point x = 0 is an almost universal convention in simple Huckel theory, however, and we shall continue to use it. 

Several different molecular orbital methods have been used in SAR investigations. These include simple Huckel theory, HT,(38) extended Huckel theory, EHT,(39) CND0,( ) NDD0,(41) MINDO/3,(42) and PCILO,(43)... 

STOs have a number of features that make them attractive. The orbital has the correct exponential decay with increasing r, the angular component is hydrogenic, and the Is orbital has, as it should, a cusp at the nucleus (i.e., it is not smooth). More importantly, from a practical point of view, overlap integrals between two STOs as a function of interatomic distance are readily computed (Mulliken Rieke and Orloff 1949 Bishop 1966). Thus, in contrast to simple Huckel theory, overlap matrix elements in EHT are not assumed to be equal to the Kronecker delta, but are directly computed in every instance. 

In analogy to extended Huckel theory, there are also charge iterative methods for simple Huckel theory. The equivalent of eq. (3.90) is... 

It has recently become clear that simple Huckel theory, as well as some more elaborate techniques such as MINDO/2, are unreliable for use in conjunction with frontier orbital theory. For example, Huckel molecular orbital coefScients suggest that acrolein (30) will dimerize to (31), but in fact the product is (32). SCF orbitals... 

One point which it is important to remember concerning the approach described in these pages is that it is based upon the ideas of simple Huckel theory. The type of problem therefore which may be viewed in terms of moments is therefore at present restricted to those for which such a topologically based theory is applicable. We have already disqual-... 

There is another way to test chemical stability hat can be applied to aromatic organic compounds. Aromaticity is usually taken to mean high stability and low reactivity. It can be quantified by calculating the resonance energy per electron (REPE). These values are usually calculated by simple Huckel theory, but they correlate well with experimental measures of reactivity. ... 

Assuming that the cohesive energy is due to the delocalization energy of partly filled bands, we can conclude that Equations (5.20), (5.22) and (5.23) are valid. We can also assume that the coulombic energy a is the same as for the free metal atoms. This is what is done in the simple Huckel theory used for other covalent bonding. Then we can write... 

The obvious qualitative model of electronic structure offullerenes is based on simple Huckel theory. The edges of the polyhedral cage are taken to be spanned by a set of two-electron a bonds, leaving to each atom one electron in an approximately radial n orbital to contribute to a surface n system. Appealing as this model is at first sight, it involves a number of assumptions that require somejustification. 

Fig. 12. Histogram representing the projected DOS on the Pb cluster (6p and 6py components). This topology gives within the frame of the simple Huckel theory (one MO per atom) 3 non bonding levels mainly localized on the A atoms.

Thus in order to calculate a value of a hyperfine splitting constant, to compare with an experimental value, it is necessary to know the appropriate spin densities and the appropriate proportionality constants. Since the spin density, rather than the unpaired electron density is required, simple HUckel theory may not be employed McLachlan s S.C.F. theory has gained wide-spread acceptance for the calculation of spin densities because even though it is relatively simple, the accuracy of its predicted spin densities generally exceeds the precision with which the proportionality constants in eqns. 4.15.1 and 4.15.2 are known. 

For monocycUc conjugated polyenes (such as cyclobutadiene and benzene) with each of Nq carbon atoms contributing an electron in a 2p orbital, simple Huckel theory gives the following expression for the energies of the resulting it molecular orbitals ... 

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