Simple Huckel method

Fig. 4.26 The simple Huckel method normally uses only one basis function per heavy atom only one 2p orbital on each carbon, oxygen, nitrogen, etc., ignoring the hydrogens. The extended Huckel method uses for each carbon, oxygen, nitrogen, etc., a 2s and three 2p orbitals, and for each hydrogen a Is orbital. This is called a minimal valence basis set...

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. 

This process alone is not, of course, sufficient to overcome all the semi-quantitative shortcomings of the simple HMO-method and, indeed, we would not expect it to be. It does, however, reduce the dipole moment to a much more manageable value, although this quantity is still overestimated by the co-technique calculation we should certainly therefore need to look at some further improvements ( 7.3 and 7.4) before we were anything like satisfied with this sort of approach. The co-technique does, however, give rise to a more realistic predicted charge-distribution than does the simple Huckel-method in the case of those molecules in which all the n-charges are not unity. 

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. 

Under such conditions two electrons are likewise removed from 9-methyl-, 9,10-dimethyl-, 2,6-dimethyl-, 9-chloro- and 9-bromoanthracenes 9-ethylanthra-cene biphenylene - and methylated biphenylenes In SbF,—SO CIF dications are formed from the polycyclic aromatics for which the energy of the highest occupied molecular orbital (HOMO) calculated by the simple Huckel method is less than 0.5 p (pentacene, naphthacene, perylene, 1,2-benzpyrene, anthracene, 1,12-benzperylene, pyrene, 1,2-benzanthracene, 1,2 5,6-dibenzanthracene). At higher... 

The simple Huckel method is usually applied only to the calculation ir electron energies in conjugated organic systems. The simple method is based on the assumptirai of the separability of the electron systems in the molecule. This is a very crude approximation and works best when the energy level pattern is determined largely by the synunetry of the molecule. (See Chapter 12.)... 

The predictions of the various approaches diverge more widely when nonben-zenoid conjugated systems are considered. The simple Huckel method using total 77-energy less the energy of the equivalent number of isolated double bonds fails. It predicts delocalization energies of the same order of magnitude for such unstable systems as pentalene and fulvalene as it does for the much more stable aromatics. Both the HMO and SCF-MO methods, which are referenced to polyenes, do much better. They show drastically reduced stabilization for such systems, and, in fact, indicate destabilization in some cases. 

Results such as these have tended to restrict use of the EH method to qualitative predictions of conformation in molecules too large to be conveniently treated by more accurate methods. However, just as the simple Huckel method underwent various refinements (such as the cjo technique) to patch up certain inadequacies, so has the EH method been rehned. Such refinements have been shown to give marked improvement in numerical predictions of various properties. The EH method has been overtaken in popularity by a host of more sophisticated computational methods. (See Chapter 11.) However, it is still sometimes used as a first step in such methods as a way to produce a starting set of approximate MOs. The EHMO method also continues to be important as the computational equivalent of qualitative MO theory (Chapter 14), which continues to play an important role in theoretical treatments of inorganic and organic chemistries (as, for example, in Walsh s Rules and in Woodward-Hoffmann Rules). 

Figure 15-20 (a) tt band of poly acetylene (simple Huckel method) with alternating C-H groups... 

HuLiS started as a Java applet and evolves to ajavascript/HTML5 script to increase the ease of use [33]. The program is available as a web application at http //ism2. univ-amu.fr/hulis, and can also be downloaded as a standalone java applet. The mobile version is available from the same address. In addition to the simple Huckel method, HuLiS implements the two methods described herein and the topological resonance module described in this section. 

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