Simple Calculations Using the Hiickel Method

Although the complexity increases rapidly there is no reason that Walsh diagrams cannot be constructed for XY3 pyramidal, XY4 tetrahedral, XYS octahedral, and other molecules. In fact, they have been prepared, but their applications will not be described here. Insofar as these diagrams are amenable to quantitative interpretation, the predictions are in accord with what we know from experimental evidence and valence bond methods. 

When dealing with carbon atoms, the coulomb integral (// ) is represented as a and the exchange integral (H, ) is represented as o. It is also assumed that interaction between nonadjacent atoms can be ignored so if i — j 15 2 the H,j = 0. Finally, in simple HMO there is complete neglect of overlap so 

If we begin with a simple molecule such as ethylene, it is apparent that the a bonded stmcture is represented as 

The useful part of the calculation in the Hiickel method is with regard to the 7r bond, 

Note that it has been assumed that H12 = H21 and that S12 = S21, which means that the two bonded atoms are identical. When S12 = S21 = 0, as has been described, after letting Hu = H22 = a and H12 = H21 = A the secular determinant becomes 

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Electron densities and bond orders for pyran-2-one, pyran-4-one and eight benzologues or dibenzologues have been calculated using the simple Hiickel, the Hiickel autocoherent and the semi-empirical Pople methods (74BSF538). Similar properties have been obtained for flavone and the electronic absorption spectra of some substituted flavones have been examined in detail (74CHE1218). Excitation is accompanied by a transfer of charge from the... 

In Table 47 we have collected RE and REPE values obtained by the ambitious VB calculations of Wu and Jiang,and those of Alexander and Schmalz, to be compared to the RE values calculated by the simple Hiickel MO method. Both VB calculations used the graphical unitary group technique that have produced highly efficient methods for ab initio calculations, the so-called graphical unitary group approach (GUGA), in which only the non-zero matrix elements are computed.One should recall that the... 

In Table 27 the simple Hiickel indices, Nr (Dewar number), Fr (free valence number) and Lr (localization energy) are given, together with the Mulliken overlap population pr, calculated by the extended Hiickel method and using the geometry of hexahelicene as determined by X-ray analysis141) to account for the non-planarity. 

It is apparent that the molecular orbital theory is a very useful method of classifying the ground and excited states of small molecules. The transition metal complexes occupy a special place here, and the last chapter is devoted entirely to this subject. We believe that modem inorganic chemists should be acquainted with the methods of the theory, and that they will find approximate one-electron calculations as helpful as the organic chemists have found simple Hiickel calculations. For this reason, we have included a calculation of the permanganate ion in Chapter 8. On the other hand, we have not considered conjugated pi systems because they are excellently discussed in a number of books. 

Fig. 4.22 A useful mnemonic for getting the simple Hiickel method pattern for cyclic n systems. Setting the radius of the circle at 2ipi, the energy separations from the nonbonding level can even be calculated by trigonometry...

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