HMO Calculations on Some Simple Molecules

As we consider larger systems, bmte-force solution of determinantal equations becomes too labor-intensive, and so such cases are always either solved on a computer or else by appeal to HMO tabulations in print. However, the above generalizations continue to be useful in understanding the MO results. 

Thus far, we have used the allyl and cyclopropenyl systems as examples. We will now describe the results of HMO calculations on some other simple but important systems. 

with the ground state electronic configuration indicated, are shown in (II). 7T-Electron densities and jr-bond order are indicated in the diagram beneath the MO sketches. Ethylene is an even alternant, so it has paired energies, unit electron densities, and coefficients related by a sign change. 

This problem can be solved by expansion to a polynomial in x and factoring, but it is simpler to use Eq. (8-49) or the decagon in a circle of radius 21. The coefficients are obtainable from Eq. (8-50). The results are 

The MOs are given in Fig. 8-12. is bonding in all bonds, 02 is bonding in the outer bonds, antibonding in the central bond. As a result, butadiene has a lower jr-bond order in the central bond than in the outer bonds. This is in pleasing accord with the 

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