Localized Bonds in SCF Wavefunctions for Polyatomic Molecules. IV. Ethylene, Butadiene, and Benzene

Ab initio molecular‐orbital wavefunctions for ethylene, butadiene, and benzene have been analyzed in terms of the localized orbitals (LMO's) defined by minimizing molecular exchange energy. The effect of conjugation on the LMO's is studied in terms of the delocalization of LMO's and the curvature of the energy surface which determines the LMO's. The degree of preference for bent double‐bond LMO's over $\mathrm{\sigma –\pi }$ double‐bond LMO's is also examined. In all cases, the former LMO's represent the correct solutions, while the latter LMO's, obtained by imposing the constraint of $\mathrm{\sigma –\pi }$ separation, correspond to saddle‐point solutions. The double‐bond LMO's for ethylene and butadiene are quite similar, whereas in the case of benzene, appreciably greater delocalization is found, and the preference for bent bonds over $\mathrm{\sigma –\pi }$ bonds is greatly reduced.