π-σ Electronic states in molecules II. The singlet spectrum of ethylene and derivatives

Abstract

It is suggested that the failure of the Heitler-London-Slater-Pauling method to give the right transition rules for the excited levels in conjugated systems is not due chiefly to shortcomings in the valence bond method (like neglect of ionic structures) but rather to the use of the Hückel approximation (see part I). This is confirmed by a detailed treatment of ethylene as a twelveelectron problem by the valence-bond method. The Hückel approximation is dispensed with, so that six canonical structures are considered. Of these, one corresponds to the perfect pairing scheme, one to π-σ resonance in the double bond and four to π-h resonance (h being the hydrogen 1s electron) in the C-H bonds. No purely σ-σ resonance is considered. Most of the necessary exchange integrals are computed in this paper. Two of them, however, are estimated. The treatment can be extended to substituted ethylenes by changing a few exchange integrals. It is necessary here to estimate another integral. A π-σ resonance energy of 0.47 eV is obtained for the ground state of ethylene. The actual positions of the peaks of absorption obtained are not very accurate, as could be expected. They are, however, of the same order as those given by the method of the antisymmetrized molecular orbitals. A first band ¹A_1g-A_1g, forbidden, is obtained. This is identified with the observed faint absorption starting at 2000 Å. The second band, allowed, is double, given by the transitions ¹A_1g-¹ B_1M and ¹A_1g¹ B_2u separated by ca. 0.2 eV (experim ental 0.06 eV). These bands are identified with the strong absorption at 1600 Å. The double nature of this band was hitherto without theoretical explanation. The distance between the first forbidden ban d and the centre of the second is 1.4 eV (experimental ca. 1.1 eV). The second band is shifted towards the red by tetra-alkyl substitution by 0.9 eV (experimental 1 eV). There is no need to have recourse to hyperconjugation to explain this last fact.