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π -σ Electronic States in Molecules. II. The Singlet Spectrum of Ethylene and Derivatives
S. L. Altmann
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences
Vol. 210, No. 1102 (Jan. 7, 1952), pp. 343-354
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/98785
Page Count: 12
You can always find the topics here!Topics: Molecules, Approximation, Orbitals, Wave functions, Electrons, Hydrogen, Ground state, Mathematical integrals, Molecular orbitals, Molecular structure
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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 Huckel approximation (see part I). This is confirmed by a detailed treatment of ethylene as a twelve-electron problem by the valence-bond method. The Huckel 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 1A1g-1A1g, forbidden, is obtained. This is identified with the observed faint absorption starting at 2000 angstrom. The second band, allowed, is double, given by the transitions 1A1g-1B1u and 1A1g-1B2u separated by ca. 0· 2 eV (experimental 0· 06 eV). These bands are identified with the strong absorption at 1600 angstrom. The double nature of this band was hitherto without theoretical explanation. The distance between the first forbidden band 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.
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences © 1952 Royal Society