LCAO Self-Consistent Field Calculation of the π-Electron Energy Levels of cis- and trans−1,3-Butadiene

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Abstract
The π‐electrons of the molecules cis‐ and trans−1,3‐butadiene are treated by the method of antisymmetrized products of molecular orbitals, the molecular orbitals being taken as linear combinations of 2pπ‐Slater atomic orbitals with effective charge 3.18. The best ground state LCAO molecular orbitals obtainable from these are found by application of a method recently proposed by Roothaan which is based on the variational theorem, and the π‐electron energy of the ground state is calculated. Including a correction for nuclear repulsions, the trans‐ form is computed to be 0.12 ev more stable than the cis‐form. Using the ground state orbitals to build up excited state wave functions, the energies of four singly excited singlet states and the corresponding triplet states are calculated, there resulting for the average of the lowest singlet and triplet states the excitation energy 5.4 ev for cis‐ and 5.7 ev for trans‐, the experimental value for the lowest singlet state (probably for trans‐) being 6.0 ev. The first ionization potential is computed to be 9.7 ev for both cis‐ and trans‐, whereas the observed value is 9.1 ev. No extra‐geometrical empirical data are used except in the calculation of ionization potentials, where the value − 11.28 ev based on atomic spectroscopic data is used for the energy of a 2pπ‐electron in a carbon atom in its valence state.