THE $\pi$-ELECTRON STATES OF BUTADIENE
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Date
1971
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Publisher
Ohio State University
Abstract
Using a Hartree-Fock representation for the $\sigma$-core (obtained from an all-electron calculation on the ground state), extensive configuration interaction calculations have been carried out on the $\pi$-electron states of trans-butadiene. The $\sigma$ basis set of contracted Gaussian functions is of double zeta quality, while the $\pi$ basis has been augmented with two diffuse functions on each carbon atom appropriate for the description of the first set of Rydberg states. It is found that the lowest two triplet states, of symetry $^{3}B_{u}$ and $^{3}A_{g}$, with calculated vertical transition energies of 3.45 e.v. and 5.04 e.v., respectively, are valence states, and that the effect of CI is in accordance with the Coulson-Rushbrooke theorem. The lowest two excited singlet states, on the other hand, are found to be Rydberg transitions from the highest occupied $\pi$-orbital of the ground state. The calculated vertical excitation energies for the four lowest singlet Rydberg states are 6.77 ev $(2^{1}A_{g}), 7.05 (1^{1}B_{u}), 7.83 (3^{1}A_{g})$ and $8.06 (2^{1}B_{u})$, with oscillator strengths of $\sim$0.2 and $\sim$0.45 for the allowed transitions ($1^{1}A_{g}\rightarrow 1^{1}B_{a}, 2^{1}B_{u}$). The Rydberg states are found to occur in sets of four with roughly the same spatial extent, e.g., for the Rydberg orbital in the four lowest singlet states, the expectation value $<{Z}^{2}>$ varies from $40 (a.u.)^{2}$, to $66 (a.u.)^{2}$, where Z is in the $\pi$-direction. These results are not in accord with the previous assignments of the spectrum of butadiene or with the basic formulation of $\pi$-electron theory as it has developed along semi-empirical lines.
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Author Institution: Battlle Memorial Institute