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The recent discovery of a low-lying transition in $\alpha ,\omega$-diphenyl-octatetraene and 2, 10-dimethylundecapentaene and its subsequent explanation on the basis of a semi-empirical calculation employing both singly- and doubly-excited configurations has led to disagreement as to the ordering of excited states in these molecules. Experiments by Kohler, Hudson and Christensen have suggested the state ordering of linear polyenes to be $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}Ag,1Ag,1Bu$, countering the H$u¨$ckel alternating $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}Ag,1Bu,1Ag$ state ordering expected for the idealized $C2h$ point group (planar geometry). This ordering was also calculated semi-empirically for butadiene, hexatriene, and octatetraene via PPP methods by Schulten and Karplus, who included all single and double excitations in configuration interaction (CI), but their findings for butadiene have been challenged by more recent, non-empirical calculations. Besides high resolution absorption and emission spectral evidence for the state ordering in this unsubstituted polyene, our present paper presents qualitatively correct ab initio theoretical description. The lowest two $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}Ag$ and $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}Bu$ state energies of 1, 3, 5-hexatriene were calculated on the POLYCAL program using a minimum basis set of Slater-type orbitals (STO ‘s). Utilizing all singly- and doubly-excited configurations arising from the six carbon $pz$ atomic orbitals. CI gave a state ordering: $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}Ag$ (ground state) These ab initio results agree qualitatively with preliminary absorption and emission experiments as well as with one previous semi-empirical calculation and experiments on larger polyenes. Therefore it is suggested that, even for a relatively inflexible basis set, the inclusion of all singly- plus doubly-excited configurations of the $\pi$-system in the CI treatment yields a qualitatively correct picture of state ordering in these molecules.