Singlet–Triplet Transition Probabilities in Aromatic Hydrocarbons. I. A→31La Transitions in Linear Polyacenes

A general expression for the transition moment of ${}^1{\mathrm{A\hspace{0.17em}\to \hspace{0.17em}}}^3{L}_a$ in linear polyacenes is derived from the matrix elements of spin–orbit interaction between $\mathrm{(\pi ,\; \pi )}$ and $\mathrm{(\pi ,\; \sigma )}$ states. Only one‐center one‐electron integrals are evaluated. The results indicate that the oscillator strength of this transition should decrease as the size of the linear polyacene increases. It is shown that this conclusion is most likely independent of the approximations employed. Interaction of $\mathrm{(\pi ,\; \sigma )}$ and $\mathrm{(\pi ,\; \pi )}$ states quantitatively accounts for the main part of the oscillator strength of ${}^1{\mathrm{A\hspace{0.17em}\to \hspace{0.17em}}}^3{L}_a$ in naphthalene.