A signature of singlet open-shell character on the optically allowed singlet excitation energy and singlet triplet energy gap is theoretically illuminated for open-shell singlet molecules. On the basis of a two-site diradical model with two electrons in two orbitals, the linear dependence of these excitation energies on the transfer integral, which is equivalent to the energy gap between the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals in the Huckel theory, is found to be broken down in the high diradical character region due to an increase in electron correlation in the open-shell singlet ground state. A series of polyacenes shows the similar behavior of the optically allowed singlet excitation energies obtained by time-dependent spin-flip density functional theory calculations and experiments, which bears testimony to the singlet open-shell character in long polyacenes.