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Electron Correlations and Two-Photon States in Polycyclic Aromatic Hydrocarbon Molecules: A Peculiar Role of Geometry

We present numerical studies of one- and two-photon excited states ordering in a number of polycyclic aromatic hydrocarbon molecules: coronene, hexa-peri-hexabenzocoronene and circumcoronene, all possessing $D_{6h}$ point group symmetry versus ovalene with $D_{2h}$ symmetry, within the Pariser-Parr-Pople model of interacting $π$-electrons. The calculated energies of the two-photon states as well as their relative two-photon absorption cross-sections within the interacting model are qualitatively different from single-particle descriptions. More remarkably, a peculiar role of molecular geometry is found. The consequence of electron correlations is far stronger for ovalene, where the lowest spin-singlet two-photon state is a quantum superposition of pairs of lowest spin triplet states, as in the linear polyenes. The same is not true for $D_{6h}$ group hydrocarbons. Our work indicates significant covalent character, in valence bond language, of the ground state, the lowest spin triplet state and a few of the lowest two-photon states in $D_{2h}$ ovalene but not in those with $D_{6h}$ symmetry.