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An Exact Solution of the PPP Model for Correlated Electronic States of Tetracene and Substituted Tetracene

Tetracene is an important conjugated molecule for device applications. We have used the diagrammatic valence bond method to obtain the desired states, in a Hilbert space of about 450 million singlets and 902 million triplets. We have also studied the donor/acceptor (D/A) substituted tetracenes with D and A groups placed symmetrically about the long axis of the molecule. In these cases, by exploiting a new symmetry, which is a combination of $C_2$ symmetry and electron-hole symmetry, we are able to obtain their low-lying states. In the case of substituted tetracene, we find that optically allowed one-photon excitation gaps reduce with increasing D/A strength, while the lowest singlet-triplet gap is only weakly affected. In all the systems we have studied, the excited singlet state, $S_1$ is at more than twice the energy of the lowest triplet state and the second triplet is very close to $S_1$ state. Thus donor-acceptor substituted tetracene could be a good candidate in photo-voltaic device application as it satisfies energy criteria for singlet fission. We have also obtained the model exact second harmonic generation (SHG) coefficients using correction vector method and we find that the SHG responses increase with the increase in D/A strength.