Truncated Transition Densities for Analysis of (Nonlinear) Optical Properties of carbo-Chromophores

The optical properties of several quadrupolar carbo-benzene derivatives are investigated at various levels of calculation (TDDFT and CASPT2) and analyzed using a new theoretical tool here disclosed: The "visualization" of the transition dipole moment from the transition density truncated to the main monoexcitations involved in the electronic transition (TTD). The experimental or calculated one-photon UV-visible absorption spectra of the carbo-benzene derivatives fit with the Gouterman model originally proposed for porphyrins, where the first four excited states involve linear combinations of monoexcitations of the same four frontier molecular orbitals. The relative intensities of the absorption bands are analyzed from the transition dipole moments calculated from the TTDs and an analogy between porphyrins and carbo-benzenes is argued. The two-photon absorption (TPA) cross section related to the third-order nonlinear optical response is calculated for each two-photon-allowed excited state |f⟩ from the contribution of all possible intermediate excited states |i⟩ using the "sum-over-state" (SOS) scheme. The quadrupolar carbo-benzene derivatives fit into the three-level model, as their TPA cross section exhibits a dominant contribution of one of the intermediate excited states. The origin of TPA efficiency (enhancement) upon carbo-merisation of the C-C link to the para-substituents is discussed from the excitation energies of the intermediate and final excited states and from the two corresponding transition dipole moments (μ0i and μif). The latter may be calculated from the TTDs.