Third-Order Nonlinear Optical Properties of Asymmetric Non-Alternant Open-Shell Condensed-Ring Hydrocarbons: Effects of Diradical Character, Asymmetricity, and Exchange Interaction

Using spin-unrestricted density functional theory, the longitudinal static second hyperpolarizability γ has been investigated for an asymmetric azulene-like open-shell condensed-ring molecule (1) as well as for its symmetric almost closed-shell and open-shell analogues (pentacene (2) and its dicyclopenta- (3) and dicyclohepta-fused (4) analogues). It is found that the symmetric systems, 3 and 4, having intermediate diradical characters show a 6-9 times enhancement of γ as compared to 2, but that this enhancement is even larger (by a factor of 30) for the asymmetric diradicaloid, 1. Geometrical, electronic, and magnetic descriptors have shown that in 1 the terminal seven- and five-membered rings display a cooperative push-pull effect, leading to a large dipole moment, that seems to reinforce its aromaticity as well as its ionic character, whereas 3 and 4 are mostly neutral diradicaloids and are less aromatic. These features have been rationalized by resorting to an asymmetric two-site model within the valence configuration interaction method. It is found that the diradical character decreases with increasing the asymmetricity and the exchange interaction. Then, an increase in the exchange interaction leads to a decrease of the asymmetricity value defining the critical point (where the diradical and ionic contributions of the ground and first excited states exchange) and increases the amplitudes of the γ extrema. The increase in asymmetricity has been realized in two ways: (i) by applying a static electric field to the symmetric nonalternant condensed-ring diradicaloid (3), and (ii) by designing an asymmetric nonalternant azulene-like condensed-ring conjugated system (1). Scheme ii gives a triplet ground state and it therefore requires large r_K, i.e., small HOMO-LUMO overlap. As a result, such an increase of r_K in scheme ii leads to a new class of asymmetric NLO systems, having a ferromagnetic ground state and a singlet first excited state. The latter has an intermediate or small diradical character y and it exhibits negative γ values with amplitudes larger than those of symmetric diradicaloids with smaller r_K.