Theoretical study on the second hyperpolarizability of open-shell singlet one-dimensional systems with a charged defect

The longitudinal static second hyperpolarizability (γ) has been investigated for models (H₃ ⁺ and H₅ ⁺) open-shell singlet one-dimensional systems bearing a charged defect. Using various ab initio molecular orbital and density functional theory methods, the γ values of these cationic symmetric hydrogen chain models having different bond-length alternations (BLAs) are analyzed as a function of the average diradical character as well as by adopting the summation-over-states scheme. These systems exhibit negative γ values, of which the amplitudes increase nonlinearly with the average diradical character while the chain-length dependence is enhanced by increasing the BLAs. This dependence of γ with the diradical character is mostly dictated by the strong decrease of the excitation energies.