Open-shell character and second hyperpolarizabilities of one-dimensional chromium(II) chains: Size dependence and bond-length alternation effect

Using the long-range corrected spin-unrestricted density functional theory (LC-UBLYP) method, we have investigated the longitudinal third-order nonlinear optical (NLO) properties, i.e., the second hyperpolarizabilities γ of open-shell singlet one-dimensional (1D) extended metal atom chain (EMAC) systems, chromium(II) chains Cr^II_2n (n = 1-4), with different metal-metal bond lengths from the viewpoint of the open-shell character dependences of each d orbital contribution (dσ, dπ, dδ) to γ and of the chain-length dependence of γ. It turns out that the chain length dependences of the open-shell characters of dπ and dδ orbitals at any metal-metal bond length are negligible, while the dσ open-shell character decreases as a function of chain length. The systems display bell-shaped behaviors of γ as a function of the metal-metal bond length, in which the γ values attain maxima for intermediate dσ open-shell character. The maximum γ value (γ_max) exhibits remarkable enhancement as a function of chain length. It is also found that the bond length alternation (BLA) significantly affects the γ values and their chain-length dependences. The present results provide the guiding principles for designing transition-metal complexes with open-shell singlet 1D metallic chains exhibiting large third-order optical nonlinearity.