Relationship between second hyperpolarizability and diradical character in open-shell singlet metal–metal multiply bonded systems

Using the coupled-cluster method with single and double excitations (CCSD), we investigate the relationship between the second hyperpolarizability (γ) and the diradical characters of dσ, dπ and dδ orbitals for the open-shell singlet Cr(II) Cr(II) quadruply bonded model system, in which d4–d4 interactions make one dσ, two equivalent dπ and one dδ molecular orbitals, and then these orbitals exhibit different diradical characters. The γ value is divided into the contributions of natural orbitals in order to reveal the contributions of dσ, dπ and dδ orbitals to γ. From these results, we elucidate a relationship among the orbital symmetry, diradical character and γ value, and thus we propose a guiding principle for designing open-shell singlet metal-metal multiply bonded complexes with highly efficient third-order nonlinear optical properties.