Density functional theory (DFT) B3LYP method based on the 6-31G(d) level were employed to optimize the structures of 13-vertex metallacarborane 4,1,6-MC₂B₁₀H₁₂. The polarizability and second-order nonlinear optical (NLO) coefficients were calculated by means of finite-field (FF) method. The results show that the second-order NLO coefficients of 1a～6a molecules have identical change with their configurations. In all metallacarboranes, the smaller the frontier molecular orbital energy gap is, the larger the second-order NLO coefficient is. For the homogeneous metallacarborane of different spin states, the dipole moments of high-spin state are larger than that of low-spin state, however, the polarizability and second-order NLO coefficient have not direct relationships with spin multiplicity. Therefore, the spin state has a little influence on NLO properties.

Key words: 13-vertex metallacarborane, geometrical structure, second-order NLO coefficient, DFT