Molecular orbital closed loops analysis of the third-order NLO response of polyanion [M8O26]4− (M = Cr, Mo, W): a TDDFT study

Abstract

Molecular orbital closed loops theory was used to explain the mechanism of the third-order nonlinear optical (NLO) response of polyanion cage structure of polyoxometalate by TDDFT study. The third-order NLO properties of three octa-polyoxometalate anion clusters of VIB group metals, β-[Cr8O26]4−, β-[Mo8O26]4−, and β-[W8O26]4−, were studied by DFT/TDDFT method systematically. The geometric structures of β-[Cr8O26]4− and β-[W8O26]4− were separately simulated by DFT method, based on the crystallographically determined geometry of the β-[Mo8O26]4− ion, and the thermo stability, and the second static hyperpolarizabilities, γ iiii , γ iijj , and γmean were calculated by finite-field method as an extension of the usual DFT energy run, and the results suggest that with no ligands coordinated, all of the three clusters possess moderately large hyperpolarizabilities, and the molybdate ion possess much larger NLO response than the chromate and the tungstate ions. In order to find out the reason of the big difference in the hyperpolarizabilities of the three polyoxometalates of the same group metals, the electronic properties were also studied by DFT method for the discussion of the origination of the NLO response, specially, the mechanism of the electronic structure change affecting the NLO response is analyzed and exhibited by the molecular orbital “closed loops” theory which has usually been used to estimate the thermo stability and redox ability of the polyoxometalate anion cages. Without the coordination by any ligands, polyanion [M8O26]4− (M = Cr, Mo, W) in high symmetry structures present moderately high third-order NLO response by TDDFT study, even higher than the one-dimensional metal–metal bond compounds Cr(II)4, Mo(II)4, and some C60 derivatives. A new thought of molecular “orbital loops” for the theoretical exploration of the mechanism of NLO response were introduced, and applied to the polyanions and proved to be an effective analyzing method .