Structure and Frontier Molecular Orbital (FMO) energies of α-Keggin-type polyoxometalate [PW12O40]3−: A systematical study with different functionals of density functional theory

Abstract To obtain more reasonable Frontier Molecular Orbital (FMO) energies of α-Keggin anion [PW 12 O 40 ] 3− , the influence of different density functional theory (DFT) functionals were systematically investigated. Except LC-ωPBE, M06HF, LC-BLYP, HF and LC-BP86, the functionals we tested overestimate the bond length with mean unsigned error (MUE) values ranging from 0.02 A to 0.03 A. All the functionals used show the typical trend that the FMO energy levels are overestimated. The hybrid generalized gradient approximation (hGGA), such as B3P86 (MUE 0.465 eV), performs better than others. The results on Na 3 PW 12 O 40 are more reasonable than those of [PW 12 O 40 ] 3− as the errors caused by the negative charge were compensated. B3P86 is superior to B3PW91 and B3LYP in the description on Na 3 PW 12 O 40 with MUE 0.461 eV and mean signed error (MSE) 0.043 eV. B3P86 with 13% HF exchange offers the reasonable MUEs (≈0.12 eV) for M 3 PW 12 O 40 , M 4 SiW 12 O 40 and M 6 P 2 W 18 O 62 (M = Na, K).