The effects of redox-active M-atoms (M=Mo, Ru and Rh) of the di-d-transition-metal-substituted gamma-Keggin polyoxometalates [(SiO4)(M-III)(2) (OH)(2)W10O32](4-), on the geometry and electronic structure of these species were evaluated at the density functional level. It was shown that open isomers (without two bridging OH ligands between the M centers) may coexist with closed isomers (with bridging OHs) only for M=Mo. The ground electronic state of the closed isomer of all the studied species is found to be the singlet (1)A(1), state in C-2v symmetry, but some of the high-spin states are very close in energy. The calculated M-M distance in the ground state increases via M = Mo (2.28 angstrom) < Ru (2.60 angstrom) < Rh (3.00 angstrom). Simultaneously the calculated M-M distances in high-spin states are very similar and are within of 3.13-3.25 angstrom. The M-O-si(1) (or M-O-si(2)) bond distances, which vary from 2.00 to 2.17 angstrom for the ground state of all compounds, elongate upon going to high-spin states. These geometry trends are explained in terms of the frontier orbitals of these species. (c) 2006 Elsevier B.V All rights reserved.