We present a quantitative evaluation of the influence of the electron transfer on the magnetic properties of mixed-valence polyoxometalates reduced by two electrons. For that purpose, we extract from valence-spectroscopy ab initio calculations on embedded fragments the value of the transfer integrals between W nearest-neighbor atoms in a mixed-valence alphaPW(12)O(40) polyoxowolframate Keggin anion. In contradiction with what is usually assumed, we show that the electron transfer between edge-sharing and corner-sharing WO(6) octahedra have very close values. Considering fragments of various ranges, we analyze the accuracy of calculations on fragments based on only two WO(5) pyramids which should allow a low cost general study of transfer parameters in polyoxometalates. Finally, these parameters are introduced in an extended Hubbard Hamiltonian that models the whole anion. It permits to prove that electron transfers induce a large energy gap between the singlet ground state and the lowest triplet states providing a clear explanation of the diamagnetic properties of the mixed-valence Keggin ions reduced by two electrons.
A mechanism for the reaction of the NO 3 radical with propene is proposed on the basis of B3LYP and CASSCF calculations. The mechanism involves initially both Markownikoff and contra-Markownikoff oriented addition on the double bond. From the initial radical adducts several interconnected pathways have been found, giving 1,2-epoxypropane, propanal, propenol, propanone, formaldehyde, ethanal, NO, and NO 2 . The geometries of the stationary points found on the potential energy hypersurface (PES) were obtained and characterized by means of density functional theory (DFT) B3LYP/6-31G* calculations. Comparison of the optimized geometries on a limited number of molecular structures was carried out with calculations at the CASSCF level of theory with the same basis set, building the active space with five electrons in six orbitals.
Intermediate Hamiltonians are effective Hamiltonians which are defined on an N-dimensional model space but which only provide n < N exact eigenvalues and the projections of the corresponding eigenvectors onto the model space. For a single root research, the intermediate Hamiltonian may be obtained from the restriction of the Hamiltonian to the model space by an appropriate, uniquely defined dressing of the diagonal energies or of the first column. Approximate self-consistent dressings may be proposed. The simplest perturbative form gives the same result as the original 2nd order intermediate Hamiltonian or the "shifted Bk" technique but it is of easier implementation. Self-consistent inclusion of higher order exclusion principle violating corrections greatly improves the results, especially for nearly degenerate problems, as shown on several illustrative applications. Possible generalizations to enlarged or reduced model spaces are discussed.
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