J.M. Clemente

Mixed-valence polyoxometalate clusters. I. Delocalization of electronic pairs in dodecanuclear heteropoly blues with keggin structure

Abstract The problem of delocalization of a pair of electrons over dodecanuclear polyoxometalate clusters with the Keggin structure is considered with the aim of explaining the spin pairing in these multi-nuclear mixed-valence systems. A general approach that considers the Coulomb interactions between the two delocalized electrons, as well as the single and double electron transfer processes which can be operative in delocalization of the electronic pairs is developed. The new approach is based on the site-symmetry concept which makes possible a group theoretical classification for the delocalized states of electronic pairs. This procedure proves to be very efficient in the calculation of the transfer matrices which are expressed in terms of the Coulomb energy, and the single- and double-transfer parameters. The influence of these electronic parameters on the spectrum of the low-lying energy levels of the cluster is discussed, and the conditions giving rise to the stabilization of a singlet ground spin state for the electronic pair are elucidated.

Mixed-valence polyoxometalate clusters. III. Vibronic problem for the 2-electron reduced heteropoly blue with the Keggin structure

Abstract A general approach to the vibronic problem of delocalized electronic pairs in mixed-valence compounds is developed and applied to understand the ways of electron delocalization in dodecanuclear polyoxometalate clusters containing two moving electrons. The interplay between electronic and vibronic interactions is examined. The electronic spectrum is shown to consist of two spin triplets 3 T 1 and 3 T 2 and three spin singlets 1 A 1 , 1 E and 1 T 2 levels determined by the double-transfer processes (parameter P ). Jahn-Teller and pseudo-Jahn-Teller problems ( 3 T 1 + 3 T 2 ) ⊗ ( e + t 2 ) and ( 1 A 1 + 1 E + 1 T 2 ) ⊗ ( e + t 2 ) have been considered in the framework of the Piepho-Krausz-Schatz model dealing with the only vibronic parameter. Several kinds of spatial electronic distribution have been found corresponding to the stable points of the energy surfaces. For spin-triplet states, potential surfaces contain six minima in e space corresponding to partially delocalized electronic pairs over four sides of the T d structure (limiting case of weak coupling), or delocalized over two opposite sides (limiting case of strong coupling). The former situation restricts electron delocalization to two of the three metal octahedra of each M 3 O 12 triad in such a way that each electron moves over a tetrameric unit in which the metal sites are alternatively sharing edges and corners. In the t 2 space the electronic pair can be either delocalized over three sides, giving rise to a trigonal-type distortion of the cluster and a partial electron delocalization over two opposite M 3 O 12 triads (four trigonal minima in the case of strong transfer or relatively weak vibronic interaction), or be completely localized (case of strong vibronic coupling). For spin-singlet states the system possesses a stable point in the high-symmetrical nuclear configuration, corresponding to a full delocalization of the electronic pairs in the Keggin cluster. The influence of vibronic interaction on the nature of the spin of the ground states is considered.

High‐nuclearity mixed‐valence magnetic clusters: A general solution of the double exchange problem

We report here a general solution of the double‐exchange problem in the high‐nuclearity mixed valence systems containing arbitrary number P of the electrons delocalized over the network of N (P<N) localized spins. The developed approach is based on the successive (chainlike) spin‐coupling scheme and takes full advantage from the quantum angular momentum theory. In the framework of this approach the closed‐form analytical expressions are deduced for the matrix elements of the double exchange interaction, two‐electron transfer, and three‐center interaction that can be referred to as the potential exchange transfer. For the arbitrary nuclearity mixed‐valence systems the matrix elements of all named interactions are expressed in terms of all relevant spin quantum numbers and 6j symbols and do not contain higher order recoupling coefficients. We describe also the combined approach taking into account both angular momentum consideration and advantages of point symmetry adapted basis set.

Mixed-valence polyoxometalate clusters. II. Delocalization of electronic pairs in 18-site heteropoly blues with Wells-Dawson structure

Abstract The problem of delocalization of two electrons in the 18-site Wells-Dawson polyoxometalate is examined from a general approach that takes into account both single- and double-transfer processes, as well as the Coulomb interactions between the two delocalized electrons. The electronic energy levels of this mixed-valence cluster are calculated and the conditions giving rise to the stabilization of a singlet ground spin state for the electronic pair are elucidated. It is shown that the spin pairing results from the simultaneous effects of single- and double-electron transfer processes, which are operative even when the two delocalized electrons are fairly widely separated in the Wells-Dawson structure.

Anisotropic exchange coupling in the Keggin derivative K8[Co2(D2O)(W11O39)] · n D2O

Abstract 20 g of the fully deuterated title compound have been prepared in polycrystalline form and investigated by inelastic neutron scattering using both thermal and cold neutrons. Magnetic dimer excitations were observed and the energy-splitting pattern resulting from the exchange coupling within the Co 2+ dimer was determined. The coupling is highly anisotropic with the parameter values J =−2.24 meV and η =0.33 based on the effective coupling Hamiltonian H =−2J[S 1z S 2z +η(S 1x S 2x +S 1y S 2y )] . The anisotropy results mainly from the single-ion anisotropy of the Co 2+ ion in the distorted octahedral coordination.

Electronic structure of high-nuclearity mixed-valence clusters

Abstract A general method is suggested for consideration of the electronic problem of high-nuclearity mixed-valence systems containing delocalized electronic pairs. A new approach based on the site symmetry concept with the electronic pairs is developed, and the magnetic properties of cluster metal oxides (heteropoly-blues) involving 12 and 18 metal sites are considered.

Electron delocalization and magnetic interactions in magnetic molecular systems. Theory and applications

Abstract Using the general computational approach based on the angular momentum theory we discuss here the magnetic properties of large magnetic clusters (polyoxometalates) and mixed-valence chains (diphtalocyanine-based materials). The interplay between electron delocalization, magnetic exchange and Coulomb interaction is examined in detail.

Magnetic excitations in polyoxometalate tetrameric clusters

Abstract The metal-oxide clusters with formula [M4(D2O)2(PW9O34)2]10− which contain a tetrameric magnetic cluster M4O16 provide an ideal series for the study of magnetic exchange interactions in polymetallic molecular clusters. To get a more direct information on the splitting of the spin states caused by the exchange interactions we have performed inelastic neutron scattering measurements on the Co, Mn and Ni clusters. Magnetic excitations have been observed in the range 0.5–6 meV. A tentative interpretation of these data from a Heisenberg exchange Hamiltonian and a single ion zero-field splitting is presented for Ni cluster.

High Nuclearity Mixed-Valence Clusters. Theoretical Approaches

Abstract A general approach is developed in order to calculate the energy levels and magnetic properties of high nuclearity mixed valence clusters. The approach considers all the relevant electronic processes, namely (i) interelectronic Coulomb repulsion between the moving electrons, which depend on the different distributions of the electronic pairs over the available metal sites; (ii) single and double electron transfer processes, which promotes the electron delocalization; (iii) magnetic exchange interactions. This approach is applied here to tetranuclear iron (II)-iron (III) clusters for symmetries comprised between tetrahedral and square planar.

Magnetic and vibronic interactions in mixed-valence clusters: A general approach based on the angular momentum theory

Abstract A general solution of the double exchange problem is given for a mixed-valence system in which one migrating electron or hole is delocalized over an arbitrary number of transition metal ions (spin-core). A new efficient way for solving the magnetic vibronic problem is suggested based on the semiclassical approach.