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Four new hexanuclear niobium cluster compounds of the general formula [Nb6Cl12(HIm)(6)](A)(n) . x(solvent molecule) (HIm=1H-imidazole, A=mineral acid anion, Cl- (n=2) (1), (SO4)(2-) (n=1) (2), (CrO4)(2-) (n=1) (3), and (HAsO4)(2-) (n=1) (4)) were prepared. Their synthesis can be done in basic ionic liquids, which form on the addition of a mineral acid, which also delivers the counter anion for the final cluster compound, to an excess of the 1H-imidazole. Some addition of an auxiliary solvent, like methanol, improves the speed of crystallisation. The cluster unit comprises a hexanuclear Nb-6 unit of octahedral shape with the edges bridged by Cl atoms and the exo sites being occupied by N-bonded 1H-imidazole ligands. The cluster cation carries sixteen cluster-based electrons. Between the NH groups of the ligands of the cluster unit, the anions and the co-crystallised water (1), or 1H-imidazole and methanol molecules (2, 3, and 4) a network of hydrogen bonds exists.
The synthesis and the crystal structure of the double cluster compound [Nb6Cl14(MeCN)(4)][Nb6Cl14(pyz)(4)]middot6CH(3)CN are described. The synthesis is based on a partial ligand exchange reaction, which proceeds upon dissolving [Nb6Cl14(pyz)(4)]middot2CH(2)Cl(2) in acetonitrile. The compound is built up of two discrete neutral cluster units, which consist of octahedra of Nb-6 atoms coordinated by 12 edge-bridging chlorido and two terminal chlorido ligands, and four acetonitrile ligands on one and four pyrazine ligands on the other cluster unit. Co-crystallized acetonitrile molecules are also present. The single-crystal structure determination has revealed a cluster arrangement in which the [Nb6Cl14(pyz)(4)] units are connected by (halogen) lone-pair-(pyrazine) pi interactions. These lead to chains of [Nb6Cl14(pyz)(4)] clusters. These chains are further connected to cluster layers by (nitrile-halogen) dipole-dipole interactions, in which the [Nb6Cl14(MeCN)(4)] and co-crystallized MeCN molecules are also involved. These cluster layers are arranged parallel to the crystallographic {011} plane.
We present general existence and uniqueness results for marked models with pair interactions, exemplified through Gibbs point processes on path space.
More precisely, we study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to R-d, and the marks are the paths of Langevin diffusions.
We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.