Experimental evidence and DFT studies of next-nearest-neighbor magnetic interactions through diamagnetic 3d and 4d ions

The copper template effect allows the preparation of tridentate ligands that chelate copper ions, leaving unoccupied the fourth basal coordination position and at least one axial position of the copper coordination polyhedron. Two such cationic complexes, [LCu](+) and [L(1)Cu](+) (L(-) = 2-{(E)-[(2-aminoethyl)imino]methyl}phenoxo] and L(1-) = 2-{(E)-[(2-aminopropyl)imino]methyl}phenoxo), react with diamagnetic polycyanometalate tectons such as Ni(CN)(4)(2-) or Ag(CN)(2)(-) to yield different neutral 1D complexes. In {[(LCu)(2)Ni(CN)(4)]}(n) (1) the four cyano nitrogen atoms are involved in coordination with copper ions in such a manner that each copper atom is pentacoordinated and linked to two cyano functions that occupy axial and equatorial coordination positions. Two L(1)Cu(+) cationic entities are linked, through their equatorial plane, to two trans cyano groups of the Ni(CN)(4)(2-) tecton in complex [(L(1)Cu)(2)Ni(CN)(4)] (2), the two uncoordinated cyano groups being involved in hydrogen bonds. 2 is a racemate, a S stereoisomer being associated with a R one in each [(L(1)Cu)(2)Ni(CN)(4)] unit. Zigzag Cu-Ag chains are present in [(LCu)Ag(CN)(2)] (3), where the copper centers are pentacoordinated and connected to the cyano groups in an alternate axial-equatorial coordination scheme. A bidimensional structure is developed by interchain argentophilic interactions. In complex 4, {(L(1)CuMeOH)(L(1)Cu)[Ag(CN)(2)](2)}, two L(1)Cu units are connected by a NC-Ag-CN bridge in an equatorial position. These resulting units exhibit argentophilic interactions with [Ag(CN(2))](-) entities that are monocoordinated in the equatorial position to the next unit, ultimately leading to a chain. Weak Cu-Cu magnetic interactions are detected in the four compounds, antiferromagnetic in the case of equatorial-equatorial copper interactions, ferromagnetic for orthogonal interacting copper orbitals (axial-equatorial interactions), while axial-axial bridges are characterized by an absence of interaction. The presence of weak ferromagnetic interactions through large NC-Ni-CN or NC-Ag-CN bridges (Cu···Cu distances larger than 10 ?) furnishes experimental evidence for the existence of next-nearest-neighbor interactions through diamagnetic centers. DFT calculations do confirm the existence of these magnetic transmission pathways through the diamagnetic metal bridge.     

Best affine unbiased response decomposition

Given two linear regression models y₁=X₁β₁+u₁ and y₂=X₂β₂+u₂ where the response vectors y₁ and y₂ are unobservable but the sum y=y₁+y₂ is observable, we study the problem of decomposing y into components and , intended to be close to y₁ and y₂, respectively. We develop a theory of best affine unbiased decomposition in this setting. A necessary and sufficient condition for the existence of an affine unbiased decomposition is given. Under this condition, we establish the existence and uniqueness of the best affine unbiased decomposition and provide an expression for it.     

Varying the metal/metal ratio in related Cu–Ca complexes

We demonstrate with the help of structural determinations and spectroscopic data that the nuclearity of Cu–Ca complexes derived from compartmental Schiff base ligands does not depend on the ionic radius of calcium. The main factors governing these reactions are the different affinities of the calcium ions for the anionic species present in solution: the tetradentate O₂O₂ coordination site of the ligand and the nitrato ions. Because these affinities do vary upon going from calcium to lanthanide ions, it is not possible to use the template effect of the trinuclear Cu–Ca–Cu complexes in order to prepare the corresponding Cu–Ln–Cu complexes.