W-knotted chain {[Cu(II)(dien)]4[W(V)(CN)8]}(5+)∞: synthesis, crystal structure, magnetism, and theory.

The self-assembly of [Cu(II)(dien)(H(2)O)(2)](2+) and [W(V)(CN)(8)](3-) in aqueous solution leads to the formation (H(3)O){[Cu(II)(dien)](4)[W(V)(CN)(8)]}[W(V)(CN)(8)](2)·6.5H(2)O (1). The crystal structure of 1 consists of an unprecedented {[Cu(II)(dien)](4)[W(V)(CN)(8)]}(5+)(∞) chain of (2,8) topology, nonbridging [W(CN)(8)](3-) anions, and crystallization water molecules. The analysis of magnetic behavior of 1 was performed by the density functional theory (DFT) method and magnetic susceptibility measurements. The DFT broken symmetry approach gave two J(CuW) coupling constants: J(ax) = +2.9 cm(-1) assigned to long and strongly bent W-CN-Cu linkage, and the J(eq) = +1.5 cm(-1) assigned to short and less bent W-CN-Cu linkage, located at the axial and the equatorial positions of square pyramidal Cu(II) centers, respectively, in the hexanuclear {W(2)Cu(4)} chain subunit. The dominance of weak-to-moderate ferromagnetic coupling within the chain was confirmed by magnetic calculations. Zero-field susceptibility of the full chain segment {WCu(4)}(n) was calculated by a semiclassical analytical approach assuming that only one W(V) out of five ½ spins of the chain unit WCu(4) is treated as a classical commuting variable. The calculation of the field dependence of the magnetization was performed separately by replacing the same spin with the Ising variable and applying the standard transfer matrix technique. The intermolecular coupling between the chain segments and off-chain [W(CN)(8)](3-) entities was resolved using the mean-field approximation set to be of antiferromagnetic character. The magnetic coupling parameters are compared with those of other low dimensional {Cu(II)-[M(V)(CN)(8)]} systems.