We demonstrate an accurate method for extracting Heisenberg exchange-coupling constants (J) from density-functional theory (DFT) calculations. We note that the true uncoupled low-spin state of a given molecule should be identified with the ground state of the system subject to a constraint on the spin density of the atoms. Using an efficient optimization strategy for constrained DFT we obtain these states directly, leading to a simple, physically motivated formula for J. Our method only depends on state energies and their associated electron densities and assigns no unphysical meaning to the Kohn-Sham determinant or individual orbitals. We study several bimetallic transition-metal complexes and find that the constrained DFT approach is competitive with, if not better than, the best broken symmetry DFT results. The success of constrained DFT in these cases appears to result from a balanced elimination of self-interaction error and static correlation from the simulation.

Accurate magnetic exchange couplings in transition-metal complexes from constrained density-functional theory

Two Molecular Tapes Consisting of Serial or Parallel Azido‐Bridged Eight‐Membered Copper Rings

Five geminal bis(phosphonates) containing an amino group in the α, γ or δ position of the carbon chain have been synthesised and their acid–base and complexation properties with Cu2+, Zn2+, Ca2+, Mg2+ and Na+ ions studied by potentiometry. Determination of the stability constants of the complexes with divalent metal ions is complicated by the formation of precipitates. The results of these studies show a negligible effect of the hydroxo group in the α position on the acid–base and complexation properties of the ligands. The presence of an amino group in the α position, however, decreases the basicity, which results in a lower complexation ability of the bis(phosphonates). The crystal structures of the three ligands with different degrees of protonation have also been determined. The structure of the triammonium salt of aminomethylbis(phosphonic acid) shows that the proton is bound to the nitrogen atom in monoprotonated species. The structure of the Cu2+ complex of pamidronate [{Cu2(H2pam)2}·H2O]n shows the presence of dimeric units with a relatively short distance (2.99 A) between the metal centres. These units form a coordination polymeric chain. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

Aminoalkylbis(phosphonates): Their Complexation Properties in Solution and in the Solid State

The mechanisms of the magnetic coupling interactions for two trigonal-bipyramid trinuclear Cu(II) complexes Cu3(mu3-X)2(mu-pz)3X3 (X = Cl and Br, respectively) and three trigonal trinuclear Cu(II) complexes Cu3(mu3-X)(mu-pz)3Cl3 (X = Cl, Br, and O) are investigated by the calculations based on density functional theory combined with broken-symmetry approach (DFT-BS). The research on the magneto-structural correlation reveals that the magnetic coupling interaction is sensitive to the Cu-(mu3-X)-Cu angle. With the Cu-(mu3-X)-Cu angle changing from 76 to 120 degrees, the magnetic coupling interaction is switched from ferromagnetic to antiferromagnetic. According to the analysis of the molecular orbitals and the variation of the spin-state energies versus the ratio of the magnetic coupling constants, it is found that there exists spin frustration phenomenon in these complexes.

Theoretical investigation on triagonal symmetry copper trimers: magneto-structural correlation and spin frustration.

Broken symmetry approach and density functional theory calculations for heterospin system consisting of copper(II) and aminoxyl radicals

The theoretical calculations on magnetic exchange interaction of the hetero-bridged tricopper(II) complex [Cu 3 (L 2 )Cl 2 ] 2+ and a related binuclear copper(II) model are carried out by using the density functional theory combined with the broken-symmetry approach. Meanwhile, one strategy computationally, so called isolated magnetic pair approach, is suggested to explore the spin frustration from geometry topology in poly-nuclear magnetic systems. It is found that the ferromagnetic coupling ( J 2 >0) of Cu1–Cu3 pair bridged by double μ–Cl ligands, in nature, is intrinsic, not resulted from geometrically spin frustration in the hetero-bridged tricopper(II) studied. However, in the whole molecule exist two competing contributions of antiferromagnetic and ferromagnetic coupling, and the antiferromagnetic coupling ( J 1 ) from Cu1–(μ–OR)–Cu2 and Cu2–(μ–OR)–Cu3 pairs dominates the magnetic behavior of the whole molecular system. On the other hand, the variation of J 1 / J 2 ratio affects significantly on magnetic properties of the system. The calculated effective magnetic moment μ eff of 2.26 μ B at the OPerdew functional level is compared to experimentally observation of 2.70 μ B in the solution. The briefly analysis of molecular magnetic orbitals demonstrated that the two local magnetic orbitals on Cu1 and Cu3 ions are orthogonal each other, and primarily responsible for the intrinsic ferromagnetic coupling between Cu1–(μ–Cl) 2 –Cu3. By comparison of spin population distributions for the Cu-triad and Cu-dimer the validity of the isolated magnetic pair approach is confirmed.

Is [Cu3(L2)Cl2]2+ a molecule with geometrically spin frustration? DFT study on magnetic competing interaction in hetero-bridged tricopper(II) complex

The magnetic exchange interaction in the quasi one-dimensional chain complex [Cu2(hedp)2]n4n− is investigated on the basis of the density functional theory combined with the broken symmetry approach. The title complex is modeled by binuclear models 1a and 1b. In the O–P–O bridged unit (model 1a), the magnetic exchange interaction exhibits antiferromagnetic characteristic, with the calculated magnetic coupling constant of −248 cm−1; while in the O atom bridged unit (model 1b), magnetic exchange interaction is ferromagnetic with the calculated magnetic coupling constant of +3.6 cm-1. In comparison with the analogue Cu2(CH3COO)4(H2O)2 it is found that in both the complexes the magnetic exchange interactions between the magnetic centers Cu(II) mainly are a super-exchange through the bridge groups, but not through a direct exchange between the Cu(II) ions. The analyses of molecular magnetic orbitals show that the magnetic exchange pathways in the two complexes are involved in σ-orbital on the bridging group, but not π-orbital. From Mulliken overlap spin population, the super-exchange interactions in both the acetate-bridged and diphosphonate-bridged Cu(II) complexes reveal a spin delocalization mechanism.

Zong-Chao Hu

Papers

Is [Cu3(L2)Cl2]2+ a molecule with geometrically spin frustration? DFT study on magnetic competing interaction in hetero-bridged tricopper(II) complex

Magnetic properties of diphosphonate-bridged binuclear copper(II) complex: a density functional theory study