A single configuration model containing nonorthogonal magnetic orbitals is developed to represent the important features of the antiferromagnetic state of a transition metal dimer. A state of mixed spin symmetry and lowered space symmetry is constructed which has both conceptual and practical computational value. Either unrestricted Hartree–Fock theory or spin polarized density functional theory, e.g., Xα theory, can be used to generate the mixed spin state wave function. The most important consequence of the theory is that the Heisenberg exchange coupling constant J can be calculated simply from the energies of the mixed spin state and the highest pure spin multiplet.

Valence bond description of antiferromagnetic coupling in transition metal dimers

Magnetism of lanthanides in molecular materials with transition-metal ions and organic radicals.

Ligand spin polarization and antiferromagnetic coupling in transition metal dimers

The application of broken symmetry density functional calculations to homobinuclear and heterobinuclear transition metal complexes produces good estimates of the exchange coupling constants as compared to experimental data. The accuracy of different hybrid density functional theory methods was tested. A discussion is presented of the different methodological approaches that apply when a broken symmetry wave function is used with either Hartree–Fock or density functional calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1391–1400, 1999

Broken symmetry approach to calculation of exchange coupling constants for homobinuclear and heterobinuclear transition metal complexes

Magnetic coupling constants (2J) of hydroxo- and alkoxo-bridged copper binuclear compounds have been evaluated to determine the accuracy of different density functional methods and to study the magnetic behavior of these compounds. Comparison between the calculated and experimental coupling constants for the complete structures of five compounds shows that the most successful computational strategy is the combination of the B3LYP method with the broken-symmetry approach. Calculations for model compounds of both families yield reasonable approximations to the values of magnetic coupling constants calculated for the full molecular structures. Our calculations show a correlation between the magnetic coupling constant and the Cu−O−Cu bridging angle and with the out-of-plane displacement of the hydroxo or alkoxo groups, in agreement with the experimental data. The counterions of the hydroxo-bridged complexes, when hydrogen bonded to the bridging hydroxo group, determine the extent of the out-of-plane displacem...

Toward the Prediction of Magnetic Coupling in Molecular Systems: Hydroxo- and Alkoxo-Bridged Cu(II) Binuclear Complexes

A molecular orbital analysis shows that the antiferromagnetic contributions to magnetic coupling, favoring a lowspin ground state for a dimer containing two weakly interacting metal centers, can be analyzed in terms of pairwise interactions of dimeric molecular orbitals, with the square of the splitting in energy between the members of a pair being a measure of the stabilization of the low-spin state. The effect of geometrical distortions, electronegativity, and variation of substituents on the magnetic interaction in dimeric systems is examined in detail for singly bridged L,M-X-ML, ( n = 3 , 4 , 5); Cu~C16~and other doubly bridged species where the bridging ligands are halogens, OR, pyridine N-oxides, oxalate, squarate; and the acetate bridged dimers C u ~ ( R C 0 0 ) 4 . The emphasis is on d9 Cu(I1) dimers, but other transition metal systems are also analyzed. Transition metal complexes containing more than one metal atom with unpaired electrons can generally be categorized according to their magnetic behavior into three main groups depending on the strength of the metal-metal interaction. In the noninteracting type the magnetic properties of the dimer (or polymer) a re essentially unchanged from the paramagnetic monomer. In the strongly interacting type formation of relatively strong metal-metal bonds occurs, and the molecule will display simple diamagnetic behavior (for even numbers of electrons). In this paper the properties of weakly interacting metal ions will be investigated. In such compounds this weak coupling between the electrons of the two metal ions leads to low-lying excited states of different spin which can be populated a t thermal energies (SI000 cm-I). The resulting magnetic behavior will be antiferromagnetic or ferromagnetic, depending on whether the low spin (spins paired) or high spin (spins parallel) state is the ground state, respectively. These interactions-often termed superexchange because of the large distances involved (3-5 A) between the metal ions-have been observed in a wide variety of compounds. I 5 In experimental studies the magnetic interaction between spins SA and Sg for atoms A and B is usually written in a form suggested originally by Heisenberg, Dirac, and Van

P. Jeffrey Hay

Papers

Orbital interactions in metal dimer complexes