The effect of the correction of the self-interaction error on the calculation of exchange coupling constants with methods based on density-functional theory has been tested in simple model systems. The inclusion of the self-interaction correction cancels the nondynamical correlation energy contributions simulated by the commonly used functionals. Hence, such correction should be important in the accurate determination of exchange coupling constants. We have also tested several recent functionals to calculate exchange coupling constants in transition-metal complexes, such as meta-GGA functionals or new formulations of hybrid functionals. The influence of the basis set and of the use of pseudopotentials on the calculated J values has also been evaluated for a Fe(III) dinuclear complex in which the paramagnetic centers bear several unpaired electrons.

About the calculation of exchange coupling constants using density-functional theory: the role of the self-interaction error.

The combination of diol-type ligands with paramagnetic transition metal ions has led to the isolation of a host of new homometallic and heterometallic clusters, high-spin molecules and single molecule magnets ranging in nuclearity from two to forty four and with spin ground states as large as S = 61/2. The ligands, whose cluster coordination chemistry is discussed in this article, are 1,3-propanediol and its derivatives, diethanolamine and its derivatives, pyridine-2,6-dimethanol and the gem-diol form of di-2-pyridyl ketone. The structural diversity of the complexes stems from the ability of the ligands to adopt a variety of bridging coordination modes depending on the positions of the two hydroxyl groups in the molecule, the presence/absence of extra donor groups and on the reaction conditions. Examples of ‘true’ reactivity chemistry involving clusters of diol-type ligands are also given. The activation of pyridine-2,6-dimethanol and di-2-pyridyl ketone by 3d-metal centres towards further reactions seems to be an emergent area of synthetic chemistry.

Diol-type ligands as central ‘players’ in the chemistry of high-spin molecules and single-molecule magnets

Polynuclear transition metal complexes containing paramagnetic cations have caught the attention of many chemists, since they are one of the main fields of study in molecular magnetism and they play important roles in the reactivity of active sites of systems of biological interest. Theoretical methods based on density functional theory due to the possibility of handling large systems are especially indicated for studying the electronic structure of this kind of molecules. At the same time, such methods provide good accuracy to allow the calculation of the small energy differences involved in the exchange interactions. It is worth noting that theoretical methods are especially important in the study of the exchange interactions in complexes with a large number of paramagnetic centers because they can provide a more detailed analysis of the interactions than experimental data can. This fact is due to the limitations in obtaining exchange coupling constants from experimental measurements for large size systems of this kind. The knowledge of the exchange interactions that controls the ground state of the system is crucial to the understanding of magnetic properties such as the single-molecule magnet character or the reactivity of an active site in a biological system.

Theoretical Study of the Exchange Coupling in Large Polynuclear Transition Metal Complexes Using DFT Methods

Single-molecule magnets (SMMs) represent a molecular approach to nanoscale magnetic materials. They are molecules possessing a large barrier (versus kT) to magnetization relaxation, and thus display magnetization versus appliedfield hysteresis loops at low enough temperatures, the diagnostic property of a magnet. SMMs derive their properties from a combination of a large ground-state spin (S) value and a significant magnetoanisotropy of the Ising (easy-axis) type. Deprotonated pyridine-2,6-dimethanol (pdmH2) has proven a versatile N,O,O chelating and bridging ligand in our manganese-cluster chemistry. It has been found as a chelate in species such as [PtCl2(pdmH2)], [2] [TcOCl(pdmH)2], [3] and [{MoO2(pdm)}n]. [4] In manganese chemistry, the alkoxide arms also act as bridging groups yielding polynuclear clusters such as [Mn4(O2CMe)2(pdmH)6] 2+ with S = 9, [Mn9(O2CEt)12(pdm)(pdmH)2(L)2] with S = 11/2, and [Mn25O18(OH)2(N3)12(pdm)6(pdmH)6] 2+

DFT Computational Rationalization of an Unusual Spin Ground State in an Mn12 Single‐Molecule Magnet with a Low‐Symmetry Loop Structure

The syntheses, crystal structures, and magnetic characterizations of three new hexanuclear iron(III) compounds are reported. Known [Fe6O2(OH)2(O2CBut)10(hep)2] (1) is converted to new [Fe6O2(OH)(O2...

Large spin differences in structurally related Fe6 molecular clusters and their magnetostructural explanation.

The local spin formalism (Clark, A. E.; Davidson, E. R. J Chem Phys 2001, 115, 7382–7392) for computing expectation values 〈SA· SB〉 that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high-spin radical centers are given by the same Heisenberg coupling constants {JAB} that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values 〈SA· SB〉 energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin-state energies in this way for polynuclear transition metal complexes using the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S) in the ZINDO program. This method is referred to as ZILSH, derived from ZINDO, Davidson's local spin formalism, and the Heisenberg spin model. Coupling constants and spin ground states obtained for 10 iron complexes containing from 2 to 6 metals are found to agree well with experimental results in most cases. In the case of the complex [Fe6O3(OAc)9(OEt)2(bpy)2]+, a priori predictions of the coupling constants yield a ground-state spin of zero, in agreement with variable-temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

Ted A. O'Brien

Papers

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes