Remarks on the Proper Use of the Broken Symmetry Approach to Magnetic Coupling

Abstract

The effect of nonorthogonality in the broken symmetry approach to magnetic coupling has been explicitly considered for the first time in Hartree−Fock and a variety of DFT methods. On the basis of the results for three different systems, representative of a variety of physical situations it is shown that the most often quoted trend concerning the much larger degree of delocalization of magnetic orbitals obtained from DFT, as opposed to Hartree−Fock, is not fully justified. A new and simple way to relate the overlap integral entering into the calculation and the spin density is proposed and tested in a variety of model systems.

Spin Symmetry Requirements in Density Functional Theory: The Proper Way to Predict Magnetic Coupling Constants in Molecules and Solids

“…The problem of computing atomic multiplet energies using DFT was analyzed in the pioneering work of Bagus and Bennet [54] extended later by Ziegler et al [55] These authors already point out the difficulties of the Kohn-Sham formalism when applied to open-shell systems and provide some rules to compute the energy of a state with a defined value of S 2 . A similar situation appears when using DFT to attempt to compute the singlet-triplet gap in an organic biradical or, equivalently, in a magnetic dinuclear complex with two unpaired electrons [4,5]. Unfortunately, the original works of Bagus and Bennet [54] and of Ziegler et al [55] have not caused the large impact they deserve and, to a large extent, have been ignored by many theoretical chemists and physicists more worried to obtain a number close to the experiment than ensuring that the calculated value does indeed represent a physical state.…”

“…In this case one has to rely on broken space and spin symmetry solutions to approximate [56,57] the low spin electronic states. This approach and its deficiencies have largely been described in previous works [4,5,26,27,58,59]. However, the use of a broken symmetry solution is still unavoidable for periodic systems.…”

“…For a large number of systems the magnetic moments are well localized on a given atom or group of atoms, referred to as magnetic centers; an effective magnetic moment, S i , can be associated to a given magnetic center i [1][2][3]. The physical description of magnetic coupling in a broad class of chemical compounds including organic biradicals, inorganic complexes and ionic solids is based on the use of the well-known phenomenological Heisenberg-Dirac-van Vleck Hamiltonian [1][2][3][4][5], which describes the isotropic interaction between localized magnetic moments S i and S j aŝ…”

“…The understanding of magnetic interactions is essential to analyze and interpret, among others, neutron diffraction experiments and magnetic susceptibility measurements. Most important is the fact that magnetic interactions are at the hearth of molecular based magnets [1][2][3][4][5][6] or of High-T c superconductivity [7] and largely dominate the chemistry of radicals [1,6,8]. Also, the description of magnetic states of damaged DNA, RNA or protein oxidation adducts by radicals has an increasing interest because of their relevance to understand the biological activity of important carcinogenic and antitumor compounds.…”

“…However, since DFT does only make reference to the one electron density matrix, the treatment of open-shell systems is not straightforward although spin-polarized DFT is almost universally used [17][18][19][20][21][22][23][24]. Several authors have recently addressed the problem of using DFT to predict the singlet-triplet gap, or equivalent energy differences, in magnetic systems [4,5,26,27]. The present work extends a previous analysis [28] and critically examines the reliability of magnetic coupling constants obtained by current implementations of DFT and show that the proper treatment of general open shell electronic states, where spin cannot be neglected, requires a revision of the current exchange-correlation potentials.…”