Zero-field splittings from density functional calculations: analysis and improvement of known methods

Several different approaches have been proposed to calculate the zero-field splitting tensor with density functional methods. In this work, our own derivation is presented in some detail, to allow a theoretical analysis and a comparison with other methods [M. R. Pederson and S. N. Khanna, Phys. Rev. B 60, 9566 (1999); F. Neese, J. Am. Chem. Soc. 128, 10213 (2006); J. Chem. Phys. 127, 164112 (2007)]. Pederson's method can be improved by properly taking into account the quantum nature of spin when extracting the zero field splitting tensor from the magnetic anisotropy. A closed-shell molecule at large distance from an open shell complex will have a spurious contribution to the zero-field splitting tensor calculated with Neese's methods. We thus have analyzed his approach in some detail and found that it can be corrected if one properly transforms the equations used in wave function based theory to a sum-over-states type expression before one interprets it as an energy derivative. If improved along these lines, Neese's and Pederson's methods become identical down to the working equations. The theoretical analysis is illustrated by sample calculations on the well-studied Mn(III)-tris-acetylacetonato complex Mn(acac)(3), both as an isolated molecule and with a Pd(II) dichloro diammine complex at large distance as an innocent spectator.