First-principles calculations of zero-field splitting parameters

Abstract

In this work, an implementation of an approach to calculate the zero-field splitting (ZFS) constants in the framework of ab initio methods such as complete active space self-consistent field, multireference configuration interaction, or spectroscopy oriented configuration interaction is reported. The spin-orbit coupling (SOC) contribution to ZFSs is computed using an accurate multicenter mean-field approximation for the Breit-Pauli Hamiltonian. The SOC parts of ZFS constants are obtained directly after diagonalization of the SOC operator in the basis of a preselected number of roots of the spin-free Hamiltonian. This corresponds to an infinite order treatment of the SOC in terms of perturbation theory. The spin-spin (SS) part is presently estimated in a mean-field fashion and appears to yield results close to the more complete treatments available in the literature. Test calculations for the first- and second-row atoms as well as first-row transition metal atoms and a set of diatomic molecules show accurate results for the SOC part of ZFSs. SS contributions have been found to be relatively small but not negligible (exceeding 1 cm(-1) for oxygen molecule). At least for the systems studied in this work, it is demonstrated that the presented method provides much more accurate estimations for the SOC part of ZFS constants than the emerging density functional theory approaches.

Detailed Ab Initio First-Principles Study of the Magnetic Anisotropy in a Family of Trigonal Pyramidal Iron(II) Pyrrolide Complexes

“…Through this mixing, SOC reintroduces some orbital angular momentum into the electronic ground state that is otherwise well known to be quenched through low symmetry. In QDPT, 63 one starts by obtaining an approximate solution of the BornÀOppenheimer (BO) Hamiltonian of a multireference type such as CASSCF in the form given by…”

“…65,66 Evaluation of the matrix elements of the orbital momentum operators between the |Ψ I SM s ae basis functions is done in terms of one-electron matrix elements within the MO basis. This procedure carries us beyond the perturbative regime and accounts for strong SOC effects to all orders.…”

A state interaction spin-orbit coupling density matrix renormalization group method

“…[77][78][79] The second, two-step, state-interaction method expands the eigenstates ofĤ in terms of the spin-pure eigenstates ofĤ SR . 53,54,80,81 The coefficients of expansion may be determined using different methods, such as perturbation theory [82][83][84][85][86] or through diagonalization (state interaction). [54][55][56][57][58] The latter corresponds to solving…”

The Density Functional Theory

“…For transition metal complexes, it was shown that DFT predicts the ZFS parameter with the correct sign but tends to underestimate its magnitude, often by a factor of 2 (Neese 2003). Meanwhile, a certain number of applications have demonstrated the usefulness of ab initio treatments for the calculation of the ZFS (Ganyushin and Neese 2006;Neese et al 2007b).…”