Systematic Theoretical Study of the Zero-Field Splitting in Coordination Complexes of Mn(III). Density Functional Theory versus Multireference Wave Function Approaches

Abstract

This paper presents a detailed evaluation of the performance of density functional theory (DFT) as well as complete active space self-consistent field (CASSCF)-based methods (CASSCF and second-order N-electron valence state perturbation theory, NEVPT2) to predict the zero-field splitting (zfs) parameters for a series of coordination complexes containing the Mn(III) ion. The physical origin of the experimentally determined zfs's was investigated by studying the different contributions to these parameters. To this end, a series of mononuclear Mn(III) complexes was chosen for which the structures have been resolved by X-ray diffraction and the zfs parameters have been accurately determined by high-field EPR spectroscopy. In a second step, small models have been constructed to allow for a systematic assessment of the factors that dominate the variations in the observed zfs parameters and to establish magnetostructural correlations. Among the tested functionals, the best predictions have been obtained with B3LYP, followed by the nonhybrid BP86 functional, which in turn is more successful than the meta-hybrid GGA functional TPSSh. For the estimation of the spin-orbit coupling (SOC) part of the zfs, it was found that the coupled perturbed SOC approach CP is more successful than the Pederson-Khanna method. Concerning the spin-spin interaction (SS), the restricted open-shell Kohn-Sham (ROKS) approach led to a slightly better agreement with the experiment than the unrestricted KS (UKS) approach. The ab initio state-averaged CASSCF (SA-CASSCF) method with a minimal active space and the most recent implementation that treats the SOC and SS contributions on an equal footing provides the best predictions for the zfs. The analysis demonstrates that the major contribution to the axial zfs parameter (D) originates from the SOC interaction but that the SS part is far from being negligible (between 10 and 20% of D). Importantly, the various excited triplet ligand field states account for roughly half of the value of D, contrary to popular ligand field models. Despite covering dynamic correlation contributions to the transition energies, NEVPT2 does not lead to large improvements in the results as the excitation energies of the Mn(III) d-d transitions are already fairly accurate at the SA-CASSCF level. For a given type of coordination sphere (e.g., elongated or compressed octahedron), the magnetic anisotropy of the Mn(III) ion, D, does not appear to be highly sensitive to the nature of the ligands, while the E/D ratio is notably affected by all octahedral distortions. Furthermore, the introduction of different halides into the coordination sphere of Mn(III) only leads to small effects on D. Nevertheless, it appears that oxygen-based ligands afford larger D values than nitrogen-based ligands.

Zero-field splitting in nickel(II) complexes: A comparison of DFT and multi-configurational wavefunction calculations

“…Similar conclusions for other Mn(III) systems were reached in other papers from Neese's group. 26,79,80 Moreover, some model Mn(III) complexes were the topic of an ab initio study by Maurice et al 81,82 The conclusion of this discussion might be that the difficult systems, with spatially nearly degenerate states, require the use of the most advanced theoretical tools, such as the NEVPT2/QDPT combination. What is surprising, to a certain extent, is the fact that our calculations for the apparently "easy" case of nickel(II), with the triplet ground state quite far below the excited states, show the same trend as the "difficult" ions.…”

“…13,14 We also reported a combination of molecular dynamics (MD) simulations and ZFS calculations yielding a time correlation function for the fluctuations of the ZFS in aqueous nickel(II) solution. 15,16 The development of the theoretical tools to calculate the ZFS parameters by quantum chemistry technique over the last decade has been quite impressive, with Frank Neese and his group as the leading team, 10,11,[17][18][19][20][21][22][23][24][25][26][27][28][29][30] but also with important contributions from other authors. [31][32][33][34][35][36][37] The development has followed two routes, making use of either efficient density functional theory (DFT) techniques or of high-end wavefunction methods based on multi-configurational SCF techniques (such as complete active space self-consistent field (CASSCF) and related extensions).…”

First principles approach to the electronic structure, magnetic anisotropy and spin relaxation in mononuclear 3d-transition metal single molecule magnets

“…Based on qualitative reasoning, the barrier was identified with 2 DS where D is the axial zero-field splitting (ZFS) parameter of the investigated multiplet (also called the 'magnetic anisotropy'). In Mn12, a net D -value of only -0.46 cm -1 arises, mainly from the coupling of the local D -values of the Mn III ions, which typically display local D -values of around≈-2 cm -1 [12]. Based on this model it was concluded that in order to obtain SMMs with higher blocking temperature, it is necessary to synthesize molecules that have a large and negative D -value and a large total spin S .…”

“…The negative D -value is necessary in order to ensure that the magnetic sublevels with the largest magnetic moments are lowest in energy and hence that the system shows a large net magnetization, while the large spin S would ensure a high barrier. A large total spin S (beyond 5/2 S = for d-elements and [16], iron [Fe 8 O 2 (OH) 12 (L) 6 ] 8+ [17] and a Mn 6 SMM, [Mn III 6 (μ 3 -O) 2 (μ 3 -ONR) 2 (μ 2 -ONR) 4 ] 2+ (reported record barrier -1 57.6 cm U = , 4 B T K ∼ [18]). Systems with up to the impressive total spin of 83/2 S = have been reported [19].…”

Density functional theory study of the magnetic coupling interaction in a series of binuclear oxalate complexes

“…A deeper understanding of the microscopic processes related to magnetic interactions has been a very interesting topic in computational chemistry since the first half of the twentieth century [1][2][3][4][5][6][7][8][9][10]. The idea of using molecules, rather than the ionic and metallic lattices of typical magnets, stems from the rapid development of functional molecular materials, and gives a better insight into the nature of coupling between paramagnetic centers.…”