Importance of Direct Spin−Spin Coupling and Spin-Flip Excitations for the Zero-Field Splittings of Transition Metal Complexes: A Case Study

This work reports the evaluation of several theoretical approaches to the zero-field splitting (ZFS) in transition metal complexes. The experimentally well-known complex [Mn(acac)3] is taken as an example. The direct spin−spin contributions to the ZFS have been calculated on the basis of density functional theory (DFT) or complete active space self-consistent field (CASSCF) wave functions and have been found to be much more important than previously assumed. The contributions of the direct term may exceed ∼1 cm-1 in magnitude and therefore cannot be neglected in any treatment that aims at a realistic quantitative modeling of the ZFS. In the DFT framework, two different variants to treat the spin−orbit coupling (SOC) term have been evaluated. The first approach is based on previous work by Pederson, Khanna, and Kortus, and the second is based on a "quasi-restricted" DFT treatment which is rooted in our previous work on ZFS. Both approaches provide very similar results and underestimate the SOC contribution to the ZFS by a factor of 2 or more. The SOC is represented by an accurate multicenter spin−orbit mean-field (SOMF) approximation which is compared to the popular effective DFT potential-derived SOC operator. In addition to the DFT results, direct "infinite order" ab initio calculations of the SOC contribution to the ZFS based on CASSCF wave functions, the spectroscopy-oriented configuration interaction (SORCI), and the difference-dedicated CI (DDCI) approach are reported. In general, the multireference ab initio results provide a more realistic description of the ZFS in [Mn(acac)3]. The conclusions likely carry over to many other systems. This is attributed to the explicit treatment of the multiplet effects which are of dominant importance, since the calculations demonstrate that, even in the high-spin d4 system Mn(III), the spin-flip excitations make the largest contribution to the SOC. It is demonstrated that the ab initio methods can be used even for somewhat larger molecules (the present calculations were done with more than 500 basis functions) in a reasonable time frame. Much more economical but still fairly reasonable results have been achieved with the INDO/S treatment based on CASSCF and SOC-CI wave functions.