A Glimpse into the Ligand Field Theory from Density Functional Perspective

Abstract

Electronic structure of transition metal complexes are commonly rationalized within the Ligand Field Theory (LFT). In LFT the Hamiltonian is parameterized in terms of one-electron (LF) parameters and two-electron repulsion integrals (Racaha's parameters) within the manifold of d-electrons. These parameters are determined from a fit to some experimental spectrum. The main drawback of LFT is its empirical nature, thus being limited to a description of the data, and predictions are often restricted to a chemical intuition. To overcome this, hybrid methodology, which combines a multideterminant DFT-based method with LFT, so called LF-DFT, has been developed. At the same time, LF-DFT successfully tackles many shortcomings of standard DFT, including orbital degeneracy and excited states. It works by evaluating DFT energies of all the Slater determinants arising from a dn configuration of the transition-metal ion in the environment of coordinating ligands using Kohn−Sham orbitals. This set of energies is then analyzed within a LF model to obtain variationally the energy and wave function of the ground and excited states. In doing so, both dynamical correlation (via exchange-correlation energy) and non-dynamical correlation (via LF CI) are considered. The quality of the LF-DFT for the calculations of d-d transitions is comparable to the high-level ab initio calculations, and in some cases, e.g. [CrF6]3-, [MnF6]2-, [Mn(H2O)6]2+, [Fe(H2O)6]3+ even outshines them. One of the main strengths of LF-DFT is accurate prediction of magnitude and sign of the Zero-Field Splitting (ZFS) parameters, as well as the orientation of the principal magnetic axes. In addition, we can pin-point the excitations that control the sign and magnitude of the ZFS parameters.Therefore, with a help from DFT based LF theory we can, hopefully, find a way to control the magnetic properties of transition metal complexes.