A Systematic Density Functional Study of the Zero-Field Splitting in Mn(II) Coordination Compounds

Abstract

This work presents a detailed evaluation of the performance of density functional theory (DFT) for the prediction of zero-field splittings (ZFSs) in Mn(II) coordination complexes. Eighteen experimentally well characterized four-, five-, and six-coordinate complexes of the general formula [Mn(L)nL'2] with L' = Cl, Br, I, NCS, or N3 (L = an oligodentate ligand) are considered. Several DFT-based approaches for the prediction of the ZFSs are compared. For the estimation of the spin-orbit coupling (SOC) part of the ZFS, it was found that the Pederson-Khanna (PK) approach is more successful than the previously proposed quasi-restricted orbitals (QRO)-based method. In either case, accounting for the spin-spin (SS) interaction either with or without the inclusion of the spin-polarization effects improves the results. This argues for the physical necessity of accounting for this important contribution to the ZFS. On average, the SS contribution represents approximately 30% of the axial D parameters. In addition to the SS part, the SOC contributions of d-d spin flip (alphabeta) and ligand-to-metal charge transfer excited states (betabeta) were found to dominate the SOC part of the D parameter; the observed near cancellation between the alphaalpha and betaalpha parts is discussed in the framework of the PK model. The calculations systematically (correlation coefficient approximately 0.99) overestimate the experimental D values by approximately 60%. Comparison of the signs of calculated and measured D values shows that the signs of the calculated axial ZFS parameters are unreliable once E/D > 0.2. Finally, we find that the calculated D and E/D values are highly sensitive to small structural changes. It is observed that the use of theoretically optimized geometries leads to a significant deterioration of the theoretical predictions relative to the experimental geometries derived from X-ray diffraction. The standard deviation of the theoretical predictions for the D values almost doubles from approximately 0.1 to approximately 0.2 cm-1 upon using quantum chemically optimized structures. We do not find any noticeable improvement in considering basis sets larger than standard double- (SVP) or triple-zeta (TZVP) basis sets or using functionals other than the BP functional.

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

“…When E = 1/3, the system is characterized by three equidistant levels and the sign of the D-value becomes undefined. 20 It may be worthwhile mentioning that the early theoretical work from our laboratory 15 was consistent with the ZFS of aqueous nickel(II) yielding, on average, a system of three equidistant levels. This observation was also employed in building simple models for NMR relaxation in aqueous nickel(II) solutions with a certain success.…”

“…Mn(II) (d 5 , S = 5/2) is characterized by a highly symmetric electronic structure and low ZFS (typically below 1 cm −1 ). Zein and Neese 20 reported a comparative study of DFT and CASSCF calculation of the ZFS in a series of Mn(II) coordination complexes. The DFT (B3LYP) calculations, using the CP approach to the SOC and including the SSC, performed here quite well, in fact more successfully than the CASSCF calculations including only the metal d-orbitals in the active space.…”

“…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).…”

On the Electronic Structure of NiII Complexes That Feature Chelating Bisguanidine Ligands

“…Indeed, in a recent systematic DFT study of the ZFS in Mn II complexes, Zein et al demonstrated that "even minor errors in the computed structure by DFT translate into significant errors in the predicted ZFS (by means of the coupled-perturbed spin-orbit coupling approach) owing to the subtle interplay of factors that contribute to the ZFS". [35] Hence, in the study by Zein et al the quality of the predicted ZFS parameters decreased markedly for the DFT-optimized structures. This again suggests that a proper theoretical treatment of spin-orbit coupling (SOC), the mixing of excited states with the ground state, and eventually also direct dipoledipole interactions of unpaired electrons (SS) [36] might be necessary for meaningful geometry optimizations of compounds that display a pronounced ZFS.…”

The Density Functional Theory

“…The intricacies in the application of DFT in this area are highlighted in a detailed evaluation of DFT performance for the prediction of ZFS in Mn(II) coordination complexes (Zein et al 2008b). The study revealed that regardless of whether the spin-orbit coupling (SOC) part of the ZFS was estimated with the Pederson-Khanna or the quasi-restricted orbitals approach, accounting for the spin-spin (SS) interaction always improves the results.…”