Calculation of electronic g‐tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin‐orbit operators

Abstract

We report the first implementation of the calculation of electronic g-tensors by density functional methods with hybrid functionals. Spin-orbit coupling is treated by the atomic meanfield approximation. g-Tensors for a set of small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using the local density approximation (VWN functional), the generalized gradient approximation (BP86 functional), as well as B3-type (B3PW91) and BH-type (BHPW91) hybrid functionals. For main group radicals, the effect of exact-exchange mixing is small. In contrast, significant differences between the various functionals arise for transition metal complexes. As has been shown previously, local and in particular gradient-corrected functionals tend to underestimate the "paramagnetic" contributions to the g-tensors in these cases and thereby recover only about 40-50% of the range of experimental g-tensor components. This is improved to ca. 60% by the B3PW91 functional, which also gives slightly reduced standard deviations. The range increases to almost 100% using the half-and-half functional BHPW91. However, the quality of the correlation with experimental data worsens due to a significant overestimate of some intermediate g-tensor values. The worse performance of the BHPW91 functional in these cases is accompanied by spin contamination. Although none of the functionals tested thus appears to be ideal for the treatment of electronic g-tensors in transition metal complexes, the B3PW91 hybrid functional exhibited the overall most satisfactory performance. Apart from the validation of hybrid functionals, some aspects in the treatment of spin-orbit contributions to the g-tensor are discussed.

DFT investigation of the effect of spin-orbit coupling on the NMR shifts in paramagnetic solids

“…One would expect the resulting larger spin density at the metal centre to enhance the g-tensor, due to larger spin-orbit contributions from the heavier centre. This is what one observes in g-tensor calculations on molecular 3d-complexes, where adding more exact exchange to a hybrid functional increases the g-tensors [57]. Then why do Hubbard +U corrections provide a change in the opposite direction?…”

“…While the same increase of the gap also occurs with increasing HF exchange in hybrid functionals, in the latter case the effect is overcompensated by the enhanced coupling terms contributed by the non-local HF exchange potential [57], leading to an overall increased linear response. Such coupling terms are absent in the DFT+U scheme, and thus the Hubbard terms move the results in the wrong direction.…”

“…For this, three hybrid exchange-correlation functionals were used: the PBE0 incorporating 25% Hartree-Fock (HF) exchange [54,55], shown to provide satisfactory performances for the electronic and magnetic structures of the class of materials of interest [53], and the related 20% HF hybrid (PBE20) and 35% HF hybrid (PBE35). The choice of studying these systems with a range of hybrid functionals was motivated by the known sensitivity of the electronic delocalisation and spin polarisation on the percent of HF exchange included [12,53,56,57]. Two levels of allelectron atom-centered basis set were used, a smaller set used for structure optimisation and a more extended one used for hyperfine calculations [12].…”

Ligand spheres in asymmetric hetero Diels–Alder reactions catalyzed by Cu(ii) box complexes: experiment and modeling

“…The choice of this functional was based on previous computations which show that it is very successful in the prediction of hyperfine coupling (HFC) and g-tensor in nitrogen and Cu(II) complexes. 48,[64][65][66] Ligand atoms were treated by Huzinaga-Kutzelnigg type basis sets BII (denoted also as IGLO-II). 67,68 For the Cu center an accurate triply polarized basis set CP(PPP) was employed.…”

Hybrid exchange correlation functionals and potentials: Concept elaboration

“…These are, e.g., the parameters of nuclear magnetic resonance (NMR) and electronic paramagnetic resonance (EPR) of transition metal complexes. As examples we can cite the iron ( 57 Fe) and ruthenium ( 103 Ru) chemical shifts in the corresponding complex compounds [58,59], as well as the electronic g tensors of metal complexes from the first transition row [60]. As mentioned above, the hybrid functionals are associated with an undesirable effect of "hyperparametrization."…”