Complicated Electronic Structures
Finding the correct representation of the electronic structures of complexes 5 and 8 , both Fe(II) high spin (S = 2), presented some challenges, which were however fully resolved. Since an Fe(II) high spin species is a likely intermediate or resting state of FeNC catalysts, we discuss these cases briefly.
For complex 5 , the geometry optimisation resulted in a structure with a Mulliken spin population of 3.74 at the iron ion. For the single point calculation however, the initially obtained orbital occupation pattern can be summarized as (xy)2(xz)1(yz)1(z2)1(x2–y2)0with a Mulliken spin population at the iron of 2.94 and the remaining spin delocalised on the ligand as indicated by significant spin population on the carbon atoms (1.01 in total). With this electronic configuration, erroneous Mössbauer parameters of δB3LYP = 0.65 mm s−1exp = 1.03 mm s−1) and ΔE QB3LYP = 1.48 mm s−1E Qexp = 4.01 mm s−1) were found. Of course, the incorrect Mulliken spin populations allowed for a quick identification of the wrong electronic structure description. To resolve this issue, specific orbitals were rotated to yield a more adequate orbital occupation pattern of (xy)2(xz)1(yz)1(z2)1(x2–y2)1with a Mulliken spin population at the iron of 3.77, which was also energetically preferred. Accordingly, the Mössbauer parameters improved to δB3LYP = 1.05 mm s−1exp = 1.03 mm s−1) and ΔE QB3LYP = 4.19 mm s−1E Qexp = 4.01 mm s−1), i.e. well within the error margins deduced above.
For complex 8 , a similar problem was encountered already at the stage of TPSS geometry optimisation with a Mulliken spin population of 2.77 instead of the expected value close to 4. With this structure, in the B3LYP single point calculation the d(x2–y2) orbital is also found to be unoccupied resulting in a Mulliken spin population of 2.91 and inaccurate predictions for the Mössbauer parameters: δB3LYP = 0.47 mm s−1exp = 1.05 mm s−1) and ΔE QB3LYP = 2.28 mm s−1E Qexp = 4.25 mm s−1). After re-optimisation and orbital rotation, an appropriate representation of the Fe(II) high spin electronic structure is found with a Mulliken spin population of 3.80. With this geometric and electronic structure, the Mössbauer parameters improve significantly to δB3LYP = 1.06 mm s−1exp = 1.05 mm s−1) and ΔE QB3LYP = 4.30 mm s−1E Qexp = 4.25 mm s−1).
In Figure 6, the electron densities and spin densities for 5 in both electronic structure variants are shown. Although the relevant quantity for Mössbauer spectroscopy is the electron density and not the spin density,72 it can be readily seen that the electron density is not suitable to discuss any electronic structure changes (Figure 6A/C). Spin density plots are sometimes used in the FeNC literature to characterize and discuss the electronic structures.131 In contrast to the indistinguishable electron densities, the spin density plots do show some discernible differences (Figure 6B/D). In the “initial”, incorrect electronic structure description where one iron α d-orbital was erroneously unoccupied, β spin density (yellow) is seen on the nitrogen donor atoms (Figure 6B). Additionally, there is α spin density (red) in the “initial” electronic structure descriptions distributed on the ligand, which can be rationalised as a contribution from a ligand-centered α orbital that is occupied but unmatched. However, purely by inspection of the spin densities, it is very difficult to ascertain that an adequate electronic structure is obtained. A spin population analysis appears much more suitable, while an analysis of the MO occupation pattern may be even preferred if an accurate description of the quadrupole splitting is of high importance.