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−1(δexp = 1.03 mm s−1) and
ΔE QB3LYP = 1.48 mm
s−1 (ΔE 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−1(δexp = 1.03 mm s−1) and
ΔE QB3LYP = 4.19 mm
s−1 (ΔE 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−1(δexp = 1.05 mm s−1) and
ΔE QB3LYP = 2.28 mm
s−1 (ΔE 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−1 (δexp = 1.05 mm
s−1) and
ΔE QB3LYP = 4.30 mm
s−1 (ΔE 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.