Figure 6. Isosurface plots of the electron density (left) and
spin density (right) for complex 5 with initial (A, B) and
final (C, D) electronic structure (for complex 8 , see Figure S4
in the Supporting Information). The cutoff radii are set to 0.2 for the
electron density and 0.005 for the spin density.
The outliers excluded from the fit presented above are complexes9 and 10 (see SI for the fit including all 20
complexes), which have been noted as outliers in previous studies as
well.20,21 The isomer shifts predicted with B3LYP
deviate by 0.077 mm s−1 (9 ) and 0.159 mm
s−1 (10 ) from experiment, the respective
quadrupole splitting values by 1.601 mm s−1(9 ) and 1.848 mm s−1 (10 ). While for9 , δ is thus predicted within the double mean absolute
deviation of 0.131 mm s−1, the calculated value for10 is outside this trust region. For both complexes, the error
in the quadrupole splitting prediction is far outside the trust region
of 0.451 mm s−1 and the maximum deviation of 0.57 mm
s−1 for the other members of the correlation line. In
both cases, the iron(II) intermediate spin (2S +1 = 3) ion is
found in the square-planar coordination sphere of a decorated porphyrin.
The difficulties in describing such Fe(II)-porphyrin electronic
structures have been known for many years, and the body of computational
chemistry literature pertaining to the correct prediction of the
relative spin states is vast.65 To briefly review the
key points of discussion, in D4h symmetry the two
lowest-lying triplet states are 3A2gwith a d-orbital occupation pattern of
(xy)2(z2)2(xz)1(yz)1(x2–y2)0and 3Eg with degenerate
(xy)2(z2)1(xz)2(yz)1(x2–y2)0or
(xy)2(z2)1(xz)1(yz)2(x2–y2)0configurations. Additionally, there is a low-lying5A2g state, and it is difficult to
predict the energetic gap between the correct triplet ground state and
the higher lying triplet and quintet states. However, for the purpose of
estimating the uncertainty of Mössbauer parameter predictions, the key
point here is not whether the energetic separation of triplet and
quintet states is predicted with quantitative accuracy, but how good the
quality of the predicted electron density for the specific triplet
states is in comparison with experimental data and in relation to the
calibration line.
Given that the use of symmetry can have significant
effects,21,132,133 Pápai and Vankó used symmetry
constraints to enforce either triplet state in a DFT calculation,
leading to quadrupole splittings of 0.40 mm s−1(10 , 3A2g) and 3.08 mm
s−1 (10 ,3Eg) with the B3LYP functional.
Lowering the symmetry to D2h led mixing of d(xy)
and d(z2) orbitals resulting in a computed quadrupole
splitting of 1.25 mm s−1, quite close to the
experimental value of 1.51 mm s−1. The electronic
structures in this manuscript were computed without any symmetry
constraints, and virtually no mixing of d(xy) and
d(z2) character is found, explaining the pronounced
deviation from experiment.
While some of the examples discussed in this section may at first glance
look almost trivial, it is important to note that an egregious error in
the electronic structure can be quickly spotted with the spin population
analysis but may be more difficult to identify based on the spin density
contour plots. In most cases, as shown above, such a scenario may be
resolved with re-optimising the geometry and/or the electronic
structure. An error of this magnitude will most likely result in a
drastic difference between the experimental and computed isomer shift.
In contrast, it is equally possible that while the spin population is
correct, the orbital occupation pattern that leads to this spin
population is incorrect. This will influence the isomer shift very
little or not at all, as was shown in the discussion of complexes9 and 10 ; however, the prediction of the quadrupole
splitting will be much more strongly affected as is expected from the
fundamental interactions at play in such a scenario. It is thus clear
that treating DFT purely like a black-box method is prone to failure,
and we hope to have shown with the above examples that a careful
inspection of the electronic structures at least at the level of a spin
population analysis, but preferably with an analysis of the MO
occupation pattern, is mandatory to achieve reliable results.