The predicted values are listed in Table 3; Figure 4 shows that all
density functionals perform almost equally well in the prediction of
isomer shifts (left) and quadrupole splitting values (right). Note that
the calibration lines shown in the main text are obtained after
exclusion of complexes 9 and 10 (shown as solid
symbols in Figure 4) as is explained in detail below. The fits including
all 20 complexes are shown in the Supporting Information (Figure S2).
Beginning with a closer inspection of the isomer shift predictions, the
experimental values range from –0.29 mm s−1 to +1.11
mm s−1. The linear fits obtained with the three
density functionals show almost identical R-values of 0.989 (TPSSh),
0.985 (B3LYP) and 0.988 (PBE0, see Table 4). With the B3LYP density
functional, the largest discrepancy with experiment is seen for complex9 (0.159 mm s−1 absolute deviation). The
maximum absolute discrepancy from the regression line for the B3LYP
functional is 0.131 mm s−1 (see Table 4).
For the quadrupole splittings, the experimental values lie between 0.23
mm s−1 and 4.25 mm s−1 in absolute
numbers, with the only negative sign reported for complex 17(–1.76 mm s−1). Since in previous studies the sign
was calculated correctly in all cases where it was measured
explicitly,21 the correlation line assumes the sign of
the experimental values to match that predicted computationally. As
expected, the scatter about the regression line is greater than for the
isomer shifts. Overall, the quality of the fit is quite satisfactory
with R-values of 0.989 (TPSSh), 0.991 (B3LYP) and 0.987 (PBE0). It can
be seen readily that the most significant outliers are complexes9 and 10 , with absolute deviations of 1.601 mm
s−1 (9 , B3LYP) and 1.848 mm
s−1 (10 , B3LYP) from the experimental value.
These much larger than usual deviations led us to exclude them from the
fitting procedure, and the underlying electronic structure reasons will
be discussed below. Among the set of 18 complexes the fit is based on,
the largest deviation is observed for complexes 6 and7 with the B3LYP density functional (0.850 mm
s−1 and 0.727 mm s−1 absolute
deviation from experiment). The maximum absolute deviation from the
B3LYP regression line is smaller at 0.570 mm s−1.
To summarize, all three density functionals yield roughly the same
quality of fit. Because B3LYP provides better predictions for the
quadrupole splitting values in terms of the mean absolute deviation and
maximum deviations while also performing very well for the isomer shift,
any specific discussion in the following makes use of the B3LYP data. We
define a trust region for the later evaluation of FeNC catalyst models
as twice the mean absolute deviation, i.e. 0.131 mm
s−1 for the isomer shift and 0.451 mm
s−1 for the quadrupole splitting using the B3LYP
density functional.