Figure 1. (A) Schematic environment of an FeNC site with the
iron ion shown as an orange circle. The extent of the graphene-like
environment (black lines) is unknown as indicated by grey dashed lines;
note that conjugation is not shown. The nitrogen (blue circle) donation
may occur from six- or five-membered rings; the latter will result in
local distortions and defects (green lines). Axial ligands may be
present, but their number and chemical character is unknown (half
blue/half red circles). (B) Generic Mössbauer spectrum showing the
definition of isomer shift δ and quadrupole splitting
ΔE Q.
A Mössbauer spectrum of a typical FeN4 environment shows
a doublet with two defining features: the isomer shift δ and the
quadrupole splitting ΔE Q, both sketched in Figure
1B.1 These arise from the interaction between the
charge densities of the iron nucleus and the surrounding electrons.
Specifically, the isomer shift reflects the electron density at the iron
nucleus, also known as the contact density, and the quadrupole splitting
is indicative of an electric field gradient, i.e. the degree of
asymmetry within the electron density. While the isomer shift provides
information about the iron oxidation state and spin state, the
quadrupole splitting can help to differentiate between different
electronic states with the same multiplicity. We note that the
simultaneous evaluation of both parameters is important to distinguish
signals of sites for which the isomer shift or quadrupole splitting by
themselves cannot provide an unambiguous assignment (see below).
The numerical values for isomer shift and quadrupole splitting expected
for iron in various oxidation and spin states are illustrated in Figure
2. While generally, the isomer shift is higher for lower oxidation
states, it can be seen that the observed regions overlap for different
oxidation states and different spin states. Fe(II) as one of the
relevant oxidation state for the resting state of FeNC-catalysts shows
good differentiability between its high spin (S = 2,δ = 0.59–1.45 mm s−1) and low spin
(S = 0, δ = –0.16–0.50 mms) states,
although intermediate spin (S = 1,δ = 0.26–0.49 mm s−1) centers are found
at the high end of the range expected for low spin complexes. Iron in
oxidation state +III is found between –0.17–0.67 mm
s−1 with some overlap in the observed regions for all
three spin states S = 1/2, S = 3/2 andS = 5/2. Since Fe(II) and Fe(III) may both be present in
FeNC catalysts, it is important to note that the isomer shift regions of
all ferric spin states overlap with those of ferrous low spin and
intermediate spin to some extent. This implies that additional
information, such as the quadrupole splitting values shown in Figure 2B,
will be needed to assign oxidation and spin states. Lower and higher
oxidation states are shown for completeness; while Fe(I) is less
relevant to the FeNC intermediates during ORR, higher oxidation states
are likely important for the later stages of catalysis.
Computationally, the isomer shift and quadrupole splitting can be
predicted with good accuracy using hybrid functionals and suitable basis
sets.14,19-22 Details on the computational approach
and the expected error margins are given below. A recurring problem in
computational iron chemistry is the prediction of the correct spin state
energies,61 the correct spin state being obviously
very important to achieve a reliable Mössbauer prediction. When using
density functional theory, the selection of an appropriate density
functional and basis set in combination with a good knowledge of ligand
field theory and MO theory appears to be sufficient to identify
shortcomings in many cases, e.g. when the electronic structure obtained
by the self-consistent field (SCF) procedure is not the lowest-lying
electronic state.61-63 In other cases of course, the
electronic structure will have non-negligible multireference character
or substantial mixing of low-lying excited states, and in such scenarios
DFT is prone to failure. Wavefunction approaches such as the complete
active space SCF or density matrix renormalisation group methods for
large active spaces in combination with extensive basis sets can lead to
accurate predictions of relative spin state
energies.64,65 The more recently introduced
multiconfiguration pair-density functional theory also shows promising
results.66,67 While one might thus think that
post-Hartree–Fock-methods are the ideal approach to obtain both more
accurate spin state energetics and more reliable Mössbauer parameter
predictions, these types of calculation remain far from routine for
large molecules with complicated electronic structures. For the problem
targeted —a screening of iron sites embedded in extended π-systems,
paralleling the strategy that has contributed greatly to resolving many
questions in bioinorganic chemistry13,15,20,23,68,69— a density functional theory based approach is clearly better suited.
Given the limitations and challenges set out above, it is however
equally clear that the reliability and pitfalls of Mössbauer parameter
predictions must be carefully calibrated specifically for
FeN4 sites.