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All MnOx were modeled by using periodic boundary conditions.
The calculations were performed with the GPAW46, 47 DFT code
(version 0.9.0.8965) at the generalized gradient approximation
level of theory. DFT using the revised Perdew–Burke–Ernerhof
functional48 in combination with a finite difference grid (grid spacing:
0.15 ) and 221 k point set were employed. For the Au
doped system the k point set was reduced to 211 owing to
a larger unit cell and a set containing only the gamma point was
used for the considered molecules. The inner electrons were approximated
by projector augmented wavefunctions49 (version
0.9.9672). Spin was treated explicitly by assuming a high spin
electron configuration with ferromagnetic coupling between the
Mn ions. A similar procedure has been employed for a number of
systems.6, 8, 14 Geometries were relaxed by using the Broyden–
Fletcher–Goldfarb–Shanno algorithm as implemented into
ASE 126.96.36.199 Convergence of the structure was assumed complete
if the forces were below 0.05 eV1. Zero-point energies and entropy
effects were included by adding constant corrections as described
previously.10 All adsorption energies were calculated by
following the procedure described by Man et al. under standard
conditions (pH 0 and T=283.15 K).10
MnO2 was modeled by using a 21 unit cell for the non-Au-doped
case and a 31 unit cell for the Au-doped case of the (110) surface
combined with a 2 monolayer (ML)-thick slab. In agreement
with previous work27 the surface was assumed to be fully oxidized,
that is, all surface manganese atoms had a formal oxidation state
of +5. The slab was terminated on the “bulk” side by *OH species
to model the bulk +4 oxidation state. Convergence of the slab
was ensured by comparison with a 3 ML slab. No significant differences
The Mn2O3 model was constructed by employing a slightly simplified
Mn2O3 unit cell similar to that used by Su et al. containing
2Mn2O3 units.27 The 2 ML slab was cut in the (11 0) direction and
terminated such that all “bulk” manganese atoms were in a formal
oxidation state of +3. Again, no differences with the results obtained
on a 3 ML Mn2O3 slab were found.
All binding energies used are shown in the Supporting Information
with the zero-point energy and entropy corrections. From the calculated
free energies, predictions of overpotentials were made by
using a previously reported method.4, 5, 18 The basis of this method
was to set the reference potential to that of the standard hydrogen
electrode and model the electrode potential (U) by shifting
the energy levels by eU. The lowest theoretical overpotential was
then the difference between U, with all steps downhill in energy,
and the equilibrium of water oxidation, 1.23 V.
The authors gratefully acknowledge financial support from the
Danish Ministry of Science’s UNIK initiative, Catalysis for Sustainable
Energy. The Center for Individual Nanoparticle Functionality
is supported by the Danish National Research Foundation
Keywords: cobalt · electrocatalysis · gold · manganese ·
density functional calculations
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