Calculations of Turnover Frequencies (TOF)
We compare the activities of literature references on the basis of turnover frequency. The definition we will
use is the number of O2 molecules produced per Mn atom per second. Due to the differences in catalyst
loading it is challenging to find meaningful ways of normalization; and therefore an upper and lower limit will
be presented.
The upper limit, TOFmax, constitutes the case where the surface is perfectly smooth and only surface atoms
take part in the reaction. With this assumption, the number of Mn atoms per cm2 is the same for all references
and the geometric current density can be used directly to obtain the TOFmax by multiplying jgeo with 1.545
������2
���� ��������.
For the lower limit, TOFmin, we instead assume that all the Mn atoms within the bulk of the electrode are
available for the reaction:
TOFmin =
����(���� ∙ ����−1) ∙ ��������������2(���� ∙ ������������−1)
4(����) ∙ ������(������������−1) ∙ 1.602 ∙ 10−19(���� ∙ ����−1) ∙ ����������������(��������3) ∙ ����������2(���� ∙ ��������−3)
Where ���� is the absolute current drawn, ����������2 the molar mass of MnO2, ������ the Avogadro’s constant, ���������������� the
volume of catalyst used and ��������������2 the density of MnO2.
As this equation indicates, we assume the thin films reported in the current paper to have the density and
molar mass of rutile MnO2. While it is amorphous, the XPS results are consistent with a dioxide stoichiometry.
Other possible oxide stoichiometries include MnO, Mn3O4 and Mn2O3. Using the densities and molar weights of
these compounds leads to a maximum error of around 50 %.
The TOF for literature references has been calculated based on the information given below:
β-MnO2 - α-Mn2O3/Morita3
From the description of the electrode preparation 10-5 moles/cm2 Mn is loaded onto the substrate by thermal
decomposition of a nitrate precursor. Activity data is taken from figure 2 in 3 where Pt is used as substrate and
the catalyst is tested in 1N H2SO4 by anodic polarization. The original potential scale used is Hg/HgSO4 in 1N
H2SO4. In order to show the data using the RHE scale the standard redox potential of 0.674 V vs. RHE has been
added. This results in a TOFmin of 0.00026 s-1 per mA/cm2.
Ca0.16Mn2(H2O)2/Najafpour4
The authors report dropcasting a solution consisting of 2.5 mg catalyst in 750 ml water with Nafion. 40 μl of
this solution is used for a 3 mm Glassy Carbon electrode. Prior to drop casting, the solution is sonicated to give
a good dispersion and this should give 1.89 mg/cm2 of the Ca0.16Mn2(H2O)2 catalyst powder. The number of Mn
atoms was then estimated by assuming a molar weight of 152.4 g/mol. These assumptions lead to a TOFmin of
0.0001 s-1 per mA/cm2. Activity data was digitized from Figure 7 in 4 where the catalyst is tested in 0.1 M HClO4
with a linear sweep.