Revealing the structure of the active sites for the electrocatalytic CO2 reduction to CO over Co single atom catalysts using operando XANES and machine learning

Operando XANES analysis assisted by machine learning, spectral decomposition approaches and DFT modelling is employed to shed light on the speciation of Co and N co-doped carbon catalyst during electrocatalytic CO2 conversion.


S3. FDMNES convolution parameters
The parameters reported in Table S1 were selected for the convolution of the calculated FDMNES spectra employing an energy dependent arc-tangent shape of the Lorentzian profile and optimised over the Co XANES K-edge of the CoO reference spectrum.
Table S1 FDMNES convolution parameters chosen for the theoretical Co K-edge XANES spectra.

S5.1. Wavelet Transform
The WT was carried out using the following equation: (Timoshenko & Kuzmin, 2009;Funke et al., 2005).Here  is the so-called mother wavelet function.One of the most suitable mother wavelet functions for the EXAFS analysis is the Morlet wavelet: 2 2 ].In this work, the Morlet parameters with  = 1 (value for the width of the Gaussian envelope), and  = 6 (frequency of the harmonic function) were chosen, allowing the optimal resolution (Funke et al., 2007) in both k-and R-spaces for the second coordination shell features.For the Morlet wavelet transform, the scale parameter  can be linked to the signal frequencies R values as  = /2.

Figure S4
Moduli of the Morlet wavelet transform calculated for the EXAFS signal of the 1 st and 3 rd pure species.The wavelet resolution parameters  and  were set to 1 and 6, respectively.Differently from the 2 nd species, for both these two cases, the second shell wavelet lobes (2-2.7 Å) are located mainly in the range within 4 and 6 Å suggesting mainly the existence of light scatterers.The wavelet transforms are not corrected for the phase shift.

S5.2. EXAFS fit
The EXAFS fit of the extracted 2 nd component was performed in the R-range between 1 and 3.5 Å.The k 2weighted signal was Fourier Transformed using a Hanning window defined in the k-space within 2.3 and 9 Å -1 .The fit was realised in Artemis (Ravel & Newville, 2005) considering 3 SS paths: Co-N, Co-C and Co-Co.The photoelectron scattering phases and amplitudes for the first two were calculated by the FEFF 6.0l code (Ankudinov et al., 1998) for the Co phthalocyanine complex (Crystallography-Open-Database) while for the third paths, calculations for the metallic Co were performed.S 0 2 factor was fixed to 1 for all the paths, on the basis of the EXAFS fit performed for the CoO reference (Hursán et al., 2023).In order to reduce the correlation between the coordination numbers and the Debye-Waller (DW) factors, the DW for the Co-Co path, was set to 0.008 Å 2 , a value already used for dispersed Cu sites in zeolites frameworks (Martini, Signorile, et al., 2020;Deplano et al., 2021;Martini et al., 2017).At the same time, it has been assumed that the N and C have the same DWs.The following variables were then guessed and refined through the EXAFS fit: the coordination numbers of the N, C and Co atoms (N N , N C and N Co ), their corresponding distances from the Co absorber, the DW of the N/C atoms and finally a common reference energy shift parameter ΔE 0 .The best-fit results are reported in Table S2 while the comparison between the EXAFS 2 nd component and the related best-fit is shown in Figure S5.
Table S2 EXAFS best fit parameters obtained from the analysis of the EXAFS spectrum of the 2 nd component.Uncertainties of the last digit are given in parentheses.

S6.1. XANES fit of the first component
Figure S9 shows the Co structure employed in the fit of the 1 st pure spectrum, corresponding to the asprepared catalyst (Figure 3 of the main text).To fit the Co K-edge XANES, we used the analogous approach to that discussed in the main text for the 3 rd pure species.For the as-prepared state of the catalyst, the training sets contained ca.1000 theoretically generated XANES, which allowed us to achieve an accuracy higher than 0.96, indicating a very good level of approximation.The comparison between the experiment and the best-fit is shown in Figure S10, while the best-fit parameters are reported in Table S5 and Table S6.S4.
Table S4 List of structural parameters for the model shown in Figure S9.These were employed in the fit of XANES spectrum for the 1 st pure species (as-prepared state of the catalyst).The inset shows the final structure obtained in the XANES fit.

Model used to
Table S5 XANES best-fit structural parameters for the model shown in Figure S9 and Figure S10.

Fitting parameters XANES best-fit values
Misfit (  ): 1.7 % p 1 (Å) -0.03(3) Table S6 Interatomic distances obtained from the XANES fit.The uncertainties are derived from the ones reported in Table S5 and are indicated in parenthesis.

Distances (average)/Angle Co K-edge XANES best-fit values
Co-N (two N atoms that are closer to Co) 1.74(4) Co-N (two N atoms that are further away from Co) 2.05(4)

S7. Reverse Monte Carlo EXAFS fit of the first and third component
To check whether the structure models derived based on XANES data fitting for the 1 st and 3 rd components (showed in Figure 6 and in Figure S10) are consistent also with the available EXAFS data, we performed reverse Monte Carlo (RMC) simulations as implemented in the EvAX code (Timoshenko et al., 2014(Timoshenko et al., , 2012)).
In the RMC-EXAFS approach, we start with a 3D structure model obtained using the XANES fitting

Figure
Figure S1 Operando Co K-edge XANES spectra for Co-N-C catalyst at the beginning and at the end of the CO 2 RR reaction (performed at -1.2 V RHE in 0.1 M KHCO 3 electrolyte) and the reference XANES spectra for CoO (Co oxidation state +2), Co(OH) 2 (Co +2) and finally CoOOH (Co +3).
Figure S3 (a) EXAFS signals weighted by a  2 factor, extracted for the three pure species.(b) Magnitude of their Fourier transformed signals.The Fourier transforms are not corrected for the phase shift.

Figure S5
Figure S5 Comparison between the experimental pure EXAFS spectrum belonging to the 2 nd component and its best fit: (a) magnitude, (b) imaginary part.

Figure S7
Figure S7 XANES changes associated to some (arbitrary) selected variation of each structural parameter shown in Figure 5 of the main text.

Figure S8
Figure S8 First derivative plot showing the pre-edge-region of Figure 3(a) of the main text together with the one reproduced using the PyFitIt code (i.e.FDMNES), see Figure 6(a).The dotted grey line indicates here the presence of a flex point deriving from a weak experimental and theoretical XANES feature at ca. 7714.5 eV.

Figure S9
Figure S9 Set of structural deformations employed for the XANES fit of the 1 st pure XANES component shown in Figure 3(a) and described in TableS4.

Figure
FigureS10(a) Best-fit of the XANES spectrum for the 1 st pure species (as-prepared state of Co-N-C catalyst) obtained using the indirect machine learning approach with a normalization parameter α of 0.025.
procedure and slightly move the atoms in the model around their initial positions in a random process in order to include the thermal and static disorder effects.The maximal allowed atom displacements from the starting atomic positions in the RMC simulations were set to 0.4 Å; thus, the overall 3D structure of the material and coordination numbers do not change in the RMC-EXAFS fit.The RMC approach allows us to fit EXAFS data and accounts explicitly for the contributions of distant coordination shells and multiple scattering effects.

Figure
FigureS11(a) Results of the RMC-EXAFS simulations using the EvAX code(Timoshenko et al., 2014(Timoshenko et al., , 2012)).Comparison of Fourier-transformed experimental Co K-edge EXAFS spectra for the 1 st and 3 rd component with the corresponding RMC-EXAFS results for the final structure models obtained through the XANES fits.The Fourier transforms are carried out in the k-range between 2 and 9 Å -1 .RMC fits are carried out in k-and R-spaces simultaneously using the wavelet transform, in the k-range between 2 and 9 Å -1 and in the R-range between 0.8 and 4.5 Å, including multiple scattering contributions with up to 5 Å.

Table S3
XANES best-fit structural parameters for the model shown in Figs.5 and 6(a) of the main text.