Ga and Zn increase the oxygen affinity of Cu-based catalysts for the COx hydrogenation according to ab initio atomistic thermodynamics

The direct hydrogenation of CO or CO2 to methanol, a highly vivid research area in the context of sustainable development, is typically carried out with Cu-based catalysts. Specific elements (so-called promoters) improve the catalytic performance of these systems under a broad range of reaction conditions (from pure CO to pure CO2). Some of these promoters, such as Ga and Zn, can alloy with Cu and their role remains a matter of debate. In that context, we used periodic DFT calculations on slab models and ab initio thermodynamics to evaluate both metal alloying and surface formation by considering multiple surface facets, different promoter concentrations and spatial distributions as well as adsorption of several species (O*, H*, CO* and ) for different gas phase compositions. Both Ga and Zn form an fcc-alloy with Cu due to the stronger interaction of the promoters with Cu than with themselves. While the Cu–Ga-alloy is more stable than the Cu–Zn-alloy at low promoter concentrations (<25%), further increasing the promoter concentration reverses this trend, due to the unfavoured Ga–Ga-interactions. Under CO2 hydrogenation conditions, a substantial amount of O* can adsorb onto the alloy surfaces, resulting in partial dealloying and oxidation of the promoters. Therefore, the CO2 hydrogenation conditions are actually rather oxidising for both Ga and Zn despite the large amount of H2 present in the feedstock. Thus, the growth of a GaOx/ZnOx overlayer is thermodynamically preferred under reaction conditions, enhancing CO2 adsorption, and this effect is more pronounced for the Cu–Ga-system than for the Cu–Zn-system. In contrast, under CO hydrogenation conditions, fully reduced and alloyed surfaces partially covered with H* and CO* are expected, with mixed CO/CO2 hydrogenation conditions resulting in a mixture of reduced and oxidised states. This shows that the active atmosphere tunes the preferred state of the catalyst, influencing the catalytic activity and stability, indicating that the still widespread image of a static catalyst under reaction conditions is insufficient to understand the complex interplay of processes taking place on a catalyst surface under reaction conditions, and that dynamic effects must be considered.


Chemical Potential in Solids and Gas Phase
The chemical potential of a substance at a temperature of 0 K and standard pressure, µ 0 i at 0 K, is the electronic energy of the substance as calculated by DFT-based calculations.
For an atom X in a bulk structure consisting of k atoms X, it is defined as the contribution of a single atom to the bulk internal energy (and thus the k th part of the electronic energy of the substance as calculated by DFT). As vibrational, rotational, and other temperaturedependent contributions to the chemical potential of a bulk material are small (when the temperature is much lower than the melting temperature of the bulk), the temperaturedependency of the bulk chemical potential can be safely neglected.
If the bulk consists of multiple elements (i.e. alloys), it is important to differentiate between the individual pure chemical potentials, which are defined according to equation (1), and the chemical potential of the elements in the alloy bulk structure, which also contains the mixing energy of the system. For systems consisting of two elements, the bulk internal S-3 energy E Xn X ,Yn Y ,bulk can be expressed as a function of the individual chemical potentials: E XnY k ,bulk = n X · µ 0 X,XnY k ,bulk + n Y · µ 0 Y,XnY k ,bulk For an equilibrium structure (energetic minima), the individual chemical potentials are related according to the Gibbs-Duhem equation: But since the Gibbs-Duhem equation only relates the individual chemical potentials, at least one chemical potential has to be known to determine the chemical potentials in the bulk structure. Alternatively, the individual bulk internal energies can be calculated explicitly without knowing the individual chemical potentials for each configuration, which can then be used to estimate the mixing energy according to equation (4) and used to correct the surface energy of the alloy slabs: Any gas can be approximated as an ideal gas for sufficiently large temperatures and sufficiently low partial pressures. The chemical potential of an ideal gas Z can be written as the sum of the chemical potential at zero temperature and standard pressure µ Z,gas (0K) (µ 0 Z,gas ) and the pressure and temperature dependent change of the chemical potential ∆µ Z,gas (T, p Z ).
The vibrational, rotational, and other temperature-dependent, but pressure-independent contributions ∆G Z (T ) can be calculated according to the following formula using the values in the thermochemical Tables. S1 S-4 The pressure-dependent term is based on the ideal gas law and has the following form: Combining these terms together gives the following equation describing the temperatureand pressure-dependency of the chemical potential of an atom in the gas phase: For molecular gases, the chemical potential of a single atom can be calculated using one of the two following methods. For molecules constructed only from multiples of the same atom, such as dioxygen (O 2 ), the chemical potential of a single atom is the atomic fraction of the molecular chemical potential.
For gases consisting of multiple different atoms, such as CO 2 , the chemical potential of a single atom is defined as the difference of the chemical potential of the whole molecule and the chemical potential of the remaining molecule without that specific atom. As an example, the chemical potential of O* in CO 2 is the difference between the chemical potential of CO 2 and the chemical potential of CO.
As seen in equations (8) and (9), the chemical potential for any atom/molecule Z directly in the gas phase or a in gas containing Z can be represented by an equation of the following S-5 form: where a Z contains all the constant terms, b Z (T ) contains all temperature-dependent but pressure-independent terms and c Z (T, p) contains all both temperature-and pressuredepending terms. For a fixed temperature T f ix , the expression in equation (10) can be further simplified into the following equation depending linearly on the logarithm of the individual partial pressures of each gas: where the chemical potential of an atom/molecule Z in the gas phase for a fixed temperature T f ix depends only on the partial pressure of the atoms/molecules in the gas phase.

Surface Energy
The surface energy γ is defined as the energy generated by a surface relative to the energy of the bulk, normalized by the surface area. The bulk energy can be expressed using the bulk chemical potential as described in equation (1). This gives as a result the following equation for the surface energy (n X atoms of bulk material X): If the bulk material consists of multiple elements, the energy of the bulk can be expressed as the individual bulk chemical potential (n X atoms of bulk material X, n Y atoms of bulk material Y) assuming ideal solids: S-6 If real solids are used, the chemical potential of the atoms in the alloy bulk structure must be used, which can be represented by the energy of an equivalent bulk structure: If an atom Z is adsorbed from the gas phase (the source of adsorbates Z), the chemical potential of the atom in the gas phase must also be subtracted giving the following equation as a result: Equation (15) shows the dependency of the surface energy on the chemical potential of both the individual bulk metals as well the gas phase molecules. If the individual chemical potentials are replaced by the chemical potential of an ideal bulk structure with the same stoichiometry using equation (1), equation (15) further simplifies to the following expression, which now only has the gas phase chemical potential µ Z,Gas as a variable: Inserting the expression in equation (11) into equation (16) results in a expression depending linearly on the logarithm of the different partial pressures, as follows: where the surface energy of a model γ n X ,n Y ,n Z (T, p) for a fixed temperature T f ix depends only on the partial pressure of the adsorbate atoms/molecules in the gas phase.
S-7 S-10 Table S1: Chemical potentials of hydrogen, CO and oxygen for selected initial hydrogen, CO and CO 2 -partial pressures (assuming a least minimal RWGSconversion) at 230°C. The influence of the ratio of CO 2 to CO onto µ O can clearly be seen. The influence of the hydrogen partial pressure onto µ H is quite small. µ CO already increases quite strongly when small quantities of CO are added to the feedstock gas.  (a) Pure CO 2 hydrogenation (X CO 2 = 1, X CO = 0). (b) CO 2 /CO hydrogenation (X CO 2 = 0.5, X CO = 0.5).

Oxygen Chemical Potential for Different Starting Conditions
(c) Pure CO hydrogenation (X CO 2 = 0, X CO = 1). It can be seen that the oxygen chemical potential does not depend linearly on the (R)WGSconversion. S-12 S-17 Figure S6: Surface stability diagram of the (100)-facet of the investigated CuGa-/CuZnmodels with both uncorrected surface energies (in blue) and corrected surface energies (in violet) depending on the chemical potential of oxygen (µ O in eV) and the equivalent oxygen partial pressure at 500 K. The yellow-red area indicates the expected oxygen chemical potential (µ O ) under CO 2 hydrogenation conditions (-3.11 eV < µ O < -2.92 eV, corresponding to an equivalent O 2 partial pressure bellow 10 −48 bar) while the green-yellow area indicates the expected µ O CO hydrogenation conditions (-4.07 eV < µ O < -3.93 eV, equivalent to an O 2 partial pressure bellow 10 −69 bar) with the colour gradient indicating the progressing (R)WGS reaction (yellow for low conversion, red/green for high conversion; compare Figure  1 in the main text as well as Figures S1 and S4 in the SI). Used slab models for the (100) S-23 Figure S7: Surface stability diagram of the (110)-facet of the investigated CuGa-/CuZnmodels with both uncorrected surface energies (in blue) and corrected surface energies (in violet) depending on the chemical potential of oxygen (µ O in eV) and the equivalent oxygen partial pressure at 500 K. The yellow-red area indicates the expected oxygen chemical potential (µ O ) under CO 2 hydrogenation conditions (-3.11 eV < µ O < -2.92 eV, corresponding to an equivalent O 2 partial pressure bellow 10 −48 bar) while the green-yellow area indicates the expected µ O CO hydrogenation conditions (-4.07 eV < µ O < -3.93 eV, equivalent to an O 2 partial pressure bellow 10 −69 bar) with the colour gradient indicating the progressing (R)WGS reaction (yellow for low conversion, red/green for high conversion; compare Figure  1 in the main text as well as Figures S1 and S4 in the SI). Used slab models for the (110) Figure S10 shows the surface slabs for the (100)-facet of the fcc-Cu 3 Ga-alloy with the lowest surface energy for specific oxygen chemical potentials (µ O ). For lower µ O , the clean, adsorbate-free surface slab has the lowest surface energy (Cu 3 Ga-slab, Fig. S10a). Regarding the spatial distribution of Ga in the slab, the structures is fully alloyed with the Ga distributed over the whole particle, but Ga is slightly enriched on the particle surface resulting in surface layer with a surface concentration of 50 % Ga. If µ O increases (more oxidising conditions), the slab partially dealloys and a GaO X surface layer is formed on top of the partially alloyed slab (Ga Layer 4 -Cu 6 Ga+5O*-slab, Fig. S10b). No slab model with a lower oxygen coverage has is stable, even as an intermediate structure. The structure with the S-33 GaO X surface layer somewhat represents the Ga 2 O 3 structure, but it is not fully crystalline but rather amorphous, since the layer is only partially oxidised.   S-36 Figure S13 shows the surface slabs for the (100) -Cu 6 Zn+4O*-slab, Fig. S13b and S13c) and the final structure is fully dealloyed (Fig. S13d. This can be explained by the different affinity of Ga and Zn for oxygen and the stoichiometry of their respective oxides (2:3 for Ga 2 O 3 vs. 1:1 for ZnO). Regarding the structure of the surface layer, the ZnO X structure is quite representative to the ZnO structure, but it is again rather amorphous, since the layer is only partially oxidised.  Finally, Figure S15 shows the surface slabs for the (111)-facet of the fcc-Cu 3 Zn-alloy with the lowest surface energy for specific µ O . As for the (110)-facet, the slabs are very similar to the CuGa-system; the slab is alloyed under reducing conditions (low µ O , Cu 3 Zn-slab, Fig.   S15a) and a completely dealloyed structure under oxidising conditions (high µ O , Zn Layer 8 -Cu + 5O*, Fig. S15b). The layer oxided layer is again structurally similar to the ZnO-structure.