CO2 adsorption on the (111) surface of fcc-structure high entropy alloys

ABSTRACT High entropy alloys (HEAs), obtained by alloying five or more elements, can exhibit unique characteristics. The CO2 adsorption capabilities of fcc structure HEAs consisting of five elements among Fe, Co, Ni, Cu, Zn, Ru, Rh, Pd, Ag, Ir, Pt, and Au were evaluated by conducting first-principles calculations of the CO2 adsorption energy. HEAs could be categorized into ‘binding’, ‘less binding’, and ‘inconclusive’ HEAs, where there were 27, 23, and 10 HEAs each, respectively, out of 60 randomly chosen HEAs. ‘binding’ HEAs are defined as having low CO2 adsorption energy sites of less than −0.08 eV, which is difficult to attain with elementary substances or binary alloys. These low adsorption energy, or more active, sites are found near on-top positions of the HEA surface, whereas CO2 does not adsorb at such positions in ‘less binding’ HEAs. Calculating CO2 adsorption energies could be a useful tool to check whether a specific HEA is ‘binding’ or ‘less binding’ prior to conducting extensive experiments. GRAPHICAL ABSTRACT

Carbon dioxide (CO 2 ) is a nontoxic and abundant C1 feedstock.The capture and further conversion of CO 2 into industrially valuable chemicals is beneficial when addressing the growing problem of global warming and promoting sustainable human development but the CO 2 molecule is thermodynamically very stable with a standard formation enthalpy of −393.5 kJ/mol.Adsorption (physisorption) of CO 2 is always the first step of its subsequent activation, such as molecule bending [26], charge repartition, or moving charge between C and O atoms [27], electron transfer to CO 2 , and hydrogen (or hydride) transfer to CO 2 [28].Investigation of the CO 2 adsorption step gives us some insight into CO 2 reduction reaction (CO 2 RR) activity.However, this step is not the potentiallimiting step compared to, for instance, reduction of CO 2 to anionic *CO 2 -and further protonation to *COOH or protonation of CO* to CHO* [29].
Transition metal elements, especially late transition metal elements, are typically used in HEAs.The huge combination of elements makes brute-force searching impossible, and the question of which elements to use will always linger.This study considered five-component HEAs out of 12 late transition metal elements.The activity of CO 2 adsorption, an important step in CO 2 hydrogenation [14,21], was investigated using first-principles density functional theory calculations.A CO 2 molecule was adsorbed on (111) surface sites of fcc-structure HEAs.Similar calculations were conducted in elementary substances or binary alloys for comparison.There were peculiar surface sites with low CO 2 adsorption energies in some HEAs, which were not found in elementary substances and most binary alloys.Such active sites may be the origin of unique activity in HEAs, and its existence in a specific HEA can be checked computationally.

Computational methods
HEAs in this study were based on a fcc lattice and were composed of five elements from Fe, Co, Ni, Cu, Zn, Ru, Rh, Pd, Ag, Ir, Pt, and Au.Guo et al. suggested that HEAs where the average d-electrons accommodated in the valence band per atom (valence electron count, VEC) is 8.0 or larger results in a fcc lattice, and the VEC of all constituent elements considered in this study is 8 or larger [30].The mole fractions of the five elements were 20% each.There are empirically determined conditions for HEA formation.Four quantities are defined: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi Here, ΔH ij is the mixing enthalpy of elements i and j, x i and r i are the mole fraction and atom radius of element i, respectively, R is the gas constant, and � r and � T m are the mole fraction-weighted average atom radius and melting temperature, respectively.The entropy of mixing, ΔS mix , may become less than −1.5R (the definition of a HEA) when there are more than five constituent elements.Adding five constituent elements with equal mole fractions, as in this study, results in ΔS mix ¼ À 1:61R.The enthalpy of mixing [31], ΔH mix , must not be too small or too large; a range of between −11.6 and 3.2 kJ/mol was suggested in Ref [32].Atoms in an HEA should have similar size (δ � 6:6 in Refs [32,33]), and a thermodynamical quantity Ω � 1:1 is proposed in Ref [33].Values of ΔH ij were based on tables in Ref [34].Although ΔH mix has been directly calculated in Ref [35].by averaging calculated results of five configurations, we used ΔH ij based on an existing table to eliminate the need for first-principles calculations before choosing combinations of constituent elements likely to form HEAs. 528 out of the 12 C 5 = 792 element combinations satisfied these conditions, and 60 randomly chosen HEAs in Supplementary Table S1 were evaluated in this study.HEA surfaces were studied using slab-and-vacuum models, namely, a 125-atom supercell as shown in Figure 1(a,c).This model was obtained by cleaving fccstructure bulk with a nearest neighbor distance of , where v i is the computationally optimized volume of element i in the most stable structure (bcc in Fe, hcp in Co, Zn, and Ru, fcc otherwise), and ffi ffi ffi 2 p ffi ffi ffi ffi ffi ffi ffi ffiffi is the distance between nearest neighbor atoms in fcc bulk.In other words, the lattice parameter of HEA bulk is a weighted average of lattice parameters of constituent elements assuming the fcc structure with the volume per atom same as the most stable structure.The spacing between the atoms of the outermost layers separated by the vacuum layer prior to relaxation was set to 20 Å.The 25 sites of the five elements, a to e in Figure 1(c), were randomly assigned.The same atom configuration in Figure 1(a,  c), but with different elements at each site, was used for calculation of all HEAs.
The issue of stability needs to be addressed.Ref [36].tested a number of supercells with random atomic occupancies, and the structure with the lowest energy at the ground state was chosen as the initial lattice of the (TaNb) 0.67 (HfZrTi) 0.33 alloy.The formation energy and free energy should, in principle, be obtained by statistical mechanics treatment of a reasonable ensemble, which is a non-trivial task.However, the efforts to obtain the bulk stability could become meaningless.It is relatively easy to calculate the formation energy of fcc Fe.In fact, paramagnetic fcc (γ-) Fe is a stable phase at elevated temperature.However, a five-layer slab of fcc Fe (111) could not be obtained computationally because the two outermost layers moved away from the three layers at the middle during relaxation.This disintegration could be attributed to the intrinsic instability of fcc Fe at 0 K, and the layers of fcc Fe were able to separate from each other in a slab calculation because the reduction of symmetry by introducing vacuum layers allowed relaxation not allowed in a cubic lattice.The extent of energy reduction by such relaxations cannot be estimated simply from bulk calculations.
End-on adsorption of CO 2 molecules on the (111) surface is the main topic of this study.Most of the late transition metals comprising HEAs take the fcc or hcp structure (the exception is Fe adopting the bcc structure at room temperature), and the densely packed triangular lattice surface is found in both fcc and hcp as the cleaved {111} and {0001} surfaces, respectively.The five layers in the supercell stack in an ABCAB pattern (Figure 1(a,c)).CO 2 molecules were positioned normal (vertical) to the slab surface at C (fcc site) and A (hcp site) positions.The O closer to the slab surface was positioned, for convenience, at 1.5 Å from the plane parallel to the slab surface that contains the outermost atom.These positions were chosen because the O is close to the largest number of metal atoms (three), thus can relax in various directions while being close to multiple metal atoms.There are 25 distinct fcc and hcp sites each in the supercell.The CO 2 adsorption energy was calculated for all 50 sites for each HEA.To obtain the adsorption energies, internal coordinates, but not lattice parameters, were relaxed using the projector augmented-wave method [37] and the Perdew-Burke-Ernzerhof exchange-correlation density functional revised for solids (PBEsol) [38] approximation to the exchange-correlation interactions as implemented in the VASP code [39,40].A relatively dense 4 × 4 × 1 k-mesh was used for slab calculations reflecting the metallic nature of HEAs.Internal coordinates of all atoms were relaxed with electronic and ionic relaxation criteria of 1 meV and 0.05 eV/Å 2 , respectively.Adding dispersion corrections is critical in standard PBE [41] for, as examples, CO 2 adsorption on TiO 2 [42,43] as well as estimation of the interlayer distance in graphite [44].However, dispersion corrections were not used in this study because PBEsol can estimate, without any dispersion correction, the lattice parameters of low-dimensional elementary substances, including graphite, with accuracy comparable to PBE-D3 [44].Spin polarization was used where spins of all atoms were initially set ferromagnetically.The initial magnetic moment, or difference between majority and minority spin, of each atom was initially set to that of one electron equivalent, and the magnetic moments of atoms were allowed to relax.Unfortunately the computation cost of the adsorption calculations are quite expensive at typically two days using 72 cores.Therefore, investigation of substantially larger numbers of HEA combinations, systematic evaluation of multiple atom configuration models, and detailed investigations on magnetic ordering were not practical.
For comparison, the CO 2 adsorption energies were also calculated for elementary substances as well as binary alloys that experimentally form a fcc or hcp structure solid solution over a broad range near atomic ratio 50%:50% according to Ref [45].Both elementary substances and binary compounds were modeled using a 125-atom supercell, where the atom positions of each element in the latter are shown in Figure 1(b,d).

Results and discussion
Adsorption sites in elementary substances are typically limited to high symmetry sites, such as top (or on-top), edge, and hollow sites.Hollow sites, where the atoms in each layer form a triangular lattice, can be divided into fcc and hcp sites.The layers in fcc {111} and hcp {0001} stack in ABCABC and ABABAB patterns, respectively.Therefore, when atoms in the topmost layer are in A positions and those in the next layer are in B positions, as in Figure 1(a,c), fcc and hcp sites are at C and B positions, respectively.
The high symmetry positions no longer possess high symmetry when the slab is disordered, for instance, when multiple elements are randomly distributed.Atoms can spontaneously relax to low symmetry positions during first-principles calculations because these are no longer bound by symmetry elements such as mirror and three-fold rotation perpendicular to the slab.Figure 2 shows how an arbitrary position on the surface can be assigned to a hcp, fcc, edge, or top site in a broad sense.The hcp, fcc, edge, and top 'high symmetry' sites (H, F, E, and T in the figure, respectively) are projected on a hypothetical plane parallel to the slab surface.This study defines a 'site' as a certain point on the hypothetical plane.'high symmetry' sites have coordinates with high symmetry when all atoms are the same element, but these sites actually do not have high symmetry in a disordered slab.Voronoi cells centered at 'high symmetry' positions are obtained, and each position is assigned to a site type, which could be either hcp, fcc, edge, or top, according to what is at the center of the Voronoi cell.The distance between an arbitrary site and the nearest 'high symmetry' position is defined as the site distance, and is scaled such that the distance between top sites, which was between 2.55 and 2.78 Å, is normalized to unity.
CO 2 adsorption energies were also obtained for elementary substances.A CO 2 molecule was adsorbed perpendicular to the surface at in-plane coordinates (1/3, 2/3) (fcc site), (2/3, 1/3) (hcp position), (0, 0) (top site), (1/2, 1/2) (one of the edge sites), and (1/3, 1/3) (site at the same distance from fcc, hcp, and top sites) in the definition in Figure 2. The last site is a low symmetry site that is equally distant from high symmetry sites, and spontaneous relaxation to all of fcc, hcp, and top sites is possible.On the other hand, CO 2 molecules adsorbed at fcc, hcp, and top sites are constrained by symmetry and cannot move to other sites.The adsorption energy versus site distance for the five adsorption calculations is plotted for Zn, as a representative result, in Figure 3(a).The results for the other elements are given in Supplementary Figures S1 and S2.For all elements other than Fe, where a Fe slab could not be obtained, the adsorption energy of CO 2 was not less than −0.02 eV, while the highest adsorption energy after relaxation from the five positions was at most 0.06 eV.
A similar result was obtained for binary alloys, where CoPd is shown as a representative in Figure 3(b) and the rest are provided as Supplementary Figures S3 and S4.The plots were derived are from 50 adsorption calculations per alloy.Many of the O adsorbing to the slab moved from the initial hcp or fcc site to top or edge site types, and the site distance (horizontal axis) took diverse values.The adsorption energy was higher than −0.04 eV except for PtRu (Supplementary Figure S4(c)) with minimum adsorption energy of −0.15 eV and FeRu where the adsorption energy was around −0.7 to −0.5 eV, a result of relaxation to different magnetic states between slabs with and without CO 2 (Supplementary Figure S4(e)).
The situation in HEAs was very dissimilar.Figures 3(c,d) shows plots for PdZnRuCoRh and AgCuNiPtRh, respectively.Plots for select HEAs are given in Supplementary Figures S5-S13.The five elements were positioned in a-e sites in Figure 1(a,c) in this order.The plot for PdZnRuCoRh (Figure 3(c activities of some HEAs may be attributed to existence of adsorption sites with low adsorption energies that cannot be usually attained with similar metals comprised of fewer elements.If this is the case, the activity of a given HEA can be checked by performing a similar computational study on adsorption energies of CO 2 starting from various positions. Projected density of states (PDOS) calculations was conducted for a number of CO 2 -adsorbed PdZnRuCoRh systems.No DOS corresponding to a bond to the HEA was found in the PDOS of O close to the HEA, suggesting physisorption than chemisorption.Our previous study on CO 2 adsorption to an O vacancy on a binary oxide substrate revealed that CO 2 undergoes dissociative adsorption only when the adsorption energy of ~-0.5 eV or less [46], and this threshold is much lower than the adsorption energies found in this study.
Figure 4 summarizes the calculation results for 60 HEAs.HEAs were classified into three categories:   'binding' HEAs with minimum adsorption energy less than −0.08 eV and the fifth largest adsorption energy less than 0.1 eV (calculations from a limited number of initial positions may have much larger adsorption energy), 'less binding' HEAs with minimum adsorption energy higher than −0.08 eV and the fifth largest adsorption energy less than 0.1 eV, and 'inconclusive' HEAs where many of the firstprinciples calculations did not converge and finish appropriately or most of the adsorption energies were not near 0 eV.The cutoff was chosen somewhat arbitrarily; there were only three HEAs with lowest adsorption energy between −0.090 and −0.067 eV, thus the density of HEAs in this energy range was relatively sparse.Among the 60 calculated HEAs, there were 27, 23, and 10 'binding', 'inconclusive', and 'less binding' HEAs, respectively.In other words, almost half of the calculated HEAs were 'binding', suggesting that mixing five elements to form a HEA has a high change of forming a 'binding' alloy with reactivity not found in elementary substances or most binary alloys.
Knowledge on constituent elements that have a higher chance of forming a 'binding' or 'less binding' HEA is practically useful information.The 'binding'/ "inconclusive"/"less binding" ratio is shown for all HEAs ('All') and for HEAs containing a particular element (Fe-Au) in Figure 4. HEAs containing Ru had a higher 'binding' ratio, while Ag-containing HEAs had a higher 'less binding' ratio.
Figure 5 plots the normalized site distance from 'high symmetry' positions versus CO 2 adsorption energy in all 'binding' or 'less binding' HEAs by 'high symmetry' position type.The maximum site distance is ffi ffi ffi 3 p � 6 � 0:289 (Figure 2).The number of points with adsorption energies between −0.3 and 0.15 eV as well as the ratio of points against all points in 'binding' and 'less binding' HEAs are shown.The distribution of points in the two HEA types were similar for hcp, fcc, and edge site types (Figure 5(a-f)); points were distributed over the entire range of allowed distances, and adsorption energies were typically between −0.05 and 0.05 eV.In contrast, there was a remarkable difference in the distribution of points in the top site type between 'binding' and 'less binding' HEAs (Figure 5(g,h)), respectively).In 'less binding' HEAs, points in the top site type mostly had site distances exceeding 0.1 and the adsorption energies were mostly between −0.05 and 0 eV.On the other hand, in 'binding' HEAs, there was an additional distribution of points with distance less than 0.15 and adsorption energies between 0 eV and as low as −0.25 eV.
The adsorption angle of adsorbed CO 2 with respect to the surface is shown in Figure 6.The adsorption angle is 0° and 90° where the adsorbed CO 2 molecule is parallel and perpendicular to the surface, respectively.There was a clear trend where, barring some outliers with adsorption angles around 40-50°, a linear relation between the normalized distance and adsorption angle was found in hcp and fcc site types (Figure 6 (a-d)).These trends suggest convergence of our calculations regarding the adsorption angle.The adsorption angle for edge site types formed a band centered at 60° (Figure 6(e,f)).The adsorption angle increased with increasing distance for top site types, while small site distance points are absent in 'less binding' systems (Figure 6(g,h)).Supplementary Figure S14 plots adsorption angles versus adsorption energies.The outlier points with adsorption angles between 40-50°in hcp and fcc tended to have lower adsorption energies compared to the 60-90° adsorption angle points (Figure S6(a-d)).A weak correlation between adsorption angle and adsorption energy was also found in edge and top sites, where small adsorption angles resulted in smaller CO 2 adsorption energies.From another point of view, CO 2 adsorption energy reduction happens when the CO 2 molecule adsorbs at a large angle from the direction normal to the surface, which is heavily discouraged at hcp and fcc sites.

Conclusions and future outlook
The CO 2 adsorption energies of fcc-structure HEAs consisting of five elements among Fe, Co, Ni, Cu, Zn, Ru, Rh, Pd, Ag, Ir, Pt, and Au were evaluated using first-principles calculations.HEAs could be categorized into 'binding', 'less binding', or 'inconclusive' HEAs.There were 27, 23, and 10 HEAs each, respectively, within 60 randomly chosen HEAs.'binding' HEAs have low CO 2 adsorption energy positions of less than −0.08 eV, which is difficult to attain with elementary substances or binary alloys.These low adsorption energy, or more active, sites are found near top positions, whereas CO 2 does not adsorb near top 'high symmetry' sites in 'less binding' HEAs.HEAs containing Ru had a higher ratio of 'binding' HEAs.Calculating CO 2 adsorption energies could be a useful tool to check whether a specific HEA is 'binding' or 'less binding' prior to conducting extensive experiments.
Further analysis on the chemistry and design principles is attractive.For example, understanding what HEA element choices and compositions as well as the coordination, chemistry, and electronic structure of local environments would enhance the reactivity of adsorption positions, and studying other reaction steps would attract much interest.Identification of simple descriptors and trends representing the activity will accelerate searching of appealing HEAs.However, more detailed analysis through increasing the size and diversity of the data pool is only possible after breakthroughs in significantly reducing computational costs of individual calculations, such as use of reliable neural-network potential models.(c,d) fcc, (e,f) edge, and (g,h) top site types in all (a,c, e,g) "binding" and (b,d,f,g) "less binding" HEAs.The percentage of points of each site type among all "binding" or "less binding" points are also given.(c,d) fcc, (e,f) edge, and (g,h) top site types in all (a,c, e,g) "binding" and (b,d,f,g) "less binding" HEAs.The angle is 0° and 90° when the adsorbing CO 2 molecule is parallel and perpendicular to the HEA surface, respectively.The percentage of points of each site type among all "binding" or "less binding" points are also given.

Figure 1 .
Figure 1.(a,b) Side and (c,d) top views of slab-and-vacuum models of (a,c) HEAs and (b,d) binary alloys used in this study.BACBA in (a,b) indicate the stacking pattern.Labels a-e in (c) and a and b in (d) shows the site of each element in the model.The edge, hcp, fcc, and top labels in (c) illustrates the "high symmetry" positions where CO 2 adsorbs perpendicular to the slab.

Figure 2 .
Figure 2. Projection of hcp, fcc, edge, and top "high symmetry" sites (H, F, E, and T, respectively) on a plane parallel to the surface of the slab.The region encompassed by orange lines indicate the Voronoi cell for each projected "high symmetry" site.

Figure 5 .
Figure 5. CO 2 adsorption energy versus normalized site distance for (a,b) hcp,(c,d) fcc, (e,f) edge, and (g,h) top site types in all (a,c, e,g) "binding" and (b,d,f,g) "less binding" HEAs.The percentage of points of each site type among all "binding" or "less binding" points are also given.

Figure 6 .
Figure 6.Angle of adsorbed CO 2 versus normalized site distance for (a,b) hcp,(c,d) fcc, (e,f) edge, and (g,h) top site types in all (a,c, e,g) "binding" and (b,d,f,g) "less binding" HEAs.The angle is 0° and 90° when the adsorbing CO 2 molecule is parallel and perpendicular to the HEA surface, respectively.The percentage of points of each site type among all "binding" or "less binding" points are also given.