Coadsorption Interfered CO Oxidation over Atomically Dispersed Au on h-BN

Similar to the metal centers in biocatalysis and homogeneous catalysis, the metal species in single atom catalysts (SACs) are charged, atomically dispersed and stabilized by support and substrate. The reaction condition dependent catalytic performance of SACs has long been realized, but seldom investigated before. We investigated CO oxidation pathways over SACs in reaction conditions using atomically dispersed Au on h-BN (AuBN) as a model with extensive first-principles-based calculations. We demonstrated that the adsorption of reactants, namely CO, O2 and CO2, and their coadsorption with reaction species on AuBN would be condition dependent, leading to various reaction species with different reactivity and impact the CO conversion. Specifically, the revised Langmuir–Hinshelwood pathway with the CO-mediated activation of O2 and dissociation of cyclic peroxide intermediate followed by the Eley–Rideal type reduction is dominant at high temperatures, while the coadsorbed CO-mediated dissociation of peroxide intermediate becomes plausible at low temperatures and high CO partial pressures. Carbonate species would also form in existence of CO2, react with coadsorbed CO and benefit the conversion. The findings highlight the origin of the condition-dependent CO oxidation performance of SACs in detailed conditions and may help to rationalize the current understanding of the superior catalytic performance of SACs.


Introduction
Single atom catalysis is emerging and growing as a new frontier in catalysis [1,2]. Similar to the metal centers in enzymes and transition metal complexes in biocatalysis and homogeneous catalysis, the transition metal species in SACs are charged and atomically dispersed on the support [3,4]. In reaction conditions, the thermodynamics-driven adsorption and reaction of substrates would change the oxidation state [5] and coordination of metal species drastically [6], and may stabilize metal species in an atomically dispersed form or promote their aggregation or redispersion [7]. This feature of transition metal species in reaction conditions were reported for Au [8][9][10][11][12], Pd [13], and Rh [14] -based SACs, etc. Apart from the potential aggregration/redispersion of metal species, the adsorption/coadsorption of the substrate may also impact the thermodynamics and kinetics for the evolution of reaction species and may lead to a switch of the pathways for substrate conversion with reactions conditions, such as temperature, substrate concentrations (partial pressures), [15][16][17][18][19] etc. For these complexities, the impact of the reaction condition to active sites and active species was seldom investigated [19].
Low temperature catalytic oxidations of CO oxidation to CO 2 are the key components in many industrial chemical processes, such as the water-gas-shift reaction [20], CO preferential oxidation in H 2 rich stream (CO-PROX) [21], exhaust gas control [22], etc. Apart from the practical applications, CO oxidation is widely used as a prototypical reaction for fundamental investigations [23] and it is also the first catalytic reaction realized on Pt 1 /FeO x [24]. Continuous efforts have been made to develop novel CO oxidation catalysts that are efficient at low temperatures [22]. Among transition metals used for CO oxidation, Au is special, as it is chemically inert in the bulk phase, and is highly active when is downsized to a sub-nano scale [25,26]. Since the supported Au nanoparticles were found active for CO oxidation in the 1980s, tremendous efforts have been put to understand the active species and mechanism pathways for the Au-catalyzed CO oxidation in operating conditions [26]. For many of these cases, the charged Au atoms, formed dynamically in reaction conditions, were proposed to be the active sites [5,[10][11][12]19,27,28]. Furthermore, it has been demonstrated that Au SACs are highly active for many reactions [29], such as the water-gas-shift [27], methanol steam reforming [30], epoxidation of ethylene, [31] acetylene hydrochlorination [32], selective hydrogenation [33], ethanol dehydrogenation reactions [34], CO oxidation [11,19,[35][36][37][38][39], etc.
Recently, we theoretically explored the reaction network for CO oxidation over Pd 1 and Fe 1 SACs on graphene and highlighted the vital role of the thermostability of reaction species in determining CO conversion and reaction pathways [55,56]. In this work, we focus on CO oxidation over AuBN to highlight the impact of coadsorbed substrates to the formation and evolution of surface species on SACs in reaction conditions with extensive first-principles-based calculations. We expect the finding would be helpful for the discovery of new reaction pathways and a rationalized understanding to the observed superior performance of SACs.

Theoretical Methods
All the first-principles-based calculations were performed using the GGA-PBE functional [57] with the DSPP pseudopotential [58] and DNP basis set [59], as implemented in DMol 3 [60,61]. CO oxidation over AuBN was investigated in a 6 × 6 supercell of h-BN. The Brillouin Zone was sampled with a Γ-centered 4 × 4 × 1 k-point grid [62]. The global orbital cutoff was set as 4.50 Å and the convergence criterion for energy and forces were 3 × 10 −4 eV and 5 × 10 −2 eV/Å, respectively. The transition states (TSs) were determined with synchronous transition methods, and further optimized and confirmed with frequency analysis, so that the only negative frequency is on the bond formation/dissociation direction [63]. The Hirshfeld scheme was adapted for population analysis [64]. With the above setup, the bulk lattice parameter of face-center-cubic Au and h-BN were calculated as 4.20 and 2.52 Å, respectively [65,66].
The formation free energy of a reaction species with stoichiometry of Au(CO) x (O 2 ) y over AuBN, under CO oxidation conditions, was calculated as: Here, x, y and z are the stoichiometry for CO, O 2 and CO 2 involved in the formation of Au(CO) x (O 2 ) y , respectively, G Au(CO) x (O 2 ) y and G BN are the free energy of Au(CO) x (O 2 ) y and B-vacancy h-BN, respectively, E Au is the energy of an Au atom, G CO and G O 2 are free energy of gas molecules calculated as G gas (T, p) = E e gas + ∆µ gas T, p 0 + k B Tln p p 0 , where E e gas is the calculated total energy of the gas molecule and ∆µ gas T, p 0 is derived from calculated partition functions of the gas molecule. The reaction conditions described by T, p were previously used to characterize the performance of SACs in CO oxidation [67].

Thermodynamics Analysis of Potential Reaction Species
We firstly evaluated the formation of Gibbs free energies (∆G) of all the potential reactants at various temperatures (T) at P CO :P O2 = 1:20 and P CO = 0.01 atm (Figure 1), which are commonly used to characterize the CO oxidation performance of a catalyst [67].

Thermodynamics Analysis of Potential Reaction Species
We firstly evaluated the formation of Gibbs free energies (ΔG) of all the potential reactants at various temperatures (T) at PCO:PO2 = 1:20 and PCO = 0.01 atm (Figure 1), which are commonly used to characterize the CO oxidation performance of a catalyst [67].

Figure 1.
The calculated atomic structures (a−i) and temperature dependence of ∆G (j) for the potential reaction species formed over AuBN in CO oxidation. Please see the context for the notation of structures. ∆G was calculated with respect to B-vacancy on h-BN, Au atom at PCO = 0.01 atm and PCO/PO2 = 1:20. The inset in (j) is the sideview of (i). In (a)-(i), the B, N, C, O and Au atoms are in green, light blue, brown, red and gold, respectively.
The calculated binding energy (Eb) of the Au atom on the B-vacancy of h-BN (AuBN, Figure 1a) in a triplet ground state is −3.54 eV and is comparable to calculated (−2.90 eV), previous theoretical (−3.03 eV) [68] and experimental results of bulk Au (−3.81 eV) [69], suggesting AuBN would be plausible over other potential Au deposition structures [52,53]. Considering the poor Eb of the Au atom (−0.11 and −0.10 eV, respectively, on top of N and B atoms on pristine h-BN), the outward diffusion of Au from AuBN would be highly endothermic (>3 eV), so it is hard to expect that the Au atom would diffuse away. In AuBN, the Au-N distances are ~2.08 Å and Au is 0.45|e| positively charged. These are in excellent agreement with the reported X-ray photoelectron spectroscopy of Au SACs [24,34,35,70], transition metal SACs on h-BN and Au/h-BN nanocomposites, where the Au and TM atoms are confirmed to be positively charged as reaction centers [41,51,71]. The thermodynamics data (Figure 1j) demonstrated that CO adsorbed on AuBN (AuCO, Figure 1b, Ead = −1.38 eV) is the most plausible at temperatures from 200 to 500 K. In AuCO, Au is 0.36 |e| positively charged, and C-O bond is in the direction nearly reverse to one of the Au-N bonds at Au-C distance of 1.93 Å and is slightly stretched (1.16 Å ). As for the adsorption of O2 (AuO2, Figure 1c, Ead =−0.90 eV), the O-O bond is elongated to 1.33 Å , parallel to the h-BN surface, and is nearly vertical to one of the N-Au bonds, forming an undercoordinated octahedral. Au is 0.53 |e| positively charged and the spin density is localized on Au and O atoms. ∆G of other potential species (Figure 1d-i) were also collected ( Figure 1j). ∆G of AuO2 and the coadsorption of CO and O2 (AuO2 + CO, Figure 1d, Ead = −1.49 eV) stand right above that of AuCO, are negative from 250 to 500 K and intersect each other at ~280 K, demonstrating that AuO2 + CO may form from AuCO via coadsorption with O2 or by an exchange of adsorbates. ∆G of other coadsorption species, such as coadsorption of 2 CO (Au(CO)2, Figure 1e), 2 O2 (Au(O2)2, Figure 1f) and the van de Waals complexes formed between adsorbed O2/CO and gaseous molecules, such as Au(O2)2 + CO(g), Au(CO)2 + O2(g) and AuO2 + CO(g) (Figure 1g-i), etc., are much higher in ∆G than those for AuO2, AuCO and AuO2 + CO (Figure 1j). Though these species may potentially exist, their coverage would be much lower than those for the AuCO, AuO2 and AuO2 + CO, and they would evolve into these more stable species by adsorbate desorption or Figure 1. The calculated atomic structures (a-i) and temperature dependence of ∆G (j) for the potential reaction species formed over AuBN in CO oxidation. Please see the context for the notation of structures. ∆G was calculated with respect to B-vacancy on h-BN, Au atom at P CO = 0.01 atm and P CO /P O 2 = 1:20. The inset in (j) is the sideview of (i). In (a-i), the B, N, C, O and Au atoms are in green, light blue, brown, red and gold, respectively.
The calculated binding energy (E b ) of the Au atom on the B-vacancy of h-BN (AuBN, Figure 1a) in a triplet ground state is −3.54 eV and is comparable to calculated (−2.90 eV), previous theoretical (−3.03 eV) [68] and experimental results of bulk Au (−3.81 eV) [69], suggesting AuBN would be plausible over other potential Au deposition structures [52,53]. Considering the poor E b of the Au atom (−0.11 and −0.10 eV, respectively, on top of N and B atoms on pristine h-BN), the outward diffusion of Au from AuBN would be highly endothermic (>3 eV), so it is hard to expect that the Au atom would diffuse away. In AuBN, the Au-N distances are~2.08 Å and Au is 0.45|e| positively charged. These are in excellent agreement with the reported X-ray photoelectron spectroscopy of Au SACs [24,34,35,70], transition metal SACs on h-BN and Au/h-BN nanocomposites, where the Au and TM atoms are confirmed to be positively charged as reaction centers [41,51,71]. The thermodynamics data ( Figure 1j) demonstrated that CO adsorbed on AuBN (AuCO, Figure 1b, E ad = −1.38 eV) is the most plausible at temperatures from 200 to 500 K. In AuCO, Au is 0.36 |e| positively charged, and C-O bond is in the direction nearly reverse to one of the Au-N bonds at Au-C distance of 1.93 Å and is slightly stretched (1.16 Å). As for the adsorption of O 2 (AuO 2 , Figure 1c, E ad =−0.90 eV), the O-O bond is elongated to 1.33 Å, parallel to the h-BN surface, and is nearly vertical to one of the N-Au bonds, forming an undercoordinated octahedral. Au is 0.53 |e| positively charged and the spin density is localized on Au and O atoms. ∆G of other potential species (Figure 1d-i) were also collected ( Figure 1j). ∆G of AuO 2 and the coadsorption of CO and O 2 (AuO 2 + CO, Figure 1d, E ad = −1.49 eV) stand right above that of AuCO, are negative from 250 to 500 K and intersect each other at~280 K, demonstrating that AuO 2 + CO may form from AuCO via coadsorption with O 2 or by an exchange of adsorbates. ∆G of other coadsorption species, such as coadsorption of 2 CO (Au(CO) 2 , Figure 1e), 2 O 2 (Au(O 2 ) 2 , Figure 1f) and the van de Waals complexes formed between adsorbed O 2 /CO and gaseous molecules, such as Au(O 2 ) 2 + CO(g), Au(CO) 2 + O 2 (g) and AuO 2 + CO(g) (Figure 1g-i), etc., are much higher in ∆G than those for AuO 2 , AuCO and AuO 2 + CO (Figure 1j). Though these species may potentially exist, their coverage would be much lower than those for the AuCO, AuO 2 and AuO 2 + CO, and they would evolve into these more stable species by adsorbate desorption or exchange. Our results ( Figure 1) clearly indicate that AuCO (Figure 1b) is the most plausible reaction species in the 200-500 K temperature range, under CO oxidation conditions. We also investigated the impact of CO and O 2 chemical potential on the relative stability in terms of the ∆G of these reaction species by varying the CO and O 2 partial pressure in the range of 0.01-0.2 atm in the same temperature interval. Though the calculated values of ∆G of these identified major reactants, namely AuCO, AuO 2 , AuO 2 + CO and Au(CO) 2 (Figure 1b-e) may shift due to the variation of reaction conditions, AuCO is still the most plausible, considering that the ∆G of AuO 2 and AuO 2 + CO remain right above that of AuCO. This is in reasonable agreement with the experimental finding that the active reaction species in SAC-catalyzed CO oxidation all originate from positively charged or even oxidized metal atoms [72][73][74][75]. We also investigated the potential impact of van der Waals interactions on the relative stability of these species within the same temperature and partial pressure range, and yielded exactly the same finding. The calculated stretching frequency of AuCO ( Figure 1b) is slightly redshifted from that of gaseous CO, i.e., from 2143 cm −1 to 2040 cm −1 , and further shifted to 2115 cm −1 in AuO 2 + CO ( Figure 1d). The calculated CO stretching frequencies correlate well with the calculated charge on Au in AuBN, AuCO and AuO 2 + CO, confirming the positively charged nature of the Au atom in AuBN. Similar redshifts of the C = O stretching frequency have been reported for CO oxidation over Au and Pd-based SACs and nanoparticles catalysts [20,[74][75][76][77]. Based on the consistent evidence for the positively charged nature of AuBN ( Figure 1a, AuBN), we moved further to investigate its performance in CO oxidation.

Revised LH Pathway for CO Oxidation over AuBN
Based on experimental and theoretical results, several pathways have been proposed for the CO oxidation over SACs [22], which can be classified into two kinds according to the involvement of support during the reaction. Pristine h-BN is chemically inert to CO and O 2 . As shown in Figure 1a, the proposed AuBN has the B-vacancy on h-BN fully passivated, there is no other defect at the chemical bond distance from Au to stabilize CO, O 2 or other reaction species. Therefore, the pathways that require support or defects on the support for stabilization and activation of CO or O 2 , and formation and stabilization of reaction species, such as the Mars-van-Krevelen type pathway and its variants that requires support oxygen to init [24,70], support-promoted CO oxidation that needs support to stabilize reactants [78], etc., are not applicable on AuBN. Another kind of CO oxidation pathway inherits the merit of Langmuir-Hinshelwood (LH) and Eley-Rideal(ER) type pathways derived from bulk metals [79,80], involving the adsorption and activation of one reactant (ER), either CO or O 2 , or both (LH) only on the metal species. We recently investigated CO oxidation over the defect-stabilized Fe and Pd SACs on graphene and demonstrated that the coadsorption of CO and O 2 would be more plausible on these SACs over van de Waals complexes and the coadsorption of 2 CO to initiate CO oxidation on ER type pathways. Thus, it would be a major reaction species with a population superior to those van de Waals complexes and is the active species to initiate CO oxidation [55,56,81]. The calculated thermodynamics stability of reaction species on AuBN (Figure 1j) also demonstrated such a trend that AuO 2 + CO is more plausible than AuO 2 + CO(g) and Au(CO) 2 , though AuCO is the most plausible species in reaction conditions. This AuO 2 + CO ( Figure 1d) satisfies the requirements to initiate reaction on LH type pathways that both O 2 and CO adsorb on AuBN and get activated for reactions. The first reported pathway of the LH type involves coadsorbed CO-assisted O 2 activation through the formation and dissociation of peroxide (OCOO) species on the metal center (revised Langmuir-Hinshelwood pathway, rLH), and was originally proposed by Iglesia et al., and was then adapted as the pathway for the CO and ethylene oxidation over Au SAC [31,39,82]. We then started with the rLH pathway from AuO 2 + CO (LH-IS1, Figure 2a).   (Figure 2f), which is more thermodynamically stable than LH-FS1. AuO will then form a van de Waals complex with gaseous CO (LH-IS2, Figure 2g). The calculated ∆E and ∆G between LH-FS1 and LH-IS2 are only 0.02 and 0.19 eV, respectively. The electrostatic interaction between C(CO) (+0.06 |e|) and O(Au)(−0.30|e|) stabilizes LH-IS2 and initiates the subsequent reaction with charge transfer from the 5σof CO to the π* on O(Au) for the reduction of Au. CO moves towards O(Au) in this process to reach the transition state (LH-TS3, Figure 2h), where the C-O(Au) distance decreases to 1.90 Å and the calculated Hirshfeld charge on C and O(Au) changes to 0.06 and −0.26 |e|, respectively, indicating a charge transfer from CO to O for the formation of the C=O bond. By crossing the energy barrier of 0.17 eV (LH-TS3), another CO 2 is formed (LH-FS2, Figure 2i). CO 2 desorption from AuCO 2 would be easy even at a low temperature, as the calculated E ad of CO 2 is only −0.07 eV and thus closes the catalytic cycle for CO oxidation along the rLH pathway.

Interference of the Coadsorption of CO or O 2 to CO Oxidation
LH-MS1 is an important intermediate on the rLH pathway with a dissociation free energy barrier of 0.51 eV at 298.15 K when P CO = 0.01 atm and P CO /P O2 = 1:20. Considering the high barrier for dissociation and a small barrier for formation, LH-MS1 would be one of the major reaction species [55]. A careful inspection of the structure shows that Au in LH-MS1 is not fully coordinated in a penta coordinated environment, implying potential coadsorption and further reactions with CO or O 2 (Figure 3). The calculated E ad for CO coadsorption with LH-MS1(LHa-IS1, Figure 3a) is −0.44 eV and ∆G is 0.22 eV (at 298.15 K, P CO =0.01 atm, P CO /P O2 = 1:20). The variation of ∆G from LH-MS1 also suggests that the adsorbed CO would be reactive for subsequent reactions [55,76]. In LHa-IS1, Au is +0.61 |e| charged to interact with 3 N at a B-vacancy of h-BN, O and C of peroxide intermediate (OOCO) and the newly adsorbed CO. The calculated C = O stretching frequency in OOCO is blue shifted from 1748 cm −1 to 1811 cm −1 , while that in CO is also blue shifted to 2125 cm −1 . These correlate well with the charge on Au. OCOO dissociation and subsequent reactions was then investigated. As aforementioned, OCOO will dissociate to form CO 2 and AuO with an energy barrier of 0.51 eV. The calculated energy barrier for OCOO dissociation in LHa-IS1 is 0.44 eV and is lowered by 0.07 eV. One may raise concern with the CO desorption during or prior to OCOO dissociation. The O(CO)-Au distance is decreased slightly from 2.09 (in LHa-IS1) to 2.05 Å in the corresponding TS (LHa-TS1, Figure 3b) and is further decreased to 2.02 Å in the product (LHa-MS1, Figure 3c) that is a coadsorption structure of atomic O and CO with a CO 2 interacting electrostatically with O(Au). The continuous decrease in the Au-C distance during this process indicates that OCOO dissociation may not drive desorption of CO but stabilize it instead. After desorption of CO 2 in LHa-MS1, further reactions may take place between coadsorbed CO and O in LHa-MS2 ( Figure 3d). As mediated by Au, the coadsorbed O and CO combine together by crossing a TS (LHa-MS2, Figure 3e) with a reaction barrier of 0.01 eV and free energy barrier of 0.05 eV, to form another CO 2 (LHa-FS1, Figure 3f). The calculated (free) energy barriers on the newly proposed pathway for the evolution of LHa-IS1 are much lower than those on the rLH pathway (Figures 2j and 3j). The decreased reaction barrier provides direct evidence for the promotion effect of CO in OCOO dissociation. By crossing the energy barrier of 0.17 eV (LH-TS3), another CO2 is formed (LH-FS2, Figure 2i). CO2 desorption from AuCO2 would be easy even at a low temperature, as the calculated Ead of CO2 is only −0.07 eV and thus closes the catalytic cycle for CO oxidation along the rLH pathway.

Interference of the Coadsorption of CO or O2 to CO Oxidation
LH-MS1 is an important intermediate on the rLH pathway with a dissociation free energy barrier of 0.51 eV at 298.15 K when PCO = 0.01 atm and PCO/PO2 = 1:20. Considering the high barrier for dissociation and a small barrier for formation, LH-MS1 would be one of the major reaction species [55]. A careful inspection of the structure shows that Au in LH-MS1 is not fully coordinated in a penta coordinated environment, implying potential coadsorption and further reactions with CO or O2 (Figure 3). The calculated Ead for CO coadsorption with LH-MS1(LHa-IS1, Figure 3a) is −0.44 eV and ΔG is 0.22 eV (at 298.15 K, PCO =0.01 atm, PCO/PO2 = 1:20). The variation of ∆G from LH-MS1 also suggests that the adsorbed CO would be reactive for subsequent reactions [55,76]. In LHa-IS1, Au is +0.61 |e| charged to interact with 3 N at a B-vacancy of h-BN, O and C of peroxide intermediate (OOCO) and the newly adsorbed CO. The calculated C = O stretching frequency in OOCO is blue shifted from 1748 cm −1 to 1811 cm −1 , while that in CO is also blue shifted to 2125 cm −1 . These correlate well with the charge on Au. OCOO dissociation and subsequent reactions was then investigated. As aforementioned, OCOO will dissociate to form CO2 and AuO with an energy barrier of 0.51 eV. The calculated energy barrier for OCOO dissociation in LHa-IS1 is 0.44 eV and is lowered by 0.07 eV. One may raise concern with the CO desorption during or prior to OCOO dissociation. The O(CO)-Au distance is decreased slightly from 2.09 (in LHa-IS1) to 2.05 Å in the corresponding TS (LHa-TS1, Figure 3b) and is further decreased to 2.02 Å in the product (LHa-MS1, Figure 3c) that is a coadsorption structure of atomic O and CO with a CO2 interacting electrostatically with O(Au). The continuous decrease in the Au-C distance during this process indicates that OCOO dissociation may not drive desorption of CO but stabilize it instead. After desorption of CO2 in LHa-MS1, further reactions may take place between coadsorbed CO and O in LHa-MS2 ( Figure 3d). As mediated by Au, the coadsorbed O and CO combine together by crossing a TS (LHa-MS2, Figure 3e) with a reaction barrier of 0.01 eV and free energy barrier of 0.05 eV, to form another CO2 (LHa-FS1, Figure 3f). The calculated (free) energy barriers on the newly proposed pathway for the evolution of LHa-IS1 are much lower than those on the rLH pathway (Figures 2j and 3j). The decreased reaction barrier provides direct evidence for the promotion effect of CO in OCOO dissociation.   Figure 3h) with a barrier of 1.00 eV and the free energy barrier of 0.92 eV, forming physisorbed O 2 and CO 2 around AuO (LHb-FS1, Figure 3i). As the OCOO dissociation barrier is increased to be much higher than E ad (∆G) for O 2 adsorption, O 2 desorption may take place with high priority and may not impact OCOO dissociation.
Apart from promoting the dissociation of OCOO, the coadsorbed CO may also react with OCOO. In LHc-IS1 (Figure 4a Figure 3h) with a barrier of 1.00 eV and the free energy barrier of 0.92 eV, forming physisorbed O2 and CO2 around AuO (LHb-FS1, Figure 3i). As the OCOO dissociation barrier is increased to be much higher than Ead (ΔG) for O2 adsorption, O2 desorption may take place with high priority and may not impact OCOO dissociation. Apart from promoting the dissociation of OCOO, the coadsorbed CO may also react with OCOO. In LHc-IS1 (Figure 4a), Au is highly positively charged (+0.61|e|), O bound to Au is negatively charged (−0.20 |e|) and C(CO) is also positively charged (+0.19 |e|). CO may interact electrostatically with O(Au) to reach a TS (LHc-TS1, Figure 4b) with energy and free energy barriers of 0.18 and 0.64 eV, respectively, for the formation of OCOOCO intermediate (LHb-MS1, Figure 4c) that was previously proposed on a threemolecule ER(ER3) type pathway for CO oxidation [53].  As Au in LHb-MS1 is also pentacoordinated, coadsorption of CO or O 2 may also take place. The impact of coadsorbed CO and O 2 for the further evolution of LHc-MS1 was also investigated. Both CO and O 2 cannot react with OCOOCO intermediate, they will retain and adsorb on AuBN after the dissociation of LHc-MS1. As Au is already positively charged in LHc-MS1, the calculated E ad for CO and O 2 coadsorption are −0.21 and −0.09 eV, respectively, while ∆G are 0.52 and 0.46 eV, respectively. This is similar to the aforementioned coadsorption of CO or O 2 with OOCO. With the coadsorption of reactants, the energy and free energy barriers for OCOOCO dissociation change to 0.49 and 0.28 eV, respectively, for CO and 0.19 and 0.15 eV, respectively, for O 2 . The variation of the reaction barrier with coadsorption of CO or O 2 once again provides direct evidence for the interference of coadsorbed CO or O 2 to the evolution of reaction species and CO conversion.
AuO is another important intermediate on the rLH pathway for CO oxidation. AuO is formed by the dissociation of LH-MS1 and may be consumed by direct reaction with gaseous CO [39]. In AuO, O is negatively charged (−0.30 |e|). Previously, such negatively charged O-containing species in mesoporous carbon materials were proposed as reactive CO 2 binding sites [84]. The calculated CO 2 E ad for CO 2 physisorption on AuO (LHd-IS1, Figure 5a) is −0.07 eV and the corresponding ∆G is 0.51 eV. These are in reasonable agreement with Pd, Fe and Au SACs on graphene [31,55,56]. In LHd-IS1, both the C-O bonds are nearly vertical to C(CO 2 )-O(Au) direction. Following the O(Au)-C(CO 2 ) electrostatic interaction, CO 2 moves to O(Au) by crossing a TS (LHd-TS1, Figure 5b) with a barrier of 0.18 eV and free energy barrier of 0.34 eV for the formation of carbonate (CO 3 , LHd-MS1, Figure 5c). The O(CO)-C-O angle also changes from 85 to~94 • , demonstrating that CO 2 is activated to interact with both O(Au) and Au in this process. The interaction is further enhanced in LHd-MS1, as the O(C)-C-O(Au) is distorted to be~120 • . Au in AuBN is also oxidized during this process, as the charge on Au changes from 0.56 |e| to 0.64 |e| in LHd-MS1. The energy and free energy change for the formation of CO 3 are −0.98 and −1.19 eV, respectively, while the calculated energy and free energy barriers for CO 3 dissociation are 1.38 and 1.28 eV, respectively. Therefore, the direct dissociation of CO 3 is rather demanding over AuBN. In this sense, CO 3 formation is plausible by the reaction of gaseous CO 2 with AuO. This pathway also connects the evolution of OCOO to thermodynamically more plausible CO 3 species and solves the concern for formation and evolution of CO 3 species in CO oxidation on SACs [73][74][75]85]. We then moved on to investigate the potential coadsorption with CO and whether CO may promote the conversion of CO 3 [56]. The CO coadsorption leads to the formation of LHd-MS2 (Figure 5d). The calculated CO E ad and ∆G are −0.42 and 0.16 eV, respectively. The small positive change of ∆G suggests coadsorbed CO would be highly reactive [55,76]. According to the charge distribution, the positively charged C(CO) may move to react with negatively charged O(Au) at the interface by crossing the TS (LHd-TS2, Figure 5e Figure 5h). During this process, 2 C(O) were oxidized and charges were transferred to Au. As aforementioned, the coadsorbed CO may also act as a spectator in CO 3 dissociation. For comparison, the dissociation of CO 3 in LHc-MS2 in this way was also investigated. In this process, the reaction proceeds through a TS (LHc-TS4, Figure 5i) with calculated energy and free energy barriers of 1.85 and 1.59 eV, respectively, to reach the product with a coadsorption of atomic oxygen, CO and a physisorbed CO 2 around the Au center (LHa-MS1, Figure 3c). The barriers at LHd-TS4 are much higher compared with the direct dissociation of CO 3 and the reaction of coadsorbed CO with CO 3 , demonstrating the influence of coadsorbed reactants to the evolution of reaction species and the CO conversion.
To this end, the coadsorbed CO, O 2 or CO 2 may lead to the formation of new reaction species with different reactivity and their evolution through pathways complementary to the rLH pathway for CO oxidation. Specifically, the coadsorbed CO or O 2 may promote the evolution of reaction intermediates, considering the CO promoted the dissociation of OCOO (LHa, Figure 3) and O 2 promoted the dissociation of OCOOCO. Or, they would react to form new reaction species, such as the formation of OCOOCO by the reaction of CO with OCOO (LHb, Figure 4) and the formation of C 2 O 4 by the reaction of CO with CO 3 (LHd, Figure 5), initiating new pathways for CO oxidation. Considering the limited E ad and ∆G of these coadsorbed species, their formation would be strongly interfered by reaction conditions. At low partial pressure and high temperature, coadsorption of reactants would be vanished and the reaction may mainly proceed with the rLH pathway ( Figure 2) with the formation and dissociation of peroxide intermediate and a direct reaction with gaseous CO. High partial pressure and low temperature may benefit the formation of coadsorbed structures of different reactivity to enable the switching of the reaction pathway. This effect would be significant for the LHb (Figure 3) pathway and promotes the CO-assisted dissociation of OCOO, as well as the CO 3 formation and evolution initiated with the reaction of AuO with CO 2 (LHd, Figure 5). CO 3 is also an important reaction species, considering the strong exothermicity for formation and its reaction with coadsorbed CO, which makes the circumvention of the potentially sluggish reaction of gaseous CO with AuO possible [86]. To this end, the coadsorbed CO, O2 or CO2 may lead to the formation of new reaction species with different reactivity and their evolution through pathways complementary to the rLH pathway for CO oxidation. Specifically, the coadsorbed CO or O2 may promote the evolution of reaction intermediates, considering the CO promoted the dissociation o OCOO (LHa, Figure 3) and O2 promoted the dissociation of OCOOCO. Or, they would react to form new reaction species, such as the formation of OCOOCO by the reaction o CO with OCOO (LHb, Figure 4) and the formation of C2O4 by the reaction of CO with CO (LHd, Figure 5), initiating new pathways for CO oxidation. Considering the limited Ea and ΔG of these coadsorbed species, their formation would be strongly interfered by re action conditions. At low partial pressure and high temperature, coadsorption of reactant would be vanished and the reaction may mainly proceed with the rLH pathway ( Figure  2) with the formation and dissociation of peroxide intermediate and a direct reaction with gaseous CO. High partial pressure and low temperature may benefit the formation of co adsorbed structures of different reactivity to enable the switching of the reaction pathway This effect would be significant for the LHb (Figure 3) pathway and promotes the CO assisted dissociation of OCOO, as well as the CO3 formation and evolution initiated with the reaction of AuO with CO2 (LHd, Figure 5). CO3 is also an important reaction species considering the strong exothermicity for formation and its reaction with coadsorbed CO which makes the circumvention of the potentially sluggish reaction of gaseous CO with AuO possible [86].

Comparison with Other Alternative Pathways
We have discussed CO oxidation over AuBN through the rLH pathway and its vari ants and would now move further to compare these with the remaining. An ER type path

Comparison with Other Alternative Pathways
We have discussed CO oxidation over AuBN through the rLH pathway and its variants and would now move further to compare these with the remaining. An ER type pathway is initiated with the adsorption and activation of one of the reactants for subsequent reaction with the other gaseous reactants. Theoretically, several ER type pathways were proposed for CO oxidation over SACs, including one molecular ER pathway(ER1), where O 2 or CO should be activated at the metal center to react with gaseous reactant for the formation of CO 2 and surface O species [87], two molecular ER(ER2) pathways where gaseous CO react with activated O 2 forming CO 3 as a stable intermediate [88] and an ER3 pathway that can be identified with the OCOOCO intermediate formed by the reaction of gaseous O 2 with two pre-adsorbed CO [53], etc. These pathways all initiate with the van de Waals complexes formed between surface species and the gaseous reactants. According to the thermodynamics data (Figure 1j), AuCO is the most plausible surface species with AuO 2 + CO ranking the second. The van de Waals complexes formed between preadsorbed CO or O 2 with gaseous reactants, such as AuO 2 + CO(g), Au(CO) 2 + O 2 (g), etc., are less plausible as compared with the corresponding surface species, such as AuO 2 + CO, etc., while Au(CO) 2 + O 2 is unstable and O 2 may desorb during structure optimization. The superior stability of reaction species on LH type pathways over those van de Waals complexes were previously reported for in CO oxidation over other SACs, where the relative stability among these reaction species were proposed to account for the dominant role of the rLH pathway in the CO oxidation [55,56]. Further to these, the charge transfer from activated O 2 to CO is required for the formation of CO 3 intermediate on the ER2 pathway, and a reaction of this kind is always accompanied with high reaction barriers. The ground state of Au(CO) 2 + O 2 (g) is of triplet symmetry, and the spin is localized on O 2 , making the formation of OCOOCO species of singlet symmetry spin-forbidden. Therefore, the reactions along ER2 and ER3 pathways on AuBN would be rather demanding as compared to those on LH type pathways. As only O 2 was activated on the ER1 pathway, the reaction is between activated O 2 and gaseous CO and the calculated energy and free energy barriers for the formation of first CO 2 are 0.71 and 0.84 eV, respectively, and are much higher as compared with those on the LH type pathways with the involvement of Au.
We fell back to consider the potential formation of the reaction species on ER type pathways and compared them with those on the rLH pathway and newly proposed variants. It is interesting to note that all reaction species, such as CO 3 , OCOOCO, etc., were already included on newly proposed variants of the rLH pathway. Furthermore, the thermostability of some reaction species on ER pathways are lower as compared with corresponding species on LH type pathways, demonstrating that their evolution to those stable species on LH type pathways by adsorbate adsorption/desorption or exchange would be thermodynamics driven. Therefore, their evolution to and on the LH-type pathways would be more reasonable, and would be strongly interfered with by the reaction conditions.

Conclusions
The reaction condition-dependent catalytic performance of a SAC has long been realized, but seldom investigated before. We investigated CO oxidation pathways over SACs in reaction conditions, using AuBN as a model with extensive first-principles-based calculations. We showed that the adsorption of reactants, namely CO, O 2 and CO 2 , and their coadsorption with reaction species on AuBN, would be condition dependent, leading to various reaction species with different reactivity and impact to the CO conversion. New pathways originating from these reaction species, complementary to rLH pathway, were proposed and may account for the CO conversion at the corresponding conditions. Specifically, the rLH pathway with CO-mediated activation of O 2 and the dissociation of the cyclic peroxide intermediate followed by the Eley-Rideal type reduction is dominant at high temperatures, while the coadsorbed CO-mediated dissociation of peroxide intermediate becomes plausible when coadsorption is allowed at low temperatures and high CO partial pressures. Carbonate species would also form in existence of CO 2 and would react with coadsorbed CO, promoting the CO oxidation. The pathways were currently proposed to investigate CO oxidation on AuBN, but can be delivered to other SACs by further integration with other alternatives pathways that require features not available on AuBN, such as the Mars-van-Krevelen type pathways and those require the involvement of the support. The findings highlight the condition-dependent CO oxidation over SACs may originate from the thermostability of reaction species in detailed conditions and may help to rationalize the current understanding to the superior catalytic performance of SACs.
Author Contributions: X.L. designed the research and wrote the manuscript. X.Z. performed the firstprinciples-based calculations and analyzed the results. X.Z. is responsible for the results presented. X.L. and C.M. provided the resources, commented on the results and proofed the manuscript. All authors have read and agreed to the published version of the manuscript.

Conflicts of Interest:
The authors declare no conflict of interest.