Adsorption of O2 on the Preferred -O-Au Sites of Small Gold Oxide Clusters: Charge-dependent Interaction and Activation

Decades of research have illuminated the significant roles of gold/gold oxide clusters in small molecule catalytic oxidation. However, many fundamental questions, such as the actual sites to adsorb and activate O2 and the impact of charge, remain unanswered. Here, we have utilized an improved genetic algorithm program coupled with the DFT method to systematically search for the structures of Au1–5Ox−/+/0 (x = 1–4) and calculated binding interactions between Au1–5Ox−/+/0 (x = 1–2) and O2, aiming to determine the active sites and to elucidate the impact of different charge states in gold oxide systems. The results revealed that the reactivity of all three kinds of small gold oxide clusters toward O2 is strongly site-dependent, with clusters featuring an -O-Au site exhibiting a preference for adsorption. The charges on small gold oxide clusters significantly impact the interaction strength and the activation degree of adsorbed O2: in the case of anionic cluster, the interaction between O2 and the -O-Au sites leads to a chemical reaction involving electron transfer, thereby significantly activating O2; in neutral and cationic clusters, the adsorption of O2 on their -O-Au sites can be viewed as an electrostatic interaction. Pointedly, for cationic clusters, the highly concentrated positive charge on the Au atom of the -O-Au sites can strongly adsorb but hardly activate the adsorbed O2. These results have certain reference points for understanding the gold oxide interfaces and the improved catalytic oxidation performance of gold-based systems in the presence of atomic oxygen species.


Introduction
Catalysis plays a substantial role in agricultural, industrial, and environmental fields, serving as one of the pivotal topics within the scope of chemical research.Notably, metallic nanocatalysts loaded on various oxides represent one of the most common forms of catalysts [1][2][3][4][5][6].Gold, perceived as an exceedingly inert metal since ancient times, was discovered, by Haruta [7][8][9] and Hutchings [10,11] at the end of the last century, to exhibit remarkable catalytic oxidation activity toward CO and other small organic molecules.This groundbreaking discovery precipitated a surge in the amount of research related to gold systems, gradually culminating in the establishment of an independent field of study.
By adopting the cluster model which boasts advantages such as controllable preparation, simplicity, and close linkage with DFT theoretical computations, we can comprehend the mechanisms of heterogeneous catalysis interacting with small molecules at the atomic and molecular level [42][43][44][45].Insights into the activation of O 2 on gold-based catalysts have been derived from comprehensive studies on the reactions between various gold clusters and O 2 , merging data from numerous experiments and calculations [18,20,[46][47][48][49][50][51][52][53][54][55].Consistent findings indicate O 2 functioning as a one-electron acceptor during its interactions with gold clusters, with electron transfer from gold to its anti-bonding π* 2p enhancing its adsorption and activation.The strong chemical interactions with O 2 are primarily due to the unpaired electrons and the low electron binding energy inherent to gold clusters.Theoretical explorations have also been conducted on gold clusters containing one or two O atoms [53,55,56].These O atoms tend to occupy terminal positions in clusters comprising no more than three gold atoms, or they bridge two peripheral gold atoms [56].It has been generally observed that gold clusters featuring two separate O atoms maintain greater stability than their counterparts which adsorb an O 2 molecule, particularly when the clusters incorporate more than three gold atoms [51,53,55].Furthermore, some small gold oxide clusters, specifically AuO 1-2 − and Au 2,4 O 2 − , have been generated within the plasma of the laser-vaporization cluster source.Combinatorial analysis using photoelectron spectrometry experiments and calculations determined their structures [52,57].The interactions between Au x O y +/− and CO have been thoroughly examined using a flow tube reactor, which illuminated several reaction channels [58][59][60][61][62].We previously explored reactivity of AuO x − (x = 1-3) with O 2 and found that only AuO − is active [63].Recently, we have indicated that -O-Au is the preferred adsorption site for O 2 on small anionic gold oxide clusters through theoretical calculations and mass spectrometry experiments, and the correlation with the global electronic characteristics is insignificant [64].
Compared with common cluster models, actual heterogeneous catalytic sites tend to be neutral or carry a small amount of charge due to charge transfer [30,65].Therefore, revealing the relationships between cluster reactivity and the polarity and amount of charge on the clusters is crucial to scrutinize reaction mechanisms on actual catalysts based on cluster reaction results.This study aims to elucidate the impact of different charge states of gold oxide systems on O 2 adsorption and activation, which is the rate-limiting step in many catalytic oxidation processes [32,[66][67][68].In this paper, we have carried out extensive theoretical calculations on the structures of Au 1-5 O 1,2 −/+/0 and the adsorption and activation of O 2 on them.The results indicate that, no matter what the charge state of the cluster is, the -O-Au site is the preferred adsorption site for O 2 , with the largest binding energy.However, due to the different valence bond interactions formed on clusters' various charge states, only the -O-Au sites in the anionic gold oxide clusters can significantly activate O 2 .The low-lying structures of Au 1-5 O 1,2 − have been reported in our previous work [64], and Figure 1 shows the lowest-lying ones.For references to other low-lying structures, please refer to Figures S1-S4 in the Supplementary Materials.In Figure 1, the O atoms in Au 1-5 O − are coordinated to one or two Au atoms, which is consistent with previous results [56]; for Au 1-5 O 2 − , when the number of Au atoms is odd, the energy of the oxide formation is energetically favorable (with O atoms dissociated), whereas when the number of Au atoms is even, the formation with an absorbed O 2 becomes the most energetically favorable structure.The most energetically advantageous adsorption site for the O 2 in Au 2,4 O 2 − is consistent with previous theoretical results [49][50][51]55,69,70].

Geometric Structures of Au
with a slightly larger number of gold atoms in Figures S2-S4, we can find 3-4-b-T eV), 3-4-c-T (Ea: 0.87 eV), and 5-4-g-T (Ea: 0.89 eV) and many other structures that with the adsorption rules.Namely, if the -O-Au site is present, the adsorption en O2 on it is the largest (approx.0.5-1.5 eV).However, if there is no such site, the ads of O2 is extremely weak, as demonstrated by 3-4-d-Quint (Ea: 0.01 eV), 4-3-b-Q ( eV), and 5-4-n-Quint (Ea: 0.01 eV) in Figure 1.Additional examples for this weak tion can be found in the Supplementary Materials (Figures S1-S4).
Figure 1.The lowest-lying structures of Au1-5Ox − (x = 1 and 2) and their most stable produ adsorbing one O2 according to calculations at the B3LYP level with the basis sets of def2-SV and def2-TZVP for O.In the labels of the structures, the first two numerals indicate the nu gold atoms and the number of oxygen atoms, respectively; the third part "G/a/b…" means structure is the lowest-lying, the second lowest-lying, or the third lowest-lying one among tural candidates; the fourth part indicates the spin-multiplicity, in which "S", "D", "T", " "Quint" stand for singlet, doublet, triplet, quartet, and quintet, respectively.The numera parentheses following the labels of the structures containing adsorbed O2 unit(s) show the tion energies (Ea, in eV) of the second O2.For the structures of Au 1-5 O 1,2 − , illustrated in the left two columns of Figure 1, only 1-1-G-S and 3-1-G-S have an -O-Au site, and adsorption of O 2 on these two structures forms 1-3-G-T and 3-3-G-T with the largest two adsorption energies of 1.45 eV and 0.77 eV, respectively (in the right two columns of Figure 1).Similar situations can also be repeatedly confirmed in the Supplementary Materials, such as the O 2 adsorption products of 1-4-G-T (E a : 1.05 eV), 2-3-b-D (E a : 1.35 eV), and 2-4-G-D (E a : 1.05 eV) in Figure S1.Also, for clusters with a slightly larger number of gold atoms in Figures S2-S4, we can find 3-4-b-T (E a : 1.15 eV), 3-4-c-T (E a : 0.87 eV), and 5-4-g-T (E a : 0.89 eV) and many other structures that comply with the adsorption rules.Namely, if the -O-Au site is present, the adsorption energy of O 2 on it is the largest (approx.0.5-1.5 eV).However, if there is no such site, the adsorption of O 2 is extremely weak, as demonstrated by 3-4-d-Quint (E a : 0.01 eV), 4-3-b-Q (E a : 0.00 eV), and 5-4-n-Quint (E a : 0.01 eV) in Figure 1.Additional examples for this weak interaction can be found in the Supplementary Materials (Figures S1-S4).The lowest-lying structures of Au 1-5 O 1,2 + are shown in the left two columns of Figure 2. In the geometric structures of Au 2-5 O + , the O atom connects three gold atoms when the number of Au atoms is odd, and it connects two gold atoms when the number of Au atoms is even.Our computational work remains consistent with previous work [56].For Au 1-5 O 2 + , the lowest-lying structures can be interpreted as the lowest-lying cationic pure gold cluster adsorbed an O 2 [71][72][73].The adsorption energies of O 2 clearly show that, with the exception of AuO 2

Geometric Structures of Au
+ (E a : 0.50 eV), the adsorption interaction here is relatively low, which is consistent with the results of Ding et al. [70].Additionally, there is a decreasing trend in adsorption energies as the number of gold atoms increases, which may be related to what we will discuss later: for cationic gold oxide clusters and neutral gold oxide clusters, the adsorption energy of O 2 on them is proportional to the amount of positive charge on the Au atom of the -O-Au sites.
number of Au atoms is odd, and it connects two gold atoms when the number of Au is even.Our computational work remains consistent with previous work [56].F 5O2 + , the lowest-lying structures can be interpreted as the lowest-lying cationic pu cluster adsorbed an O2 [71][72][73].The adsorption energies of O2 clearly show that, w exception of AuO2 + (Ea: 0.50 eV), the adsorption interaction here is relatively low, w consistent with the results of Ding et al. [70].Additionally, there is a decreasing t adsorption energies as the number of gold atoms increases, which may be related we will discuss later: for cationic gold oxide clusters and neutral gold oxide clust adsorption energy of O2 on them is proportional to the amount of positive charge Au atom of the -O-Au sites.
As shown in the right two columns of   As shown in the right two columns of Figure 2, the adsorption energies of O 2 on the -O-Au sites of 1-1-G-T and 2-1-G-D remain high, at approximately 0.78 eV (1-3-G-Quint) and 0.64 eV (2-3-G-D), respectively.The adsorption energies of O 2 on the -O-Au sites of 3-1-G-S, 4-1-G-D and 5-1-G-S are 0.56 eV (3-3-G-T), 0.53 eV (4-3-G-Q), and 0.51 eV (5-3-G-T), respectively.This observed preference is similar to our prior findings regarding anionic gold oxide clusters [64].Apart from the ones shown in Figure 2, Figures S5-S8 in the Supplementary Materials provide other examples to repeatedly confirm this preference (such as the adsorbed O 2 in 2-4-G-Q, 2-4-c-D, 3-3-b-Quint, 3-4-a-Quint and 5-4-a-Quint).In a word, the adsorption energy of O 2 on the -O-Au site is higher than that on other sites, with the majority of clusters' adsorption energies around 0.5 eV.
In the absence of the -O-Au site, the adsorption will be weak.As portrayed in Figure 2, the structures 2-4-a-Q, 3-4-G-Quint, 4-4-G-Q, and 5-4-G-Quint exhibit adsorption energies of merely 0.25 eV, 0.24 eV, 0.19 eV, and 0.16 eV, respectively.In Figure 2   The lowest-lying structures of Au 1-5 O 1,2 are shown in the left two columns of Figure 3.For the clusters with one or three gold atoms, the O is mono-coordinated, whereas when the number of gold atoms is equal to 2, 4, or 5, the O atom is di-coordinated.The lowest-lying structures obtained by our calculations are consistent with previously reported results [56].For Au 1-5 O 2 , the lowest-lying structures are those with molecular oxygen adsorbed onto pure gold clusters.It is noteworthy that when the number of gold atoms is three or five, peroxide adsorption forms, with adsorption energies of 0.49 eV and 0.64 eV being found.These two peroxide structures are consistent with previous results [70], and their O 2 units are highly activated: the O-O bond length, O-O vibration frequency, and NPA charge on O 2 are 1.281 Å, 1199.00 cm −1 , and −0.427 a.u.for Au 3 O 2 , and 1.316 Å, 1161.80 cm −1 , and −0.540 a. u. for Au 5 O 2 .
As shown in the right two columns of Figure 3, the corresponding adsorption structures of 1-1-G-D, 2-1-G-S, and 4-1-G-S are 1-3-G-Q, 2-3-G-T, and 4-3-a-T, respectively.The original structures all have active -O-Au sites, and the adsorption energies of O 2 on these sites are 0.39 eV, 0.38 eV, and 0.36 eV, respectively.Aside from those shown in Figure 3, there are other examples in the Supplementary Materials.As can be seen in Figure S9, the corresponding adsorption structure of 2-2-a-T is 2-4-b-Quint, and the adsorption energy on its -O-Au site is 0.40 eV.Some additional examples include 3-4-b-Q and 3-4-e-Q from Figure S10; 4-3-e-T, 4-3-h-T and 4-4-j-Quint from Figure S11; and 5-4-i-Q from Figure S12.In a word, if there is an -O-Au site, the adsorption energy of O 2 is maximal (relative to other sites), and the adsorption energies on these sites are typically slightly less than 0.4 eV.
If there is no -O-Au site, adsorption of O 2 is extremely weak.As depicted in Figure 3, the corresponding adsorption structures of 3-1-G-D and 5-1-G-D are 3-3-a-Q and 5-3-c-Q with the adsorption energies of 0.10 eV and 0.01 eV, respectively.There are other examples in the Supplementary Materials (Figures S9-S12), which are not all enumerated.The adsorption energies of the second O 2 on Au 1-5 O 2 are nearly identical to the previous theoretical results predicted by Ding et al. [70].

Charge-Dependent Bonding Strengths and Activation Degrees
To summarize and compare the adsorption energies and the activation degree on the -O-Au sites in the structures depicted in Figures 1-3, we present related calc parameters of the adsorbed O2 in Table 1.Anionic gold oxide clusters exhibit the l binding energies for O2 among the three series, along with the longest O-O bond l (above 1.32 Å).The calculated bond length of a free O2 stands at 1.204 Å (1.208 Å ported in an experiment by [74]), so anionic gold oxide clusters show a significant s ing of the O-O bond.Simultaneously, the O2 units on anionic gold oxide clusters ac late more than 0.6 a.u.negative charges, and their spins are close to 1.0.All these p eters indicate that the adsorbed O2 on the -O-Au sites of these anionic gold oxide c gain an electron onto its π* anti-bonding orbital, which significantly activates th bond.For cationic gold oxide clusters, apart from 1-3-G-Quint and 2-3-G-D, which adsorption energies of 0.78 eV and 0.64 eV, respectively, the rest of the structures t have adsorption energies slightly higher than 0.50 eV.The O-O bond lengths of t sorbed O2 on these cationic gold oxide clusters are around 1.21 Å, which is very c that of a free O2; the adsorbed O2 units are slightly positively charged, and their sp

Charge-Dependent Bonding Strengths and Activation Degrees
To summarize and compare the adsorption energies and the activation degree of O 2 on the -O-Au sites in the structures depicted in Figures 1-3, we present related calculated parameters of the adsorbed O 2 in Table 1.Anionic gold oxide clusters exhibit the largest binding energies for O 2 among the three series, along with the longest O-O bond lengths (above 1.32 Å).The calculated bond length of a free O 2 stands at 1.204 Å (1.208 Å as reported in an experiment by [74]), so anionic gold oxide clusters show a significant stretching of the O-O bond.Simultaneously, the O 2 units on anionic gold oxide clusters accumulate more than 0.  In Figure 4a,b, we summarized the variations of the adsorption energies (E a ) and the stretching frequencies of the adsorbed O 2 vs. the NPA charges localized on the Au atom of the -O-Au sites in Au 1-5 O x −/+/0 (x = 1 and 2).The considered structures include the lowest-lying ones shown in Figures 1-3 S1-S12.For anionic Au 1-5 O x − (x = 1 and 2), a roughly inverse correlation was observed between the adsorption energies (E a ) and the NPA charges.The E a values decrease from around 1.5 eV to around 0.5 eV when the NPA charges increase from around −0.1 a.u. to around +0.4 a.u.The stretching frequencies of the adsorbed O 2 on the -O-Au sites concentrate in the range of 1100 to 1200 cm −1 .These values are much lower than the calculated stretching frequencies of a free O 2 , which stands at 1637 cm −1 (1580 cm −1 as reported in experiment [74]), and there is not a clear correlation between these frequencies and the NPA charges.For cationic gold oxide clusters Au 1-5 O x + (x = 1 and 2), an approximately positive correlation exists between the E a values and the NPA charges on the Au atoms of -O-Au sites.The E a values increase from around 0.4 eV to around 0.8 eV when the NPA charges increase from around +0.6 a.u. to around +1.0 a.u.The stretching frequencies of the adsorbed O 2 on the -O-Au sites concentrate in the range of 1500 to 1600 cm −1 .These values are very close to that of a free O 2 , and there is not a clear correlation between these frequencies and the NPA charges.For neutral Au 1-5 O x (x = 1 and 2), the adsorption energies (E a ) concentrate around 0.4 eV, which is lower than the E a values of the anionic and cationic Au 1-5 O x −/+ (x = 1 and 2).The correlation between E a and NPA charges of neutral Au 1-5 O x (x = 1 and 2) can be viewed as an extension of the positive correlation of cationic Au 1-5 O x + (x = 1 and 2) toward the small NPA charge values.The stretching frequencies of the adsorbed O 2 on the -O-Au sites in neutral clusters spread from 1300 cm −1 to 1500 cm −1 , which is between the values of the anionic and cationic species.The results of the anionic, the neutral, and the cationic species are shown by the black, the blue, and the green symbols, respectively.
Insights from the results of AuO − (1-1-G-S), AuO3 − (1-3-G-T), Au3O − (3-1-G-S), and Au3O3 − (3-3-G-T) presented in Figure 5a,b,g,h, reveal that the two up-spin and one downspin components originating from the π2p* of O2 are occupied in the adsorption products.These observations suggest that a single electron has been transferred from the anionic gold oxide clusters to the adsorbed O2, which follows a pattern reminiscent of O2 adsorption on active Aun − [51].It is crucial to note that an excess electron on the π2p* of O2 may substantially weaken the O-O bond strength, echoing the findings shown in Table 1 and Figure 4.The interaction process between AuO − (1-1-G-S) or Au3O − (3-1-G-S) and O2 can be elaborated as follows: an electron located on one HOMO (π*//) of the anionic cluster is excited to its LUMO (the σ orbital enclosed by a blue frame).Consequently, the occupied σ orbital, which extends externally, showcases a high propensity for σ bond formation.Subsequently, the interaction between this σ orbital and one singly occupied π* orbital of O2, results in an occupied σ orbital and an unoccupied σ orbital.This newly formed occupied σ orbital boasts bonding characters predominantly comprised of the π* orbital of O2, and the newly formed unoccupied σ orbital exhibits antibonding characters mainly originating from the LUMO of AuO − or Au3O − .These chemical bonding figures can account for the strong bonding strengths and the high activation degrees of O2 in these anionic species.
According to the calculated DOSs of AuO + (1-1-G-T), AuO3 + (1-3-G-Quint), Au3O − (3-1-c-T), and Au3O3 + (3-3-b-Quint) shown in Figure 5c,d,i,j, the up-spin and down-spin components on the cluster moiety and the O2 do not apparently change during the adsorption reactions, and marginal electron transfer can be distinguished.The bonding interaction The results of the anionic, the neutral, and the cationic species are shown by the black, the blue, and the green symbols, respectively.

Analyses on the Bonding Patterns
In order to understand the charge-dependent bonding strengths and activation degrees of O2 on the -O-Au sites of various clusters, we conducted an analysis of the density of states (DOSs).This analysis allowed us to identify the bonding patterns in several representative structures with differing charge polarities.The density of states (DOSs) of AuO − (1-1-G-S), AuO + (1-1-G-T), AuO (1-1-G-D), Au3O − (3-1-G-S), Au3O + (3-1-c-T), and Au3O (3-1-a-D) are shown in Figure 5a,c,e,g,i,k, respectively.The density of states (DOSs) of their adsorption products, AuO3 , and Au3O3 (3-3-G-Q), and the partial density of states (PDOSs) of the adsorbed O2 are shown in Figure 5b,d,f,h,j,l, respectively.
Insights from the results of AuO , and Au3O3 − (3-3-G-T) presented in Figure 5a,b,g,h, reveal that the two up-spin and one downspin components originating from the π2p* of O2 are occupied in the adsorption products.These observations suggest that a single electron has been transferred from the anionic gold oxide clusters to the adsorbed O2, which follows a pattern reminiscent of O2 adsorption on active Aun − [51].It is crucial to note that an excess electron on the π2p* of O2 may substantially weaken the O-O bond strength, echoing the findings shown in Table 1 and Figure 4.The interaction process between AuO − (1-1-G-S) or Au3O − (3-1-G-S) and O2 can be elaborated as follows: an electron located on one HOMO (π*//) of the anionic cluster is excited to its LUMO (the σ orbital enclosed by a blue frame).Consequently, the occupied σ orbital, which extends externally, showcases a high propensity for σ bond formation.Subsequently, the interaction between this σ orbital and one singly occupied π* orbital of O2, results in an occupied σ orbital and an unoccupied σ orbital.This newly formed occupied σ orbital boasts bonding characters predominantly comprised of the π* orbital of O2, and the newly formed unoccupied σ orbital exhibits antibonding characters mainly originating from the LUMO of AuO − or Au3O − .These chemical bonding figures can account for the strong bonding strengths and the high activation degrees of O2 in these anionic species.
According to the calculated DOSs of AuO + (1-1-G-T), AuO3 + (1-3-G-Quint), Au3O − (3-1-c-T), and Au3O3 + (3-3-b-Quint) shown in Figure 5c,d,i,j, the up-spin and down-spin components on the cluster moiety and the O2 do not apparently change during the adsorption reactions, and marginal electron transfer can be distinguished.The bonding interaction ) and other structures (the cross symbols +) with the -O-Au sites in the Supplementary Materials.The results of the anionic, the neutral, and the cationic species are shown by the black, the blue, and the green symbols, respectively.

Analyses on the Bonding Patterns
In order to understand the charge-dependent bonding strengths and activation degrees of O 2 on the -O-Au sites of various clusters, we conducted an analysis of the density of states (DOSs).This analysis allowed us to identify the bonding patterns in several representative structures with differing charge polarities.The density of states (DOSs) of AuO −  5a,b,g,h, reveal that the two up-spin and one downspin components originating from the π 2p * of O 2 are occupied in the adsorption products.These observations suggest that a single electron has been transferred from the anionic gold oxide clusters to the adsorbed O 2 , which follows a pattern reminiscent of O 2 adsorption on active Au n − [51].It is crucial to note that an excess electron on the π 2p * of O 2 may substantially weaken the O-O bond strength, echoing the findings shown in Table 1 and Figure 4.The interaction process between AuO − (1-1-G-S) or Au 3 O − (3-1-G-S) and O 2 can be elaborated as follows: an electron located on one HOMO (π* // ) of the anionic cluster is excited to its LUMO (the σ orbital enclosed by a blue frame).Consequently, the occupied σ orbital, which extends externally, showcases a high propensity for σ bond formation.Subsequently, the interaction between this σ orbital and one singly occupied π* orbital of O 2 , results in an occupied σ orbital and an unoccupied σ orbital.This newly formed occupied σ orbital boasts bonding characters predominantly comprised of the π* orbital of O 2 , and the newly formed unoccupied σ orbital exhibits antibonding characters mainly originating from the LUMO of AuO − or Au 3 O − .These chemical bonding figures can account for the strong bonding strengths and the high activation degrees of O 2 in these anionic species.
The specific implementation process is as follows: (1) In our search program, we specify the number of gold and oxygen atoms and the multiplicity of the clusters.Based on the complexity of cluster searching, we determine the type and number of initial structures as initial random structures with diverse motifs.We have designed a module capable of generating seven typical motifs for a defined cluster size: the space-free motif, the close packing motif, the simple cubic packing motif, the cage motif, the solid sphere motif, the ring motif, and the specially defined motif through atomic coordinates.The latter allows users to input specially defined or previously reported structures.
(2) The initial random structures undergo relaxation using an incomplete optimization approach and are screened using the competition method under the small basis set we specify.The surviving structures become the offspring of the first generation.(3) The first-generation results undergo multiple iterations of crossover and mutation under the genetic algorithm framework, generating a substantial number of offspring.After deduplication and competition, the next generation of structures is produced.This cycle continues until a global minimum is attained under the specified convergence limit.The structure optimizations at this stage were performed using a relatively coarse DFT method.Specifically, the B3LYP hybrid functional [80,81] with the LANL2DZ basis set [82] for Au and the 6-31+G* basis set [83][84][85] for O were utilized.For each Au 1-5 O x −/+/0 (x = 1-2), the program explored structure candidates in the two lowest-lying spin multiplicities, and for each Au 1-5 O x −/+/0 (x = 3-4), the program explored structure candidates in the three lowest-lying spin multiplicities.When conducting a structural search for the system containing three to four O atoms, the randomly generated structures consist of either all the O atoms being randomly dispersed or two of the O atoms combined as an O 2 unit being adsorbed on the remaining gold oxide clusters containing a single O atom or two O atoms.(4) All structures that were relatively stable (within approximately 1.0 eV of the lowestlying one) underwent further optimization and scrutiny at a more sophisticated theory level, in which the B3LYP hybrid functional in combination with the def2-SVP basis set for Au and the def2-TZVP basis sets for O [86,87] was utilized.Scalar and spinorbital relativistic effects of Au were addressed through energy consistent relativistic pseudopotentials.The ultimate global minima were validated via vibrational mode analysis, confirming the absence of imaginary frequencies.(5) The adsorption energies of O 2 on specific structures were calculated based on the Hartree-Fock energies corrected by the zero-point energies from frequency analyses.The formula for calculating the adsorption energy is the sum of the energies of the gold oxide cluster and O 2 , minus the energy of the compound after adsorption.The distribution of charges localized on the adsorbed O 2 and the Au atom of the -O-Au sites were examined using the Natural Bond Analysis method [88].The density of state (DOS) spectrum was obtained by broadening the calculated Kohn-Sham (KS) orbitals from the more sophisticated theory level using the Gaussian function with a FWHM of 0.1 eV.The position of HOMO in the DOS spectrum has been corrected using the clusters' vertical detachment energy (VDE) values.All DFT calculations were performed using the Gaussian 09 program [89], and the DOS spectra were generated from the calculation results using the Multiwfn software [90].

Conclusions
Using an improved genetic algorithm program combined with DFT methods, we conducted extensive calculations on the structures of Au 1-5 O 1,2 −/+/0 and their corresponding products after adsorbing an O 2 , Au 1-5 O 3,4 −/+/0 .The preferred adsorption sites and the charge-dependence of the adsorption strengths and the activation degrees were analyzed.The conclusions are as follow: 1.
Regardless of the charge states of gold oxide clusters, the -O-Au sites are inevitably the primary sites for O 2 adsorption.

2.
The charge states of gold oxide clusters determine the bonding strengths and the activation degrees of the adsorbed O 2 .For anionic gold oxide clusters, the occurrence of electron transfer from the -O-Au sites to the adsorbed O 2 leads to the formation of typical chemical bonds and high activation degrees of O 2 .For both cationic and neutral gold oxide clusters, their interactions with O 2 are predominantly electrostatic.More positive charges on the Au atom of -O-Au sites in the cationic clusters lead to stronger binding energies than those of corresponding neutral ones.Meanwhile, the lower electron densities around the Au atom of -O-Au sites in the cationic clusters make electron transfer to O 2 more unlikely, and O 2 activation on the cationic gold oxide clusters is less effective than those in neutral species.
These findings could deepen the understanding of intricate charge effects on the ability of active sites on gold-based catalysts to activate O 2 and offer pivotal information to reveal their catalytic mechanisms at the atomic and molecular level.

Figure 1 .
Figure 1.The lowest-lying structures of Au 1-5 O x − (x = 1 and 2) and their most stable products after adsorbing one O 2 according to calculations at the B3LYP level with the basis sets of def2-SVP for Au, and def2-TZVP for O.In the labels of the structures, the first two numerals indicate the number of gold atoms and the number of oxygen atoms, respectively; the third part "G/a/b. .." means that this structure is the lowest-lying, the second lowest-lying, or the third lowest-lying one among all structural candidates; the fourth part indicates the spin-multiplicity, in which "S", "D", "T", "Q", and "Quint" stand for singlet, doublet, triplet, quartet, and quintet, respectively.The numerals in the parentheses following the labels of the structures containing adsorbed O 2 unit(s) show the adsorption energies (E a , in eV) of the second O 2 .

Figure 2 .
Figure 2. The lowest-lying structures of Au1-5Ox + (x = 1 and 2) and their most stable produ adsorbing one O2 according to calculations at the B3LYP level with the basis sets of def2-SVP

Figure 2 .
Figure 2. The lowest-lying structures of Au 1-5 O x + (x = 1 and 2) and their most stable products after adsorbing one O 2 according to calculations at the B3LYP level with the basis sets of def2-SVP for Au, and def2-TZVP for O.The meanings of the labels and the numerals are the same as those in Figure 1.
, the Au 1-5 O 4 + clusters can be regarded as pure gold clusters adsorbing two molecular oxygen.The values of adsorption energies in this study align well with those reported by Ding et al., with only minor discrepancies observed in the adsorption sites of 4-4-G-Q and 5-4-G-Quint [70].As shown in Figure S6, the 3-2-b-T encompasses both an -O-Au site and an -O-Au-Au site, and the adsorption energy at the active site is 0.51 eV (3-4-b-Quint), whereas that on the -O-Au-Au site is only 0.10 eV (3-4-c-Quint).In Figure S7, 4-1-b-D has a gold triangle and an -O-Au site, and the adsorption energy of O 2 on its gold triangle and -O-Au site is calculated to be 0.17 eV (4-3-g-D) and 0.50 eV (4-3-d-Q), respectively.An analogous weak adsorption scenario can be observed in many other adsorption structures like 3-3-g-Quint, 5-3-a-T, and 5-4-c-Quint in Figures S6 and S8 .

Figure 3 .
Figure 3.The lowest-lying structures of Au1-5Ox (x = 1 and 2) and their most stable produc adsorbing one O2 according to calculations at the B3LYP level with the basis sets of def2-SVP and def2-TZVP for O.The meaning of the labels and the numerals are same as those in Figu

Figure 3 .
Figure 3.The lowest-lying structures of Au 1-5 O x (x = 1 and 2) and their most stable products after adsorbing one O 2 according to calculations at the B3LYP level with the basis sets of def2-SVP for Au, and def2-TZVP for O.The meaning of the labels and the numerals are same as those in Figure 1.
6 a.u.negative charges, and their spins are close to 1.0.All these parameters indicate that the adsorbed O 2 on the -O-Au sites of these anionic gold oxide clusters gain an electron onto its π* anti-bonding orbital, which significantly activates the O-O bond.For cationic gold oxide clusters, apart from 1-3-G-Quint and 2-3-G-D, which have adsorption energies of 0.78 eV and 0.64 eV, respectively, the rest of the structures tend to have adsorption energies slightly higher than 0.50 eV.The O-O bond lengths of the adsorbed O 2 on these cationic gold oxide clusters are around 1.21 Å, which is very close to that of a free O 2 ; the adsorbed O 2 units are slightly positively charged, and their spins are close to that of free O 2 .All these parameters indicate that the O 2 units on the -O-Au sites of the cationic gold oxide clusters are almost not activated.Neutral gold oxide clusters show adsorption energies slightly lower than 0.4 eV, with corresponding O-O bond lengths distributed around 1.225 Å, which is between those of the aforementioned anionic and cationic ones.Their O 2 units carry a slight negative charge.Compared to free O 2 , the spins of the adsorbed O 2 on these neutral gold oxide clusters decrease a little, implying the weak activation of O 2 on the neutral species despite its relatively weak binding.

Figure 4 .
Figure 4. (a) The correlations between the adsorption energies (Ea) of O2 and the NPA charges localized on the Au atoms of -O-Au sites and (b) the correlations between the frequencies (cm -1 ) of the adsorbed O2 and the NPA charges localized on the Au atoms of the -O-Au sites.The data are those of the lowest-lying structures of Au1-5Ox −/+/0 (x = 1 and 2) shown in Figures 1-3 (the square symbols □ + ) and other structures (the cross symbols +) with the -O-Au sites in the Supplementary Materials.The results of the anionic, the neutral, and the cationic species are shown by the black, the blue, and the green symbols, respectively.

Table 1 .
The adsorption energies (E a ), the bond lengths (BL O-O ), the NPA charges (Charge O-O ), and the spins (Spin O-O ) of the O 2 units adsorbed on the -O-Au sites of the Au n O −/+/0 shown in Figures 1-3.