coatings First-Principle Study of Co-Adsorption Behavior of H 2 O and O 2 on δ -Pu (100) Surface

: The surface corrosion of plutonium in air is mainly the result of the interaction with O 2 and H 2 O in air. In this paper, the co-adsorption behavior of O 2 and H 2 O on a δ -Pu (100) surface is studied by the ﬁrst-principle method. Two different cases of preferential adsorption of H 2 O and O 2 are considered, respectively. Bader charge analysis and adsorption energy analysis are carried out on all stable adsorption conﬁgurations, and the most stable adsorption conﬁgurations are found under the two conditions. The results of differential charge density analysis, the density of states analysis and Crystal Orbital Hamilton Populations (COHP) analysis show that the two molecules can promote each other’s adsorption behavior, which leads to the strength and stability of co-adsorption being far greater than that of single adsorption. In the co-adsorption conﬁguration, O atoms preferentially interact with Pu atoms in the surface layer, and the essence is that the 2s and 2p orbitals of O overlap and hybridize with the 6p and 6d orbitals of Pu. H atoms mainly form O–H bonds with O atoms and hardly interact with Pu atoms on the surface layer. from O , the H atom is not separated from the O1 atom. The total charge of H1, H2 and O1 atoms is between 0.036 e and 0.188 e . This shows that the greater the dissociation degree of H 2 adsorbed preferentially, the greater the number of charges obtained and the greater the degree of interaction with other atoms. Among the six stable adsorption conﬁgurations, compared with the conﬁguration before adsorption, the outermost Pu atoms on the surface of δ -Pu (100) generally lose charge, and the charge amount changes the most, ranging from − 2.634 e to − 2.460 e . Pu atoms in the subsurface layer also generally lose charge, and the change of charge is smaller than that in the outermost layer, ranging from − 0.269 e to 0.001 e . The general charge of Pu atoms in the third layer is much smaller than that the two layers on the surface, from 0.001 e to 0.044 . The charge Pu the bottom layer is also common, and the change of charge is almost the same as the third layer, ranging from 0.012 e to 0.050 e . It be seen that the change charge the surface of δ -Pu (100) decreases layer by layer, the charge transfer between co-adsorbed atoms and molecules mainly occurs in two layers of the


Introduction
Plutonium plays a key role in the fields of national defense and energy. It is located at the boundary between light actinides with delocalized 5f electrons and heavy actinides with localized 5f electrons [1,2]. Plutonium is chemically active and tends to interact with gases such as O 2 , CO 2 , H 2 and H 2 O in the air, which affects its service life severely [3][4][5][6][7]. Some experimental studies [8,9] showed that the corrosion rate of Pu in humid air is much higher than that in dry air. In order to reveal the mechanism of this phenomenon, many scholars have studied the high-speed oxidation mechanism of Pu in humid air [10][11][12]. The results show that the plutonium hydride PuH x is produced by the interaction between H 2 O and O 2 in humid air and the surface of plutonium. H atoms released by this reaction will not form H 2 molecules but will react with the inner Pu to form PuH x , and the generated H 2 O molecules will continue to interact with the surface of plutonium, repeating this reaction process, resulting in rapid corrosion of plutonium., i.e., H 2 O molecules in the air catalyze the corrosion of plutonium. The adsorption behavior of H 2 O and O 2 molecules on the surface of plutonium is the first step of the interaction. Therefore, it is of great importance to study the single adsorption and co-adsorption behavior of H 2 O and O 2 molecules on the surface of plutonium for understanding the corrosion mechanism of plutonium in air.
Due to the strong toxicity and radioactivity of plutonium, experimental research is facing great difficulties. Therefore, in recent years, many scholars have completed a lot of research works on the adsorption behavior of active atoms or molecules on the surface of pure plutonium or correspondence compounds. Taking the adsorption of CO molecules on δ-Pu (100) surface as an example, Delley et al. studied this problem by using the firstprinciple method under the framework of density functional theory (DFT) [13,14] and DMOL 3 program [13,15]. The results show that the adsorption of CO on δ-Pu (100) surface is the most stable, and the interaction between them is mainly located at the first layer of the surface model, and the essence of the interaction is the overlapping hybridization of the hybrid orbitals of CO molecules with the orbitals of Pu5f, Pu6d and Pu7s [16,17]. Meanwhile, Gérald et al. [18] studied the adsorption behavior of H 2 O on the surface of PuO 2 (110) by DFT calculation combined with the GGA+U method. The results show that the adsorption energy of H 2 O on the surface of PuO 2 (110) is −0.87 eV, and the molecular adsorption state is only a metastable state. H 2 O will dissociate at last, and the dissociation energy is −1.12 eV. After dissociation, H atoms in H 2 O molecules combine with an O atom on the surface of PuO 2 (110) to form hydroxyl OH, which is adsorbed on the surface together with the remaining hydroxyl OH. Huda et al. [19,20] revealed that the most stable adsorption sites of O atoms on δ-Pu (100) and δ-Pu (111) surfaces are hollow sites, and the adsorption of O 2 molecules increase the work function of the plutonium surface and make it more difficult for electrons to escape from the surface.
Plutonium polymorphs have six phase structures, among which δ-Pu has the best ductility [2,21]. δ-Pu has two low index crystalline surfaces, namely, (100) surface and (111) surface. The localization degree of 5f electrons on the (100) surface is higher than that on the (111) surface [22]. In the present work, we intend to study the co-adsorption behavior of O 2 and H 2 O on δ-Pu (100) surface by the first-principle method. First of all, it is necessary to build a variety of co-adsorption models for optimization to obtain a stable adsorption configuration and calculate its adsorption energy. Then, the adsorption strength will be analyzed by comparing the structural changes of H 2 O and O 2 and δ-Pu (100) surface before and after adsorption. Bader charge analysis, differential charge density analysis, electronic density of states analysis and COHP calculation will be carried out on the most stable adsorption configuration in order to reveal the charge transfer, bonding strength and bonding nature in the adsorption process. The adsorption properties will be judged according to the final analysis results. This work will provide a necessary reference for revealing the influence of the combined action of O 2 and H 2 O on the corrosion behavior of plutonium.

Calculation Method
All the optimization calculations in this paper are completed by using the material calculation software VASP [23,24] based on first-principle. The plane wave basis set is expanded by the Projection Addressed Wave (PAW) [25,26] method, and the exchange correlation effect is described by Generalized Gradient Approximation (GGA) [27] method. PAW-PBE pseudopotential is used to treat H, O and Pu elements. Under this pseudopotential, 16 electrons (6s 2 7s 2 6p 6 6d 2 5f 4 ) of Pu element are regarded as valence electrons, and 6 electrons (2s 2 2p 4 ) of O element are regarded as valence electrons. When the crystal unit cell is optimized, the K-point grid in the Brillouin zone is set to 7 × 7 × 7, and when the surface model is optimized and the adsorption configuration is optimized, the K-point grid in the Brillouin zone is set to 5 × 5 × 1; when calculating the density of states, the K-point grid in the Brillouin zone is set to 11 × 11 × 3, and all are generated by the Monkhorst-Pack method [28]; the plane wave truncation energy is uniformly set to 500 eV.
Adsorption energy is an important parameter to investigate adsorption stability. In this paper, the adsorption energy of each optimized adsorption configuration is compared to determine whether the adsorption configuration can exist stably. Negative adsorption energy indicates that adsorption is exothermic and adsorption configuration can exist stably, while regular adsorption energy indicates that adsorption is endothermic and adsorption configuration cannot exist stably, and the configuration with the most heat release is the most stable adsorption configuration. The calculation method of adsorption energy is shown in Formula (1).
In the above formula, E a represents adsorption energy, E t represents the total energy of the optimized adsorption configuration, E 1 represents the energy of H 2 O molecule optimized separately, E 2 represents the energy of O 2 molecule optimized separately and E s represents the energy of four-layer δ-Pu (100) surface optimized separately.

Computational Model
The δ-Pu crystal has an fcc structure, and the lattice constants optimized in this paper are a = b = c = 4.776 Å, α = β = γ = 90 • . The lattice constants obtained from experiment [18] are a = b = c = 4.637 Å, α = β = γ = 90 • . The difference between them is about 2.9%, which shows that the calculation in this paper is in good agreement with the experiment. When determining the surface model, we performed a supercell test on the δ-Pu (100) surface and calculated the surface energy of the p(2 × 2), p(2 × 3) and p(3 × 3) supercells. The corresponding coverage is 0.25 ML, 0.14 ML and 0.1 ML, respectively. The results show that the surface energies of p(2 × 2), p(2 × 3) and p(3 × 3) supercells are 0.047 eV/Å 2 , 0.043 eV/Å 2 and 0.036 eV/Å 2 , respectively. The difference is very small, which has no significant influence on the main results of this paper. In order to improve the calculation efficiency, we use p(2 × 2) supercell as the surface base for calculation. Some literature [16,17] also used p(2 × 2) supercells and obtained good calculation results. Thus, in this paper, a 4-layer p(2 × 2) supercell plate periodic model is used to simulate the surface of δ-Pu (100), and the two layers on the surface are relaxed for optimization, while the lower two layers are fixed for optimization. After optimization, the relaxed two layers all declined to varying degrees. As shown in Figure 1a,  O molecules on δ-Pu (100) surface and found the most stable adsorption structure of the two gas molecules on δ-Pu (100) surface. O 2 will dissociate after adsorption, and its most stable adsorption structure is that two O atoms occupy two bridge sites of the outermost atoms on the surface of δ-Pu (100), and the adsorption energy is −7.281 eV. As shown in Figure 1b, the bond lengths of the four Pu-O bonds are all 2.054 Å. H 2 O is adsorbed on the inclined top of the top surface of δ-Pu (100) in a molecular state. The adsorption energy of its most stable adsorption configuration is −0.305 eV, and its adsorption strength is far less than that of O 2 . As shown in Figure 1c  As for the single adsorption behavior of O 2 molecule on the surface of δ-Pu (100), the calculation results of Jijun G et al. [29] show that O 2 molecule initially placed in parallel to the heart position is dissociated after adsorption, and the two dissociated O atoms are stably adsorbed on a heart position and a bridge position on the surface of δ-Pu (100), which is the most stable, with adsorption energy of 7.290 eV. According to the calculation results of M N Huda and A K Ray [20], O 2 molecule initially placed in the heart position and parallel to the surface of δ-Pu (100) also undergoes dissociation after adsorption, and the dissociated two O atoms are stably adsorbed at the two heart positions on the surface of δ-Pu (100), respectively, with adsorption energy of 8.236 eV. There is a paper [30] showing the adsorption of a single O atom on δ-Pu (111). The results show that O atom is preferentially adsorbed at the heart site, and the adsorption energy is 6.153 eV. With regard to the single adsorption behavior of H 2 O molecule on δ-Pu surface, the literature [31] studies the adsorption behavior of H 2 O molecule on δ-Pu (111) surface by DMOL 3 software and WIEN2K program. The results show that H 2 O molecule will be adsorbed on the top site of δ-Pu (111) surface in parallel, which is also a weak physical adsorption. The research results of Hongyuan W [32] also show that the adsorption of water on δ-Pu (100) and δ-Pu (111) surfaces is weak physical adsorption. Therefore, although there are slight numerical differences between our results and those of previous scholars, the basic results obtained are not much different. The adsorption of O 2 molecule on δ-Pu surface is a strong chemical adsorption, and virtually all of them will be dissociated, and the dissociated two O atoms will be preferentially adsorbed at the bridge position and the heart position. The adsorption of water on δ-Pu surface is a weak physical adsorption and tends to be parallel adsorption.
Two main situations are considered when constructing the co-adsorption model. Firstly, in the case of H 2 O preferential adsorption, the O 2 adsorption model is constructed; that is, the most stable adsorption configuration of H 2 O single adsorption is taken as the substrate. Secondly, in the case of O 2 preferential adsorption, the H 2 O adsorption model is constructed; that is, the most stable adsorption configuration of O 2 single adsorption is taken as the substrate.
When the most stable adsorption configuration of H 2 O single adsorption is used as the substrate, we place the O 2 molecule on the three adsorption positions of bridge (B), center (H) and top (T) on the surface of δ-Pu (100). The O 2 molecule at each adsorption site can be divided into two cases: parallel (P) to the surface of δ-Pu (100) and vertical (V) to the surface of δ-Pu (100). At the same time, the connecting line between O 2 molecule and two H atoms in H 2 O molecule in the matrix is considered to be parallel (P) or vertical (V). Based on this consideration, nine initial adsorption configurations are constructed, such as B-P-v, which represents that O 2 molecules were placed at the bridge position on the surface of δ-Pu (100), parallel to the surface of δ-Pu (100) and perpendicular to the connecting line of two H atoms. All initial adsorption configurations based on the most stable adsorption configuration of H 2 O single adsorption are shown in Figure 2. When the most stable adsorption configuration of O 2 single adsorption is taken as the substrate, we also consider placing H 2 O molecule on the bridge (B), heart (H) and top (T) adsorption sites of δ-Pu (100) surface, respectively. H 2 O molecule at each adsorption site can be divided into two cases: O atom facing down (D) and perpendicular to δ-Pu (100) surface and O atom facing up (U) and perpendicular to δ-Pu (100) surface. At the same time, the connection between two H atoms in H 2 O molecule and the connection between two O atoms in matrix is considered to be parallel (P) or perpendicular (V). Therefore, 12 initial adsorption configurations were constructed, such as B-D-p, representing that H 2 O molecule is placed at the bridge position on the surface of δ-Pu (100) and is perpendicular to the surface of δ-Pu (100), with O atoms facing downwards. The connecting line of two H atoms in H 2 O molecule is parallel to the connecting line of two O atoms in the matrix. All initial adsorption configurations based on the most stable adsorption configuration of O 2 single adsorption are shown in Figure 3.

Adsorption Configuration and Adsorption Energy
In the case of preferential adsorption of H 2 O, nine initial adsorption configurations in Figure 2 are optimized, and finally, six stable adsorption configurations are obtained, as shown in Figure 4. In these six stable adsorption configurations, all O 2 molecules dissociate into two O atoms (O 2 and O 3 ). The naming of stable adsorption configuration is based on the adsorption positions of δ-Pu (100) surface occupied by O 2 atoms and O 3 atoms, respectively, after dissociation (B stands for bridge position, H stands for heart position and T stands for top position), the relative position between the connecting line of O2 and O3 atoms and δ-Pu (100) surface (S stands for tilt, P for parallel and V for vertical), the total number of bonds between all H atoms and neighboring Pu atoms on δ-Pu (100) surface and the total number of bonds between all O atoms and the δ-Pu (100) surface. HB-S-H2O8, for example, indicates that the O2 atom occupies the center position of the δ-Pu (100) surface, the O3 atom occupies the bridge position of the δ-Pu (100) surface, and the connecting line between the O2 atom and O3 atom inclines to the δ-Pu (100) surface; the total number of bonds between the H atom and neighboring Pu atoms is two and the total number of bonds between the O atom and neighboring Pu atoms is eight. In the case of preferential adsorption of O 2 , 12 initial adsorption configurations in Figure 3 were optimized, and finally, 6 stable adsorption configurations were obtained, as shown in Figure 5. In these six stable adsorption configurations, H 2 O molecules do not dissociate, but the bond length and bond angle have changed in different degrees. The naming of stable adsorption configuration is based on the adsorption position of the δ-Pu (100) surface occupied by H 2 O molecule (B stands for bridge position, H stands for heart position and T stands for top position), the relative position of the H 2 O molecule plane and δ-Pu (100) surface (S stands for tilt, P for parallel and V for vertical), the total number of bonds between all H atoms and neighboring Pu atoms on the δ-Pu (100) surface and the total number of bonds between all O atoms and the δ-Pu (100) surface. For example, T-P-H2O2 means that the H 2 O molecule occupies the center of the δ-Pu (100) surface, and the plane of H 2 O molecules is parallel to δ-Pu (100) surface. The total number of bonds between H atoms and neighboring Pu atoms is two, and the total number of bonds between O atoms and neighboring Pu atoms is five.  Table 1, the co-adsorption model obtained under the condition of preferential adsorption of H 2 O is analyzed. From the point of view of adsorption energy, the adsorption energy of six stable co-adsorption configurations is all less than that of the most stable adsorption configuration of O 2 single adsorption (−7.281 eV). This shows that the adsorption of O 2 after preferential adsorption of H 2 O will release more heat than the adsorption of O 2 alone on the pure δ-Pu (100) surface, and the adsorption will be more stable. The preferential adsorption of the H 2 O molecule will promote the adsorption of O 2 to a great extent. At the same time, the adsorption energies of the six stable adsorption configurations are not much different, and the heat released by adsorption is more than 8 eV. The BH-S-H4O10 configuration with the smallest adsorption energy is only 1.596 eV lower than the HB-S-H2O7 configuration with the largest adsorption energy. It can be considered that the co-adsorption of O 2 and H 2 O can coexist in the case of preferential adsorption of H 2 O. The adsorption configuration BH-S-H4O10 gives off heat up to 9.731 eV, in which the adsorption distance of O atoms and H atoms is the smallest among the six configurations, and the total number of bonds between O atoms and H atoms and Pu atoms near the surface is also the largest. Based on these phenomena, we can conclude that BH-S-H4O10 is the most stable adsorption configuration based on the most stable adsorption configuration of H 2 O single adsorption. After optimization, O 2 molecules dissociate, and the dissociated O2 and O3 atoms tend to occupy the bridge position and heart position of the δ-Pu (100) surface. Among the six stable adsorption configurations, except the HH-P-H1O9 configuration, H 2 O molecules preferentially adsorbed in the other five configurations also undergo dissociation. In HH-P-H1O9 configuration, the bond length and bond angle of H 2 O molecule preferentially adsorbed also increased to a small extent, and its plane is no longer parallel to the δ-Pu (100) surface, but there is a slight inclination, which indicates that H 2 O molecules are activated to a greater extent. It is worth noting that the O atom dissociated from the O 2 molecule and occupying the bridge site on the surface of δ-Pu (100) will generally combine with an H atom dissociated from an H 2 O molecule to form a hydroxyl group (OH) to be adsorbed on the bridge site, while the O atom occupying the center of δ-Pu (100) will form at least five Pu-O bonds with neighboring Pu atoms. These phenomena are the key factors to improve adsorption stability and cause adsorption exotherm. It can be seen from the data in Table 1 that the average bond length of Pu-O bonds with six stable adsorption configurations ranges from 2.277 Å to 2.481 Å, which is slightly larger than that of Pu-O bonds in plutonium oxide crystals (PuO: 1.830 Å, PuO 2 : 1.810 Å) [33,34]. The average bond length of Pu-H bonds ranges from 2.821 Å to 2.996 Å, which is also slightly larger than that of Pu-H bonds in plutonium hydride crystals (PuH 2 : 2.340 Å, PuH 3 : 2.388 Å) [35,36]. This shows that when H 2 O is preferentially adsorbed, O atoms and H atoms in O 2 and H 2 O will have strong bonding with Pu atoms on the surface of δ-Pu (100), thus greatly improving the adsorption stability.
Similarly, combined with the data in Figures 3 and 5 and Table 1, the co-adsorption model obtained when O 2 is preferentially adsorbed is analyzed. From the point of view of adsorption energy, the adsorption energy of the six stable co-adsorption configurations is far less than that of the most stable adsorption configuration of H 2 O single adsorption (−0.305 eV). This shows that the adsorption of H 2 O after preferential adsorption of O 2 will also release more heat than the adsorption of H 2 O on pure δ-Pu (100) surface, and the adsorption will be more stable. The preferential adsorption of O 2 molecules will greatly promote the adsorption of After optimization, compared with single adsorption, the bond length of two bonds of the H 2 O molecule is no longer the same, and the bond angle has changed to a greater extent, and its symmetry has been destroyed. In the six stable adsorption configurations, the bond lengths of two bonds of H 2 O molecules have increased or decreased in different degrees, but the range of increase or decrease is no more than 0.01 Å. In comparison, the bond angles vary from −4.775 • to 4.092 • . This shows that the preferential adsorption of two O atoms increases the activation degree of H 2 O molecules. Among the six stable adsorption configurations, H 2 O molecules in three configurations are adsorbed on the bridge position of the δ-Pu (100) surface; two are located at the top position and one is located at the heart position, which indicates that the co-adsorption of O 2 and H 2 O can coexist with multiple adsorption configurations and preferentially adsorb on the bridge position. At the same time, according to the adsorption energy, H 2 O molecules tend to obliquely adsorb on δ-Pu (100) surface. The adsorption of H 2 O molecules also affects the adsorption symmetry of O atoms on the substrate to a small extent, and the two O atoms preferentially adsorbed are still in the original bridge position, but the bond lengths of the four Pu-O bonds formed by them and the adjacent Pu atoms are no longer completely the same, and the variation range is no more than 0.2 Å. It can also be seen from Table 1 that the average bond length of Pu-O bonds in six stable adsorption configurations ranges from 2.067 Å to 2.325 Å, which is closer to the bond length of Pu-O bonds in plutonium oxide crystals than that in the co-adsorption model when H 2 O is preferentially adsorbed, and the average bond length of Pu-H bonds ranges from 2.728 Å to 2.947 Å, which is also closer to the bond length of Pu-H bonds in plutonium hydride. These phenomena also indicate that the strong bonding between O atoms on the substrate and H atoms in H 2 O and between O atoms and δ-Pu (100) surface is the key factor to improve the adsorption stability.
To sum up, for the co-adsorption of O 2 and H 2 O on the surface of δ-Pu (100), the preferentially adsorbed molecules will greatly promote the adsorption of the post-adsorbed molecules, thus greatly increasing the heat released by adsorption and improving the adsorption stability. The interaction between H atoms in H 2 O and O atoms dissociated from O 2 and the interaction between all H atoms and O atoms and Pu atoms adjacent to the δ-Pu (100) surface are also the key factors to improve adsorption stability. It is worth noting that in the case of preferential adsorption of O 2 , the adsorption energy of three optimized stable adsorption configurations is lower than that of the most stable adsorption configuration of O 2 because the interaction between H atoms in H 2 O and O atoms on the substrate weakens the adsorption stability to a certain extent.

Bader Charge Distribution Analysis
The adsorption of atoms and molecules on the surface of δ-Pu (100) is bound to be accompanied by the mutual transfer of charges with Pu atoms, and the analysis of charge transfer is very helpful for understanding the nature of adsorption [15,37]. Bader charge calculation [38][39][40] is a commonly used charge analysis method, and its calculation formula is as follows.
In Formula (2), Q net represents the net charge of atoms, Q bader is the calculated Bader charge and Q valence is the number of pseudoelectrons of each element determined by the pseudopotential method. The net charge numbers of the six stable adsorption configurations obtained under H 2 O preferential adsorption are shown in Table 2, and the net charge numbers of the six stable adsorption configurations obtained under O 2 preferential adsorption are shown in Table 3. The negative value of net charge means that the system has lost electrons and is positively charged, and the corresponding valence is positive. If the value of the net charge is regular, it means that the system has obtained electrons which are negatively charged, and the corresponding valence is negative.  Combining the data in Table 2 with Figures 4 and 6, it can be seen that when coadsorption is carried out under the condition of preferential adsorption of H 2 O, on the whole, the atoms or molecules co-adsorbed on the surface of δ-Pu (100) receive electrons, the Pu atoms in the four layers of δ-Pu (100) lose electrons and the charge is transferred from the surface of δ-Pu (100) to the adsorbed atoms or molecules. Among the six stable adsorption configurations, when the two O atoms produced by O 2 dissociation are located at the bridge position and the heart position, the charge transfer amount is large, ranging from 2.640 e to 2.769 e. When the two O atoms produced by O 2 dissociation are located in the heart, the charge transfer amount is small, which is 2.613 e. When two O atoms produced by O 2 dissociation are located at the bridge position, the charge transfer amount is the smallest, which is 2.467 e. After the completion of co-adsorption, among the six adsorption configurations, only the H 2 O molecules preferentially adsorbed in the HH-P-H1O9 configuration do not dissociate, and the number of charges obtained by H 2 O molecules is also the smallest, which is 0.036 e. Only two H atoms of H 2 O molecules preferentially adsorbed in BH-S-H2O2 configuration are dissociated from O1 atoms, but the total charge of H1, H2 and O1 atoms is the largest, which is 0.188 e. In the other four adsorption configurations, one H atom of H 2 O molecule preferentially adsorbed is separated from the O1 atom and combined with one O atom dissociated from O 2 , while the other H atom is not separated from the O1 atom. The total charge of H1, H2 and O1 atoms is between 0.036 e and 0.188 e. This shows that the greater the dissociation degree of H 2 O adsorbed preferentially, the greater the number of charges obtained and the greater the degree of interaction with other atoms. Among the six stable adsorption configurations, compared with the configuration before adsorption, the outermost Pu atoms on the surface of δ-Pu (100) generally lose charge, and the charge amount changes the most, ranging from −2.634 e to −2.460 e. Pu atoms in the subsurface layer also generally lose charge, and the change of charge is smaller than that in the outermost layer, ranging from −0.269 e to 0.001 e. The general charge of Pu atoms in the third layer is much smaller than that in the two layers on the surface, ranging from 0.001 e to 0.044 e. The charge of Pu atoms in the bottom layer is also common, and the change of charge is almost the same as that of Pu atoms in the third layer, ranging from 0.012 e to 0.050 e. It can be seen that the change of charge on the surface of δ-Pu (100) decreases layer by layer, and the charge transfer between co-adsorbed atoms and molecules mainly occurs in two layers of the surface. Similarly, when the data in Table 3 are analyzed in combination with Figures 5 and 7, it can be found that, similar to H 2 O preferential adsorption, when co-adsorption is carried out under the condition of preferential adsorption of O 2 , the atoms or molecules co-adsorbed on the surface of δ-Pu (100) receive electrons, and the Pu atoms in the four layers of δ-Pu (100) lose electrons and the charge is transferred from the surface of δ-Pu (100) to the adsorbed atoms or molecules. However, the charge transfer amounts of the six stable adsorption configurations are generally smaller than those of the adsorption configurations with preferential adsorption of H 2 O. The total charge transfer numbers of the six stable adsorption configurations are all between 2.2 e and 2.3 e, and the total charge transfer numbers of H 2 O molecules at the bridge position are generally higher than those at the heart position and the top position. After co-adsorption, H 2 O molecules generally receive an electric charge, but compared with before adsorption, the electric charge has little change, ranging from 0.018 e to 0.064 e. The two O atoms preferentially adsorbed are also universally obtained electrons. Compared with those before adsorption, the charge of the O1 atom ranges from 1.050 e to 1.098 e, and that of the O2 atom ranges from 1.120 e to 1.137 e. It can be seen that the charge of Pu atoms on the surface of δ-Pu (100) mainly transfers to two O atoms preferentially adsorbed, and the amount of transfer to H 2 O molecule adsorbed afterward is very small. By analyzing the surface delamination of δ-Pu (100), it is found that the charge of the outermost Pu atom ranges from −2.281 e to −2.136 e, that of the subsurface Pu atom ranges from -0.059 e to 0.123 e, that of the Pu atom in the third layer ranges from −0.128 e to 0.023 e and that of the bottom Pu atom ranges from −0.065 e to 0.049 e. It can be seen that the charge change of the topmost Pu atoms is much larger than that of the following three layers, which indicates that the charge transfer mainly occurs between the topmost Pu atoms and the co-adsorbed atoms and molecules, while the other three layers have less charge transfer.

Differential Charge Density Analysis
The differential charge density diagram can more intuitively show the charge gain and loss of each region in the adsorption configuration and plays an important role in analyzing the charge transfer and bonding between adsorbed molecular atoms and Pu atoms on the surface of δ-Pu (100) [41,42]. The formula for calculating the differential charge density is as follows.
In the above formula, ∆ρ represents differential charge density, ρ t represents charge density of stable adsorption configuration, ρ a represents charge density of all the H atoms and O atoms after adsorption and ρ s represents charge density of δ-Pu (100) surface after adsorption. Figure 10a,b shows differential charge density diagrams of the most stable adsorption configuration optimized for H 2 O preferential adsorption and the most stable adsorption configuration optimized for O 2 preferential adsorption, respectively. Comparing and analyzing Figure 10a,b, it can be concluded that among the two most stable adsorption configurations obtained by preferential adsorption of H 2 O (BH-S-H4O10) or O 2 (B-S-H2O4), the charge transfer degree between the δ-Pu (100) surface and adsorbed atoms or molecules is greater when H 2 O is preferentially adsorbed than when O 2 is preferentially adsorbed. It is possible that O3 atoms in the BH-S-H4O10 configuration and Pu8 atoms in the subsurface layer also have a large degree of charge transfer, while the charge transfer in the B-S-H2O4 configuration mainly occurs between adsorbed atoms and molecules and Pu atoms in the outermost layer. It may be due to the fact that the O3 atom in BH-S-H4O10 configuration and the Pu8 atom in the subsurface layer also have a large degree of charge transfer, while the charge transfer in the B-S-H2O4 configuration mainly occurs between adsorbed atoms and molecules and Pu atoms in the outermost layer. Generally speaking, in the two most stable adsorption configurations, the decreased degree of charge density around all adsorbed O atoms is far less than the increased degree, which indicates that there is a high concentration of charge distribution around O atoms. Similarly, the charge density around all Pu atoms nearest to the O atom changes obviously. The charge density on one side near the O atom generally decreases and on the other side generally increases. From O to Pu along the Pu-O bond, the charge density first decreases and then increases, which means that the Pu-O bond has ionic behavior. In the BH-S-H4O10 configuration, the charge density around two H atoms decreases, which indicates that the charge of H atoms obviously transfers to O atoms and the O-H bond also has ionic bond behavior. In the B-S-H2O4 configuration, the charge density around two H atoms is almost unchanged. These phenomena indicate that in the process of co-adsorption, charge transfer mainly occurs between Pu atoms and O atoms in the two layers of the surface, and there is also a weak charge transfer between H atoms and O atoms, while there is almost no charge transfer between H atoms and Pu atoms. These conclusions are consistent with the results of the Bader charge analysis.

Electronic Density of States Analysis
By analyzing the total density of states (TDOS) and partial density of states (PDOS) of the system, it is possible to more specifically understand the electronic structure of the adsorption system and the nature of the bonding between the adsorbed molecules or atoms and the adsorbed surface atoms [43]. It can be seen from t1 and p1 in Figure 11 that the electronic structure on the surface of pure δ-Pu (100) is strongly localized, and the electronic states are mainly localized in three energy regions: −47 eV~−44 eV, −21 eV~−17 eV and −5 eV~0.5 eV, with a large number of electronic states in the high energy region. The electronic states in the energy range of −47 eV~−44 eV are mainly contributed by Pu7s orbitals, those in the energy range of −21 eV~−17eV are mainly contributed by Pu6p orbitals and those in the energy range of −5 eV~0.5 eV are mainly contributed by Pu5f and Pu6d orbitals. In the most stable co-adsorption model obtained by preferential adsorption of H 2 O, the broadening and peak value of the low-energy region of TDOS decreased, while the broadening and peak value of the middle-energy region and high-energy region increased. Comparing figure t2 with figure p2, it can be concluded that the change of states density in the low-energy region is due to the decrease of peak and broadening of Pu7s orbitals, the change of states density in the middle-energy region is due to the occupation of O2s orbitals and the increase of Pu6p orbitals and the change of state density in the high-energy region is due to the occupation of O2p orbitals, the increase of Pu6p orbitals and the increase of peak and broadening of Pu5f orbitals. Comparative analysis of figure t2 and figure t3 shows that in the most stable co-adsorption model obtained by preferential adsorption of O 2 , the peak value of low energy region of TDOS increases and the broadening decreases, which is mainly due to the increase of peak value and the decrease of broadening of Pu7s orbitals. The broadening of the middle energy region increases and the peak value decreases, which is due to the occupation of O2s orbitals and the decrease of Pu6p orbitals broadening and the increase of peak value. In the highenergy region, the broadening increases and the peak value decreases, which is due to the occupation of O2p orbitals, the decrease of peak value and the increase of broadening of Pu5f and Pu6d orbitals. Generally speaking, no matter the preferential adsorption of H 2 O or O 2 , after co-adsorption, the electronic structure of the system retains the local characteristics of the pure surface before adsorption, but the broadening and peak value of each element orbitals have some changes. From these phenomena, we can find that the H1s orbitals contribute little to the total density of states, and the interaction between the δ-Pu (100) surface and adsorbed atoms mainly occurs between Pu atoms and O atoms. In order to compare the interaction intensity between adjacent atoms in the two most stable adsorption configurations after adsorption more intuitively, we calculated COHP (Hamiltonian population of crystal orbit) and ICOHP [44,45] of the interaction between adjacent atoms by using the LOBSTER program [46,47]. The value of -COHP is positive for bonding and negative for anti-bonding. ICOHP is the integral value of COHP from negative infinity to Fermi level, which can represent the interaction intensity between atoms. The more negative ICOHP value indicates the stronger bonding between atoms, and the more positive ICOHP value indicates the stronger anti-bonding between atoms.
According to the analysis of Figure 12a combined with Figure 4 and the calculated ICOHP value, in the BH-S-H4O10 configuration, there are bonding interactions between H atoms and O atoms and between Pu atoms and O atoms below the Fermi level. Among them, the interaction between H atom and O atom is the strongest; the ICOHP value of H1-O1 is −3.74661 and the ICOHP value of H2-O2 is −3.95609. The interaction between the Pu atom and O atom at the bridge site is also strong; the ICOHP value of Pu16-O1 is −2.09331 and the ICOHP value of Pu15-O2 is −1.84934. The interaction between the Pu atom and O atom at bridge position is the weakest; the ICOHP value of Pu15-O3 is −0.01555. Therefore, when H 2 O is preferentially adsorbed, the phenomenon that O atoms combine with H atoms to form hydroxyl groups will make adsorption more stable, and O atoms at the bridge position are more likely to interact with neighboring Pu atoms than O atoms at the heart position. It can be seen from Figure 13a that the interaction between H atoms and O atoms is due to the overlapping hybridization of H1s orbitals and O2p and O2s orbitals, and the essence of the interaction between Pu atoms and O atoms lies in the overlapping hybridization between Pu6p and O2s orbitals and Pu6d and O2p orbitals.  Similarly, by analyzing Figure 12b with Figure 5 Figure 13b that the electronic structure of H1s orbitals is more localized than that of BH-S-H4O10 configuration, and there are obvious hybridization peaks between H1s orbitals and O2p and O2s orbitals at −6 eV. The strong interaction of the H-O bond is due to the overlapping hybridization of H1s orbitals with O2p and O2s orbitals. Consistent with the BH-S-H4O10 configuration, the essence of the interaction between the Pu atom and O atom is also the overlapping hybridization of O2s and Pu6p orbitals and O2p and Pu6d orbitals.

Surface Work Function Analysis
By analyzing the data in Table 4 and Figure 14, it can be seen that among the six stable adsorption configurations optimized for preferential adsorption of H 2 O, except for the configuration BB-S-H4O5, the surface work function increases, and the other five configurations decrease to a small extent, with the decreasing range being between 0.022 eV and 0.059 eV. It can be seen that the co-adsorption during H 2 O preferential adsorption has little effect on the work function of δ-Pu (100) surface; that is, it has little effect on the difficulty of electrons escaping from the surface, but the high probability will make electrons escape from the surface more easily and make the surface relatively stable. Among the six stable adsorption configurations optimized under the condition of preferential adsorption of O 2 , except for B-V-H1O6 configuration and B-V-H0O5 configuration, the surface work functions of the other four configurations all increased more, ranging from 0.577 eV to 2.764 eV, and the degree of increase is heart position > bridge position > top position. This shows that the co-adsorption when O 2 is preferentially adsorbed tends to decrease the surface stability of δ-Pu (100) and increase the difficulty of electrons escaping from the surface. Based on these phenomena, we can conclude that different types of preferential adsorption molecules have different influences on the co-adsorption process, which proves that it is reasonable for us to consider two different preferential adsorption methods. Figure 15 more intuitively shows the most stable adsorption configuration in two cases and the change of electrostatic potential on the pure δ-Pu (100) surface.  E vacuum : the distance between H atom and O atom, E Fermi : Fermi level, φ: surface work function (φ=E vacuum -E Fermi ), ∆φ: the difference of surface work function between adsorption configuration and pure δ-Pu (100) surface.

Conclusions
In this paper, the co-adsorption behavior of O 2 and H 2 O on the δ-Pu (100) surface is studied by the first-principle method. The results are in good agreement with the experimental facts. Compared with single adsorption, the co-adsorbed two molecules promote each other, and the adsorption stability and strength are greatly increased.
Firstly, by comparing the adsorption energy of each stable adsorption configuration, the two most stable adsorption configurations, BH-S-H4O10 and B-S-H2O4, are obtained when H 2 O is preferentially adsorbed and O 2 is preferentially adsorbed. At the same time, we find that the co-adsorption in both cases coexisted with multiple adsorption configurations. When the H 2 O preferential adsorption is used as the substrate for coadsorption, two O atoms dissociated from O 2 molecules interacted and bonded with Pu atoms adjacent to the surface and H atoms dissociated from H 2 O molecules, which greatly improved the adsorption stability. When co-adsorption is carried out on the basis of O 2 preferential adsorption, H 2 O molecules will preferentially adsorb at the bridge site in an inclined state. The difference is that the adsorbed H 2 O molecules do not have much influence on the adsorption configurations of the two O atoms preferentially adsorbed.
Secondly, the results of charge analysis show that whether H 2 O or O 2 is preferentially adsorbed, the charge transfer mainly occurs between Pu atoms on the surface and adsorbed atoms and molecules. Pu atoms on the surface generally lose electrons, O atoms generally gain electrons and H atoms generally lose electrons.
Thirdly, through the analysis of electronic structure, we find that both the Pu-O bond and H-O bond in the co-adsorption configuration have ionic bond behavior, and the H-O interaction is stronger than the Pu-O interaction. The essence of the Pu-O interaction is the overlapping hybridization between O2s and O2p orbitals and Pu6p and Pu6d orbitals. Coadsorption of the two molecules does not change the localization of the electronic structure on the surface of δ-Pu (100). In contrast, the surface work function of the optimized coadsorption configuration is smaller when H 2 O is preferentially adsorbed, and electrons escape from the surface more easily. After co-adsorption, the surface is more stable.