The Adsorption Behavior of Hydrogen on the PuO₂(111) Surface: A DFT+U Study

Abstract

Based on density functional theory, a first-principles study of the adsorption behavior of hydrogen atoms on the PuO₂(111) surface is carried out in this work. Models for three different surface morphologies of PuO₂(111) are established. It is found that the surface with the outermost oxygen atom (sub outer Pu atom) morphology has the best stability. Based on this model, the adsorption energy, bader charge, and electronic density of the states of a hydrogen atom at different adsorption sites are calculated. Finally, we analyzed the process of hydrogen dissociation into hydrogen atoms on the surface using the cNEB method. The results indicate that the top position of the outermost oxygen atom and the bridge position of the second outermost plutonium atom are relatively stable adsorption configurations, where hydrogen atoms lose electrons and release heat, forming O-H bonds with oxygen atoms. The density of states of O-p orbital electrons will undergo significant changes, reflecting the hybridization of O-p and H-s orbital electrons, forming a stable bonding effect. The dissociation of hydrogen molecules into two hydrogen atoms adsorbed on the top of oxygen atoms requires crossing an energy barrier of 1.06 eV. The decrease in total energy indicates that hydrogen tends to exist on the PuO₂(111) surface in a hydrogen atom state. The research results lay the foundation for theoretically exploring the hydrogenation corrosion mechanism of the PuO₂(111) surface, providing theoretical support for exploring the corrosion aging of plutonium oxide, predicting the material properties of plutonium oxide under extreme and special environments.

1. Introduction

Plutonium is an important material in the nuclear industry system, with strong physical and chemical activity. Numerous experimental studies have shown that when a plutonium surface is exposed to a certain atmosphere, it is highly susceptible to interaction with gas molecules in the environment, resulting in corrosion [1,2,3,4]. In the air, similar to aluminum, plutonium can quickly form oxide layers on its surface. Initially, people believed that these oxide layers were mainly composed of the outer layer of PuO₂ and the inner layer of Pu₂O₃ [5,6]. Later, with the enrichment of research methods, nonstoichiometric plutonium oxides were also confirmed to be real [7,8,9,10,11,12]. In fact, compared to oxidation, hydrogenation corrosion of plutonium is considered catastrophic. This process is highly reactive and significantly increases the oxidation rate. Severe hydrogenation corrosion will lead to material failure, which is also the reason why plutonium hydrogenation is highly concerned.

Based on experimental methods, the plutonium hydrogenation process is divided into four stages: incubation period, nucleation period (aggregation period), block hydrogenation, and end period [13,14]. The incubation period is considered the key to determining the progress of the entire process, which can be divided into six stages [5].

The first step in the hydrogenation corrosion of plutonium is the interaction between hydrogen and the outermost layer of PuO₂ on the surface of plutonium, then gradually passing through the oxide layer and finally interacting with pure metal plutonium. Fortunately, PuO₂ can effectively block the entry of H, making it the most important barrier for plutonium hydrogenation corrosion and the foundation for the existence of the incubation period. The low valent oxides inside cannot effectively organize the infiltration of hydrogen [15,16]. Zhang’s team conducted a series of studies on the differences between PuO₂ and Pu₂O₃ in their interaction with hydrogen, revealing the micro-mechanisms underlying the differences in hydrogen inhibition efficiency between the two [17,18]. In Zhang’s latest research, concerned about the issue of hydrogen molecules precipitated after water splitting on the surface of plutonium oxide [19]. Yu studied the adsorption and dissociation process of H₂ on the surface of PuO₂(110) and found that H₂ exhibits weak adsorption on the surface of PuO₂(110), but may dissociate to form H atoms under certain conditions. H atoms can form physical and chemical adsorption with the surface at different adsorption points [20,21]. Tang performs systematic ab initio molecular dynamics calculations to reveal the microscopic mechanism of Pu oxides over metallic Pu in resisting hydriding reactions [22].

The stability of various surfaces of PuO₂ is the foundation for the interaction between hydrogen and PuO₂, and there are few public reports on this topic. In view of this, this work first analyzes the stability of PuO₂(100), PuO₂(110), and PuO₂(111) surfaces, and finds that PuO₂(111) is the most stable surface, which is the most likely surface to exist. Among the three forms on the surface of PuO₂(111), the most likely one is the outer layer with O atoms and the second layer with Pu atoms. Five possible adsorption configurations of H atoms are constructed, and the adsorption mechanism of H atoms on the PuO₂(111) surface is studied from three aspects: adsorption energy, charge transfer, and density of states. The climbing nudged-elastic-band (cNEB) method is used to analyze the dissociation process of H₂ molecules on the surface.

2. Methods and Computational Details

The calculations in this article are carried out using the VASP (vienna ab initio simulation package) program based on density functional theory [23]. The interaction between electrons and ions is described using the projection augmented wave (PAW) method, and the exchange correlation energy is calculated using the PBE (Perdew Burke Ernzerhof) exchange correlation functional in the generalized gradient approximation (GGA) [24,25]. The strong correlation between 5f electrons in Pu atoms makes it difficult for traditional DFT to deal with it. It is necessary to add a Hubbard correction term and use the DFT+U method for processing. Based on existing research experience, it is known that using U = 4 in the PuO₂ system is more effective [20,21,26]. For PuO₂ magnetic settings, we use the “↑↓↑↓” method to simplify, as shown in Figure 1. Sampling within the irreducible Brillouin zone is conducted using the Monkhorst Pack (MP) scheme [27]. The cutoff energy is set to 520 eV. When optimizing the structure, the conjugate gradient method [28] is used to search for the minimum energy value, and the energy convergence is interpreted as 1 × 10⁻⁵ eV, the force convergence criterion is set to 0.01 eV/Å.

The PuO₂ crystal cell is a CaF₂ structure with the group space code Fm-3m [29]. When optimizing PuO₂ single crystal cells, a 7 × 7 × 7 k-point grid is used. The obtained lattice parameters match well with the experimental values. The surfaces of PuO₂(100), PuO₂(110), and PuO₂(111) are obtained by cutting the PuO₂ crystal cells along the [100], [110], and [111] directions, respectively. To avoid mutual influence between layers, a 15 Å vacuum layer is set. For the optimization of surface model and adsorption configuration, a 5 × 5 × 1 k-point grid is used. For the 5-layer surface model, we fix the 2 lower layers of atoms, and release the top 3 layers without changing the volume and shape of the model.

Surface energy is a measure of the chemical bond damage caused by the surface of a substance during its creation process, which is of great significance for analyzing surface stability.

The surface energy of PuO₂(XXX) is defined as:

$$E_{\mathrm{surf}\left(\mathrm{Pu}{\mathrm{O}}_2\mathrm{XXX}\right)}=\frac{1}{2A}(E_{\mathrm{slab}}-N{E}_{\mathrm{bulk}})$$

(1)

Among them, $E_{\mathrm{slab}}$ represents the total energy of the surface model, $E_{\mathrm{bulk}}$ represents the energy of a single crystal cell, and N represents the number of single crystal cell units in the surface model.

3. Results and Discussion

3.1. Surface Energy

Structural optimization was carried out on the models corresponding to the surfaces of PuO₂(100), PuO₂(110), and PuO₂(111), and energy data was substituted into the calculation formula to obtain surface energies of 0.435 V/Ų, 0.430 V/Ų, and 0.423 V/Ų (the maximum of the three forms) for each surface. Surface energy measures the disruption of intermolecular chemical bonds when creating a material surface. The smaller the surface energy, the better the stability of the surface. It can be judged that PuO₂(111) has the best surface stability. The following focus will be on the study of PuO₂(111) surface.

The surface of PuO₂(111) has three forms: the outermost layer is a Pu atom, the outermost layer is an O atom (with a secondary layer being an O atom), and the outermost layer is an O atom (with a secondary layer being a Pu atom), as shown in Figure 2. The surface energies of the three forms are 0.308 eV/Ų, 0.423 V/Ų, and 0.271e V/Ų, respectively. Among the three forms, the surface with the outermost O atom (the second outermost Pu atom) has the best stability and is most likely to appear. Therefore, the following calculations on the PuO₂(111) surface will be carried out for this form.

3.2. Hydrogen Atom Adsorption Configuration and Adsorption Energy

Adsorption energy refers to the energy released or absorbed by molecules or atoms adsorbed on the surface, which is an important reflection of the strength of the interaction between molecules or atoms and the target surface. When the adsorption energy is negative, it indicates that the adsorption process has released energy, and when the adsorption energy is positive, it indicates that the adsorption process has absorbed energy. The calculation formula for adsorption energy is:

$$E_{\mathrm{ads}}=E_{\mathrm{slab}+\mathrm{H}}-E_{\mathrm{slab}}-E_{\mathrm{H}}$$

(2)

Among them, $E_{\mathrm{ads}}$ is the adsorption energy, $E_{\mathrm{slab}+\mathrm{H}}$ is the total energy of the system after H atom adsorption, $E_{\mathrm{slab}}$ is the base energy before H atom adsorption, and $E_{\mathrm{H}}$ is the energy of H atom.

After analysis, we found that there are five possibilities for hydrogen atoms to adsorb on the surface of PuO₂(111), as shown in Figure 3. Among them, pos1 is the top position of the oxygen atom, pos2 is the top position of the Pu atom, pos3 is the acupoint of the O atom, pos4 is the bridge position of the Pu atom, and pos5 is the bridge position of the O atom.

Table 1. Adsorption energies for the five adsorption configurations.

Adsorption Site	pos1	pos2	pos3	pos4	pos5
Adsorption Energy (eV)	−2.486	−1.186	−0.756	−2.466	−1.186

shows the adsorption energies corresponding to the five adsorption configurations. It can be observed that the adsorption energies of each model are negative, indicating that the adsorption process releases energy outward. The adsorption energies of Position1 and Position4 are greater than the other three adsorption configurations, and the two are relatively close. Further analysis revealed that the adsorbed configurations of Position1 and Position4 are shown in Figure 4, where both H atoms form O-H bonds with O atoms (experimental value 0.99 Å), leading to chemical adsorption. Other configurations are physical adsorption.

3.3. Bader Charge

During the adsorption process, there is charge transfer between atoms, which can further describe the interaction between atoms. Here, the Bader charges of H atoms before and after adsorption on the surface of PuO₂(111) were calculated. The net charge of an atom can be calculated using Bader charge, with the formula:

$$q_{\mathrm{atom}}=q_{\mathrm{Bader}}-q_{\mathrm{valence}}$$

Among them, $q_{\mathrm{atom}}$, $q_{\mathrm{Bader}}$, $q_{\mathrm{valence}}$ represents the net atomic charge, Bader charge, and the number of valence electrons outside the nucleus, respectively. When the calculated net charge is negative, it indicates that the atom has lost electrons, and the numerical value is the amount of charge transfer. When the calculated net charge is positive, it indicates that the atom has obtained electrons, and the numerical value is the amount of charge transfer.

Table 2. Bader charge distribution number of H-PuO₂ system. q_H are the Bader charge number of the hydrogen atom. q_1st q_2nd q_3rd q_4th q_5th represent the total Bader charge number of first to fifth layers on the PuO₂(111).

Surface Model	qH	q1st	q2nd	q3rd	q4th	q5th
Complete Surface Model	-	0.0330	−0.0027	−0.0145	0.0156	−0.0344
Position1	−0.5942	0.4354	−0.0304	0.1836	−0.0118	0.0174
Position2	0.2984	−0.4228	−0.0658	0.2077	−0.0088	−0.0087
Position3	0.3128	−0.1909	−0.2985	0.1836	−0.0093	0.0022
Position4	−0.5991	0.4680	−0.0576	0.1738	−0.0122	0.0272
Position5	0.2970	−0.3803	−0.1012	0.1990	−0.0092	−0.0053

shows the net charges of each layer atom and H atom in each model. It can be observed that in the two configurations Pos1 and Pos4, the H atom loses charge and the charge reaches more than 0.5e, indicating a large amount of charge transfer. This indicates that in these two configurations, the H atom has a strong interaction with the surface atom, forming a chemical bond. The charge transfer amounts of pos2, pos3, and pos5 configurations are relatively small, indicating that the interaction between H atoms and surface atoms is relatively weak in these three configurations. Generally speaking, the larger the charge transfer amount, the more heat is released during the adsorption process, and the stronger the adsorption effect. Comparing the adsorption energy of each postion, it can be found that the charge transfer amounts of pos1 and pos2 configurations with higher adsorption energy are also higher, further confirming the previous conclusion.

3.4. Density of States

From Figure 5, it can be observed that the density of states of Pu-f orbital electrons in the three systems is relatively close, indicating that Pu-f orbital electrons do not participate in bonding before and after adsorption. The density of electronic states in the O-p orbital varies. The peak intensity, position, and shape of the density of states before and after the adsorption of the H atom on the top position (position1) of the O atom have undergone significant changes. The peak intensity decreases in the range of −6 eV to −3 eV, and new peaks appear locally near −8 eV. Based on the density of states map of the H atom in Figure 5, it can be observed that the corresponding orbitals of the O atom and the H atom have undergone some changes, the O atom forms a stable bond with the H atom. Before and after the top position of the Pu atom adsorbs the H atom, there is no significant change in the density of states, indicating that there is no strong interaction between the H atom and the O atom in this adsorption configuration, which is consistent with the previous analysis.

3.5. Dissociation of H₂ Molecules on the Surface of PuO₂

The adsorption sites of H₂ molecules on the surface of PuO₂ are similar to those of H atoms, but due to the presence of chemical bonds in H molecules, there are two possibilities when approaching the surface: vertical and parallel. Therefore, there may be six situations for the adsorption of H₂ molecules on the surface of PuO₂, namely approaching the Pu atomic top, the O atomic top, and the O atomic acupoints in vertical and parallel states (Figure 6).

After optimization, the final stable adsorption configurations at each point were obtained. The adsorption energy of each point and the H-H bond length after adsorption are shown in

Table 3. Adsorption energies for the six adsorption configurations.

Surface Model	H2	P-O-O	V-O-O	P-Pu	V-Pu	P-S-O	V-S-O
Adsorption Energy (eV)	N/A	−0.133	−0.234	−0.302	−0.171	−0.205	−0.095
H-H bond length (Å)	0.741	0.750	0.752	0.755	0.751	0.752	0.750

. From the final stable adsorption configuration, it can be seen that the H₂ molecule has not dissociated at various adsorption points on the PuO₂ surface, and the interaction mode is van der Waals force, manifested as physical adsorption with relatively low adsorption energy. Compared with the H-H bond length in separately placed H₂ molecules, the adsorption configuration at each point has a certain elongation, indicating that H₂ molecules have a certain dissociation trend on the surface of PuO₂. With certain external capabilities provided, the H-H bond can break and dissociate into H atoms, forming chemical adsorption with the surface. Compared with the H-H bond length in separately placed H₂ molecules, the adsorption configuration at each point has a certain elongation, indicating that H₂ molecules have a certain dissociation trend on the surface of PuO₂. With certain external capabilities provided, the H-H bond can break and dissociate into H atoms, forming chemical adsorption with the surface.

Based on the above analysis, we take P-Pu, which has the most stable adsorption, as an example and use the transition state search method to explore the dissociation process of H₂ molecules. The cNEB method requires determining the initial state (IS) before dissociation and the final state (FS) after dissociation, with other intermediate states being transition states (TSs). Before decomposition, hydrogen gas is adsorbed in a molecular state at the most likely position, which is the stable adsorption site. The final state after decomposition is the two hydrogen atoms at their most likely positions, which are the stable adsorption sites. We select the stable adsorption state of the optimized H₂ molecule at P-Pu as the initial state for dissociation, and select the stable adsorption state of two H atoms at adjacent oxygen atom top positions as the final state.

The minimum energy path (MEP) of the dissociation process is shown in Figure 7. It can be observed that from the initial state to the transition state, the distance between the two H atoms that make up the H₂ molecule gradually increases, exhibiting hydrogen bond breakage in the transition state, and the energy barrier that needs to be crossed is 1.06 eV at TS3. Subsequently, the distance between hydrogen atoms further increases, and the molecule completely dissociates, gradually approaching the corresponding surface O atom, and finally stably adsorbs on the top position of the O atom, forming O-H bonds. From the IS to the FS, the total energy of the entire system decreased by 0.31 eV. Although external energy is required to cross the energy class during the process, the entire process releases energy outward, indicating that molecules tend to exist in an H atomic state on the PuO₂(111) surface, which affects the subsequent internal diffusion process. From a macro perspective, hydrogen gas adsorbs on the surface of plutonium oxide, undergoes hydrogenation reactions, and reaches the initial stage of hydrogen corrosion.

4. Conclusions

The adsorption behavior of hydrogen atoms on the PuO₂(111) surface was studied using the DFT+U method. We have identified stable adsorption sites for hydrogen atoms and analyzed the electronic states before and after adsorption. We also obtained the energy barriers that hydrogen decomposition needs to cross and the energy changes before and after.

(1)

Among the common surfaces of PuO₂, the surface of PuO₂(111) is the most stable. Among its three possible forms, the outer layer with O atoms and the second layer with Pu atoms have the best morphological stability and the highest possibility of existence.

(2)

There are five possible adsorption sites for H atoms on the surface of PuO₂(111), among which the top position of the outermost O atom and the bridge position of the second outer Pu atom are relatively stable adsorption configurations, forming O-H bonds with O atoms, indicating chemical adsorption. The other three adsorption configurations are physical adsorption.

(3)

Through the analysis of charge transfer, it was found that both H atoms in the two configurations undergoing chemical adsorption lost electrons, and the amount of charge transfer was relatively large. During the chemical adsorption process, there was a greater heat release, indicating a higher adsorption energy.

(4)

The density of states results indicate that during chemical adsorption, there is a significant change in the density of states of the O-p and H-s orbital electrons, leading to hybridization and stable bonding. When physical adsorption occurs, the change in the density of states is not significant.

(5)

The dissociation process of hydrogen molecules on the surface was analyzed using the transition state search method. Research has found that hydrogen molecules cross the energy barrier of 1.06 eV from the most stable adsorption state and dissociate into two hydrogen atoms adsorbed on the top of the O atom. The overall energy of the system is somewhat reduced, and hydrogen tends to exist in an atomic form on the surface of PuO₂(111).