First-Principles Study of Nitrogen Adsorption and Dissociation on PuH2 (111) Surface.

Plutonium mononitride is one of the main fuels for Generation IV reactors and can be prepared from nitrogenation of plutonium hydride. We investigated the adsorption and dissociation of nitrogen on PuH2 (111) surface to elaborate the initial stage of nitrogenation. The adsorption energies varied greatly with respect to the adsorption sites and orientations of the adsorbed molecule. The nitrogen exhibited preferential adsorption above the ccp site, where the molecular nitrogen was nearly parallel to the PuH2 surface and pointed to the nearest Pu atom. The orbital hybridization and the electrostatic attraction between the Pu and N weakened the N-N bond in the adsorbed molecule. The mechanism of the dissociation process was investigated within transition state theory, and the analysis of the activation barrier indicated that dissociation of nitrogen is not the rate-determining step of nitrogenation. These findings can contribute to a better understanding of the nuclear fuel cycle.


Introduction
With the increasing social concern about energy consumption and environmental pollution, nuclear energy has attracted renewed attention in recent years. Therefore, it is crucial to understand the chemical and physical properties of both civilian and weapons materials at various stages of the nuclear fuel cycle. Plutonium is one of the main materials used in nuclear applications, and considerable experimental and theoretical efforts have been devoted to studying the structures and properties of elementary plutonium as well as its compounds [1][2][3][4][5]. For the safety of long-term storage of plutonium, a series of reactions may be involved, such as Pu + x /2O 2 → PuO x , Pu + x /2H 2 → PuH x , Pu + xH 2 O → PuO x + xH 2 , PuH x + 1 /2N 2 → PuN + x /2H 2 [6][7][8][9][10].
Calculations using density functional theory (DFT) [11,12] have provided a significant opportunity to advance the understanding of Pu-related material structures and reaction mechanisms [3,[13][14][15][16]. Huda and Ray presented a useful study of atomic hydrogen adsorption onto δ-Pu (100) and (111) surfaces, and found the preferential adsorption [17]. Their influential investigations of molecular hydrogen interaction with δ-Pu are of great significance, as they compared the dissociation barriers with different surfaces and found the most favorable dissociation channel [18,19]. Goldman's innovative calculation provided valuable insight into the H 2 dissociation pathways with an energy map, and also indicated that the dissociation reaction is highly active even at ambient conditions [20,21]. In a thorough study of H 2 interaction with PuO 2 , Yu and Meng compared various adsorption sites to evaluate H 2 into account, because these exposed hydrogen atoms were located above the Pu layer and exhibited a high degree of surface mobility without forming the hydride product [17,21]. The plutonium and hydrogen atoms of the bottom layer were frozen in the positions of their crystal lattice while other atoms were allowed to relax in the optimization of the slab. Following this, the adsorption and dissociation of nitrogen were investigated. To further verify the reliability and effectiveness of our calculation, the adsorption of hydrogen atom on the δ-Pu (111) surface was investigated with the same parameters. The adsorption energies of the ccp and hcp site were −2.57 and −2.61 eV, which were consistent with the previous results, −2.487 and −2.509 eV [21].

Results and Discussion
We first discuss the adsorption of molecular nitrogen onto PuH2 surfaces, then focus on the situation of atomic nitrogen, and finally provide the most favorable process for nitrogen dissociation.

Molecular Adsorption
The adsorption of molecular nitrogen onto PuH2 surfaces was investigated, and the optimized geometries with different adsorption sites and orientations are shown in Figure 2. The four different adsorption sites were (i) directly above a surface plutonium atom (top site); (ii) on the middle of two nearest-neighbor surface plutonium atoms (bridge site); (iii) at the hollow site on top of a Pu atom on the second layer (hcp site); and (iv) at the hollow site on top of a Pu atom on the third layer (ccp site). For each of these sites, we considered three different orientations of N2 molecule for adsorption: (i) To further verify the reliability and effectiveness of our calculation, the adsorption of hydrogen atom on the δ-Pu (111) surface was investigated with the same parameters. The adsorption energies of the ccp and hcp site were −2.57 and −2.61 eV, which were consistent with the previous results, −2.487 and −2.509 eV [21].

Results and Discussion
We first discuss the adsorption of molecular nitrogen onto PuH 2 surfaces, then focus on the situation of atomic nitrogen, and finally provide the most favorable process for nitrogen dissociation.

Molecular Adsorption
The adsorption of molecular nitrogen onto PuH 2 surfaces was investigated, and the optimized geometries with different adsorption sites and orientations are shown in Figure 2. The four different adsorption sites were (i) directly above a surface plutonium atom (top site); (ii) on the middle of two nearest-neighbor surface plutonium atoms (bridge site); (iii) at the hollow site on top of a Pu atom on the second layer (hcp site); and (iv) at the hollow site on top of a Pu atom on the third layer (ccp site). For each of these sites, we considered three different orientations of N 2 molecule for adsorption: (i) parallel to the surface and pointing to the nearest Pu atom (Ori1); (ii) parallel to the surface and vertical to Ori1 (Ori2); and (iii) vertical to the surface (Ori3). These adsorption sites and orientations of N 2 molecule were the same as the calculations with δ-plutonium (111) surface, and the Molecules 2020, 25, 1891 4 of 13 plutonium and hydrogen atoms were frozen in their optimized slab positions [21,47,48]. Following the geometry optimizations with spin polarization, the adsorption energies were then calculated from the following equation.
where E(PuH 2 − slab + N 2 ), E(N 2 ), and E(PuH 2 − slab) are the total energies of the PuH 2 slab with adsorbed N 2 , N 2 molecule in gas phase, and the PuH 2 slab, respectively. The probability of adsorption can thus be suggested by the magnitude of the absolute value of the adsorption energy. The adsorption energies and the optimized adsorption parameters for different adsorption sites and orientations are provided in Table 1. The Brillouin zones of the slabs were sampled by 2 × 2 × 1 k-point meshes, and increasing the k-point meshes to 3 × 3 × 1 changed the total energy and adsorption energy by only 0.001 eV/atom and 0.01 eV. The distances r N shown in the table are the N-N distances in the adsorbed N 2 molecule, while the distances r d are the vertical distance from the PuH 2 surfaces to the closest N atoms.
Molecules 2020, 25, 1891 4 of 13 parallel to the surface and pointing to the nearest Pu atom (Ori1); (ii) parallel to the surface and vertical to Ori1 (Ori2); and (iii) vertical to the surface (Ori3). These adsorption sites and orientations of N2 molecule were the same as the calculations with δ-plutonium (111) surface, and the plutonium and hydrogen atoms were frozen in their optimized slab positions [21,47,48]. Following the geometry optimizations with spin polarization, the adsorption energies were then calculated from the following equation.
where PuH -slab + N , N , and PuH -slab are the total energies of the PuH2 slab with adsorbed N2, N2 molecule in gas phase, and the PuH2 slab, respectively. The probability of adsorption can thus be suggested by the magnitude of the absolute value of the adsorption energy. The adsorption energies and the optimized adsorption parameters for different adsorption sites and orientations are provided in Table 1. The Brillouin zones of the slabs were sampled by 2 × 2 × 1 k-point meshes, and increasing the k-point meshes to 3 × 3 × 1 changed the total energy and adsorption energy by only 0.001 eV/atom and 0.01 eV. The distances rN shown in the table are the N-N distances in the adsorbed N2 molecule, while the distances rd are the vertical distance from the PuH2 surfaces to the closest N atoms.   There was no obvious change in the adsorption of the top site compared with the predesigned structures. The molecular nitrogen exhibited less favorable adsorption at this site than the other three sites. The adsorption parameters of the two parallel orientations were almost identical. The adsorption energy of Ori2 orientation was only 0.01 eV lower than that of Ori1 orientation, while the distance r d was 0.02 Å closer. The bond lengths r N were both slightly stretched from the theoretically optimized results 1.10 Å. In the case of vertical orientation, the N 2 molecule showed shorter vertical distance to the PuH 2 surface, and adsorption energy also increased accordingly. Similar results have been reported in previous studies of oxygen adsorption on Pu (111) surface, and the reasonable explanation for this is that the adsorbate interacts with only one plutonium atom [47].
Significant differences were found in the adsorption of ccp site. The Ori1 orientation revealed the lowest adsorption energy, and was the most stable configuration. In this orientation, N 2 was very close to the PuH 2 surface, and the bond length was strongly stretched. Additionally, the orientation of the nitrogen molecule was also tilted. One nitrogen atom moved towards the surface, and almost completely occupied the ccp site. The other nitrogen atom was slightly further from the surface, and the nitrogen molecule deviated from the original adsorption position. Finally, the angle of the nitrogen molecule to the surface was about 19 • . It was inferred from these results that the ccp site had a low adsorption energy with the nitrogen atom. The Ori2 orientation also exhibited strong chemisorption, with the distance r d of 1.48 Å and bond length r N of 1.25 Å. Unlike Ori1 orientation, Ori2 remained almost parallel to the surface. There were similarities between the ccp site and top site expressed by adsorption energies of vertical orientation, but the former provided longer N-N bond lengths. This adsorption energy seemed inconsistent with the above result that nitrogen atoms were strongly adsorbed at ccp site. However, the nitrogen atom further from the surface was less affected, and revealed the opposite attraction to closer nitrogen atom, resulting in weak adsorption. According to these data, it could conceivably be hypothesized that no vertical adsorption would be strong chemisorption.
The adsorption parameters and the configurations of molecular nitrogen in the hcp site with different orientations presented similarly to those of the ccp site. The Ori1 orientation revealed the lowest adsorption energy and the shortest vertical distance, while the Ori3 orientation offered the opposite adsorption capacity and bond length. The results reported in Table 1 also suggest that the adsorption capacity of hcp site was between that of the ccp site and the top site.
For case of the bridge site, Ori2 was the preferred orientation. Although the center of the molecular nitrogen was placed at the bridge site, there were noticeable variations in the chemical environments Molecules 2020, 25, 1891 6 of 13 of the two nitrogen atoms. One nitrogen atom was close to the ccp site, while the other was near the hcp site. Drastic changes took place in the adsorption position and orientation of the nitrogen molecule due to the difference of adsorption capacity between the two sites, resulting in the adsorption of the ccp site with Ori1 orientation. Thus, the X and Y directions of the nitrogen molecule with Ori2 orientation were fixed, and the adsorption parameters are shown in Table 1. The Ori1 orientation was also no longer parallel to the surface, and the two nitrogen atoms coordinated with different Pu atoms. The adsorption energy was −0.65 eV, and N-N bond was extended to 1.17 Å.
To further evaluate the dispersion corrections, we performed calculations using the DFT-D3 method [49], based on the optimized configurations. The adsorption energies contributed by the inclusion of the corrections are denoted as E D3 , as shown in Table 1. The adsorption energies decreased by 0.18-0.21 eV due to the D3 dispersion corrections, and the order of adsorption energies remained unchanged, suggesting little dependence between the adsorption sites and orientations. These results were similar to Kaltsoyannis's work, in which the adsorption of water onto PuO 2 was investigated [50].
In all these cases, the adsorption was molecular in nature, and there were similarities between the attitudes expressed by the adsorption configurations in this study and those described by Ray in the investigation of H 2 interaction with the Pu [19]. The adsorption energies varied greatly with respect to the various adsorption sites and the orientations of nitrogen molecules, and suggest a moderate adsorption capacity compared with the adsorption of H 2 and O 2 onto Pu surface [19,47]. We also observed that for almost all the cases, the adsorption energy and the bond length were shown to vary in response to each other, while noticeable discrepancy was found in the vertical distance r d . This inconsistency may be explained by the chemical environments of the different nitrogen atoms. In general, the adsorption of nitrogen onto the PuH 2 surface was exothermic, and the most stable geometry was at the ccp site, where the molecular nitrogen was nearly parallel to the surface and pointed to the nearest Pu atom. The suboptimal adsorption site was hcp with a similar orientation. Figure 3 plots the partial density of states (PDOS) of the PuH 2 (111) surfaces with and without nitrogen adsorption. For the sake of brevity, only the most favorable nitrogen-adsorbed case (ccp Ori1) is shown. The smearing width was set to 0.2 eV and the Fermi levels were set at zero. It was clear that the main peak of the PuH 2 (111) surface at the Fermi level was dominated by the Pu−5f orbitals, while the main peak of N 2 at the Fermi level was a combination of N-2s and N-2p. Variations appeared in the Pu-6d orbitals near the Fermi level upon nitrogen adsorption, and the Pu-5f orbitals remained nearly undisturbed. The PDOS of N 2 revealed that the valence states of N (2s and 2p orbitals) shifted to the lower levels. Moreover, the peak above the Fermi level disappeared. These results suggest that hybridizations took place between the Pu-6d and N-2p orbitals, and that the antibonding orbitals in N 2 accepted electron density transferred from Pu-6d orbitals. Similar results were also described by Hirshfeld [51] charge analysis, which provided evidence that N 2 molecules gain electrons form PuH 2 slab, revealing that the ionic aspect of Pu-N bonding plays a significant role in the adsorption product.

Dissociative Adsorption
To further illustrate the adsorption capacity and predict the dissociation process of the nitrogen molecule on the PuH2 (111) surface, the adsorption of atomic nitrogen was investigated. The four specific adsorption adsorption sites were top, bridge, ccp, and ccp site, as presented above. After the geometry optimizations, the adsorption energies were then evaluated from = PuH -slab + nN − PuH -slab − n × N where PuH -slab + nN , PuH -slab , and N are calculated with spin polarization, and n represents the number of nitrogen atoms. The chemisorption energies and the equilibrium geometries of the N atom to the PuH2 surface are given in Table 2, and Figure 4, respectively.

Dissociative Adsorption
To further illustrate the adsorption capacity and predict the dissociation process of the nitrogen molecule on the PuH 2 (111) surface, the adsorption of atomic nitrogen was investigated. The four specific adsorption adsorption sites were top, bridge, ccp, and ccp site, as presented above. After the geometry optimizations, the adsorption energies were then evaluated from where E(PuH 2 − slab + nN), E(PuH 2 − slab), and E(N) are calculated with spin polarization, and n represents the number of nitrogen atoms. The chemisorption energies and the equilibrium geometries of the N atom to the PuH 2 surface are given in Table 2, and Figure 4, respectively. geometry optimizations, the adsorption energies were then evaluated from = PuH -slab + nN − PuH -slab − n × N where PuH -slab + nN , PuH -slab , and N are calculated with spin polarization, and n represents the number of nitrogen atoms. The chemisorption energies and the equilibrium geometries of the N atom to the PuH2 surface are given in Table 2, and Figure 4, respectively.   The nitrogen exhibited preferential adsorption above the ccp site, closely followed by the bridge and hcp sites. For the ccp site, spin polarized calculation indicated an adsorption energy of −6.85 eV with a vertical distance of 0.45 Å. The nitrogen atom embedded itself in the surrounding plutonium atoms, yielding three Pu-N bonds, and the average bond lengths were about 2.23 Å. In the case of the two-fold coordinated bridge site, adsorption was slightly less favored than at the ccp site. The nitrogen experienced the most unfavorable adsorption at the top site, where the nitrogen atom was bonded to only one Pu atom. These results suggest that the adsorption energies strongly depend on the number of Pu-N bonds. However, this conclusion cannot be applied to the hcp site. Similar Pu-N bonds were found at the ccp and hcp sites, while their adsorption energies differed by more than 1 eV. This rather contradictory result may be interpreted in terms of the electronic structures of PuH 2 . The ionic character of Pu-H bond was investigated by Hirshfeld analysis, revealing that electrons were transferred from Pu to H atoms. When a nitrogen atom with a larger electronegativity was adsorbed directly above the hcp H atom (1.18 Å), it gained −0.43 e from the PuH 2 slab and formed strong Coulombic repulsion with the hcp H atom, resulting in less favored adsorption than at the ccp site. To further reveal the bonding characteristics in this adsorption site, we plotted the charge density difference contour map along the (110) plane, as shown in Figure 5. The ionic nature of the Pu−H bond was clearly revealed, while abnormal charge density was found in the direction of the axis of the N-H bond, suggesting strong repulsion between N and H atoms. The nitrogen exhibited preferential adsorption above the ccp site, closely followed by the bridge and hcp sites. For the ccp site, spin polarized calculation indicated an adsorption energy of −6.85 eV with a vertical distance of 0.45 Å. The nitrogen atom embedded itself in the surrounding plutonium atoms, yielding three Pu-N bonds, and the average bond lengths were about 2.23 Å. In the case of the two-fold coordinated bridge site, adsorption was slightly less favored than at the ccp site. The nitrogen experienced the most unfavorable adsorption at the top site, where the nitrogen atom was bonded to only one Pu atom. These results suggest that the adsorption energies strongly depend on the number of Pu-N bonds. However, this conclusion cannot be applied to the hcp site. Similar Pu-N bonds were found at the ccp and hcp sites, while their adsorption energies differed by more than 1 eV. This rather contradictory result may be interpreted in terms of the electronic structures of PuH2. The ionic character of Pu-H bond was investigated by Hirshfeld analysis, revealing that electrons were transferred from Pu to H atoms. When a nitrogen atom with a larger electronegativity was adsorbed directly above the hcp H atom (1.18 Å), it gained −0.43 e from the PuH2 slab and formed strong Coulombic repulsion with the hcp H atom, resulting in less favored adsorption than at the ccp site. To further reveal the bonding characteristics in this adsorption site, we plotted the charge density difference contour map along the (110) plane, as shown in Figure 5. The ionic nature of the Pu−H bond was clearly revealed, while abnormal charge density was found in the direction of the axis of the N-H bond, suggesting strong repulsion between N and H atoms. Following the calculations of the adsorption of the nitrogen molecule and a single nitrogen atom, dissociative adsorption was investigated to explore the nitrogen dissociation process. Since the ccp site had the largest adsorption capacity, one of the dissociated nitrogen atoms was assumed to occupy this position. We then focused on the question of which site was preferred by the other nitrogen atom. Based on the above discussion, the top site was excluded for its instability compared Following the calculations of the adsorption of the nitrogen molecule and a single nitrogen atom, dissociative adsorption was investigated to explore the nitrogen dissociation process. Since the ccp site had the largest adsorption capacity, one of the dissociated nitrogen atoms was assumed to occupy this position. We then focused on the question of which site was preferred by the other nitrogen atom. Based on the above discussion, the top site was excluded for its instability compared with other adsorption sites, and the final adsorption geometries were determined as follows: (i) both atoms were at ccp sites (ccp-ccp site); (ii) one atom was at a ccp site, and the other was at a bridge site (ccp-bridge site); (iii) one atom was at a ccp site and the other was at the ortho hcp (ccp-hcp1 site); (iv) one atom was at a ccp site and the other was at the para hcp (ccp-hcp2 site).
The adsorption and dissociative adsorption energies with related parameters are shown in Table 3. The dissociative adsorption energies are defined as E dis = E(PuH 2 − slab + nN) − E(PuH 2 − slab + N 2 ). The results indicated that the dissociative adsorption of ccp site molecular nitrogen was exothermic, and the ccp-ccp site was the most favorable dissociative adsorption site. In fact, the adsorption energy of the ccp-ccp site was twice that of the ccp site when a single nitrogen atom was adsorbed, indicating little interaction between the two nitrogen atoms. Nearly identical vertical distances and bond lengths of Pu-N also clearly supported and confirmed this conclusion. For the case of ccp-bridge site, the bridge site atom was not stable and fixed, similarly to the case of molecular adsorption at bridge site and Ori2 orientation. Finally, we compared the adsorption energies of the two ccp-hcp sites. The nitrogen atom exhibited slightly less preferred adsorption at the ortho hcp site. This relationship may be interpreted by the repulsion of the two negatively charged nitrogen atoms. Additional evidence arises from the fact that the distance between two nitrogen atoms in ccp-hcp1 was a little larger than that of the exact ccp-hcp. Furthermore, noticeable discrepancies were also found in the adsorption energies between dissociative adsorption and two monoatomic adsorption. All these results suggest that the ccp-ccp site was most favorable dissociative adsorption site, and the ratio of nitrogen atom to plutonium atom was 1:1. This result is consistent with the previous literatures where only one stoichiometric plutonium nitride was formed [32]. Table 3. Adsorption and dissociative adsorption energies of the possible dissociative adsorptions of nitrogen onto PuH 2 (111) surface. Adsorption parameter r d is the vertical distances from the surface and r Pu-N is the average distances of Pu-N. The subscript A denotes the ccp site atom, and B denotes the other. According to these data, we performed a transition state search with the complete linear synchronous transit/quadratic synchronous transit algorithm [52]. To avoid complicated and worthless calculations, the preferential adsorption of molecular nitrogen with the ccp site and Ori1 orientation was treated as our starting point (R) of the dissociation channel, considering its large adsorption energy and high probability. The potential energy profile is shown in Figure 6. Following the reaction coordinate, the activation barrier for the dissociation process was 1.02 eV, and the dissociated nitrogen atoms were located at the ccp-ccp site, forming the product P. The reaction path was confirmed by nudged elastic band (NEB) method, and similar N 2 dissociation results have been reported on a body-centred cubic Fe surface with a higher reaction energy barrier [53]. Our results indicate that the adsorption and dissociation of nitrogen onto PuH 2 (111) surface is energetically favorable, and the strong chemisorption weakens the N-N bond, allowing the dissociation to take place even at room temperature. Muromura and Ouchi suggest that the rate-determining step of nitrogenation of plutonium hydride is the dehydrogenation process rather than the dissociation of nitrogen [8].

Site E ads (eV) E dis (eV) r d-A (Å) r Pu-N-A (Å) r d-B (Å) r Pu-N-B (Å)
To further illustrate this issue, the dehydrogenation products (P-deH 2 ) were optimized and the calculations suggested a large energy penalty (1.6 eV) for dehydrogenation. Our theoretical calculations are consistent with the experimental results.
Molecules 2020, 25, 1891 10 of 13 Figure 6. The potential energy profile of the nitrogen dissociation. The preferential adsorption of molecular nitrogen with the ccp site and Ori1 orientation was chosen as the starting point R, and the ccp-ccp was the product P. P-deH2 represents the dehydrogenation product.

Conclusions
In the present work, we investigated the adsorption and dissociation of nitrogen onto PuH2 (111) surface. Noticeable variations in the adsorption energies were shown in the molecular adsorption, and the most favorable adsorption took place at a ccp site, where the molecular nitrogen was nearly parallel to the PuH2 surface and pointed to the nearest Pu atom. Both the orbital hybridization and the ionic electrostatic attraction played significant roles in the adsorption product, and the nitrogen-nitrogen bond was greatly weakened. Atomic nitrogen also exhibited preferential adsorption above the ccp site and the dissociative adsorption was strongly exothermic. The mechanism of the dissociation and diffusion process of nitrogen was investigated by transition state search with the complete synchronous transit/quadratic synchronous transit algorithm. The relatively low activation barrier indicated that this dissociation can take place even at ambient temperature. These results also suggest that the rate-determining step of nitrogenation is the dehydriding process rather than dissociation of nitrogen, and future experiments and calculations should devote their efforts to the dehydrogenation process. Further attention should also be paid to the acceleration of dehydrogenation, such as via temperature, pressure, and catalyst, to accelerate the nitrogenation of plutonium hydride. Our calculations represent the initial stage of formation of plutonium nitride, and further studies of the nitrogenation of plutonium hydride are currently underway.

Conflicts of Interest:
The authors declare no conflict of interest. Figure 6. The potential energy profile of the nitrogen dissociation. The preferential adsorption of molecular nitrogen with the ccp site and Ori1 orientation was chosen as the starting point R, and the ccp-ccp was the product P. P-deH 2 represents the dehydrogenation product.

Conclusions
In the present work, we investigated the adsorption and dissociation of nitrogen onto PuH 2 (111) surface. Noticeable variations in the adsorption energies were shown in the molecular adsorption, and the most favorable adsorption took place at a ccp site, where the molecular nitrogen was nearly parallel to the PuH 2 surface and pointed to the nearest Pu atom. Both the orbital hybridization and the ionic electrostatic attraction played significant roles in the adsorption product, and the nitrogen-nitrogen bond was greatly weakened. Atomic nitrogen also exhibited preferential adsorption above the ccp site and the dissociative adsorption was strongly exothermic. The mechanism of the dissociation and diffusion process of nitrogen was investigated by transition state search with the complete synchronous transit/quadratic synchronous transit algorithm. The relatively low activation barrier indicated that this dissociation can take place even at ambient temperature. These results also suggest that the rate-determining step of nitrogenation is the dehydriding process rather than dissociation of nitrogen, and future experiments and calculations should devote their efforts to the dehydrogenation process. Further attention should also be paid to the acceleration of dehydrogenation, such as via temperature, pressure, and catalyst, to accelerate the nitrogenation of plutonium hydride. Our calculations represent the initial stage of formation of plutonium nitride, and further studies of the nitrogenation of plutonium hydride are currently underway.