Structural evolution and stability of plutonium oxide clusters

ABSTRACT Plutonium oxide clusters have attracted great interest as potential complex for the separation or storage of radioactive plutonium elements. However, the structural stability, chemical bonding mechanism and maximum oxygen adsorption capacity for plutonium oxygen clusters are not well understood due to the difference between the radial distribution function and orbital energy of the plutonium atom. Here, we systematically study the structural evolution and electronic properties of plutonium oxygen clusters with cluster sizes n from 2 to 15 by using the CALYPSO cluster structural prediction method in combination with density functional theory (DFT) calculations. The low-lying isomers searched by the CALYPSO method are re-optimised at the theoretical level of B3LYP/ECP60MWB(Pu)/aug-cc-pVTZ(O). Relative stability results indicate that the PuO8 cluster with CS symmetry is the most stable cluster due to the large HOMO–LUMO gap (of 4.84 eV). The high stability of PuO8 cluster is predominantly attributed to the strong interactions between Pu-5f orbitals and O-2p orbitals. The Pu atom can chemically adsorb up to eight O atoms, and the corresponding adsorption energy is −3.84 eV. The present findings shed light on the complex chemical bonding and structural evolution mechanisms of plutonium oxide clusters, which may facilitate the rational design and the synthesis of other actinide-oxygen clusters. Plutonium chemically adsorbs eight oxygen atoms, and its high stability is attributed to the interactions between Pu-5f and O-2p orbitals. GRAPHICAL ABSTRACT


Introduction
Over the past few decades, transition metal oxide clusters have been extensively studied due to their unique [1][2][3][4].Compared with transition metal oxides, the study of actinide (An) oxide clusters presents certain challenges.On the one hand, actinides are radioactive and toxic, making it difficult to experimentally explore actinide clusters.On the other hand, actinide is a typical heavy element, and its complex electron correlation and relativistic effect cannot be ignored in theoretical calculations, which makes it difficult to theoretically confirm the true ground-state structures of actinide oxide clusters.Meanwhile, actinide oxide clusters have attracted extensive interests as potential complexing agents for the separation or storage of radioactive elements used in military or industrial applications [5][6][7][8].
Actinides are similar to the early transition metals in their low electronegativity of 1.1-1.5, indicating that actinides are likely to form stable oxide clusters, nitride clusters and fluoride clusters [9][10][11][12][13].As well known, the An-5f orbitals are more contracted than the 7s and 6d orbitals, but less contracted than the 4f orbitals of lanthanides [14,15].In addition, the abundant valence orbitals of actinides can form covalent bonds with other metal elements or ligands and thus play an important role in the formation of stable clusters.The oxidation state is another important factor related to the stability of actinide clusters [16,17].Previous studies [18,19] have shown that oxygen atoms are usually symmetrically distributed around actinide cations with coordination numbers of 6-12 or higher when the actinide cation has a valence of IV or lower.Actinide cations with +V and +VI valence states are usually bonded with two 'yl' O atoms (O atom on the actinyl unit of structure formed by actinide and oxygen atoms) to form linear dioxo actinyl cations, rather than the typical bending configuration like transition metals [20][21][22].In a word, the 6d and 5f orbitals of actinide atom contribute to bonding with the oxygen atoms, which in turn leads to the formation of stable actinide oxide clusters.
Plutonium, one of the core elements of nuclear energy, is located between the early and later actinides [23].Its 5f electron is on the transition line between delocalisation and localisation, so Pu is considered a mysterious and complex element.Due to the large amount of valence electrons and orbital radial construction, plutonium compounds exhibit various complex electronic structures and oxidation states [24][25][26][27].As the actinide atomic number and valence electrons increase, plutonium is in the transition boundary from the valence state up to down, which is called the 'plutonium turn [28]'.Plutonium has abundant valence states, usually represented as +III, +IV, +V and +VI, and its highest valence state in the aqueous solution is +VII [29][30][31].Its high valence states are generally found in metal complexes with highly electronegative ligands such as oxygen or fluorine.Due to the ubiquity of plutonium oxide in the nuclear industry, particular attention has been paid to the development of plutonium oxide research [32].A series of theoretical studies [33][34][35][36] reported that the ground state of the PuO molecule is X 5 − under relativistic effective atomic real potential approximation for Pu and all-electron basis function 6-311G * for O, with its average nuclear spacing of 0.183 nm.Based on the MP2 method, it is found that the ground state of PuO 2 (X 5 g + ) presents a linear configuration of O-Pu-O (D ∞h ), and the equilibrium nuclear distance is 0.180 nm.In the study of the structure and spectrum of PuO 3 molecule, it is found that its ground state ( 7 B 1 ) is Y shaped with C 2v symmetry, and PuO 3 may also have a metastable state of D 3h symmetry.However, there are some different results in the theoretical study of PuO 3 and PuO 4 .In 2001, Straka et al. [37] firstly reported the T-shaped structure of PuO 3 ( 1 A 1g ) and the planar PuO 4 with D 4h symmetry using the DFT method.Subsequently, Andrei Zaitsevskii et al. [38][39][40] by applying twocomponent relativistic DFT calculations predicted the T-shaped configuration of PuO 3 (triplet) and studied the stability of PuO 4 isomers.The geometric parameters of PuO 3 are consistent with those of the 1 A 1g state reported by Straka et al [37].As for the H 0 298 and G 0 298 of PuO 4 , the thermodynamic stability of planar PuO 4 with D 4h symmetry is inferior to that of plutonyl superoxide PuO 2 (O 2 ) [39].Therefore, they proposed that the structural stability order of PuO 4 is C 2v plutonyl superoxide (PuO 2 + )(η 2 -O 2 − ), then D 2h planar tetroxide PuO 4 and finally C 2v peroxide derivative Pu 4 + (η 2 -O 2 2− ) 2 [40].At the same time, a number of studies [41][42][43] theoretically indicated the isomers of PuO 4 by using quantum chemical approaches, such as quasi-relativistic DFT, MP2, CCSD(T) and CASPT2, and found that ground state of PuO 4 is a quintuple state (PuO 2 ) + (O 2 ) − complex with C 2v symmetry, while the previously proposed planar D 4h -Pu(VIII)O 4 is a metastable state.In 2017, theoretical studies about PuO 3 conducted by both Attila Kovacs [44] and Katharina Boguslawski et al. [45] clarified that the ground electronic state of T-shaped PuO 3 is 3 B 2 .Recently, Kervazo et al. [46] discussed the electronic ground state at the scalar relativistic and spin-orbit levels for PuO 2 and PuO 3 .They predicted the enthalpy of formation of PuO 2 , PuO 3 and PuO 2 (OH) 2 , and confirmed that the ground state of PuO 2 molecule is mainly characterised by 5 g + and the experimental value of the adiabatic ionisation energy of PuO 2 .In the latest study for PuO 4 , Gibson et al [47] estimated the electron affinity of PuO 4 and gave the relative energies and structures of six PuO 4 isomers (singlet, triplet and quintuple).Among them, the triplet C 2v superoxide form (triplet lower than 0.104 eV) is the lowest energy structure, which is not consistent with the results of previous studies [41][42][43].It can be seen that there are still many paradoxes in the theoretical study results of PuO 3 and PuO 4 molecules, mainly due to the difficulty in conventional quantum chemical calculations for the complex electronic structure of plutonium oxide compounds.However, PuO n compounds are significant not only for general f -block chemistry but also for nuclear science and technology.Therefore, it is of great significance to study the stability and bonding property of plutonium oxides in a wide range of dimensions in plutonium chemistry.
In this work, we mainly focus on the plutonium oxygen clusters PuO n (n = 2-15) and discuss the following issues: (1) exploring the stable geometric configuration of medium-sized oxygen clusters doped with plutonium, and their structural evolution pattern with the increase of oxygen atoms; (2) analysing the stability of plutonium oxygen clusters and their ability to adsorb oxygen atoms and electronic properties; (3) finally, determining the most stable cluster of PuO n clusters (n = 2-15) and then analysing its stability mechanism through frontier molecular orbital characteristics and chemical bonding patterns.

Methodology
Extensive low-lying structure searches for PuO n clusters (n = 2-15) were carried out using CALYPSO code, which is based on the particle swarm optimisations (PSOs).CALYPSO package applies a series of special techniques, such as symmetry constraints, bond characteristic matrices, atomic centre symmetry functions, structural random generation and others [48][49][50][51].It provides structural prediction based only on the chemical composition of the material and has been widely used for innovative design of crystals, surfaces (including two-dimensional single/multilayer materials), interfaces, clusters, transition states and interface, as well as material design for functional orientation (such as energy gap, hardness and electron density) [52][53][54][55][56][57][58][59].CALYPSO randomly generates a large number of initial structures under symmetric constraints during the search process for PuO n clusters (n = 2-15).In each generation, the structure generated by particle swarm optimisation algorithm accounts for about 60%, and other 40% is randomly generated.After 50 generations of structural search, the total number of isomers to be tested is about 1000.Candidate structures were selected for re-optimisation according to the following four criteria: (a) Trial structures with the relative lower energy.(b) Trial structures with good symmetry.(c) Select similar structures to the published similar cluster systems.(d) Ensure structural diversity.The electronic configuration of the Pu atom is [Rn]5f 6 7s 2 , considering the electron correlation effect and strong relativistic effect of Pu.Therefore, the selected candidate structures are re-optimised at the B3LYP level with the ECP60MWB [60][61][62] relativistic effective core potential (RECP) developed by Stuttgart-Cologne groups and ECP60MWB_ANO [61,62] basis sets for Pu, and augcc-pVTZ [63] for O.These plutonium oxide clusters are computationally quite challenging, mainly due to the 5f, 6d and 7s orbitals with close energies, and relativistic effects need to be considered.To confirm the reliability of the calculation results, the bond length and vibration frequency of small plutonium oxygen clusters are listed in Table S1 in Supporting Information and compared with experimental data.The agreements with the experimental data confirm the reliability of the present theoretical level.Different spin multiplicities (singlet, triplet, quintet and septuple) and vibration frequency are considered in the optimisation process to determine the truly global minima structures.All reported energy values are corrected by zero energy.In the Multiwfn 3.5 [64] program, chemical bonds are analysed using the natural bond orbital (NBO) and the adaptive natural density partitioning (AdNDP) [65] method to better understand the bonding characteristic.The Gaussian 09 [66] program was applied to all calculations.

Geometric configuration of PuO n clusters (n = 2-15)
The ground state and metastable isomers of PuO n (n = 2-15) clusters are shown in Figure 1, as well as their symmetry and relative energy difference.Each isomer is labelled as na, nb or nc (n represents the number of O atoms, and the letters a, b and c represent energy order).Through analysing their vibration frequency, all structures are confirmed as stable energy minimums.The calculated total energy and lowest frequency of all ground and metastable isomers are listed in Table S2 in the Supporting Information.Moreover, the point group symmetry and electronic states of the ground-state structure are listed in Table 1.
As shown in Figure 1, for n = 2, the 2a ground state of PuO 2 cluster is a stable linear structure O-Pu-O (D infh ), which is consistent with the PuO 2 molecular structure previously reported by Gao et al [34].In analogy to the case of PuO 2 , the ground-state 3 B 2 -3a is consistent with the structural characteristics of the ground-state PuO 3 in recent studies [44,45], which adapts T-shaped configuration with C 2v symmetry.The ground-state 3 B 1 -4a of PuO 4 cluster with symmetry of C 2v can be seen  as plutoniumyl (V) unit (PuO 2 ) plus O 2 ligand, which is consistent with the research results of earlier studies [41][42][43].The planar structures of two metastable isomers 4b and 4c have been reported in previous researches [41][42][43]. 5A-5a with C 1 symmetry structure is also composed of plutonyl (V) unit PuO 2 plus O 3 molecule.In the PuO 6 cluster, the ground-state 5 B 2u -6a has a high symmetry of D 2h , which seems to be based on the 5b structure plus an O atom.For the PuO 7 cluster, the most stable structure 3 A-7a has low symmetry C 1 .In PuO 8 cluster, the geometry of 3 A'-8a with C S symmetry contains three O 2 units complexed with a linear dioxo plutonyl unit.
On the basis of isomer 8b, trioxide ligand O 3 replaces dioxygen unit O 2 on 8b to form 5 A-9a isomer with C 1 symmetry.The ground states of both PuO 10 and PuO 11 clusters are of C 1 symmetry and triplet.The geometry of 10a contains the configuration of 6b isomer and two dioxygen molecules O 2 , in which one oxygen atom is connected to the central plutonium atom.It is worth noting that starting from 11a, the oxygen atoms in the plutonium oxygen cluster began to move away from the central plutonium atom to varying degrees.The electronic state and symmetry of the PuO n cluster (n = 2-15) are 1 A and C 1 , respectively.Among them, the main frame of the ground-state structure of 12a and 14a is similar to 10c isomer, and other oxygen atoms are in the form of oxygen molecules.In addition, for 12a and 13a, three pairs of oxygen molecules are far away from the central plutonium atom.Likewise, four pairs of oxygen molecules are also far away from the central plutonium atom in 14a and 15a.Generally, the small-sized plutonium oxygen clusters possess higher symmetry, and with the increase of oxygen atoms, the symmetry of plutonium oxygen clusters of n ≥ 9 decreases to C 1 .In addition, spin multiplicities of the small-sized oxygen clusters doped with plutonium are mostly 3 or 5, while for larger size, the ground state is more prefer to adopt low spin multiplicity.It is worth noting that central plutonium atom is bonded with up to eight oxygen atoms in the form of separate oxygen atoms, dioxygen molecules O 2 or trioxide molecules O 3 .However, other oxygen atoms are randomly detached in the form of oxygen molecules in the ground-state geometry of the PuO n cluster when n ≥ 11.

Stability analysis
After analysing the geometry of the PuO n cluster (n = 2-15), we plot E b (the average binding energy) and 2 E (the difference of second-order energy) versus the cluster size (number of oxygen atoms) to analyse the relative stability of the PuO n cluster, as shown in Figure 2. The equations used for the calculation of E b and 2 E are as follows: where E(Pu) and E(O) represent the energy of plutonium and oxygen atoms, and E(PuO n ) represents the total energy of the PuO n cluster.E b is an effective criterion for the thermodynamic stability of clusters.It can be seen from Figure 2 The 2 E is an important parameter that reflects the relative stability between adjacent clusters.In Figure 2(b), there are obvious peaks when n is even number, except for n = 11 and 12.For n < 10, the PuO n cluster showed a tendency of odd and even oscillation, which indicates that the PuO n cluster with an even number of oxygen atoms is more stable than the corresponding neighbouring plutonium oxygen cluster when n < 10.In the 2 E curves, the obvious 2 E peak found in PuO 4 , PuO 6 , PuO 8 , PuO 11 , and PuO 14 are consistent with the peaks (including minor peaks) found in E b , indicating that their relative higher stability than the adjacent clusters.In addition, a large energy gap (E gap ) between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) indicates a high-energy cost of electron excited from HOMO to LUMO, and also indicates that the corresponding structure is chemically inert.We listed the HOMO-LUMO E gap in Table S3 in Supporting Information and found that PuO 8 clusters have a large E gap (4.84 eV) and exhibit good stability.

Adsorption capacity and charge transfer analysis
To explore the adsorption capacity of oxygen in plutonium-oxygen clusters, we evaluated the adsorption energy (E ads ) of each oxygen atom by using the following formula: where E represents energy of the corresponding single atom or cluster.The results of average oxygen adsorption energy of the PuO n cluster (n = 2-15) are shown in Table 1 (the adsorption energy corrected by ZPE of PuO n clusters are listed in Table S4 in the Supporting Information).The difference in adsorption energy corrected by ZPE and calculated by formula (3) is not significant, which proves the reliability of our datum.From Table 1, it can be found that all the adsorption energies are negative and the absolute values are 3.59-6.22eV (negative values represent the release of energy), which means the strong binding interaction between O and Pu atom.In addition, the plutonium atoms adsorb oxygen atoms by bonding with oxygen atoms, which is chemical adsorption.For even better observation, we have plotted the absolute value of adsorption energy in Figure 3(a).The significant downward trend in the curve demonstrates that the released energy decreases when a large number of O atoms are absorbed separately by Pu atoms.Notably, with the increase of O atoms, the absolute value of E ads exhibits an irregular decrease.Thus, the chemical oxygen adsorption capacity of plutonium-oxygen cluster decreases with the increase of O atom.
To better understand the electronic structure of plutonium-oxygen clusters, we employed natural population analysis (NPA) to explore the charge transfer between plutonium and oxygen atoms.The results of charge on Pu atoms in the PuO n clusters (n = 2-15) are shown in Figure 3(b) and listed in Table 1.The whole charge transfer curve is positive, and the attenuation of irregular oscillation shape occurs with the increase of n.The obvious peaks appear at n = 5, 9, 11, 14, where n = 5 is the maximum peak.It is known that the electronegativity of plutonium and oxygen atom is 1.28 and 3.44, respectively.Thus, the plutonium atom always loses electrons and is an electron donor, since the electronegativity of the oxygen atom is much greater than plutonium atom.In addition, the changes in the cluster size and geometric configuration of plutonium-oxygen clusters affect the interactions between atoms and charge transfer.The overall change trend shows that with the increase in the PuO n cluster size, oxygen atom distribution is scattered and far away from the central Pu atom, and the interactions between Pu and O atoms are getting weaker, resulting in less charge transfer.For large-sized plutonium oxygen clusters, additional oxygen atoms are far away from the central Pu atom, and the charge on the Pu atom is similar to that with analogous geometric configuration.For example, in PuO 12 and PuO 14 , the charge on plutonium is approximately the same, and they are geometrically similar.

Molecular orbitals and chemical bonding analysis
According to the previous relative stability analysis of PuO n (n = 2-15) clusters, the PuO 8 cluster exhibit better symmetry and relative higher stability.To further understand the bonding properties of plutonium-oxygen clusters, we take the PuO 8 cluster as an example to analyse its molecular orbitals (MOs) and chemical bonding patterns through NBO and AdNDP methods.
As shown in Figure 4, the PuO 8 cluster has a large HOMO-LUMO gap of 4.84 eV.The largest contribution to LUMO is atomic orbitals (AOs) of Pu, accounting for 92.35%, of which 5f (s2) orbital accounts for 87.33%.However, the largest contributor to HOMO is 2p x orbital of O atoms, while the Pu-AOs contribute only 31.59% (Pu-5f (s3) orbital account for 25.56%).HOMO-k (k = 1-4, 7-9) are also mainly contributed by O-2p AOs, and Pu AOs contribute a little.The occupied MOs contributed by O-2p y orbital include HOMO-1, HOMO-3, HOMO-7 and HOMO-9.As for HOMOs, the O-2p x orbital is the largest contributor to HOMO-8.The remaining HOMO-2 and HOMO-4 are formed primarily by the O-2p z orbital.Notably, in HOMO-5 and HOMO-6, the contributions of the Pu-AOs are 95.76%(5f (c2) orbital is 88.29%) and 59.99% (5f (0) orbital is 52.85%).In a word, it can be found that in these MOs of PuO 8 clusters, the stability of PuO 8 clusters benefits from the strong interaction between Pu-5f AOs and O-2p AOs.
As shown in Figure 5  maintaining the overall stability of the PuO 8 cluster.Hence, the aforementioned analysis suggests that there are strong chemical bonds between Pu and O atoms rather than van der Waals forces, leading to an enhanced stability of the C S -PuO 8 cluster.

Conclusions
In summary, we conduct a systematic study of the geometric evolution, stabilities and electronic properties of PuO n clusters (n = 2-15) by CALYPSO structure searches combined with DFT calculations at the theoretical level of B3LYP/ECP60MWB_ANO(Pu)/aug-cc-pVTZ(O).The reliability of the theoretical method is confirmed by the good agreement between the calculated bond lengths and vibration frequencies and their corresponding experimental values.The relative stabilities of plutonium oxide clusters indicate that large-sized clusters possess lower stability and symmetry compared to their smaller sized clusters.The PuO 8 cluster exhibits stronger stability with a large HOMO-LUMO gap of 4.84 eV, which is attributed to the strong interactions between Pu-5f and O-2p orbitals.Notably, the metallic Pu atoms can chemically adsorb up to eight O atoms, and the adsorption energy of the PuO 8 cluster is −3.84 eV.These findings offer valuable information for understanding the structural evolution of plutonium oxide clusters and stimulate the experimental design and synthesis of other actinide-based nanomaterials.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Figure 1 .
Figure 1.The geometry, point group symmetry and relative energy (eV) of optimised PuO n cluster (n = 2-15).The yellow and red spheres represent plutonium and oxygen atom, respectively.M represents the spin multiplicity.

Figure 2 .
Figure 2. (a) Average binding energy E b and (b) second-order difference 2 E of the ground state of PuO n clusters.
(a) that the E b value of the ground state of plutonium oxygen clusters decreases with the increase of O atoms, indicating that large-sized PuO n clusters are less thermodynamically stable than smaller ones, and smaller PuO n clusters are easier to form.It should be noted that E b is irregularly monotonically reduced, and there is a less obvious trend of odd and even oscillations, except for n = 12, where n is an even number with obvious tiny peaks in the E b curve.Within the study scope of PuO n clusters, the difference between the minimum E b value (n = 15) and the maximum E b value (n = 2) is 1.47 eV.

Figure 3 .
Figure 3. (a) Absolute value of adsorption energy and (b) charge on the Pu atom in the lowest-energy of PuO n cluster.
, the AdNDP analysis results indicate that the chemical bonding pattern of the PuO 8 cluster can be divided into types: eight lone pairs (LP) and 18 two centre-two electron bonds (2c-2e).The eight lone pairs with ON = 1.88-1.96|e|on each O atom are mainly 2s electrons of O atoms.The 18 localised 2c-2e bonds (ON = 1.97-2.00|e|)contain four kinds of bonds: O-O σ bond, O-O π bond, Pu-O σ bond and Pu-O π bond.Among them, three localised 2c-2e σ O-O bonds (ON = 1.99-2.00|e|)and three localised 2c-2e π O-O bonds (ON = 1.97-1.98|e|)are responsible for bonding between dioxygen units.In addition, four localised 2c-2e π Pu-O bonds (ON = 1.99|e|) and two localised 2c-2e σ Pu-O bonds (ON = 2.00|e|) are responsible for the connection between two separate oxygen atoms and central plutonium atom, which form a stable plutonyl unit.Finally, the remaining six localised 2c-2e Pu-O σ bonds (ON = 1.97-1.99|e|)describe the strong bonding between the central Pu atom and dioxygen units,

Figure 5 .
Figure 5. AdNDP analysis for PuO 8 cluster, and ON indicates the number of occupied electrons.