Bonding Properties and Oxidation States of Plutonium in Pu2On (n = 1

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Bonding Properties and Oxidation States in PuO (n=1-8) Molecules Studied by Using Screened Hybrid Density Functional Theory Cui Zhang, Shuxian Hu, Haitao Liu, Yu Yang, and Ping Zhang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b12324 • Publication Date (Web): 11 Apr 2018 Downloaded from http://pubs.acs.org on April 11, 2018

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The Journal of Physical Chemistry

Bonding Properties and Oxidation States of Plutonium in Pu2On (n=1-8) Molecules Studied by Using Screened Hybrid Density Functional Theory Cui Zhang,1 Shu-Xian Hu,2 Hai-Tao Liu,1 Yu Yang,1, ∗ and Ping Zhang1, ∗ 1

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing 100088, People’s Republic of China 2

Beijing Computational Science Research Center, Beijing, 100193, People’s Republic of China

Abstract The structural and electronic properties of Pu2On (n=1-8) molecules have been systematically studied within the screened hybrid density functional theory. On the basis of the calculations, plutonium and oxygen generally prefers forming Pu-O and Pu-O-Pu bonds over to Pu-Pu or O-O bonds. In the ground-state geometries, we find that the highest oxidation state for plutonium atoms is Pu(VI). Through fragmentation studies, we find that the Pu2O and Pu2O2 molecules are energetically stable among all studied compounds. When fixing the Fermi level to be energy zero, the Pu-5f states always distribute at the two sides of the Fermi level. With increasing the number of oxygen atoms and the oxidation state of plutonium, the Pu-6d states shift down from above to below the Fermi level.

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I.

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INTRODUCTION

The chemistry of the actinide elements has been concerned by chemists for a long time, not only because of their essential role in nuclear energy and environmental issues, but also due to their rich oxidation states1,2 . Along the actinide series, plutonium (Pu) is extremely important for its irreplaceable role in nuclear fission reactors and national defense affairs. A thorough understanding of the chemistry of Pu is needed to predict and manipulate environmental migration, degradation of stockpile and disposition forms, physiological effects, and so on3 . A Pu atom can be seen as eight valence electrons [5f 6 7s2 ] distributing around a soft Rn core4 . The the 5f orbital of Pu is energetically in proximity to its 6d and 7s orbitals. Therefore electrons easily jump between theses orbitals, resulting in very distinctive and diverse chemical properties of Pu-based materials4 . At another side, the 5f orbital of Pu is quite contracted in radial distribution and penetrates inside the 6sp semicore shell5 . This nature increases the complexity of Pu chemistry. For example, the plutonium metal exists in six allotropic forms below its remarkably low melting point of 640◦ , the most among all metal substances6–8 . When bonding with different elements under different chemical environments, the Pu 5f electrons show different and complex localization/itinerancy characters after orbital mixing. The complex electronic characters also lead to intricate bonding properties of Pu compounds, like valence-varying oxides, hydrides, as well as plutonium monoxide monohydride (PuOH)9–12 . Recently, several theoretical studies explored the possible oxidation states for Pu atom in differently designed molecules13 . Li’s group systematically investigated the possibility of Pu(VIII) valence state in PuO4 and PuOn F8−2n systems5,14–16 . They find that the ground states of PuO4 and PuOn F8−2n molecules did not contain octavalent Pu(VIII), while the species of Pu element in VIII oxidation state are unstable or meta-stable only. These researches enriches our knowledge on chemical bonding theories and actinide chemistry. But differently for most Pu compounds, there exist nonzero spins around each Pu atom and magnetic interactions between neighboring Pu atoms17,18 . Therefore studying the bonding characters within molecules containing more Pu atoms might be closer to revealing the chemical behavior of Pu-5f electronic states in Pu compounds. Zaitsevskii et al. took a try by studying the possible stabilities of Pu2 O6 and Pu2 O8 molecules against isolated PuO3 2


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and PuO4 molecules19,20 . Nevertheless, geometries considered in their work for Pu2 O6 and Pu2 O8 molecules were all with high symmetries. In our previous work on uranium oxide clusters, we found that for clusters with high uranium valence states, the geometries were all with low symmetries21 . These backgrounds motivate our present work on Pu2 On (n = 1 ∼ 8) molecules. Through wide structure searching, we determine the ground-state geometries for different Pu2 On molecules. Fragmentation energies and electronic properties are calculated and discussed to show the stabilities and bonding characters of Pu2 On molecules. Note that different magnetic orders as well as spin-orbit coupling effects are all considered.

II.

COMPUTATIONAL METHOD

The results presented in this work are obtained using the projector augmented wave (PAW) method22 as implemented in the Vienna ab initio simulation package (VASP)23 . The HSE06 range-separated hybrid functional24 is applied for our calculations. Simultaneously, the GGA calculations with the Perdew-Burke-Ernzerhof (PBE) functional25,26 are also performed to examine the distinct effect of the hybrid functional. A plane wave basis set with a cutoff energy of 400 eV is adopted, and the plutonium 6s2 6p6 5f 6 7s2 and oxygen 2s2 2p4 electrons are treated as fully relaxed valence electrons. A Fermi broadening27 of 0.05 eV is chosen to smear the occupation of the bands around the Fermi energy (Ef ) to improve the convergence of the self consistent calculation for such complex systems, and the results at T = 0 K are extrapolated at the end. Since relativistic effects are crucial for heavy elements like Pu, spin-orbit coupling is included in all self consistent calculations based on a second-order approximation28 when added to the scalar relativistic DFT Hamiltonian29,30 . The supercell containing the Pu oxide molecules is chosen to be without symmetry, and the cell size along each direction is larger than 15 ˚ A to make the interaction between neighboring images negligible. A quasi-Newton algorithm is used to relax the Pu and oxygen ions for all molecules, with the force convergence criteria of 0.01 eV/˚ A in PBE calculations and 0.03 eV/˚ A in HSE calculations. Recently, the Heyd-Scuseria-Enzerhof (HSE)31–33 based hybrid density functional has shown excellent performance of describing the electronic structures of actinide oxide materials34–37 . The calculated electronic band gaps of different actinide oxides are in the

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best agreement with the latest experimental results. The HSE functional defined by31–33 1 3 HSE Exc = ExHF,SR (µ) + ExPBE,SR (µ) + ExPBE,LR (µ) + EcPBE 4 4

(1)

separates the Hartree-Fock (HF) exchange into short-range(SR) and long-range (LR) contributions, and the LR portion is replaced by the corresponding DFT exchange part. The µ parameter is an adjustable screening parameters for the partition of the SR and LR con˚−1 is adopted within the HSE06 functional24 . The tributions, and the specific value of 0.2 A HSE functional has been extensively applied to calculate ground-state properties and adsorption energetics of molecular systems, and has been proven to be better than the LDA and GGA functionals in describing finite molecular systems21,38,39 . Therefore, we adopt the HSE method in our present study on Pu oxide molecules.

III.

RESULTS AND DISCUSSIONS

Both the ground state and low-energy states of Pu2 On (n=1-5) are presented in Fig. 1(a) to 1(e). As expected, the ground state of Pu2 O exhibits a triangle structure with two Pu-O bond lengths of 2.082(3) ˚ A, and a Pu-Pu distance of 3.671 ˚ A . According to previous theories40,41 , such Pu-O bond lengths indicate the formation of Pu1+ oxidation state. In this ground state, the local electron spins around each Pu atoms are 4.81 µB , while the orbital magnetic moments at each Pu sites are 3.54 µB . Both electron spins and orbital magnetic moments are antiferromagnetically ordered. Different from the U2 O molecule adopting a UU-O linear structure (with a 2.469 ˚ A U-U bond length) as a second low-energy structure21 , there is no second stable geometry for the Pu2 O molecule. This result indicates different bonding features in U2 O and Pu2 O. As a result of actinide contraction, the Pu-5f orbital has a lower energy distribution than the U-5f orbital, and contracts along the radial direction5,42 . Then direct Pu-Pu bonding is harder to form than U-U bonding. In the ground state of Pu2 O2 , two Pu atoms are connected by two bridge oxygen atoms (Ob ) forming a planar rhombic structure with an energy stabilization of 3.05 eV than the one with two isolated PuO molecules. The four Pu-O bond lengths are shorter than those in Pu2 O, around 2.068 ˚ A, but still in the range for Pu1+ oxidation state40,41 . The bond angle of Pu-O-Pu in Pu2 O2 is found to be 77.5◦ . This rhombic structure of Pu2 O2 is energetically favorable and performs as a growth unit in larger Pu2 Ox molecules. As for the 4


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electronic structure, the local electron spins around two Pu atoms are both 4.76 µB , arranged antiferromagnetically, while the orbital magnetic moments both have the value of 3.38 µB . Different from Pu2 O2 , the next stable U2 O2 isomer adopts an asymmetrical structure, where one O atom is shared by two uranium atoms but another O atom is only connected with one uranium atom21 . Similar to U2 O3 , Pu2 O3 adopts a spindle ground-state geometry, with two Pu atoms occupying two poles and three O atoms distributing uniformly at the equator, giving a three oxygen coordination for each plutonium atom. The Pu-O bond lengths of 2.103 ˚ A for top Pu and 2.091 ˚ A for bottom Pu are in the range of Pu-O single bond range40,41 , indicating the Pu(III) oxidation state for both Pu atoms. Interestingly, the O-Pu-O angle in Pu2 O3 is 77.0◦ , very close to that in Pu2 O2 . The second and third stable isomers for Pu2 O3 can be obtained by adding an oxygen atom to Pu2 O2 . The isomer with an additional O atom along one O-Pu direction has an electronic energy of 0.16 eV, lower than that with an additional O atom along the Pu-Pu direction. In U2 Ox clusters where the U2 O3 spindle structure acts as a growth unit in U2 O4 and U2 O5 molecules21 . Differently for Pu2 On molecules, the Pu2 O2 rhombic structure instead of the Pu2 O3 spindle acts as the growth unit for Pu2 O4 and Pu2 O5 , as shown in Fig. 1(d) and 1(e). The ground-state structures for Pu2 O4 and Pu2 O5 are constructed by adding two and three oxygen atoms (Ot , terminal oxygen atoms) to the Pu2 O2 unit, respectively. In the ground state structure of Pu2 O4 , two additional Ot atoms bond to one plutonium atom (Pu1) of the Pu2 O2 rhombus with the same bond length of 1.775 ˚ A, which is typical for the Pu2+ oxidation state40,41 . Consequently, the lower two sides nearer to the additional two Ot atoms are enlarged to be 2.267 ˚ A, while the other two sides diminish to 1.956 ˚ A. However, both the elongated and shortened lengths are still in the range of Pu1+ oxidation state. So the formal oxidation state of Pu1 can be assigned to +VI and that of Pu2 is +II, which is supported by the nonzero total spin population of 2. In the second stable structure of Pu2 O4 , the additional two O atoms bond with two Pu atoms. In the third stable isomer, the additional two O atoms bond with the same Pu atom with different bonding angles than the ground-state structure. In the ground state of Pu2 O5 , another O atom is added to the Pu2 atom in the groundstate structure of Pu2 O4 , forming a strong Pu-O bond with the bond length of 1.76 ˚ A, contributing a Pu2+ oxidation state. Different from Pu2 O4 , one Pu-O bond between Pu1 5



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and one Ob atom is elongated to be 2.428 ˚ A, indicating an almost broken bond with very weak ionic interaction. And this Ob atom bonds with the Pu2 atom with a bond length of 1.832 ˚ A, similar to that between an Ot atom and a Pu atom. Therefore the Pu1 and Pu2 atoms in Pu2 O5 are both in the oxidation state of Pu(V), resulting in a zero total spin population in the antiferromagnetic state. The next stable isomer of Pu2 O5 is the structure of two O-Pu-O chains connected by another Ob atom. The other isomers of Pu2 O5 are all over 2 eV higher than the ground state. As shown in Fig. 2(a), the ground-state structure of Pu2 O6 also contains a Pu2 O2 rhombus and each Pu atom is bonded with another two Ot atoms. One of the newly formed O-Pu-O bond is chain-like, while the other is triangle-like with an apex angle of 92◦ . In the next and third stable isomers of Pu2 O6 , the two newly formed O-Pu-O bonds are both chainlike and triangle-like, respectively. The other Pu2 O6 isomers are over 3 eV higher than the ground state. In the previous theoretical work by Zaitsevskii et al.19,20 , it has been pointed out that forming a close-shell O2− 2 subsystem is energetically favorable for Am2 O6 (Bk2 O6 ), but energetically unfavorable for Pu2 O6 . This is in accordance with our result. In fact, in the obtained ground states of Pu2 On (n = 1 ∼ 6) molecules, peroxo (O2− 2 ) or superperoxo (O− 2 ) groups are all unfavorable. As we will discuss in the following, it is because that the plutonium and oxygen generally prefers forming Pu-O and Pu-O-Pu bonds over to Pu-Pu or O-O bonds. Pu2 O7 is the only molecule within our studies that adopts a lower symmetry geometry as the ground-state structure. As shown in Fig. 2(b), the ground state of Pu2 O7 can be built by adding a new oxygen atom to the second stable structure of Pu2 O6 , forming an additional O-O bond. The newly formed O-O bond has a bond length of 1.305 ˚ A, which is 5,43 within the range of an O1− . Therefore the oxidation states of the two Pu atoms 2 ligand

in Pu2 O7 are both Pu(VI). And the total spin population in the antiferromagnetic state is zero. The next stable structure of Pu2 O7 is very similar to the ground state with slightly different bonding lengths within the center Pu2 O2 rhombus. Geometrically, the third and fourth stable Pu2 O7 isomers are more symmetric and each of them contains a PuO4 unit. In the series of Pu2 On (n = 1 ∼ 7), the Pu2 O7 molecule is the one that contains the most energy-close isomers to the ground state, which is probably because of their low symmetries compared with other molecules. As shown in Fig. 2(c), the ground-state geometry of Pu2 O8 is the one that contains two 6


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O-O dimers forming a planar structure with two Pu atoms and each two of the other four O atoms bond with a Pu atom along the normal direction of that plane. The next stable structure of Pu2 O8 is composed of two PuO4 molecules with a very close electronic energy to the ground state. In the previous work by Zaitsevskii et al., they also built up a symmetric molecular structure for Pu2 O8 , which we find out to be the third stable molecular structure. Interestingly, our calculations reveal that without considering the spin-orbit coupling effects, the third stable isomer will become the next stable structure. The spin-orbit coupling energy around the two Pu atoms is 0.78 eV lower in the isomer composed of two PuO4 molecules than in the third stable isomer. The bond lengths of the two O-O bonds are 1.288 and 1.289 5,43 ˚ A, belonging to the O1− . Therefore the oxidation states of the two Pu atoms 2 ligand type

in Pu2 O8 are both Pu(VI). In the third stable isomer, the two Ob atoms actually behave like two Ot atoms, mainly bonding with one Pu atom with the bond length of around 1.825 ˚ A. As a result, the two Pu atoms in the third isomer are indeed in the Pu(VIII) oxidation state. The bonding lengths in the third isomer also indicate that it can easily dissociate into two PuO4 isomers. In our previous study of Un Om clusters, we found that the formations of U-O-U and isolated U-O bonds are energetically more stable than that of pure U-U bond21 . Here we find that this regularity also applies for Pu2 Ox molecules. Nevertheless, there are three differences in the structural characters of Un Om and Pu2 Ox molecules. Firstly, no Pu-Pu bonds can be found in low energy structures of Pu2 On molecules. Secondly, the U2 O3 fragment containing three U-O-U bonds is very stable and commonly seen in larger Un Om clusters, while the Pu2 O2 fragment containing two Pu-O-Pu bonds is the most stable fragment and commonly seen in Pu2 Ox molecules. Thirdly, the isolated U-O bonds tend to distribute away from each other while the Pu-O bonds tend to pair up forming O-Pu-O bonds. As a result, the ground-state structures of Ux Oy clusters are always nonsymmetric, while the ground-state structures of Pu2 Ox molecules are always symmetric. In order to further discuss the relative stabilities of different Pu2 Ox molecules, we calculate their dissociation energies. We define the dissociation energy ∆E as the fragmentation energy along the most energetically favorable dissociation channel. The fragmentation energy along the dissociation channel A → B + C is defined as ∆f E = EB + EC − EA . In this way, a negative/positive fragmentation energy means that the fragmentation process is exothermic/endothermic. Firstly we check the accuracy of our method by calculating the dis7



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sociation energies of PuO and PuO2 molecules. The dissociation energies for PuO→Pu+O and PuO2 →Pu+PuO at 0 K are calculated to be 6.74 eV and 5.73 eV. In comparisons, the theoretical results obtained by A. Kovács et al. are 6.20 eV and 5.96 eV44 , and the experimental results obtained at 298 K are 6.82 eV and 6.21 eV44,45 . For the studied Pu2 Ox molecules, as shown in Table I, our calculations reveal that the rhombus Pu2 O2 structure has the largest dissociation energy among all considered Pu2 On molecules. This result is consistent with the fact that it is the most commonly found structural unit for larger molecules. As shown in fragmentation energy calculations, both Pu2 O7 and Pu2 O8 are energetically unstable and they can spontaneously dissociate into Pu2 O6 , releasing an energy of 0.38 and 0.70 eV, respectively. Comparing this result with our previous study21 , we find Pu2 On molecules show quite different structural properties from U2 On . Among U2 On , the U2 O5 is the most stable molecule. Instead, the Pu2 O2 is the most stable cluster among Pu2 On . Moreover, the U2 O3 spindle is the basic structure unit for larger uranium oxide molecules, while the Pu2 O2 rhombus is the basic unit for larger plutonium oxide molecules. According to the structural characters, we define three different types of oxygen atoms in Pu2 On (n = 1 ∼ 8) molecules: the first type denoted as Ot represents for terminal oxygen atoms that only bond with one Pu atom; the second type denoted as Ob represents for bridge oxygen atoms that simultaneously bond with two plutonium atoms; and the third type denoted as Od represents for oxygen atoms in O-O dimers. Such definition is used in the following electronic structure and charge transfer studies. Applying the Bader topological charge analysis developed by Henkelman et al.46,47 , which decomposes the charge density into atomic components based on topological features of the real-space charge density distribution, we systematically compute the atomic charges for every atom in the plutonium oxide molecules of interest, reported in Table II. Mostly the oxygen atoms gain electrons from plutonium atoms during formation of molecules and from the electron transfer quantities, one can easily distinguish different types of oxygen atoms. The quantity of electrons gained by Ot type are between 0.84 and 1.04, comparing to that obtained by Ob type that are between1.00 and 1.50. Attributed to the participation in covalent O-O bondings, Od type gain the least electrons (≤0.46). Except the energetically unstable molecule Pu2 O7 and Pu2 O8 , the quantity of electrons that plutonium atom loses is increasing from molecule Pu2 O to Pu2 O6 , accompanied by the decrease of electron quantity gained by oxygen. 8


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Energy levels and orbital resolved projected density of states (PDOS) are then computed to explore electronic properties of Pu2 Ox molecules. Spin-orbit couplings are included in all self-consistent calculations. The calculated PDOS for different Pu2 On molecules are shown in Fig. 3. Note that the Fermi levels are all set to 0. For the Pu2 O and Pu2 O2 molecules, there is weak orbital mixing between O-2p and Pu-5f states in the low energy range from -4.5 to -6.5 eV. Right below the Fermi level, the highest occupied states mainly compose of Pu-5f states. And above the Fermi level, the lowest unoccupied states are Pu-5f and Pu-6d mixed states. The ground-state electronic structure of Pu2 O3 is very similar to that of two former molecules. In addition, strong orbital mixing of O-2p and Pu-5f states distribute between -2.5 and -5.0 eV. From Pu2 O4 to Pu2 O6 , the Pu-6d states also mixes with O-2p and Pu-5f states, and together contribute to the highest occupied states below the Fermi level. At the same time, the lowest unoccupied states become Pu-5f states with negligible Pu-6d contributions. Lastly for Pu2 O7 and Pu2 O8 , the 2p states of the Od distribute at the low energy range around -7.5 eV, without orbital mixing with electronic states of Pu.

IV.

CONCLUSIONS

In this work, first-principles calculations with the HSE method have been performed to study the geometries and electronic structures of possible Pu2 On molecules (n=1-8). Based on an extensive search, we find that the Pu-O-Pu connection and the isolated Pu-O bond are common components in the ground-state structures, and the Pu2 O2 rhombus plays as a basic unit for larger Pu2 On molecules. Fragmentation analysis shows that the Pu2 O and Pu2 O2 molecules are the most stable molecules with the largest dissociation energy. Through electronic structure calculations and wavefunction analysis, we reveal that the highest occupied and the lowest unoccupied states mainly composed of Pu-5f states for all molecules considered in this study. The O-2p states locate in the low energy range and mix with Pu-5f and Pu-6d states.

Acknowledgments

We would like to thank Prof. Haitao Liu very much for his great helps when building the initial molecular structures and constructive discussions. This work was supported by

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the President Fund of China Academy of Engineering Physics under Grant No. 201402034, by the National Natural Science Foundation of China under Grants No. 21503019, No. U1530258, and No. 11374038, and by Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum physics under Grant No. KF201514.

∗

To whom correspondence should be addressed. E-mail:

yang [email protected] and

zhang [email protected] 1

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Prodan, I. D.; Scuseria, G. E.; Martin, R. L. Assessment of metageneralized gradient approximation and screened Coulomb hybrid density functionals on bulk actinide oxides. Phys. Rev. B 2006, 73, 045104.

35

Prodan, I. D.; Scuseria, G. E.; Martin, R. L. Covalency in the actinide dioxides: Systematic study of the electronic properties using screened hybrid density functional theory. Phys. Rev. B 2007, 76, 033101.

36

Wen, X. D.; Martin, R. L.; Roy, L. E.; Scuseria, G. E.; Rudin, S. P.; Batista, E. R.; McCleskey, T. M.; Scott, B. L.; Bauer, E.; Joyce, J. J.; Durakiewicz, T. Effect of spin-orbit coupling on the actinide dioxides AnO2 (An=Th, Pa, U, Np, Pu, and Am): A screened hybrid density functional study. J. Chem. Phys. 2012, 137, 154707.

37

Wen, X. D.; Martin, R. L.; Henderson, T. M.; Scuseria, G. E. Density Functional Theory Studies of the Electronic Structure of Solid State Actinide Oxides. Chem. Rev. 2013, 113, 1063.

12


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Nieminen, R. M. Issues in first-principles calculations for defects in semiconductors and oxides. Modelling Simul. Mater. Sci. Eng. 2009, 17, 084001.

39

Yang, Y.; Liu, H. T.; Zhang, P. Structural and electronic properties of Scn Om (n = 1 − 3, m = 1 − 2n) clusters: Theoretical study using screened hybrid density functional theory. Phys. Rev. B 2011, 84, 205430.

40

Pyykkö, P. Additive Covalent Radii for Single-, Double-, and Triple-Bonded Molecules and Tetrahedrally Bonded Crystals: A Summary. J. Phys. Chem. A 2014, 119, 2326.

41

Liu, J. B.; Chen, G. P.; Huang, W.; Clark, D. L.; Schwarzb, W. H. E.; Li, J. Bonding trends across the series of tricarbonato-actinyl anions [(AnO2 )(CO3 )3 ]4− (An=U-Cm): the plutonium turn. Dalton Transactions 2017, 46, 2542.

42

Kramida, A.; Ralchenko, Y.; Reader, J., et al. NIST ASD Team NIST Atomic Spectra Database; National Institute of Standards and Technology: Gaithersburg, MD, 2012; http://physics.nist.gov/asd.

43

Menconi, G.; Kaltsoyannis, N. Time dependent DFT study of the electronic transition energies of RuO4 and OsO4 . Chem. Phys. Lett. 2005, 415, 64.

44

Kov´ acs, A.; Pog´ any, P.; Konings, R. J. M. Theoretical Study of Bond Distances and Dissociation Energies of Actinide Oxides AnO and AnO2 . Inorganic Chemistry 2012, 51, 4841.

45

Konings, R. J. M.; Morss, L. R.; Fuger, J. Thermodynamic Properties of Actinides and Actinide Compounds. In The Chemistry of the Actinide and Transactinide Elements; Edelstein, N. M., Fuger, J., Morss, L. R., Eds.; Springer: Dordrecht, The Netherlands, 2006; Vol. 4, 2113.

46

Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: New York, 1990.

47

Tang, W.; Sanville, E.; Henkelman, G. A grid-based Bader analysis algorithm without lattice bias. J. Phys.: Condens. Matter 2009, 21, 084204.

13



Page 14 of 20

TABLE I: The most favorable fragmentation channels and dissociation energies (∆E, in units of eV) of the Pu2 On (1 ≤ n ≤ 8) molecules. All results are obtained by employing the HSE method, and spin-orbit couplings are included in all self-consistent calculations. molecule

Fragmentation channels

∆E

Pu2 O

Pu+Pu+O

+6.03

Pu2 O2

Pu2 O+O

+6.05

Pu2 O3

Pu2 O2 +O

+4.09

Pu2 O4

Pu2 O3 +O

+2.05

Pu2 O5

Pu2 O4 +O

+2.54

Pu2 O6

Pu2 O5 +O

+0.32

Pu2 O7

Pu2 O6 +O

-0.38

Pu2 O8

Pu2 O6 +O2

-0.70

14


Page 15 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TABLE II: Atomic charges for the Pu2 On (1 ≤ n ≤ 8) molecules obtained by using the Bader topological method. Spin-orbit coupling is included during the self consistent calculations of the charge densities. A positive (negative) value indicates that the atom gain (lose) electrons during formation of the molecule. Ot , Ob , and Od represent for three types of oxygen atoms: bonding with only one Pu atom, bonding with two Pu atoms, and bonding with another O atom, respectively. The integer in each parenthesis means that such number of oxygen atoms are in the same charge state. molecule

QPu (e− )

QOt (e− )

QOb (e− )

QOd (e− )

Pu2 O

-0.75, -0.75

-

+1.50

-

Pu2 O2

-1.34, -1.34

-

+1.34 (2)

-

Pu2 O3

-1.86, -1.86

-

+1.24 (3)

-

Pu2 O4

-1.82, -2.66

+1.04 (2)

+1.20 (2)

-

Pu2 O5

-2.56, -2.60

+0.99 (2), +0.96

+1.06, +1.16

-

Pu2 O6

-2.64, -3.00

+0.84 (2), +0.98 (2)

+1.00 (2)

-

Pu2 O7

-2.70, -2.84 +1.00 (2), +0.86, +0.89

+1.03

+0.23, +0.46

Pu2 O8

-2.63, -2.69 +0.91, +0.97, +1.00 (2)

-

+0.23, +0.25, +0.44, +0.46

15



Page 16 of 20

List of captions

Fig.1

(Color online). (a)-(e) The low-energy structures of Pu2 On (n = 1 ∼ 5) molecules.

Blue and red balls represent the plutonium and oxygen atoms, respectively. The bond length is in unit of ˚ A. The number in parenthesis is the relative energy (in eV) with respect to the corresponding ground state. Note that the spin multiplicity is also given in the parenthesis.

Fig.2

(Color online).

(c) Pu2 O8 molecules.

The low-energy structures of (a) Pu2 O6 , (b) Pu2 O7 , and

Blue and red balls represent the plutonium and oxygen atoms,

respectively. The bond length is in unit of ˚ A. The numbers in parenthesis are the relative energy (in eV) with respect to the corresponding ground state and the spin multiplicity.

Fig.3

(Color online). (a)-(h) The orbital-resolved projected density of states for Pu2 On

(n = 1 ∼ 8) molecules. Ot , Ob , and Od represent for three types of oxygen atoms: bonding with only one Pu atom, bonding with two Pu atoms, and bonding with another O atom, respectively. The Fermi energies are all set to be zero.

16


06

1.814

1.814 3.676

7

2.

06

77.5°

6

2.

06

06

2.

(0.00 eV, M=0)

8

(b)

2.

2.0 82 2 . 0 123.6° 8 3 3.67 1

(a)

(0.00 eV, M=0)

(3.05 eV, M=0) 2.0

2.1

3

8

2

2.07 4

02

2.09

1.

7 7 .0 °

8

47

2.

4

1. 2

3.284 13

2.122 ° 3.6 10 280 3. 2.053

9

2.

2.091

8 1.

10

80

17

2.12

04

2.

08

8

88.3 °

0 9 99 1 . 103.5° 0

2 .0 5 3

2.1

2.1

2.06

2.09 2

03

(c)

(0.00 eV, M=0)

(1.22 eV, M=2)

(1.38 eV, M=2)

(5.93 eV, M=2)

1. 77 5

1.7 76

Ot

(0.00 eV, M=4)

2.3

6

82

07

1.7

5 1.7 73

1.4

2 .1 7 2

8

37

1.

(3.57 eV, M=2)

81

(2.71 eV, M=0)

31

2.2 71 6 1 2 2 . 3.489

38.1°

4

3.387

90

3.358

(2.71 eV, M=3)

2.

11 1.4

2.28

1.

8 2.3

109.4°

29

1.

93

1.

6

(3.82 eV, M=1)

FIG. 1:

17


2.1 7 64 01 106.8°

2 2 . 2. 2 2 367

0 25

8 1.

71

2.

1 .7 6 2

1 .7 6 3

1 .7 6 3

28 2.4 2 1 . 8. 1 3 7 40

20

1

9

63

2.0

48

3.089

2.

2 34 8 2. .34 2

9

(1.59 eV, M=0)

2.

35

1.7

80

35

16 2 . 4. 0 5 8 2

2.

(2.77 eV, M=1)

2.1

2.

4

3 00 2.

2

4 20

40°

3.394

83

81

2 .0 9 5

2. 14 3

1 .4 5 7

09

3.390 95

6 96 1 . 107°

1.

103.1° 3.35 6

2.1

1.76

2

1. 47 0

76

159.3°

2 .0 9 4

8 1 .7 6 8

(0.00 eV, M=0)

2.

13

2 .111

Pu2

Pu1

1.76

104.9°

(1.94 eV, M=4)

1.

(e)

(0.75 eV, M=0)

2.3

5

109 .9°

2.26

Pu1

1.

95

1.

7

3.30 4

1.9

10 2 . 1 105.1° 9 1.814 1.814 2 . 1 3.349 9 0 09 2.1

24

67

Ot

1.

2.

09

1.8

56

56

1.9

Ob

Ob

3

Pu2

(d)

2.2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


9

Page 17 of 20

80

1

1.815


1 .7 8 8 98

1.

81

14

69 1.4

9 81

2. 1 3.44 4 3 9 2. 45 3

0 20

3.47 3

7 23 2.

1 .7 4 6

1 .7 4 6

61

2.1

1.74 5

1.744

1. 80 1

5

80

2.2

3.69 7 2.6 01 2. 43 9

1.754

7 76 1. 7

7

8

1.3

38

1.746 1 . 747

1.

76

1.7 64

1.

00

78

74

2 . 4 3.462 6 58 82 1.

2.1

63

2.2

1.7 64

63

5 2.4 57 82 107.0°

20

7 1.

1.

1. 75 5

1.755

8

(0.002 eV, M=0)

(1.31 eV, M=0)

FIG. 2:

18


1.

403

9 34 2.

3 12 2. 01 1.4

2.38

2.3

5

16 1.3

35

3.284

2.2 50 3.63 2

1

1.8

02

6 .78 38

2.2

75 1.

76

1. 75 5

1.7 44 1 .7 4 1

77

0

1.

1.

0 47 2 .3 5 2 2.

1.

(2.70 eV, M=2) 03

4

3.87 9

1. 74 5

8

2 4 7 1. 75

1.8

2 .4 3 7

08 12

(1.88 eV, M=0)

2. 20 9

1

1 .7

1.4

(0.00 eV, M=0)

2 .2 1 2

1.7 51

3.384

1.760

48

32

11

2.

1.4

2.

2.4

04

9

1.429

2.1

2.17

75

1

1.2 88

1.4

2.2

2.

32

1.44

33

3

07

3

2.385

(4.04 eV, M=3)

1.9 57 16 15 1.7 108.5° 92.5° 3.358 11 . 7 2.3 3 70 99 1.8

2.45

7

7

(0.59 eV, M=0)

(1.32 eV, M=0)

3 2.39 31 .0 ° 2 .4 3 0

90

1.

41

74

2.27

5

2.2

38 2 . 2. 0 9 1 2

35

. 2.392 4 0 1 7 . 1

1.2 89

3

1.8

1.7 55

1. 75 0

(c)

1.

29

1.

0 74

1

38.4°

3.357 1.7 70 30 99 1.8

(0.60 eV, M=0)

02

0

(3.72 eV, M=1)

2.1 55 70 3 . 2 2 . 1 3.398 14 51 2.0

2.3

2.3

1.7 58

43

20

8

13 1 2 . 2 108.6° 5

2.

2.

1.83

1.77

1.38 1

2.09

1.7 45 7 80 1.

1. 46 2

1.806

(0.19 eV, M=0)

1.4

2. 08 5 2.

2 1.48 6

9

35

31

2

2.

3

2.

7

29

2.3

39 2 .4 3

2.

15

83

(0.00 eV, M=0)

1.9

(2.32 eV, M=0)

1.8 2.1

9

12

2 3.284 . 3 3 1

28

2.3

2.3

2.3

05 1.3 2 .49 38 7 .3 1.7 46 2 93.6° 1.7 57 1.7 46 1 3.284 57 1.7 .95 1 12 2.3

1.

9

2.0

2 86

97

2.0

2.

54

(3.51 eV, M=0)

(b)

9

8

1.48 6

81

(0.14 eV, M=0)

1.83

3 2.

1.

1 .7 8 8

1.788

(0.00 eV, M=0)

2. 09 98 9 2.0 105.0° 2 . 3.284 8 09 09 8 2.

105.1°

9 81 104.6°

1.

1.

3.359 33

99

2.3

69 .7 11. 76 9

2.0

1.7 55

99 3.284

1.8 32 62 2.3 105.9°

1.7 55

1.788

2.0

(a)

2.3

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 20

(1.37 eV, M=0)

Ob-2p Pu-6d Pu-5f

6

Pu2O 3

Ob-2p Pu-6d Pu-5f

6

Pu2O2

3

Energy (eV)

5

10

Ot-2p

Pu2O4

Pu-6d Pu-5f

6

3

0

9

-5

(e)

0

Energy (eV)

5

(g)

0

Energy (eV)

5

Ot-2p Pu-6d Pu-5f

6

10

Pu2O5

Ot-2p

Pu2O7

Ob-2p Od-2p

6

Pu-6d Pu-5f

3

0

9

-5

(h)

0

Energy (eV)

5

10

Ob-2p Od-2p Pu-6d Pu-5f

6

Pu2O8

3

0 -10

-5

0

Energy (eV)

5

10

Pu2O3

3

9

-5

(f)

0

5

10

0

5

10

Energy (eV) Ot-2p Ob-2p Pu-6d Pu-5f

6

3

Pu2O6

0 -10

PDOS (arb. unit)

-5

Ob-2p Pu-6d Pu-5f

-10

0 -10

(c)

6

10

Ob-2p

3

9

0 -10

PDOS (arb. unit)

(d)

0

PDOS (arb. unit)

PDOS (arb. unit)

-5

Ob-2p

9

(b)

0 -10

9

9

PDOS (arb. unit)

(a)

PDOS (arb. unit)

9

0

PDOS (arb. unit)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


PDOS (arb. unit)

Page 19 of 20

-10

-5

0

Energy (eV)

5

10

FIG. 3:

19


-10

-5

Energy (eV)


Pu 2O 1

Pu 2O 2

Pu 2O 3 Pu 2O 4

Pu 2O 5

Pu 2O 6

Pu 2O 7 Pu 2O 8

Page 20 of 20

The structures and electronic properties of Pu2 On (n=1-8) molecules are studied within the screened hybrid density functional theory. We show that the formation of Pu-O-Pu bondings and that of isolated Pu-O bonds are energetically more stable than Pu-Pu and O-O bondings. In the ground-state geometries, we find that the highest oxidation state for plutonium atoms is Pu(VI). The Pu2 O7 and Pu2 O8 molecules are unstable and spontaneously dissociate to be Pu2 O6 .

20


Bonding Properties and Oxidation States of Plutonium in Pu2On (n = 1

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