Plutonium Oxidation States in Complex Molecular Solids

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Plutonium Oxidation States in Complex Molecular Solids Bingyun Ao, Ruizhi Qiu, and Shu-Xian Hu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01527 • Publication Date (Web): 24 Apr 2019 Downloaded from http://pubs.acs.org on April 24, 2019

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The Journal of Physical Chemistry

Plutonium Oxidation States in Complex Molecular Solids Bingyun Ao,*1,2 Ruizhi Qiu,*1 and Shu-Xian Hu*2 1Science

and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621908,

Sichuan, China 2Beijing

Computational Science Research Center, Beijing 100094, China

*Corresponding

authors

Email: [email protected] (BA); [email protected] (RQ); [email protected] (SXH).

ACS Paragon Plus Environment

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ABSTRACT: Oxidation state is a key chemical quantity that allows the understanding and prediction of the majority of chemical reactions; however, the main deficiency using the formal oxidation state comes from the materials containing multivalent metals. Among them the most complicated element Pu is an outstanding instance. Here we calculate the orbital occupation numbers under the frameworks of first-principles DFT + U methods to quantitatively determine Pu

oxidation

state

of

in

the

recently

reported

complex

molecular

solids:

[K(crypt)]Pu[C5H3(SiMe3)2]3, Pu3(DPA)5(H2O)2 and Pu3(DPA)6H. The results show that the oxidation states of Pu is extremely low Pu2+ in the former, and mixed Pu3+/Pu4+ in the latter two compounds, consistent with the experimental identifications. The steric effects and the environmentally sensitive localization → delocalization transition of Pu 5f electrons can rationally elucidate the formation of the unusual oxidation states. Such atomic-resolution quantitative determination of the unusual Pu oxidation states in the complex molecular solids offers an alternative for the further exploration of peculiar Pu solid-state materials.


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1. INTRODUCTION Searching for novel materials has been largely focused on the multivalent elements involved systems because the elements assume sensitive responses to the physical and chemical surroundings. Two representative examples are d block Mn-based and f block Ce-based materials, which have been technologically and industrially used in a broad domain, and expected to have more application potentials.1,2 Physically, the fascinating properties originate from the intricate and flexible electron structures, and the quantitative determination of valence is crucial and some electron structure related techniques have indeed opened the way.3 Notwithstanding, the openshell d or f orbitals are generally non-integrally occupied, thus the valence is not pragmatic especially for chemistry.4 In this regard, oxidation state (OS) fills the gap to some extent despite that OS is physically ill-defined and unobservable because the textbook definition (formal oxidation state, OSf) is based on the unphysical assumption that all bonds in a compound were 100% ionic.5 As a result, some fundamental problems regarding OSf remain for the multivalent elements and there is little doubt that the most complicated Pu is the most notorious object.6-12 Indeed, even the OSf of Pu in some relatively simple compounds such as PuCn (n = 1, 1.5, 2), PuBn (n = 2, 4, 6, 12) and plutonates such as Na5PuO6 cannot be rationally assigned in terms of ionic approximation.13-16 Pu exhibits many anomalous properties which are physically rooted from the competition between delocalization and localization of 5f electrons. Considerable researches, especially the direct measurements of electron structures, have demonstrated that the valence electron configurations associated with OS of Pu sensitively depend on the surroundings.3 Essentially, in most of alloys and intermetallic compounds three outer valence electrons of Pu participate into bonding, resulting in the approximate 5f5 configuration associated with trivalent-like Pu ion; an


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intuitive example is that the trivalent Ga, Al and Ce can stabilize Pu alloys due to the electronmatch principle.17 This holds for the some non-metallic elements such as H and N with weak oxidizability judged from their borderline compounds PuH3 and PuN.13 Pu2+ had not been detected in the binary compounds for a long time;18 even the instable PuH2 and PuO (exactly, stabilized by C, i.e., PuCxO1-x) were determined to be trivalent-like Pu ion with a surplus 5f conduction electron, resulting in the metallic states of PuH2 and PuO whereas PuH3 and Pu2O3 are semiconducting states.19-22 Clearly, the valence or OS can be readily changed by more electronegative elements. With the transition of Pu2O3 → PuO2 → PuO2+x,23,24 Pu 5f electrons become more delocalized with the typical feature of fewer 5f states below Fermi energy (EF), and are expected to be further delocalized in the crystallographically identified Pu-O-F ternary solid compounds such as PuO2F, PuO2F2 and PuOF4. However, the OS of Pu in the three compounds cannot be intuitively assigned to be Pu5+, Pu6+ and Pu6+, respectively. In fact, solid state PuO2F2 is determined to be formatted as Pu4+[O-]2[F-]2 instead of the widely-accepted actinyl-like [Pu6+O24-]2+F22-, suggesting the strong electronic interactions between F and O. On the other hand, even the OSf of Pu or other multivalent metals in the complexes are more elusive due to the complicated coordination effects and multi-component interactions.7 As mentioned above, OS is physically unobservable and the available experimental determination based on the chemical shift to the reference material is not strict to some extent. In this regard, considering the scientific and technologic importance of OS to the exploration of novel Pu-based materials, the rigorous quantum-mechanics method is specially required to assign the unambiguous OS and we here denote it as OSqm. In this paper we aim to quantitatively calculate the OSqm of Pu in the known complex solidstate compounds in terms of counting 5f orbital occupation numbers under the frameworks of


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first-principles DFT + U methods. The breakthrough multi-component molecular solids with unusual OS of Pu, i.e., [K(crypt)]Pu[C5H3(SiMe3)2]3 (denoted as Pu2+-1 or Pu-1; Me = methyl.),25 Pu3(DPA)5(H2O)2 (denoted as Pu3+,4+-2 or Pu-2; DPA = 2,6-pyridinedicarboxylate.) and Pu3(DPA)6H (denoted as Pu3+,4+-3 or Pu-3),26 come to our attentions. The former was the first report on the existence of Pu2+ since Pu3+ had ever been acknowledged as the lowest OS. The latter two are the Pu3+/Pu4+ mixed compounds which are rather rare despite that the multivalent nature of Pu is expected to favor the formation of mixed compounds; in fact, only the ill-established PuO2-x had been previously classified as the Pu3+/Pu4+ mixed oxides due to oxygen vacancy induced the localization of Pu 5f electrons.23,24,27-29 The OS of Pu in the three molecular solids were determined by combining experimental absorption spectra with non-periodic quantum chemistry calculations; yet, the inherent weakness in quantitatively determining the OS of solid ions by the experimental techniques and the renaissance of actinide solid-state science spurs us to conduct periodic DFT calculations. Among the periodic electron-structure calculation methods for actinide solid materials, the classic DFT + U method could be viewed as the optimal choice as a consequence of the compromise between computation accuracy and efficiency. We hope that the simple and efficient determination of OSqm of Pu in the complex molecular solids is extendable to the majority of Pu-based solids, and of great theoretical and practical significance for solid-state Pu chemistry. 2. COMPUTATIONAL APPROACH All DFT + U calculations in Dudarev formalism are performed using the Vienna Ab initio Simulation Package (VASP), Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and projector augmented wave (PAW) pseudopotential.30-33 An effective U value of 4.0 eV is used for Pu 5f electrons; this value or thereabouts has been widely used and proven by ourselves


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and other researchers to be reasonable in describing the localization degree of Pu 5f electrons in a variety of solid-state compounds.12,18,21,22,34-39 In fact, our calculation tests show that U values in the range of 3 ~ 5 eV do not influence the assignments of OSqm despite that the occupation numbers slightly increase with the increase in U. Relaxations for the large molecular crystals are constrained to volume optimization and Monkhorst-Pack Γ-point sampling, and the convergence is reached when the total energies converge within 1 × 10−5 eV and Hellmann-Feynman forces on each ion are lower than 0.02 eV/Å. A plane-wave kinetic energy cutoff of 500 eV which is higher than the default value in PAW potential is used to give accurate convergence of total energies. A series of calculation tests on PuO2 show that Pu OSqm is largely independent of U values (3 ~ 5 eV), pseudopotentials (LDA, PBE, PW91 or hybrid DFT), spin-orbit coupling (SOC) interaction, relaxation scheme, magnetic order and much more, implying the insensitivity of calculation parameters on OSqm. The conclusion holds for the calculation test on van der Waals (vdW) dispersion correction despite that the weak interaction might play a role in stabilizing Pu molecular solids.40 For the calculation of OSqm, here we expand the orbital occupation number method which was successful in the qualitative determination of OSqm of TMs to f-block elements.41,42 The core of the method is that the occupied Kohn-Sham orbitals and the atomic orbitals of interest such as Pu 5f orbitals can be separately computed; the wisdom allows us to separate the contribution from metal-ligand orbital mixing to the charge allocated to an ion. The occupation number of a 5f orbital can be obtained by projecting of all occupied orbitals onto the atomic 5f orbital. Certainly, a 7 × 7 occupation matrix by the projection scenario can be defined to obtain all occupation numbers of 5f orbitals. One occupied or unoccupied Pu 5f orbital corresponds to the occupation number being 1 or 0, respectively. By counting the occupied numbers of Pu 5f orbitals and


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comparing with its electronic configuration, the OSqm of Pu can be determined without much ambiguity. Taking PuO2 as the illustration, the occupation numbers of 5f orbitals of each Pu ion are 4, or four localized 5f electrons do not contribute to the bonding with oxygen; consequently, considering that delocalized 6d and 7s electrons tend to participate into bonding, we assign a robust Pu4+ OSqm irrespective of the flexible outer valence configurations 5f6-x6dx7s2 (0 ≤ x ≤ 1) of Pu atom. However, the occupation number of an occupied or an unoccupied Pu 5f orbital may deviate from unity 1 or 0 because of the primogenic quantum problems of open-shell 5f orbitals; in this regard, we assign a 5f orbital as occupied if the orbital has the occupation number greater than 0.8, a critical value proposed for d-block elements. 3. RESULTS AND DISCUSSION The crystal structures of Pu-1, Pu-2 and Pu-3 are shown in Figure 1.25,26 It is important to point out that we test a series of Pu and other actinide solid-state compounds to check the reliability of the approach for calculating OSqm. Specifically, [K(crypt)]An2+[C5H3(SiMe3)2]3 (An = U, Np, denoted as U-1, Np-1) molecular solids as the analogues of Pu-1,43-46 and PunO2n-2 (n = 7, 9, 10, 11, 12; the nominal compositions are determined to be (n-4)Pu4+O2•2Pu3+2O3 which are particularly rare mixed-valent Pu compounds like Pu-2 and Pu-3, are calculated. In addition, we select the precursors or products regarding the syntheses of Pu-1, Pu-2, Pu-3, i.e., Pu3+[C5H3(SiMe3)2]3 for Pu-1, [Pu3+(DPA)(H2O)4]Br and Pu4+(DPA)2(H2O)3·3H2O for Pu-2 and Pu-3.25,26 To be brief, the calculated OSqm of Pu, U and Np are labeled in the structural formulas and the theoretical method appears to be reliable in actinide solid-state compounds with unusual OS. Pu-1 is the first Pu2+ compound that has been well isolated and identified by single-crystal X-ray diffraction. Its fundamental synthetic route is the reduction of Pu3+[C5H3(SiMe3)2]3 by potassium graphite (KC8) and other auxiliary chemicals, yielding the formation of weaker Pu-C


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bonds. On the other hand, the fundamental synthetic routes for Pu-2 and Pu-3 adopt the staged and judicious oxidation of [Pu3+(DPA)(H2O)4]Br, resulting in that the Pu3+:Pu4+ ratio of 1:2 in the latter is reversed from the former with the ratio of 2:1. As previously mentioned, the experimental uncertainties in sample preparation and characterization of the extremely intractable Pu compounds complicate the interpretation of unusual OS behavior, albeit with quantum-chemistry results. Quantitative orbital occupation numbers based on periodic DFT methods are required to be calculated for verification.

K Pu2+ Pu3+

Si O N

Pu4+

C H

(a)

(b)

(c)


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Figure 1. (Color online) Primitive cells of Pu molecular solids. (a) [K(crypt)]Pu[C5H3(SiMe3)2]3 (Pu2+-1 or Pu-1) in a triclinic P1 structure. (b) Pu3(DPA)5(H2O)2 (Pu3+,4+-2 or Pu-2) in a monoclinic C2/c structure. (c) Pu3(DPA)6H (Pu3+,4+-3 or Pu-3) in a monoclinic C2/c structure. Pu ions marked with different colors and sizes correspond to different calculated oxidation states. The crystal structures CIF files of An-1, Pu-2, Pu-3 and the precursor of Pu-1 can be referred in Refs. 25 and 26. The OSqm of Pu ions in Pu-1, Pu-2 and Pu-3 are quantitatively assigned in terms of the calculated occupation numbers of 5f orbitals, as listed in Table 1. The associated results of U-1, Np-1, PuO, Pu2O3, PuO2, Pu7O12 as the prototype of PunO2n-2, and PuC are presented for comparison or for verification. It is important to point out that one of the notorious questions about electron structures of actinides is the valence fluctuation or multiple electron configurations; an illustrative example is whether Pu adopts 5f66d07s2, 5f56d17s2 or intermediate 5f6-δ6dδ7s2 configuration. Clearly, the uncertainties are unworthy of being mentioned for the assignment of OS of Pu3+ or higher owing to the low-lying 5f orbitals; this is why the roles of 6d orbitals in Pu compounds have rarely been discussed until the discovery of Pu2+ compound in which 6d orbital population should be counted to obtain the correct OS. This is particularly important for U-1 and Np-1 because the commonly accepted electron configurations contain one 6d electron, i.e., 5f36d17s2 and 5f46d17s2 for U and Np, respectively, whereas 6d orbitals of Pu are essentially unoccupied. In this regard, the occupation numbers of 6d orbitals of An-1 (An = U, Np, Pu) are provided as well. Taking the most common PuO2 as the illustration for the assignment of OSqm, there are four occupied 5f orbitals; consequently, one can readily assign Pu4+ in term of the outer valence configuration of Pu atom−5f66d07s2 because four electrons (5f27s2) contribute to the Pu-O bonds. For the relatively simple binary oxides, the number of


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electron participating into bonding depends on the number of oxygen atom; likewise, Pu ions in PuO and Pu2O3 adopt Pu2+ and Pu3+, respectively, consistent with the OSf in the ionic limit. In other words, more oxygen atoms induce more delocalized 5f electrons. The occupation numbers of Pu7O12 show that there are three Pu4+ and four Pu3+ ions, characteristic of mixed valence behavior and inequivalent Pu atoms. Essentially, the two electrons left after the formation of one oxygen vacancy tend to be localized at the two nearest neighboring Pu atoms, a typical feature of mixed valence metal oxides. Furthermore, Pu ion in PuC adopts Pu4+, consistent with the valence electron configuration of carbon; however, this does not mean that additional carbon atoms would increase the OS of Pu. Indeed, our calculations show that Pu ions in the borderline carbide PuC2 and the intermediate carbide Pu2C3 both with the existence of C-C bonds adopt Pu4+ as well. The weak oxidizability and the strong clustering tendency of carbon are essential for the stabilization of low OS of Pu such as Pu-1 in which Pu-C interactions play the dominating role, as will be detailed later. Table 1. Calculated occupation numbers of 5f and 6d orbitals and OSqm of An (An = U, Np, Pu) ions in the solids. The occupation numbers are listed as ascending order and the numbers for full occupancy are marked with bold, and the occupation numbers of 6d are marked with italic. The fractional numbers in the parentheses represent the atomic ratio of Pu ion with the OSqm. Bader charge of An ions and the nearest-neighboring bond distances of dominant bonds are presented for the illustration of OSqm. Note that we give the average values of charge and bond distance for the crystals containing inequivalent Ann+ ions.


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Crystals PuO Pu2O3 PuO2

Pu7O12

PuC

U-1

Np-1

Pu-1

Pu-2

Pu-3

Occupation numbers of 5f and 6d orbitals 0.004 0.020 0.002 0.053 0.026 0.078 0.006 0.046 0.002 0.146 0.003 0.153 0.000 0.007 0.076 0.126 0.001 0.014 0.006 0.053 0.001 0.023 0.005 0.034 0.005 0.034 0.008 0.056 0.005 0.023 0.008 0.086

0.005 0.882 0.011 0.076 0.026 0.126 0.009 0.068 0.019 0.168 0.011 0.153 0.001 0.008 0.076 0.126 0.001 0.020 0.013 0.061 0.001 0.977 0.006 0.040 0.006 0.050 0.019 0.112 0.009 0.032 0.018 0.112

0.005 0.882 0.012 0.993 0.030 0.232 0.011 1.000 0.020 0.215 0.012 0.236 0.002 0.025 0.076 0.126 0.002 0.908 0.039 0.063 0.002 0.980 0.025 0.040 0.009 0.884 0.020 0.134 0.011 0.908 0.018 0.117

0.005 0.950 0.012 1.000 0.042 1.000 0.014 1.000 0.030 0.999 0.012 0.987 0.003 0.031 0.076 0.126 0.004 0.922 0.040 0.066 0.003 0.984 0.025 0.042 0.012 1.000 0.027 1.000 0.015 0.960 0.020 0.999

0.015 1.000 0.030 1.000 0.046 1.000 0.014 1.000 0.070 1.000 0.026 0.990 0.006 0.969 0.076 0.126 0.004 0.976 0.050 0.071 0.003 0.997 0.033 0.044 0.013 1.000 0.045 1.000 0.016 0.967 0.043 1.000

0.016 1.000 0.034 1.000 0.050 1.000 0.022 1.000 0.076 1.000 0.035 0.992 0.006 0.973

0.016 1.000 0.051 1.000 0.077 1.000 0.034 1.000 0.120 1.000 0.035 0.992 0.006 0.977

0.005 0.980

0.005 0.982

0.004 1.000

0.015 1.000

0.018 1.000 0.048 1.000 0.020 0.985 0.048 1.000

0.022 1.000 0.052 1.000 0.020 1.000 0.052 1.000

OSqm

Bader charge (|e|)

Bond distance (Å)

2+

+1.463

2.479

3+

+2.01

2.395

4+

+2.42

2.337

3+(4/7)

+2.05

2.382

4+(3/7)

+2.41

2.317

4+

+1.620

2.485

2+

+1.500

2.805

2+

+1.485

2.801

2+

+1.414

2.796

3+(2/3)

+2.235

2.461

4+(1/3)

+2.574

2.354

3+(1/3)

+2.298

2.460

4+(2/3)

+2.564

2.358

Based on the above assignment method of OSqm of Pu in the binary compounds, the OSqm of An ions in An-1, Pu-2 and Pu-3 can be readily derived according to the calculated occupation numbers, as shown in Table 1. The striking features are: 1) the valence electron configurations of An cations and the calculated occupancies on the metal centers imply that the energy levels of An 5f electrons in An-1 are inert, indicative of the weak oxidizing ability of [C5H3(SiMe3)2] (Cp”)


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ligand, and 2) the occupation numbers of 5f orbitals in mixed valence Pu-2 or Pu-3 have nonequivalent distribution, i.e., 5 and 4, corresponding to Pu3+ and Pu4+, respectively. The OSqm derived here for Pu-1, Pu-2 and Pu-3 are well consistent with the previously reported experimental data,25,26 suggesting that the present approach is valid in these complex systems and can

be

extended

to

other

single

molecular

crystal

systems.

In

view

of

the

aforementioned importance of 6d populations in An2+, the occupation numbers of 6d orbitals are counted as well. However, none of 6d orbital is fully occupied since all the occupation numbers are far less than 1, which does not mean that there is no 6d electron in the valence electron configuration. This is presumably because 6d electron is essentially itinerant and not restricted to one orbital despite that 6d electron does not directly take part in the An-ligand bonding, resulting in the rather low 6d orbital occupation numbers. Even so, the sum of 6d orbital occupation numbers decreases in the sequence of U → Np → Pu; indeed, the sum for U is approximately equal to 1 whereas lower than 0.3 for Pu. On these grounds, the widely accepted point that 5fn6d1 to 5fn+16d0 crossover of actinide series occurs near Pu holds for the present DFT + U calculations; that is, U, Np and Pu in An-1 adopt 5f36d17s2, 5f57s2, 5f67s2 valence electron configurations, respectively.3,13,25, 43,44 The conclusion that 6d orbitals do not contribute to increase the OSqm of An in An-1 is further supported by the analysis of Bader charge despite that there is no quantitative correlation between charge and OS.4,47 The non-integer charge is always lower than that of OSqm, suggesting a typical mixed ionic covalent bonding. Interestingly, charge is an index for the same binary compounds such as Pu oxides with a relatively simple bonding feature. The OSqm of Pu in Pu oxides are in approximate proportion to the charge of Pu, as can be deduced from Table 1. However, the scaling factor derived from binary oxides cannot be extended to multi-component


12

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compounds with more complicated interplay among atoms, and cannot even be extended to other complicated binary compounds such as PuC1+x (0 < x ≤1) with the presence of complicated C-C bonding. The OSqm assignment here is Pu(IV) in PuC; however, the charge of Pu ion is approximately at the level of PuO. This is a consequence of the difference in bonding strength, i.e., more electronegative oxygen tend to withdraw more electrons from Pu than carbon; an intuitive example is that Pu4+C exhibits conducting state whereas Pu4+O2 insulating state because of more conducting electrons in the former. For An-1 with the dominating An-C bonds, An ions take about 1.5 e+ which are most likely resulted from the loss of 7s2 electrons, and the lowcharge states are suggestive of no direct bonding contribution of 6d electrons. On the whole, the trend of charge of Pu in Pu-1, Pu-2 and Pu-3 is basically consistent with that of Pu binary oxides. However, Pu ions (Pu3+ and Pu4+) in Pu-2 and Pu-3 are more positively charged with comparison to Pu binary oxides. We propose that the coordinated oxygen atoms in Pu-2 and Pu3 require more charge to stabilize the bonding between oxygen and other nonmetallic atoms, which is evidenced by the more negatively charged oxygen atoms with comparison to Pu binary oxides. OS could be viewed as a multifactorial quantity and the electronegativity difference between metal and ligand, which correlates with bonding strength, is no doubt one of the key descriptors, particularly for the simple binary compounds. In brief, bond distance associates with bond strength: shorter bonds are stronger, which particularly holds for the comparison of compounds with structural similarity. Notwithstanding, the metal-ligand (M-L) bonding factor could be counterbalanced or surpassed by the remarkable steric effects in the complicated multicomponent systems such as An-1, Pu-2 and Pu-3 of our interest. The Pu-C distance in Pu-1 is significantly longer than that in PuC, reflecting the differences of Pu OSqm. However, the


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correlation between Pu OSqm and Pu-O distances in Pu-2 and Pu-3 is somewhat indistinct. As can be found in Table 1, the Pu-O distances are longer than those in the binary oxides with the same Pu OSqm; as previously discussed, the interactions between O and other nonmetallic atoms could account for the weakening of Pu-O bonding despite that Pu ions in Pu-2 and Pu-3 are more positively charged. In particular, the Pu3+-O distances in Pu-2 and Pu-3 are very close to the Pu2+-O distance in PuO, implying the relatively unstable Pu3+-O bond and the further oxidation of Pu3+. In order to further understand the correlation between Pu OSqm and local structure, we give the basic structure units of Pu-1, Pu-2 and Pu-3, as shown in Figure 2. The detailed structures of those molecular solids can be referred to Refs. 25, 26. The striking feature of the precursor of Pu-1 is the cage-like structure in which a Pu3+ ion locates at the center of the cage (see SI). Despite of the relatively long Pu-C distances, the steric effects are strong enough to stabilize Pu3+, and only the strong reducers such as KC8 can break the cage-like structure, resulting in the formation of lower-OSqm Pu2+, characteristic of three Pu-(C5-ring centroid) units per Pu2+ ion. The semi-closed Pu-1 complex with unusual and high-lying Pu2+ ions is bound to be highly susceptible towards oxidation, as evidenced by experimental observations. The long Pu-C distances which could be viewed as the upper-limit bonding distances, further support the aforementioned conclusion that steric effects prevail over chemical bonding in the stabilization of Pu2+. For Pu-2 and Pu-3 with mixed Pu3+/Pu4+ ions, there are crystallographically nonequivalent Pu sites possessing noticeably different coordination environments, as detailed by Cary et al.25 The basic structure unit of Pu-2 features a 3D framework hinged by O-C-O bridge bonds, suggesting a degree of electron interactions among Pu ions. As shown in Figure 2(c), the low-symmetry and distorted framework structure suggests a relatively unstable state; especially,


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the relatively long O-C-O bridged bonds associated with weak bond strength reflect the structural instability. Indeed, Pu3+ ions in Pu-2 can gradually transfer to Pu4+ under the judicious selection of oxidation conditions, which is accompanied with the gradual break of C-O bonds and the weakening of electron interactions among Pu ions. Breaking one C-O bond yields one Pu4+ ion; consequently, Pu-3 is formed. From the perspective, the further oxidation of Pu-3 results in the formation of the end product with crystallographically equivalent Pu4+ ions and high-symmetry structure, as characterized experimentally. In this regard, both Pu-2 and Pu-3 are the intermediate complexes between pure Pu3+ and Pu4+ in the complex series, similar to the existence of Pu3+,4+O2-x between Pu2O3 and PuO2.48 Furthermore, considering the wide-range distances between Pu and its nearest neighboring atoms, the bond distances and radial distribution functions (RDF) are presented for the illustration of the crystal structures. We suggest that the longest C-O bonds either in Pu-2 or Pu-3 have the highest priority to be broken. After the disappearance of all O-C-O bridge bonds associated with the full transition of Pu3+ → Pu4+, the electron interactions among Pu ions disappear as well.


15


Pu-1 (Precursor, Pu3+-C) Pu-1 (Pu2+-C)

2.0 1.5

Pu2+

1.0 0.5

Pu3+

2.521

0.0 Pu-2 (Pu3+-O) Pu-2 (Pu4+-O)

2.0

+1.414|e| Pu2+ 2.869 2.737

Pu4+

2.509

Si

RDF

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 16 of 25

1.5 1.0 0.5 0.0

O

2.536

Pu-3 (Pu3+-O) Pu-3 (Pu4+-O)

2.0 1.5

C

1.0 0.5 0.0

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Pu-ligand Distance (Å)

(a) Pu-1

(b) RDF

2.417 1.269

+2.235|e| 2.436 2.485

1.244

2.475 2.480

1.244

1.265

Pu3+ 2.417

+2.564|e| 2.405 2.302 1.285

Pu4+ 2.405 1.285 1.235

1.245 1.265

2.476 2.368 2.340

2.302

1.235 2.476

2.437 +2.298|e|

2.354 +2.574|e|

(c) Pu-2

(d) Pu-3

Figure 2. (Color online) Basic structure units of Pu2+-1, Pu3+,4+-2 and Pu3+,4+-3 for the illustration of Pu oxidation states. Only Pu, its nearest neighboring atoms and some bridge atoms are shown and other atoms are omitted for clarity. The bond distances in Å and Bader charge of Pu are provided for comparison. Radial distribution functions (RDF) between Pu and its nearest neighboring atoms are shown in Figure 2(b), and the average bonding distances are listed in Table 1. Having discussed the correlations between OSqm and local structures, the OSqm behaviors associated with the electron structures are further interpreted by the analysis of electronic density


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of state (DOS). It is important to point out that the detailed electronic structures of the extremely complicated Pu-based materials are highly sensitive to the theoretical methods and calculation parameters, whereas OSqm behavior does not show the strong dependence on method. This conclusion has been proven by our calculations on the OSqm of a rich variety of Pu binary and ternary solid-state compounds: DFT + U, hybrid DFT and dynamical mean field theory (DMFT) point to the same answer regarding OSqm despite that the occupation number of each 5f orbital slightly varies with method. Considering the extraordinary overloading in the computation of complicated Pu-1, Pu-2 and Pu-3, here we decide to leave the detailed electron structures out of the discussion, but focus on the Pu 5f states which capture the main features of Pu-based materials. The projected DOS of Pu 5f orbitals in the three crystals along with 6d orbitals in Pu-1 are plotted in Figure 3. As expected, the contribution from 6d orbitals in Pu-1 is negligible, consistent with above conclusion drawn from occupation number distribution. For the electron structures of Pu-based materials, an overwhelming standpoint is that its 5f electrons just locate at the critical position of the transition from delocalization to localization across the actinide series, and the fractional ratio of delocalization to localization of Pu 5f electrons is very sensitive to physical and chemical surroundings.3 Clearly, the diverse characteristics of Pu 5f electrons are reflected in the DOS spectra of Pu-1, Pu-2 and Pu-3. The 5f electrons in Pu-1 are highly localized with the typical sharp and strong DOS peaks just below EF. The DOS profiles of Pu 5f states in Pu-2 and Pu-3 distribute in a wider range due to the existence of inequivalent Pu atoms with a wider range of energy level of 5f electrons. The high-lying Pu3+ and low-lying Pu4+ 5f states in Pu-2 and Pu-3 are basically separated with the exception of some weak overlaps which characterize of some weak hybridization (or electronic interaction) between Pu3+ and Pu4+ ions, as previously discussed. The high-lying localized 5f states tend to be delocalized and particulate


17


into chemical reactions under oxidation conditions, similar to the oxidation of metallic Pu, i.e., Pu → Pu2O3-x → Pu2O3 → PuO2-x → PuO2 → PuO2+x. Indeed, as shown in Figure 3, the ratio of localized 5f states decreases with the increase in Pu OSqm. From the perspective, when the remaining Pu3+ ion is oxidized to Pu4+, the localized 5f states below EF would disappear, similar to the electron states of PuO2.34

16

Pu2+ 5f Pu2+ 6d

Pu-1

Pu3+ 5f Pu4+ 5f

Pu-2

12 8 4 0

DOS (states/eV)

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 25

16 12

EF

8 4 0 Pu3+ 5f Pu4+ 5f

16

Pu-3

12 8 4 0

-8

-6

-4

-2

0

2

4

6

8

Energy (eV)

Figure 3. (Color online) Atom-resolved projected density of state (DOS) of Pu 5f states in Pu-1, Pu-2 and Pu-3. The projected DOS of Pu2+, Pu3+ and Pu4+ 5f states are distinguished by different color lines. Pu 6d states are presented only in Pu-1 for the expression of Pu ground-state electronic configurations. Fermi energy (EF) is denoted by the vertical dash line.


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4. CONCLUSIONS In summary, this work aims to quantitatively determine the unusual oxidation state of Pu in the recently discovered complex molecular solids by counting the occupation numbers of Pu 5f orbitals under the framework of first-principles DFT + U method. The results show that Pu ions in [K(crypt)]Pu[C5H3(SiMe3)2]3 (Pu-1), Pu3(DPA)5(H2O)2 (Pu-2) and Pu3(DPA)6H (Pu-3) adopt Pu2+, 2Pu3+•Pu4+ and Pu3+•2Pu4+ oxidation state configurations, respectively, consistent with the available experimental measurements. The steric effects are proposed to be the important reason for the stabilization of the extremely low oxidation state of Pu2+ in Pu-1 with the typical structural feature of three Pu-(C5-ring centroid) units per Pu2+ ion and the relatively weak Pu-C bondings. The co-existence of Pu3+ and Pu4+ ions in Pu-2 and Pu-3 is originated structurally from the O-C-O bridge bonds and electronically from the fluctuation between 5f5 and 5f4 configurations due to the dual localization-delocalization nature of 5f electrons; the ratio of Pu3+/Pu4+ depends on redox conditions, in other words, strong oxidation conditions can break OC-O bridge bonds, resulting in the Pu3+ → Pu4+ transition. Charge transfer and electronic structures show that Pu 5f electrons occur localization → delocalization transition with the increasing Pu oxidation state. AUTHOR INFORMATION Corresponding Authors Email: [email protected] (BA); [email protected] (RQ); [email protected] (SXH). Notes The authors declare no competing financial interests.


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ACKNOWLEDGMENTS The research was supported by the Science Challenge Project of China (No. TZ2016004), the National Natural Science Foundation of China (Nos. 21771167, and 21701006), the Foundation of President of China Academy of Engineering Physics (No. YZJJSQ2017072), and the Foundation of Science and Technology on Surface Physics and Chemistry Laboratory (No. WDZC201802). The computer facilities received from Institute of Computer Applications of China Academy of Engineering Physics are greatly acknowledged. REFERENCES (1) Stoerzinger, K. A.; Risch, M.; Han, B.; Shao-Horn, Y. Recent insights into manganese oxides in catalyzing oxygen reduction kinetics. ACS Catal. 2015, 5, 6021–6031. (2) Montini, T.; Melchionna, M.; Monai, M.; Fornasiero, P. Fundamentals and catalytic applications of CeO2-based materials. Chem. Rev. 2016, 113, 5987−6041. (3) Moore, K. T.; Laan, G. V. Nature of the 5f States in Actinide Metals. Rev. Mod. Phys. 2009, 81, 235−298. (4) Walsh, A.; Sokol, A. A.; Buckeridge, J.; Scanlon, D. O.; Catlow, C. R. A. Electron counting in solids: Oxidation states, partial charges, and iconicity. J. Phys. Chem. Lett. 2017, 8, 2074−2075. (5) Jøgensen, C. K. Oxidation Numbers and Oxidation States; Springer: Berlin, 1969. (6) Riedel, S.; Kaupp, M. The highest oxidation states of the transition metal elements. Coord. Chem. Rev. 2009, 253, 606–624. (7) Neidig, M. L.; Clark, D. L.; Martin, R. L. Covalency in f-element complexes. Coord. Chem. Rev. 2013, 257, 394–406. (8) Walsh, A.; Sokol, A. A.; Buckeridge, J.; Scanlon, D. O.; Catlow, C. R. A. Oxidation states and iconicity. Nature Mater. 2018, 17, 958−964. (9) Leinders, G.; Bes, R.; Pakatinen, J.; Kvashinina, K.; Verwerft, M. Evolution of the uranium chemical state in mixed-valence oxides. Inorg. Chem. 2017, 56, 6784−6787.


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(47) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, 1990. (48) Pugmire, A. L.; Pugmire, D. L.; Moore, D. P.; Venhaus, T. J. Understanding the oxide layer on plutonium under ambient conditions. In Proceeding of Plutonium Future–The Science 2016, Baden-Baden, Germany, 2016; pp 188–189.


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TOC Graphic

Pu2+ C Si

Pu3+

Pu3+

O

Pu4+

Pu4+

Pu4+

Pu3+


25

Plutonium Oxidation States in Complex Molecular Solids

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