Molecular oxides of high-valent actinides

Abstract

The past decade has been very productive in the field of actinide (An) oxides containing high-valent An. Novel gas-phase experimental and an impressive number of theoretical studies have been performed, mostly on pure oxides or oxides extended with other ligands. The review covers the structural properties of molecular An oxides with high (An^≥V) oxidation states. The presented compounds include the actinide dioxide cations [AnO₂]⁺ and [AnO₂]²⁺, neutral and ionic AnO_x (x = 3–6), oxides with more than one An atom like neutral dimers, trimers and dimers from cation–cation interactions, as well as large U-oxide clusters observed very recently in the gaseous phase.

Introduction

The actinide (An) group contains the heaviest chemical elements occurring in nature (Th, U) and produced in appreciable quantities in nuclear reactors (Pu, Am) for important practical applications. The other actinides of the group are mostly used only for research purposes, where the required amounts are produced in nuclear reactors or particle accelerators [1].

The actinides occur most frequently in the form of oxides, these compounds being also often the products of the synthesis. Accordingly, the oxides are the best characterized actinide compounds. Best known are the physical and chemical properties of the solid Th, U, and Pu oxides. In contrast, considerably less information is available on the gas-phase properties of actinide oxides. The main reasons are the extraordinary challenges in the gas-phase studies like the required special experimental setups due to the high evaporation temperatures, and the extreme safety requirements in handling radioactive materials. Consequently, such experiments require enormous costs. In addition, further complications in the experiments are caused by the complexity of the vapors, by the variety of accessible oxidation states of An and the very high reactivity of atomic An with oxygen and moisture. The above difficulties are absent in quantum chemical modelling, which technique developed considerably due to the progress of both hardware and software in the past decades. On the other hand, the modelling also has its own challenges caused by the relativistic effects and high density of electronic states in An. Therefore, sophisticated theoretical levels have to be applied and the results have to be analyzed carefully and critically. Nevertheless, nowadays the majority of new chemical data on molecular actinide compounds are provided by modelling.

Experimental and theoretical data on binary oxides have been reviewed in several publications in the past [2,3,4,5,6,7,8,9,10,11,12,13,14] Since the latest comprehensive review [14], a considerable progress has been achieved in the field of oxides containing high-valent actinides (An^≥V), deserving an overview of the structural and other molecular properties of these interesting and exotic molecules. The grouping of compounds covered by the present review is the following:

• 1. Actinide dioxide cations [AnO₂]⁺ and [AnO₂]²⁺

• 2. Neutral and ionic AnO₃

• 3. Neutral and ionic AnO₄

• 4. Neutral and ionic AnO₅

• 5. Neutral and ionic AnO₆

• 6. Neutral dimers and trimers

• 7. Dimers from cation–cation interactions (CCIs)

• 8. Large U-oxide clusters observed in the gaseous phase

The present review focuses on the structural properties of the above compounds. They can vary considerably due to the flexible An electronic structure, facilitating different coordination environments [15]. In them, however, a frequent motif is the AnO₂ moiety appearing in most known An multioxides.

Note that an introduction of the advanced experimental and theoretical methods used in modern actinide research is omitted here. For interested readers, recent compilations [14, 16] are recommended.

Actinide dioxide cations [AnO₂]⁺ and [AnO₂]²⁺

Due to the small size and simple structure of these cations, they have been subjected to numerous experimental and theoretical studies in the past. The molecular data on the geometry, electronic structure, vibrational, and other properties have been compiled in detail in a recent review [14] and are therefore omitted here. In the present work, only two new comprehensive studies are added, which investigated the stabilities of these species across the actinide row by means of high-level ab initio calculations.

Systematic computations on AnO₂⁺ cations for An = Pa-Lr were performed at the CCSD(T) level elucidating the stabilities and structural preferences [17]. According to these calculations, actinides in the first half of the row have actinyl(V)-type [O=An=O]⁺ ground-state structures, while Cm and actinides beyond Es prefer the triangular structure with side-on bonded η²-O₂. The high stability of [Cm(η²-O₂)]⁺ is in agreement with the 5f⁷ configuration of Cm^III. In the triangular structures Cm, Bk, Cf, and Lr appeared as An^III peroxides with a formal charge distribution of [An³⁺(O₂²⁻)]⁺ while Es, Fm, Md, and No as An^II superoxides with a formal charge distribution of [An²⁺(O₂⁻)]⁺. The two oxidation states could be well distinguished by the considerably longer An-O bond distances in the superoxides (cf. Fig. 1). In the r(An-O) bond distances of the actinyl forms notable trends included the slight gradual decrease from Pa to Pu and the significant increase from Md to Lr. The latter feature is in agreement with oxidation states No^IV and Lr^III. In fact, this LrO₂⁺ species is non-actinyl and is bent with a bond angle of 107°.

Fig. 1

Bond dissociation energies for the reaction AnO₂⁺ → AnO⁺ + O (D, kcal/mol) and An-O bond distances (r, Å) for the [An(η²-O₂)]⁺ and [O=An=O]⁺ structures from CCSD(T) [17] and for the [O=An=O]²⁺ structures from B3LYP [18] calculations. The experimental dissociation energy values for BkO₂⁺ and CfO₂⁺ could be determined only as lower limits (indicated by the arrows)

Dau et al. reported in this paper also the first preparation and observation of BkO₂⁺ and CfO₂⁺ by electrospray ionization mass spectrometry, confirming experimentally the high stabilities of Bk^V and Cf^V in these oxides [17]. The dissociation energies demonstrated a gradual decrease from Pa to Cm. The high stability of Cf^V (in the actinyl structure) is due to its 5f⁷ configuration. Somewhat unexpected was, however, the comparable stability of Bk^V. The increasing stability of the [An(η²-O₂)]⁺ forms for the late actinides was explained by the increased stabilization of the 5f electrons, letting the bonding activities to the (other valence) 6d and 7s subshells.

Dixon et al. performed CCSD(T) energy calculations on geometries optimized by density functional theory (DFT) of AnO₂²⁺ dications of twelve actinides (An=U–Lr) [18]. The (incidentally) multiconfigurational nature of the compounds was taken into account using starting orbitals from the DFT calculations. In the study, all the relevant spin multiplicities and actinide oxidation states were considered. The effect of spin-orbit coupling on the relative stabilities was also investigated. Altogether eight structural isomers were found on the potential energy surface (Fig. 2). The largest number of different dication species (7) were found for U; the number of species decreased along the actinide row.

Fig. 2

Plausible minimum structures of AnO₂²⁺ ions [18]. An atoms are depicted in cyan, O in red. The most frequent oxidation states of An in the characteristic structures and the symmetries are given too

The relative energies of the various structures are depicted in Fig. 3. The main conclusions from the study include the superiority of oxidation state VI for the U, Np, and Pu oxide dications with the linear [O=An=O]²⁺ structure. Oxidation state III is preferred for An = Cm, Bk and Lr with a [An(η²-O₂)]²⁺ superoxide C_2v structure. The other six actinides prefer oxidation state II in [An(η¹-O₂)]²⁺ containing a physisorbed O₂ in a C_s or C_∞v arrangement (cf. Fig. 2). The preference of low oxidation states for transplutonium actinides is the consequence of the stabilization of the 5f orbitals. The f¹⁴ configuration explains the remarkably high stability of divalent No.

Fig. 3

AnO₂²⁺ relative energies from spin-orbit-free CCSD(T) calculations [18]

The computed An=O bond distances of the linear [O=An=O]²⁺ structures can be compared with those of the linear [O=An=O]²⁺ cations in Fig. 1. The trends (while obtained at different theoretical levels) agree very well from U to Fm. A notable feature is the drastic bond distance increase in [O=No=O]²⁺, caused by the reduction of the oxidation state of No from IV in [O=No=O]⁺ to II.

Neutral and ionic AnO₃

The three characteristic isomers of AnO₃ are presented in Fig. 4, while selected computed geometrical data are compared in Table 1.

Fig. 4

AnO₃ isomers: a T- or Y-shaped (C_2v, C_3v), b oxoperoxide (C_s), c oxosuperoxide (C_s). An atoms are depicted in cyan, O in red

Table 1 Optimized geometrical parameters of the ground and selected other states of AnO₃ molecules

ThO₃ and ThO₃⁻

The ThO₃⁻ anion obtained by laser vaporization of solid ThO₂ was studied by photoelectron spectroscopy in combination with DFT and CCSD(T) calculations [19]. Photoinduced electron loss of ThO₃⁻ resulted in neutral ThO₃. The measured adiabatic detachment energy (ADE, 3.31 eV) was in good agreement with the CCSD(T) value of 3.26 eV. The structure of ground-state ThO₃ can be derived by a side-on (η²) attachment of ThO to an O₂ molecule (Fig. 4c). The trioxide T-shaped form with C_2v symmetry (Fig. 4a) was calculated to be higher in energy by 51 kJ/mol. In contrast, the ground-state ThO₃⁻ molecule proved to have a T-shaped structure, and the η² form (Fig. 4c) was found to be higher in energy by 118 kJ/mol. Bond order and natural population analyses were performed to clarify the bonding in the studied species. The hybridization of 6d and 5f orbitals resulted in seven bonding molecular orbitals for ThO₃ and ThO₃⁻ which, however, does not mean that each of them corresponds to a single bond. The oxidation state of Th does not exceed IV in these oxides.

PaO₃⁻

PaO₃⁻ was part of a theoretical study on d and f elements with five valence electrons [20]. The scalar relativistic PBE calculations confirmed the stability of the Pa^V oxidation state in a C_3v trioxo structure (Fig. 4a) of singlet PaO₃⁻. The triplet PaO₃⁻ was found to have a similar structure but with C_2v symmetry and calculated to be higher in energy by 174 kJ/mol. The bond distances of the two structures were quite similar being in the expected range of Pa=O double bonds. The authors assigned oxidation state Pa^IV in triplet PaO₃⁻; a reasoning was not given. Additional reported molecular data included the vibrational frequencies.

De Jong et al. computed PaO₃⁻ using the PBE0 functional [21]. The data (computed energies, structures, vibrational frequencies) deposited in the Supporting Information without discussion in the text supported the singlet ground electronic state.

UO₃ and UO₃⁻

The neutral UO₃ molecule was detected in matrix-isolation IR spectra of mixtures of uranium oxides [22,23,24,25,26,27]. Several studies were performed in solid Ar [22,23,24,25,26,27] reporting five from the six fundamentals of U¹⁶O₃. Experiments using mixture of ¹⁶O and ¹⁸O isotopes coupled with normal coordinate analysis pointed out the T-shaped C_2v molecular geometry with a near-linear OUO moiety (Fig. 4a) [24, 28]. The structure and the vibrational assignments were confirmed by quantum chemical calculations [27, 29,30,31,32,33]. The U^VI oxidation state was confirmed by DFT-based adaptive natural density partitioning (AdNDP) analysis resulting in three 2-center-2-electron σ and six 2-center-2-electron π U-O bonds [32].

Already early quantum chemical calculations on UO₃ using Hartree-Fock (HF) theory and relativistic large-core pseudopotentials [29] predicted the ¹A₁ ground electronic state and reasonable geometrical parameters. Later DFT calculations provided more accurate structural data and a good agreement between the computed and experimental frequencies (taking into account both the matrix shift and anharmonicity) [27, 31]. The electronic structure and excited states of UO₃ were investigated by multireference CASPT2 calculations [34] confirming the ¹A₁ spin-orbit-free (SF) ground electronic state and its closed-shell character. It forms exclusively the spin-orbit (SO) ground state. Triplet states were predicted at very high energies, above 160 kJ/mol [34]. High-energy triplet structures include the T-shaped one (Fig. 4a) as well as forms with peroxide motif (Fig. 4b) [33].

The UO₃⁻ anion was detected early in a secondary ion mass spectrometric investigation of uranium oxides using a cesium sputter source [35]. Its presence was confirmed by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry in the vapor above solid UO₃ and (NH₄)₂U₂O₇ upon laser ablation [36]. In recent laser vaporization experiments of Su et al., UO₃⁻ was formed from surface oxide impurities on a uranium disk target [32]. In the latter work, the mass-selected anion was subjected to a photoelectron spectroscopic (PES) analysis using laser beams operating at various wavelengths. Upon laser irradiation well-resolved electron detachment transitions occurred from the anionic electronic ground state to the ground and low-lying excited states of neutral UO₃. Combined with Franck-Condon simulations, the electron affinity of UO₃ was determined to be 1.12 ± 0.03 eV. In addition, the vibrational resolution of the spectra facilitated the experimental determination of the symmetric stretching frequency of UO₃ (850 ± 30 cm⁻¹). Five low-lying excited states with geometries similar to that of UO₃⁻ were observed and vertical detachment energies between 3.2 and 6.3 eV were determined. Regarding neutral UO₃, a large energy separation of 1.8 eV was measured between the ground and first excited states, pointing to a large HOMO-LUMO gap in agreement with the closed-shell nature of the molecule [32].

Theoretical studies of the UO₃⁻ anion include the DFT one by Zaitsevskii for evaluation of the adiabatic electron affinity of UO₃ [31]. The effects of the excess electron on the geometry (Fig. 4a) are manifested in considerably (by ca. 0.1 Å) lengthened U-O bond distances and a slightly smaller O₁-U-O₁ bond angle (cf. Table 1). The geometry features were confirmed by the DFT calculations of Su et al. [32]. The electronic structure of UO₃⁻ is similar to that of UO₃, the main difference being the single occupation of a 5f-based B₂ orbital by the extra electron. The valence molecular orbitals (MOs) are of dominant O(2p_σ,π) character with ca. 20% U(6d) or U(5f) contribution. The low-energy unoccupied MOs have generally dominant U(5f) character except for one with dominant U(7s) character. The assignment of the detachment band in the PES spectrum was performed on this basis to the singly occupied B₂ MO [32].

NpO₃

The only information on the geometry and electronic structure of NpO₃ comes from a CASPT2 study of the ground and low-lying excited electronic states [34]. The calculations resulted in a C_2v ground-state geometry (Fig. 4a, Table 1). The doublet ²A₂ SF ground state gave the main component of the SO ground state. The quartet states were predicted to appear above 100 kJ/mol.

PuO₃, PuO₃⁺, and PuO₃⁻

A detection of the PuO₃ molecule was reported from a mass spectrometric analysis of the sublimation products of solid PuO₂ [37]. It was observed in a very low concentration; therefore, a confirmation from new experiments would be desirable. No experimental data on its molecular properties are available.

The first theoretical studies on PuO₃ provided some contradicting results, reflecting the difficulties of routine quantum chemical calculations for the complex electronic structure of Pu. The very first DFT study from 2001 reported a T-shaped structure (Fig. 4a) for the ¹A_1g state of PuO₃ [38]. Gao et al. calculated quintet, septet, and nonet states by HF and DFT (using the less-reliable large-core pseudopotential for Pu) and found a ⁷B₁ ground electronic state with an Y-shaped C_2v structure (Fig. 4a) [39]. Two-component relativistic DFT calculations on triplet PuO₃ predicted a T-shaped structure [40, 41] with geometrical parameters in good agreement with those reported by Straka et al. [38] for the ¹A_1g state (cf. Table 1). The ³B₂ character of the ground electronic state was clarified recently by CASPT2 [34] and CASSCF [42] calculations. In the latter study, the most important valence orbitals for the active space in multireference ab initio calculations were also determined using the density matrix renormalization group (DMRG) algorithm [43].

The multireference calculations [34, 42] pointed out the very complex electronic structure of PuO₃ (most complex from the five AnO₃, where An = U-Cm [34]) with several low-lying excited electronic states. An extensive mixing was shown between the SF ground ³B₂ and first excited ³A₂ states forming the SO ground and first excited states. The singlet states appeared as notable contributions in the SO states above 130 kJ/mol, while the quintet ones above 180 kJ/mol.

After two failed studies on PuO₃⁺ [44, 45] Gao et al. reported a ⁶B₂ ground electronic state with a C_2v Y-shaped structure (Fig. 4a) for this cation [39]. However, as the used theoretical level was the same which led to erroneous results on the neutral PuO₃ molecule (vide supra), an independent confirmation of the data on PuO₃⁺ would be desirable.

DFT results on PuO₃⁻ were published in [46]: relative energies and structures of three states with doublet, quartet, and sextet spin multiplicities were deposited in the Supporting Information without discussion in the text. The geometrical parameters are included in Table 1. From them, the T-shaped (Fig. 4a) C_2v quartet form was found to be the most stable followed by the doublet and sextet higher in energy by 47 and 68 kJ/mol, respectively.

AmO₃

The geometry and bond dissociation energy of AmO₃ were predicted by two-component relativistic DFT calculations without providing details on the electronic structure [41]. CASPT2 calculations predicted the SF ground state of T-shaped (Fig. 4a) AmO₃ being a sextet ⁶B₂, which formed almost exclusively the SO ground state [34]. The quartet states appeared at quite low energies, from ca. 42 kJ/mol, while the octet ones much higher, above 190 kJ/mol. The geometrical parameters from the two studies [34, 41] are in good agreement (cf. Table 1).

CmO₃

The CmO₃ molecule was indirectly inferred from a thermochromatographic measurement [47]. No molecular data are available for CmO₃ from experiment.

Two-component relativistic DFT calculations [48] provided the first molecular data on CmO₃ including the geometrical parameters of a T-shaped structure (Fig. 4a) and bond dissociation energy. Subsequent relativistic SO-PBE0 calculations [49] predicted the oxosuperoxide isomer (Fig. 4c) to be more stable by 31 kJ/mol than the T-shaped one.

The electronic structure of T-shaped CmO₃ was investigated by CASPT2 calculations. The lowest-energy SF state showed a ⁷A₂ character, this state forming nearly exclusively the lowest-energy SO state [34]. Compared with other AnO₃ molecules (An = U-Am), the neighboring (quintet and nonet) spin multiplicities appeared here at the lowest energies: the quintet ⁵B₂ was the major component in the first SO excited state at 28.5 kJ/mol, while the nonet ⁹B₁ appeared in the second SO excited state at 54 kJ/mol. The CASPT2 geometrical parameters were in good agreement with the DFT ones from [48].

BkO₃, CfO₃

These trioxides were investigated by Zaitsevskii by relativistic SO-PBE0 calculations [49] reporting the structures and dissociation enthalpies. For BkO₃ the T-shaped structure (Fig. 4a), for CfO₃ the oxosuperoxide isomer (Fig. 4c) was predicted to be the most stable.

Comparison of some properties of AnO₃ molecules

This comparative analysis is facilitated by systematic calculations on AnO₃ molecules performed in [34, 49].

An interesting problem is the variation of the structure across the An row. Towards the heavier actinides, the trivalent character gets stronger; consequently, the features characteristic for An^VI (e.g., the trioxo T-shaped structure) become less favored. The stability of the three isomers (Fig. 4) was investigated by Zaitsevskii in the series PuO₃-CfO₃ using relativistic SO-PBE0 calculations [49]. The oxoperoxide isomer (Fig. 4b) has a formal charge distribution of (AnO)²⁺(O₂)²⁻ in agreement with the oxidation state An^IV. The oxosuperoxide isomer (Fig. 4c) with one unpaired electron localized on the O₂ fragment has a formal charge distribution of (AnO)⁺(O₂)⁻, corresponding to oxidation state An^III.

The relative stabilities were assessed by the ${\Delta H}_0^o$ enthalpies of dissociation to AnO₂ + ½O₂. Figure 5 shows the variation of the ${\Delta H}_0^o$ enthalpies from Pu to Cf. The oxoperoxide form had the highest energy from the three isomers and, due to the positive ${\Delta H}_0^o$ values, was thermodynamically unstable. The T-shaped structure was preferred for Pu, Am, and Bk, while the oxosuperoxide isomer was predicted to be the most stable for Cm and Cf.

Fig. 5

Calculated ${\Delta H}_0^o$ enthalpies of dissociation to AnO₂ + ½O₂ of the three AnO₃ isomers; data from [49]. For the structures, see Fig. 4

The above characteristics were rationalized on the basis of effective atomic configurations derived using the concept “atoms in compounds” [50]. The high stability of Bk^VO₃ with respect to its neighbors Cm^VO₃ and Cf^VO₃ is in agreement with the high number (6) of unpaired 5f electrons in Bk^V. In Cf^V an enhanced 5f electron pairing was observed (deviating from the known high-spin 5f⁷ ground state of the Cf⁵⁺ ion), which can destabilize the T-shaped structure.

Trends in the geometrical parameters of T-shaped AnO₃ (An = U, Pu-Cf) molecules can be assessed on the basis of the SO-PBE0 results [31, 49] in Table 1. The main features are the decrease of An-O₁ bond distances, the increase of the An-O₂ bond distances, and the increase of the O₁AnO₁ bond angles from U to Am (in agreement with CASPT2 data on UO₃-CmO₃ from [34], cf. Table 1, Fig. 6). No systematic changes can be recognized beyond Am. Particularly interesting are the two distinct ranges of the An-O₂ bond distance (around 1.84 Å in the lighter U, Np, and Pu trioxides and around 2.1 Å in the heavier AnO₃ molecules) in which only marginal variations occur. The considerable lengthening refers to a significant difference in the bonding, i.e., the replacement of the double bond by a single bond. On the basis of this lengthened An-O₂ bond and the formal charge of O₂ a pentavalent character of Am and Cm was suggested [41, 49] in these trioxides. The considerably longer Am-O₂ bond with respect to the analogous Pu-O₂ one is in agreement with the by ca. 80 kJ/mol smaller bond dissociation energy of the Am-O₂ bond [41], supporting its considerably weaker character.

Fig. 6

Trends in the An-O₁ and An-O₂ bond distances in T-shaped AnO₃ molecules from SO-PBE0 [31, 49] and SF-CASPT2 calculations [34]. For the numbering of atoms, see Fig. 4

The above noted long An-O₂ bonds in heavier AnO₃ (An = Am-Cf) molecules were consistent with the effective atomic configuration data [50], i.e., with the decrease of the paired 5f electron population between Pu^VIO₃ and Am^VO₃ by ca. 1 e and the parallel increase of the unpaired 5f population by ca. 2 e (Fig. 7).

Fig. 7

Effective populations of the 5f atomic subshells. Data from [50]

A detailed analysis of the valence molecular orbitals in [34] showed a gradually increasing number of unpaired non-bonding 5f electrons from UO₃ to PuO₃ (from 0 to 2, respectively). In contrast, in T-shaped AmO₃ and CmO₃ the lowest-energy states were composed of four and five non-bonding unpaired 5f electrons, respectively, and a singly populated B₂ bonding π orbital between the An and O₂ atoms. This replaced the analogous, but doubly occupied, B₂ π orbital in the U/Np/Pu trioxides, explaining the longer Am-O₂ and Cm-O₂ bonds.

Neutral and anionic AnO₄

Gas-phase experimental reports were published for neutral UO₄ and the UO₄⁻, NpO₄⁻, and PuO₄⁻ anions. In addition, several theoretical studies on An tetroxides were carried out. According to them, AnO₄ molecules can form numerous interesting isomers as depicted in Fig. 8. From them, the η²-O₂-coordinated structure in Fig. 8a represents two bonding types: depending on the O-O distance this structure can mean the peroxo form with O₂²⁻-ligand (O-O bond around 1.45 Å) or the superoxo one with O₂⁻-ligand (O-O bond around 1.31 Å).

Fig. 8

Main structural isomers of neutral and ionic AnO₄ molecules. An atoms are depicted in cyan, O in red. Structures with the following symmetries are discussed in the review: a C_2v; b C_2v; c D_2d, C_2v; d D_2d, C_2v; e D_4h, D_2h; f C_s; g C_2v, C_s, C₁; h T_d

PaO₄⁻

The PaO₄⁻ anion was investigated recently using the PBE0 hybrid functional [21]. From the various considered isomers, the lowest-energy one proved to be the structure consisting of a bent protactinyl and an η²-coordinated O₂ (Fig. 8a). No symmetry was assigned to this species in the paper, but according to the given Cartesian coordinates, the optimized structure is very close to C_2v. Characteristic on this structure is the considerable bending of the protactinyl moiety compared with the heavier actinide analogues (cf. Table 2). This is the consequence of the Pa^V oxidation state in this anion (composed formally of PaO₂⁺ and peroxide O₂²⁻) unlike the heavier actinides which can access higher oxidation states. In the Supporting Information of [21] the relative energies and structures of 13 additional (singlet and triplet) PaO₄⁻ species were given without discussion, several of them corresponding to excited electronic states. For comparison, a few selected low-energy ones are included in Table 2. From them, the planar peroxide derivative, formed by a 90° turn of O₂ (Fig. 8b), is the closest is energy, being higher by 15 kJ/mol.

Table 2 Selected computed geometrical parameters of ground-state neutral and ionic AnO₄

UO₄, UO₄⁻, UO₄²⁻, and UO₄⁺

Because the U atom reached its maximum oxidation state VI in UO₃, the higher oxides can be formed incorporating either open-shell oxyl ligands (with electron holes in the 2p subshell) or η¹- or η²-coordinated O₂ ligands.

Neutral UO₄ was observed in the matrix-isolation IR study of Zhou et al. [27], assigning the IR absorption band at 905.1 cm⁻¹ in Ne matrix to the UO₂(O₂) form on the basis of the good agreement with the computed frequency. Two other IR bands were assigned to higher UO₂(O₂)_x species. DFT calculations were performed on UO₄, and on the basis of the calculated wavefunction a superoxo (UO₂⁺)(O₂⁻) character (Fig. 8a) was suggested for the ¹A₁ ground state.

UO₄ was also produced in laser-induced electron detachment measurements on UO₄⁻ by Su et al. [32] (vide infra). The experiments resulted in the electron affinity of 3.60 ± 0.03 eV for UO₄. The U-O symmetric stretching frequency of UO₄ was measured to be 770 ± 30 cm⁻¹. The frequency and electron affinity of an unidentified excited state were also measured.

DFT calculations in the latter study confirmed the ¹A₁ ground electronic state of UO₄ having an η²-O₂ ligand attached to the bent uranyl moiety in a C_2v arrangement (Fig. 8a). The tetrakis-oxo isomer (Fig. 8c) was higher in energy by 70 kJ/mol according to CCSD(T) single-point calculations on the B3LYP geometry. These calculations suggested a peroxo O₂²⁻ character of the η²-ligand, contradicting the previously suggested [27] superoxo nature of the ground electronic state. A superoxo UO₄ structure was obtained for a high-lying excited electronic state [32].

Anionic UO₄⁻ was reported from several experimental studies. It was first observed by Gibson et al. using FT-ICR mass spectrometry [36, 51]. The molecule showed a remarkable abundance in the vapor phase above solid UO₃ and (NH₄)₂U₂O₇ subjected to laser ablation. UO₄⁻ was formed also in the gas-phase oxidation reaction UO₃⁻ + N₂O under thermal conditions. Sokalska et al. obtained UO₄⁻ by collision induced dissociation of ions from laser desorption/ionization of various solid uranyl-salts, followed by detection by mass spectrometry [52]. Several spin states and structural isomers were probed by MP2 and DFT calculations. They predicted a doublet ground electronic state with distorted planar structures, revised later by more sophisticated calculations (vide infra).

Su et al. prepared UO₄⁻ by laser evaporation of solid uranium followed by reaction with O₂ in He carrier gas [32]. The anion was identified by mass spectrometry and further characterized by photoelectron spectroscopy and quantum chemical calculations. De Jong et al. [21] prepared UO₄⁻ by gas-phase reaction of UO₂(C₂O₄)⁻ (from electrospray ionization) with O₂ in an ion trap. The anion was detected by mass spectrometry and characterized by DFT computations.

The structure and bonding properties of UO₄⁻ were clarified by quantum chemical calculations carried out parallel with experiments in the above studies.

The ²B₁ ground electronic state of UO₄⁻ proved to be a tetrakis-oxo structure with C_2v symmetry (Fig. 8d) [21, 32, 51] resembling the tetraoxo anions of heavy transition metals with oxidation states ≥VI [53, 54]. In this structure, the radical electron is delocalized between the two “equatorial” oxygen atoms resulting in slightly larger U-O₂ vs U-O₁ bond distances (cf. Table 2) [51]. Yet, these weakened U-O₂ bonds are still stronger than a single bond [21]. The radical electron enters a dominantly O(2p)-type LUMO differing from the lower UO_x⁻ (x ≤ 3) anions where this extra electron occupies an U(5f)-type LUMO. This feature is associated with a significantly higher electron affinity of UO₄ compared with UO₃ [32].

Important additional isomers of UO₄⁻ include those consisting of an η²-O₂ ligand (Fig. 8a): The ²A₁ peroxide form with a formal O₂²⁻ ligand was calculated to be higher in energy by over 130 kJ/mol according to DFT calculations [21, 51] as well as by CCSD(T) energies on the B3LYP geometries [32]. The ⁴A₂ superoxide with a formal O₂⁻ ligand and considerably larger U-O₂ distance was even higher in energy (by 282 kJ/mol) [32]. In the Supporting Information of [21], the relative energies and structures of altogether 11 additional (doublet and quartet) UO₄⁻ species were given, several of them corresponding to excited electronic states. Selected ones are included in Table 2. From them, the C₂ (distorted S₄) form (Fig. 8d) was the closest is energy, computed to be higher only by 7 kJ/mol. The planar (Fig. 8e) and double-peroxi (Fig. 8g) isomers were obtained very high in energy (209 and 578 kJ/mol, respectively).

The square planar isomer of UO₄²⁻ (Fig. 8e) was investigated at the HF level by Pyykkö and Zhao [55] in a comparative study of various uranium oxide ions. Calculations by Bolvin et al. [56] a decade later using various wavefunction theory and DFT methods resulted consistently in a tetrahedral ground-state (Fig. 8h) with a flat potential energy surface around the minimum. The high symmetries of the probed T_d and D_4h structures (Fig. 8e, h, respectively) facilitated geometry optimizations at the highest CCSD(T) level (Table 2). The D_4h form was found to be less stable by 91.5 kJ/mol. The study included also low-energy excited states and analysis of valence molecular orbitals.

Huang et al. [57] performed a comparative analysis of isoelectronic UO₄²⁻, NpO₄⁻, and PuO₄ using the B3LYP method focusing on the relative energies of the three main structures: singlet T_d (Fig. 8h), singlet D_4h (Fig. 8e), and triplet and quintet C_2v (Fig. 8a). The study supported the ground-state character of the singlet T_d isomer of UO₄²⁻ and the preference of U^VI over U^III oxide. The D_4h and C_2v isomers proved to be low-energy structures. No geometrical parameters were published for UO₄²⁻.

The free UO₄⁺ molecule was not observed experimentally, while in the gas phase, Groenewold et al. found UO₂⁺(O₂) species coordinated by additional two or three electron donor ligands (acetone, H₂O, DMSO) [58, 59]. This observation was explained by the electron acceptor character of O₂: it requires excess electron density on the metal center which could be provided by the mentioned additional ligands.

Bryantsev et al. proposed for UO₄⁺ an (UO₂²⁺)(η²-O₂⁻) structure (Fig. 8a), corresponding to a uranyl(VI) superoxo compound on the basis of B3LYP calculations [60]. This structure, stabilized by a 2-electron-3-centered bond between the singly occupied U(5f_φ) orbital and the O₂(π*) orbital in the equatorial plane, was favored by 46 kJ/mol over the (UO₂⁺)(η¹-O₂) C_s isomer (Fig. 8f). The calculated enthalpy and Gibbs-free energy for O₂-addition to UO₂⁺ were − 52 and − 20 kJ/mol, respectively [61].

UO₄⁺ ions complexed by a few Ar atoms were produced in a supersonic molecular beam by laser vaporization of uranium in Ar containing a few percent of O₂ [62]. Such gas-phase complexes resemble matrix-isolation situations (molecules captured in a cryogenic matrix) but, due to the less Ar neighbors, they can provide better approximations of the molecular vibrations. Excitation of the UO₄⁺Ar₂ complexes with an IR-OPO laser system in the range of the O-U-O and O-O stretching vibrations facilitated the experimental determination of these vibrational frequencies. The asymmetric O-U-O stretching of the UO₂ moiety appeared as an intense band at 1015 cm⁻¹ while the symmetric stretching as a weak one at 930 cm⁻¹. The found infrared activity of this latter vibration (being inactive in linear OUO) is due to a slight bend of the uranyl core upon coordination of O₂. The O-O stretching band of the η²-coordinated O₂ appeared at 1163 cm⁻¹. Two isomers of UO₄⁺ (Fig. 8a, d) were computed by DFT and the calculated frequencies of the lower-energy doublet C_2v isomer agreed very well with the experimental spectrum [62]. The calculated O-O bond distance of the η²-O₂ moiety (1.297 Å) was close to the one in the superoxide O₂⁻ ion (1.34 Å [63]).

NpO₄⁻ and NpO₄⁺

The highest known oxidation state of Np is VII, reported in the gaseous phase first for NpO₃(NO₃)₂⁻ [64]. Recently, Gibson et al. synthesized NpO₄⁻ by the gas-phase reaction of NpO₂(C₂O₄)⁻ with O₂ in an ion trap [46]. The detection was done by mass spectrometry while the heptavalent oxidation state was supported by reactivity studies and DFT calculations. In the experimental studies, the slow rate of water addition suggested the high stability of NpO₄⁻ which can happen in a structure with four Np=O quasi-double bonds (according to Np^VII). These experimental findings were consistent with calculated reaction energies [64].

The square planar D_4h structure of singlet NpO₄⁻ (Fig. 8e) was proposed by early relativistic extended Hückel calculations of Pyykkö et al. [65] and confirmed by Bolvin et al. using various wavefunction theory and DFT methods [56]. The latter authors performed geometry optimizations of the D_4h and T_d (Fig. 8e, h) isomers using 10 different methods including CCSD(T), and obtained a preference of D_4h by 105 kJ/mol at the latter level. Analysis of molecular orbitals revealed the determining role of 5f orbitals for the planar structure, because removing them from the basis set changed the structure to a tetrahedral one. The promoting role of 5f orbitals in the covalent bonding was associated with their relatively low energy.

The DFT calculations in [46] agreed too with the singlet square planar structure. The Mulliken atomic spin population of Np corresponded to 5f⁰ configuration, i.e., to Np^VII.

Huang et al. performed a comparative analysis of isoelectronic UO₄²⁻, NpO₄⁻, and PuO₄ with the B3LYP method [57] focusing on the relative energies of the three main structures: singlet T_d (Fig. 8h), singlet D_4h (Fig. 8e), and triplet and quintet C_2v (Fig. 8a). The study confirmed the ground-state character of the D_4h isomer as Np^VIIO₄⁻ while the T_d transition state and the C_2v minimum corresponded to low-energy structures. The data indicated the preference of Np^VII over Np^IV oxide. No geometrical parameters were published for NpO₄⁻.

NpO₄⁺ was studied by Rios et al. [61] using B3LYP calculations. The lowest-energy open-shell singlet and quintet states were found to be practically degenerate in energy (within 4 kJ/mol), with the singlet state being slightly favored. The calculated enthalpy and Gibbs-free energy for O₂ addition to NpO₂⁺ were −24 and +2 kJ/mol, respectively. The obtained structure contained an O₂ molecule in a very weak η¹-arrangement to NpO₂⁺ (Fig. 8f), the O-O bond lengths being almost the same as in the free O₂ molecule. Hence, this weakly bound neptunyl−dioxygen complex retained the Np^V oxidation state of NpO₂⁺, in contrast to the uranyl−dioxygen superoxo complex in which U^V was oxidized to U^VI.

PuO₄ and PuO₄⁻

Neutral PuO₄ molecule was inferred by Domanov et al. [66, 67] on the basis of gas thermochromatographic measurements of volatile oxidation products of Pu. The suggested composition (Pu^VIIIO₄) of the detected species with unusually low deposition temperature was based on the similar deposition zones of well-known octavalent transition metal oxides, OsO₄ and RuO₄, supposing an analogous tetrahedral structure [68] for PuO₄. However, the formation of PuO₄ could not be confirmed in a similar independent experiment [69]. The detection of Pu^VIIIO₄ was questioned also by Zaitsevskii et al. [41] who obtained a non-tetrahedral structure for PuO₄ by DFT calculations (vide infra).

The formation of PuO₄ in the gaseous phase was assumed in an ozonation treatment of Pu^VI hydroxo complexes tracked by α-spectrometry [70]. However, in another ozonation experiment on Pu^VI, no Pu^VIII compounds could be detected by X-ray photoelectron spectroscopy [71]. A critical analysis of the experimental reports on PuO₄ was published by Shilov et al. [72] with the conclusion that no unambiguous experimental proof is available for the existence of Pu^VIII in the gaseous phase.

The first theoretical study of PuO₄ was performed by Straka et al. [38] using wavefunction theory (HF, MP2, CCSD(T)) methods. The geometry optimizations resulted consistently in a planar D_4h structure (Fig. 8e, in contradiction with the tetrahedral one assumed by Domanov et al. [67]) with bond distances close to those of PuO₂ and PuO₃. Accordingly, this singlet planar PuO₄ form was assumed to contain Pu^VIII. On the other hand, the calculations indicated also a multiconfigurational electronic structure, calling for confirmation by multiconfigurational calculations. As additional molecular data, Pu-O stretching frequencies, the standard enthalpy of formation and the bond dissociation energy were reported [38]. The planar PuO₄ structure was considered also in DFT studies of the molecular geometry and thermodynamic stability [40] as well as in modelling of solution structures with a PuO₄ motif [73]. The latter study assessed the redox potential of the Pu^VII/Pu^VIII couple in alkaline and acidic solutions. In acidic medium, the Pu^VII/Pu^VIII redox potential was found to be too high to get the Pu^VIII valence state. In contrast, Pu^VIII may be synthesized in strong alkaline solution, but it seems to be unstable and can easily be reduced back to Pu^VII by the solvent water molecules.

In another study, Zaitsevskii et al. investigated the stability of PuO₄ isomers using two-component relativistic DFT [41]. According to the calculated ΔH⁰₂₉₈ and ΔG⁰₂₉₈ data, planar PuO₄ (Fig. 8e) proved to be thermodynamically less stable by ca. 70 kJ/mol than the plutonyl superoxide, PuO₂(O₂) (Fig. 8a).

Huang et al. performed DFT, MP2, CCSD(T), and SO-CASPT2 calculations on possible structural isomers of PuO₄ providing details also on the electronic structure and spectroscopic properties [57]. From the two minima found on the potential energy surface, the quintet PuO₂(O₂) (Fig. 8a) was found to be superior to singlet PuO₄ (Fig. 8e) by 68 kJ/mol at the CCSD(T) level. The electronic structure of the global minimum corresponded formally to (PuO₂⁺)(η²-O₂⁻), i.e., to a plutonyl(V) (5f³) unit coupled to a superoxido O₂⁻(π*³) ligand. Its stability indicated that it may likely be detectable as a transient species in gas-phase reactions.

A comparative analysis using the B3LYP method in the same study [57] revealed the following trends in the relative stabilities of the main structures of isoelectronic UO₄²⁻, NpO₄⁻, and PuO₄ molecules: the singlet T_d isomer, being the ground-state structure of UO₄²⁻, became a gradually destabilized transition state for NpO₄⁻ and PuO₄. The singlet D_4h isomer, being the ground-state structure of NpO₄⁻, was found to be a low-energy isomer for UO₄²⁻ and PuO₄. The stability of the quintet C_2v isomer increased gradually from UO₄²⁻ towards PuO₄, corresponding to the ground-state structure of the latter molecule. These results further supported the preference of Pu^V over Pu^VIII oxide.

Zaitsevskii and Schwarz investigated the stability of PuO₄ isomers [74] using two-component relativistic DFT. The considered structures were the plutonyl superoxide (PuO₂⁺)(η²-O₂⁻), the planar tetroxide PuO₄ and the peroxide derivative Pu⁴⁺(η²-O₂²⁻)₂ (Fig. 8a, e, g), corresponding to this stability order. The reported comparison with the analogous AmO₄ and CmO₄ isomers is presented below in the “AmO₄ and CmO₄” section.

The D_4h and C_2v isomers of PuO₄ were included in two additional theoretical studies using B3LYP, CCSD(T), CASSCF, and CASPT2 methods. The stability of Pu^VIII was probed on a set of PuO_nF_8-2n (n = 0–4) models taking advantage of the high oxidizing nature of F [75]. The relevance of Pu^VIII could not be confirmed, because even the decomposition of PuF₈ to PuF₆ + F₂ was found to be considerably exothermic (ΔE = −377 kJ/mol without thermal corrections). A subsequent comparative study on the highest oxidation states in selected MO₄ molecules (M = Fe, Ru, Os, Hs, Sm, Pu) [76] revealed the inferiority of f-elements to heavy d-elements. The Ru^VIIIO₄, Os^VIIIO₄, and Hs^VIIIO₄ oxides are stabilized by closed-shell electronic structures having empty metal d⁰ valence shells bonded to O²⁻ ligands. In contrast, the light d- and the f-elements prefer partial occupation of their valance shells. Accordingly, Pu prefers the 5f³ configuration and thus the superoxide (Pu^VO₂⁺)(η²-O₂⁻) form. The reason for the larger stability of this electronic structure is the low energy of 5f orbitals, making very difficult to remove the last few 5f electrons of Pu.

The electron affinity of PuO₄ was estimated in the PBE0 study of PuO₄⁻ by Gibson et al. [46], vide infra. In the Supporting Information of [46], the relative energies and structures of six (singlet, triplet, quintet) PuO₄ species were given without discussion. The triplet and quintet superoxide forms (Fig. 8a) were the lowest-energy structures (the triplet being lower by 10 kJ/mol, with marginally differing geometrical parameters, cf. Table 2), while the singlet planar form (Fig. 8e) was computed to be higher by 107 kJ/mol. These results are in reasonable agreement with the more sophisticated ones of Huang et al. ([57], vide supra).

The experimental observation of PuO₄⁻ was reported recently [46]. It was synthesized by the gas-phase reaction of PuO₂(C₂O₄)⁻ with O₂ in an ion trap, detected subsequently by mass spectrometry. The slow rate of water addition suggested the high stability of Pu^VIIO₄⁻ in agreement with a structure containing four Pu=O double bonds. These experimental findings were consistent with the DFT calculated structure and reaction energies. The computed reaction products of water addition indicated slightly less stability of Pu^VII with respect to Np^VII, in agreement with the estimated difference between the Pu^VII/Pu^VI and Np^VII/Np^VI reduction potentials [15].

The PBE0 calculations in Ref. [46] resulted in a doublet square planar ground state for PuO₄⁻ (Fig. 8e). The Mulliken atomic spin population of Pu agreed with a 5f¹ configuration, i.e., with Pu^VII. Calculations on the conversion of Pu^VO₄ to Pu^VIIO₄⁻ by electron addition suggested an exothermic reaction with ΔE = − 247 kJ/mol, the value corresponding to the computationally predicted electron affinity of PuO₄. In the Supporting Information of [46], the relative energies and structures of 18 additional (doublet, quartet, sextet) PuO₄⁻ species were given without discussion. For comparison, selected ones are included in Table 2. From them, the quartet peroxide (Fig. 8a) was computed to be the closest to the ground state, being higher in energy by 121 kJ/mol. The sextet double superoxide (Fig. 8g) was found to be higher in energy by 375 kJ/mol.

AmO₄ and CmO₄

Experimental information on AmO₄ is not available hitherto. An assumed detection of Cm^VIIIO₄ in a gas thermochromatographic study was reported in [77]. Because this report was based on an analogous experience with PuO₄, the reliability was strongly questioned [72].

The first theoretical study of AmO₄ was published by Zaitsevskii et al. [41] using two-component relativistic DFT, reporting the structure (Table 2) and the bond dissociation energy. According to calculated gas-phase reaction energies at 298 K, AmO₄ was found to be thermodynamically unstable and should spontaneously decay to AmO₂ and molecular O₂. From the studied two minimum structures, AmO₂(η²-O₂) superoxide and planar AmO₄ (Fig. 8a, e), the former one was energetically preferred. The Am-O bonds were found to be slightly shorter than those in the analogous Pu tetroxides. Comparing the energy data of Pu and Am tri- and tetraoxides, for both actinides the (formal) oxidation states VI and VII appeared to be more favorable than VIII. Am has less propensity for the higher oxidation states than Pu as a result of the increasing stability of the 5f subshell across the actinide row.

In a subsequent computational study at the same theoretical level Zaitsevskii and Schwarz investigated systematically the structures and stabilities of PuO₄, AmO₄, and CmO₄ isomers [74]. Three isomers were considered: the planar tetroxide AnO₄ (Fig. 8e), the actinyl superoxide (AnO₂⁺)(η²-O₂⁻) (Fig. 8a) and the double-peroxide derivative Anⁿ⁺(η²-O₂)₂ⁿ⁻ (n = 3 or 4, Fig. 8g). For all the three actinides, the superoxide form proved to be the most stable (Fig. 9). In this C_2v structure, the actinides are in oxidation state V. The next in the stability order was planar AnO₄ for Pu and Am, in which the metals would have formally oxidation state VIII. This oxidation state did not seem to be feasible for Cm because the CmO₄ structure had two-two Cm-O double and single bonds (D_2h symmetry) corresponding to Cm^VI. Moreover, this structure was higher in energy than the Cm³⁺(η²-O₂²⁻)(η²-O₂⁻) peroxide-superoxide form. This peroxide-superoxide isomer was the highest-energy one for Am, while in this isomer class the tetravalent Pu formed a diperoxide Pu⁴⁺(η²-O₂²⁻)₂ structure with C_2v symmetry. The study supported the gradually decreasing stabilities and An oxidation states for the three actinides.

Fig. 9

Calculated dissociation enthalpies ΔH°₀ of various AnO₄ isomers to AnO₂ + O₂. Reproduced from [74] with permission from the PCCP Owner Societies

Zaitsevskii and Schwarz investigated also the reaction of AnO₂(O₂) (An=Pu, Am, Cm) molecules with O₂ and concluded that they can exothermally bind a second O₂ [74]. For more details of the AnO₂(O₂)₂ molecules, see the “Neutral and ionic AnO₆” section.

PaO₅⁻, UO₅, UO₅⁻, and PuO₅⁻

De Jong et al. computed PaO₅⁻ using the PBE0 functional and obtained a triplet ground electronic state [21]. The structure was a square-based pyramid with close to C₂ symmetry (Fig. 10d). The data (computed energies, structures, vibrational frequencies) of the triplet and singlet states were given in the Supporting Information without discussion.

Fig. 10

Main structural isomers of neutral and ionic AnO₅. An atoms are depicted in cyan, O in red

UO₅⁻ was prepared by reaction of laser vaporized uranium disk and O₂ in He carrier gas and investigated using photoelectron spectroscopy and quantum chemical calculations [32]. In electron detachment experiments on UO₅⁻, the neutral UO₅ could be obtained, and in this way, the electron affinity of the latter molecule be measured, resulting in 4.02 ± 0.06 eV [32]. The electron affinities of uranium oxide molecules covered in the paper increase gradually in the UO₃ < UO₄ < UO₅ row in good agreement with spin-orbit-coupled CCSD(T) energy calculations.

The structures of UO₅ species were elucidated by B3LYP calculations [32]. Neutral UO₅ can be derived from UO₃ by η¹- or η²-coordination of an O₂ molecule in the equatorial plane. The η¹ U-O₃ bond in the triplet global minimum structure (Fig. 10a) is very weak, as indicated both by the large U-O₃ and the O₃-O₃’ bond distances, the latter being very close to that of free O₂. The triplet superoxo (UO₃⁺)(O₂⁻) isomer with η²-coordinated O₂ molecule in the equatorial plane (Fig. 10b) was only by 24 kJ/mol higher in energy according to CCSD(T) single-point calculations. The singlet pentakis-oxo isomer was much higher in energy (Fig. 10c, 254 kJ/mol) [32].

The B3LYP calculations on UO₅⁻ predicted similar structures to those of the neutral UO₅ molecule [32]. However, the CCSD(T) energy order of the η¹- and η²-isomers (Fig. 10a, b) was interchanged, where the η¹-O₂ isomer was computed to be higher in energy by 71 kJ/mol. In the ²A″ ground state, the unpaired electron occupies a molecular orbital of O(2p) character in the η²-O₂ moiety.

Su et al. performed also a comparative bonding analysis of several UO_x (x = 3–6) isomers [32]. In UO₃ and in the η²- and η¹-coordinated larger oxides, the uranyl moiety is preserved. In the tetra/penta/hexakis-oxide isomers with separate O ligands, however, the uranyl moiety is strongly deformed losing its linear character and decreasing the bond order. In the small UO₃⁻ anion the excess electron was found to be localized on the U atom, while in the larger anions (x = 4–6), it was localized on the O₂ ligands. In all these oxides, the U atom had oxidation state VI.

De Jong et al. published DFT data (relative energies, geometries, vibrational frequencies) on doublet and quartet UO₅⁻ in the Supplementary Information of [21] without discussion in the text. The optimized structure of both spin states was a square-based pyramid (Fig. 10d), differing from the η¹- and η²-ones reported earlier by Su et al. [32] (vide supra). Different initial structures for the geometry optimization may be the reason for the discrepancy.

DFT data on PuO₅⁻ were published in [46]: relative energies and structures of three spin multiplicities (doublet, quartet, and sextet) can be found in the Supporting Information without discussion in the text. From the three states, the quartet one proved to be the most stable followed by the doublet and sextet at 3 and 21 kJ/mol, respectively. Similarly to the above results on the UO⁵⁻ ion by the same group [21], all the optimized structures correspond to square-based pyramids with C_2v symmetry (Fig. 10d). For comparison, selected geometrical parameters are given in Table 3. The only significant difference is the considerable lengthening of the Pu-O₂ bond in the sextet, indicating a reduction of the Pu oxidation state.

Table 3 Computed geometrical parameters of ground-state neutral and ionic AnO₅ species

Neutral and ionic AnO₆

Hexacoordinated U is a frequent structural motif in solid U^VI oxides, formally being UO₆⁶⁻. The molecular hexakis-oxo UO₆⁶⁻ anion (Fig. 11a) was studied using simple relativistic HF calculations by Pyykkö and Zhao [55] as part of the analysis of the trend in U-O bond distances. The UO₆⁶⁻ anion was found to be a minimum on the potential energy surface having cubic symmetry. The U-O bond distance is considerably increased with respect to square planar UO₄²⁻ and, particularly, to UO₂²⁺ calculated at the same level of theory. The study supported that the trend found in crystalline structures with different UO_x (x = 2–6) coordinations is of intramolecular nature.

Fig. 11

Characteristic structures of neutral and ionic AnO₆ with symmetries a O_h, b D_2h, c C_2v, d D₃, and e ~C_s. An atoms are depicted in cyan, O in red. U-O bond distances (Å) from [79] (a–d, UO₆) and [62] (e, UO₆⁺) obtained by SO-PW91/B and PBE/A calculations, respectively

The octahedral isomer of neutral UO₆ (Fig. 11a) seemed to be an appropriate model for the highest oxidation state of U (probing U^XII) [78]. The computed bond distances at various quasirelativistic wavefunction theory and DFT levels agreed with U-O double bonds. However, the electronic structure was found to have some multiconfigurational character, therefore the necessity of multireference calculations was noted. Other structures were not considered in [78] but later studies showed that this hypothetical structure has no relevance.

Recent detailed relativistic DFT studies of Xiao et al. accompanied by single-point CCSD(T) energy calculations indicated the local minimum character of this ¹A_1g octahedral isomer lying very high (ca. 540 kJ/mol) in energy compared to the ³B₂ uranyl peroxide form, U^VIO₂(η²-O₂)₂ (Fig. 11b) [79]. Similar peroxide motifs exist in several uranium minerals [80]. Other high-energy isomers include the species ³B_3u UO₄(η²-O₂) and ¹A₁ U(η²-O₂)₃ (Fig. 11c, d) [79]. Such uranium peroxide molecules were earlier tentatively reported from experiment: two IR bands in the Ne matrix from deposition of laser ablated U with O₂ were assigned to UO₂(O₂)_x species by Zhou et al. [27].

UO₆⁺ ions were produced in a supersonic molecular beam by laser vaporization of uranium in Ar containing a few percent of O₂ [62]. In the obtained UO₆⁺Ar₂ gas-phase complex, due to the very weak effect of Ar atoms, the molecular parameters approximate well those of the isolated UO₆⁺ ion. The UO₆⁺Ar₂ complexes were excited with an IR-OPO laser system in the ranges of the O-U-O and O-O stretching vibrations. In the IR spectrum, three characteristic bands were observed, providing important clues on the structure of UO₆⁺: they were the asymmetric O-U-O stretching, the O-O stretching band of an η²-coordinated O₂, and that of an O₂ interacting weakly with the UO₂(η²-O₂)⁺ ion. The lack of the symmetric OUO stretching band suggested an O-U-O core closer to linear than in UO₂(O₂)⁺. DFT calculations supported the end-on attachment of an O₂ bonded by van der Waals forces to U (Fig. 11e) in the quartet electronic state.

The enthalpies of formation of AnO₂(η²-O₂)₂ (An=Pu, Am, Cm) molecules (Fig. 11b) from AnO₂(η²-O₂) were calculated using two-component relativistic DFT to be −38, −44, and −19 kJ/mol, respectively. Other molecular data were not reported in [74].

Neutral dimers and trimers

In the solid phase, the actinides have generally high coordination numbers. In oxygen-containing inorganic and metal-organic compounds, Th^IVO_x polyhedra were found with 4 ≤ x ≤ 12 [81], while U^VIO_x polyhedra with 5 ≤ x ≤ 9 [82]. Np and Pu in various (III, IV, V, VI, VII) oxidation states form AnO_x coordination polyhedra with 6 ≤ x ≤ 12 [83, 84]. The coordination of the heavier Am, Cm, Bk, Cf, and Es atoms in crystal structures amounts to 6 ≤ x ≤ 9 [85, 86]. This high coordination occurs usually in the form of bridging An-O-An bonds.

Molecules with An-O-An bridging include the small neutral and cation-cation clusters. Such molecules have not been detected in the gaseous phase, yet the molecular parameters of various species were predicted by quantum chemical calculations. Their analysis at adequate theoretical levels revealed important information on the characteristics of An-O-An bonding.

U-oxide clusters

Yang et al. carried out a detailed survey of the potential energy surfaces of U₂O_n (n = 1–6) and U₃O_m (m = 1–9) clusters [33]. The calculations were performed with the VASP code developed for periodic systems [87], but with appropriate parameter settings able to model isolated molecular systems too. The paper lacked calculated Hessians or vibrational frequencies; therefore, the results of [33] should be treated with caution until confirmation of the minimum characters. Nevertheless, the geometries of the monomer UO, UO₂ and UO₃ molecules were reproduced well by the DFT calculations using the HSE06 functional. As the present review covers An^≥V oxidation states, only the most stable dimer U₂O_n (n = 5–6) and trimer U₃O_m (m = 7–9) structures are presented. They were reproduced by B3LYP calculations (using the Gaussian09 code) in the present work and the calculated vibrational frequencies confirmed their minimum characters.

The discussed low-energy structures do not have any U-U bonding (cf. Figs. 12, 13, 14, 15, and 16), the U atoms are connected by U-O-U bridges with U-O distances between 1.9 and 2.4 Å. Particularly interesting are the terminal oxo groups with U-O bonds of around 1.8 Å: they are mostly involved in quasilinear uranyl moieties where the bridging U-O components have bond distances increased to ca. 1.9 Å.

Fig. 12

Characteristic structures of An₂O₅ with symmetries a C₂ and b C_s. An atoms are depicted in cyan, O in red. Bond distances (Å) from SO-HSE06 calculations in [33] (U) and [88] (Pu, italics)

Fig. 13

Characteristic structures of An₂O₆ with symmetries a D_2h, C_2v; b C_2v; c C_2v; and d C_2h. An atoms are depicted in cyan, O in red. Bond distances (Å) in structures a, c, and d from SO-HSE06 calculations in [33] (U) and [88] (Pu, italics). Bond distances in structure b from SO-PBE0/A calculations in [49] (Am plain, Bk italics)

Fig. 14

Characteristic structures of a U₃O₇ (~C₃), b U₃O₈ (C₁), and c U₃O₉ (C_2v). U atoms are depicted in cyan, O in red. Bond distances (Å) from SO-HSE06 calculations in [33]

Fig. 15

Characteristic structures of An₂O₇ (An = Pu, Am) with C_s symmetry. An atoms are depicted in cyan, O in red. The bond distances of Pu₂O₇ (Å) are from SO-HSE06 calculations in [88]

Fig. 16

Characteristic structures of An₂O₈ with symmetries a, b C_2h and c C_2v. An atoms are depicted in cyan, O in red. The bond distances of Pu₂O₈ (Å) are from SO-HSE06 calculations in [88]

All the found most stable dimer structures have at least two U-O-U bridges [33]. The lowest-energy structure of U₂O₅ has C₂ symmetry with three U-O-U bridges and one terminal oxo group on each U atom (Fig. 12a). The double-bridged C_s structure with a terminal oxo group and a perpendicular uranyl moiety (Fig. 12b) proved to be a local minimum somewhat higher (by 28 kJ/mol) in energy.

The double-bridged lowest-energy structure of U₂O₆ [33] has D_2h symmetry and has two quasi-linear terminal uranyl moieties perpendicular to the bridging U-O-U plane (Fig. 13a). It can be derived from T-shaped UO₃ molecules by bonding through the equatorial oxygens. The monomeric equatorial U-O bond distance of ca. 1.85 Å was increased to ca. 2.1 Å in the bridge. Interesting (symmetric) low-energy minima are formed by turning the terminal uranyl moieties into the U-O-U plane (Fig. 13c, d) accompanied by a drastic decrease of the ca. 165° terminal uranyl bond angles to ca. 100°, the latter resembling those of the planar UO₄ species. These changes, however, had marginal effect on the U-O bond distances (cf. Fig. 13).

The lowest-energy U₃O_m (m = 7–9) structures have compact character in which the three U atoms are arranged as peaks of a triangle connected by three or four bridging oxygens [33]. In U₃O₇ (slightly deformed from C₃ symmetry), each U atom has one terminal oxo group (Fig. 14a), in the triple-bridged U₃O₉ with C_2v symmetry each U atom is involved in quasilinear O-U-O moieties (Fig. 14c), while in the four-bridged asymmetric U₃O₈, an intermediate situation with two oxo groups and one quasilinear terminal O-U-O moiety is formed (Fig. 14b). The terminal oxo groups in these structures can be considered as components of quasilinear uranyl moieties with lengthened bridging U-O distances. The above structures have several low-energy (2–100 kJ/mol) isomers (see [33]) with three or four U-O-U bridges.

The shown lowest-energy dimer and trimer structures had singlet spin multiplicities except for U₃O₇, which was triplet. (Note that the M values in the figure captions of [33] correspond to spin polarization instead of spin multiplicity.) Most low-lying states were singlets too, the triplets were characteristic only on the low-energy U₃O₇ and U₃O₈ species, which consist of formally mixed-valence U atoms. The calculated dissociation energies of the clusters were between 200 and 380 kJ/mol. Clusters with U/O ratios between 2 and 2.5 were computed to be the most stable, in agreement with the solid-phase experience that the UO_2+x hyperoxides are energetically stable. In the study [33], electronic energy levels were also determined using the orbital-resolved projected density of states model.

Dimers of Pu and Am oxides

Symmetric dimer structures of neutral Pu and Am oxides with compositions Pu₂O₆, Am₂O₆, Pu₂O₇, Am₂O₇, Pu₂O₈, and mixed ones PuAmO₆, PuAmO₇, and PuAmO₈ were first computed by Zaitsevskii et al. [40, 41]. The ground-state character was checked by swapping higher occupied and lower virtual orbitals, while the minimum character of the structures was confirmed by calculation of the Hessian matrices. However, no spin multiplicities and other details of the electronic structure were reported, which can make a comparison with other related studies difficult.

In all of these structures the actinide atoms are connected by two bridging oxygens. Computation of the AnO₃ and AnO₄ monomers in the same study [41] facilitated a straightforward assessment of the geometrical changes upon dimer formation. A common feature of most studied dimer structures was that the AnO₂ actinyl moieties of the monomers were retained, only slight changes in these O-An-O angles and An-O distances were observed.

The D_2h structures of Pu₂O₆ and Am₂O₆ agreed with the global minimum structure of U₂O₆ (Fig. 13a) by Yang et al. [33]. Upon dimer formation the equatorial Pu-O bond of the monomer was increased considerably (by ca. 0.2 Å) while the Am-O bond only marginally (by 0.01 Å). The replacement of the equatorial Pu-O formal double bond of PuO₃ by two Pu-O formal single bonds in the dimer confirmed that the hexavalent character of Pu is retained in Pu₂O₆. On the other hand, the Am^V oxidation state in the monomer increased to Am^VI in the dimer due to the two bridging Am-O single bonds attached to the americyl moieties. The structure of the heterooxide PuAmO₆ resembled those of Pu₂O₆ and Am₂O₆ with the D_2h symmetry lowered to C_2v and slight changes observed in the geometrical parameters. The calculated dissociation enthalpy was somewhat larger than the average of the respective homodimers.

In a subsequent study Zaitsevskii probed two isomer structures for Pu₂O₆, Am₂O₆, and Bk₂O₆ [49]. While for Pu₂O₆ the calculated enthalpy of dissociation to monomers supported the global minimum character of the above shown D_2h isomer [40, 41], for Am₂O₆ and Bk₂O₆, a new C_2v structure (Fig. 13b) was found to be more stable. This isomer has an η²-O₂ peroxide moiety between the actinyl groups, while the geometrical parameters resemble in character those in the oxoperoxide monomers. Accordingly, the oxidation states in this dimer structure, Am^V and Bk^V, agreed with those in their T-shaped monomers.

Recently, Zhang et al. [88] performed a detailed survey of the potential energy surfaces of Pu₂O_x (x = 1–8) molecules using the same computational techniques like in their earlier U₂O_x (x = 1–6) paper [33], vide supra. Beyond several low-energy structures and their energies, favorable fragmentation channels, Bader atomic charges and orbital resolved projected densities of states were reported. However, lacking appropriate information, the minimum characters of the optimized structures are unclear, similarly the characters of the obtained electronic states. The latter issue is rather critical in the case of Pu-containing compounds, because softwares can converge from the initial guesses to low-lying excited electronic states, which can have significantly different structures from those of the ground states. In order to verify the lowest-energy structures from [88] for this review, they were reproduced in this work by B3LYP calculations (using the Gaussian 09 code). Application of the keyword Stable supported the ground-state character of the structures discussed in this review, while the frequency analyses confirmed the minimum characters on the potential energy surfaces (except for one structure, vide supra). However, a few differences were obtained in the spin multiplicities: while the Pu₂O₆, Pu₂O₇, Pu₂O₈ ground states in [88] were characterized as singlets (with the M values in the figure captions taken as spin polarization), the present B3LYP calculations predicted triplet ground states for Pu₂O₆ and Pu₂O₈.

The ground-state structure of Pu₂O₅ [88] agreed in character with that of the low-energy U₂O₅ isomer in Fig. 12b from [33]. A triple-bridged structure, most stable for U₂O₅ (cf. Fig. 12a), was not found for Pu₂O₅. Instead, several high-energy ones were reported which contain an O₂ moiety.

For Pu₂O₆, the HSE06 calculations of Zhang et al. [88] resulted in a different energy ordering with respect to the results in [40, 41]. The lowest-energy Pu₂O₆ structure was the C_2v isomer shown in Fig. 13c, while the D_2h one (Fig. 13a, most stable in [40, 41]) proved to be slightly higher (by 13.5 kJ/mol) in energy. The discrepancy may be due to the different theoretical levels and the case should be clarified with more sophisticated calculations.

For Pu₂O₇, Zhang et al. [88] obtained a C_s ground-state structure with two parallel actinyl moieties connected by two bridging oxygens, where one oxygen is part of a superoxo moiety (Fig. 15a). A characteristic local minimum (Fig. 15b, higher in energy by 57 kJ/mol [88]) is composed of AnO₄ + AnO₃ moieties by bonding of two AnO₄ oxygens to An in the equatorial plane of AnO₃. Zaitsevskii et al. considered only the latter local minimum structure for both Pu₂O₇ [40, 41], Am₂O₇ and the mixed PuAmO₇ [41]. On the basis of the high energy of the Pu₂O₇ local minimum (vide supra), this structure may not correspond to the ground-state global minimum form of Am₂O₇ and PuAmO₇ either. Zaitsevskii et al. found Pu₂O₇ to have a remarkable stability [40, 41], that of Am₂O₇ was somewhat lower [41].

For Pu₂O₈, the HSE06 calculations predicted a double-bridged structure close to C_2h symmetry consisting of two PuO₂(O₂) moieties (Fig. 16a) [88] as most stable. The bonding is analogous to the one observed in the Pu₂O₇ ground state, where the bridging oxygen is part of a superoxo moiety. The isomer consisting of two facing PuO₄ moieties (Fig. 16b) studied in [41] was found by Zhang et al. [88] considerably higher in energy (126 kJ/mol). In the latter study, a C_2v structure with perpendicular PuO₄ arrangement (Fig. 16c) [88] was predicted to be quasi-degenerate with the ground-state structure. According to frequency calculations in the present study, this structure is a saddle-point on the potential energy surface.

Calculations on Am₂O₈ could not be found in the literature. For the PuAmO₈ heterodimer a structure with facing PuO₄ and AmO₄ moieties (Fig. 16b) was reported, pointing out its very low stability [41]. The structure in Fig. 16a was not probed for PuAmO₈. In addition to the structure and bonding, the thermochemistry of the formation of the presented dimers from the monomer oxides as well as from each other was evaluated in [41].

Dimers from CCIs

Cation–cation interactions (CCIs) can appear between highly polarized ionic molecules, hence between actinyl cations and their derivatives too. Although the oxo ligand is usually seen as chemically inert, the negatively charged oxygens can interact with the metal cation center of another actinyl moiety. CCIs between AnO₂ⁿ⁺ ions (mainly UO₂⁺ and NpO₂⁺) have been widely observed in solutions [89,90,91,92,93,94,95] and in inorganic solid compounds [96,97,98,99]. The sizes of CCI oligomers reach usually from dimers to tetramers in solution [100] while in the solid state up to three-dimensional frameworks [98]. The interaction strongly affects the structural and electronic properties and can well be recognized in the UV-Vis and IR spectra.

Quantum chemical modelling of CCIs in the gaseous and aqueous phases was restricted to the dications. They appear in two isomer forms, shown in Fig. 17. Selected geometrical parameters are compiled in Table 4.

Fig. 17

The a T- (C_2v) and b diamond-shaped (C_2h) structures of (AnO₂)₂ⁿ⁺ CCI dimers. An atoms are depicted in cyan, O in red

Table 4 Computed geometrical parameters of ground-state T- and diamond (D)-shaped CCI dimers

An early quasirelativistic calculation of the (UO₂)₂²⁺ dimer by Pyykkö and Zhao [55] predicted a week interaction between U and O of two facing cations with a distance of 2.386 Å (in good agreement with the sum of covalent single bond radii of U and O, 2.33 Å [101]). The probed diamond-shaped structure (Fig. 17b) was subjected to a partial optimization (distances and angles between two constrained UO₂⁺ monomers) only.

Isolated and solvated CCIs between various actinyl cations were modelled by DFT calculations using the COSMO solvation model [102]. Because in solution only T-shaped structures were observed [96], the geometry optimizations were restricted to this C_2v isomer (Fig. 17a). Beside the electrostatic attraction between the negatively charged oxygen and the partially positive An, a contribution to the bonding from molecular orbital interactions (in the form of donation/backdonation) was also observed. The formation of CCI complexes in the gaseous phase proved to be endothermic in terms of absolute energies at 0 K. Solvation favored the complexes (NpO₂)₂²⁺(aq) and (NpO₂)₂³⁺(aq) over the solvated monocations NpO₂⁺(aq) and UO₂²⁺(aq). For (UO₂)₂⁴⁺, the T-shaped structure could not be obtained as a minimum in the gas-phase calculations, explained by the large intrinsic electrostatic repulsion between the units. The large solvation effects could though stabilize the (UO₂)₂⁴⁺ dimer, but its formation was still endothermic. Explicit consideration of the first solvation shell at a lower DFT level resulted in a qualitative agreement with the COSMO approach.

The CCI dimers formed by uranyl(VI) and uranyl(V) were investigated by Tecmer et al. by scalar relativistic DFT calculations using the COSMO solvation model [103]. The reported relative stabilities obtained by most functionals indicated the significant preference of the T-shaped structures (Fig. 17a) for the most stable spin multiplicities: the triplet (UO₂)₂²⁺, doublet (UO₂)₂³⁺, and singlet (UO₂)₂⁴⁺. The structural characteristics were analyzed on the basis of BP86 calculations. The study confirmed the characteristic significant elongation of the donor UO bonds in both structures upon CCI. The general trend observed for the studied species was the increase of the inter-unit U-O bond with increasing charge. According to the calculated electronic transitions, the spectral characteristics of the UO₂²⁺ and UO₂⁺ building blocks would largely preserved for the CCI dimers, facilitating the identification of the oxidation state of the U atom in solutions containing CCI clusters.

Compounds with diamond-shaped (Fig. 17b) neptunyl CCI dimer motifs are very rare in the nature. Examples found in the solid phase include Na₄[NpO₂)₂C₁₂O₁₂]·8H₂O [104] and K[(NpO₂)(OH)₂]·2H₂O, the latter being the first 2D neptunyl structure stabilized by side-on CCI [105]. In the latter paper, Gagliardi et al. investigated the electronic structure of various diamond-shaped neptunyl CCI dimer models including also the simple (NpO₂)₂²⁺ ion using DFT and multiconfigurational calculations. The neptunyl moieties proved to have 5f² configuration and the SF-CASPT2 calculations predicted degenerate singlet, triplet and quintet states for the dimer. From them, in the SO ground state the triplet had the largest contribution. The SO ground state of (NpO₂)₂²⁺ was preserved during the conversion to the T-shaped (Fig. 17a) isomer, the latter lying higher in energy by a few kcal/mol. The topological analysis of the electron densities revealed two bond critical points (BCPs) between Np and O of the other moiety. The characters of the BCPs pointed to ionic interactions with some covalent (dative) character. No Np-Np bond was found. The contribution of Lewis acid/base interaction in the CCI bond was confirmed by the extended transition state (ETS) method combined with natural orbitals for chemical valence (NOCV) theory, revealing substantial donation from the occupied O(2p) orbitals to the empty 6d orbitals of Np. OH ligands tend to strengthen this donation compared to H₂O and organic ligands.

A detailed DFT and multi-reference study of neptunyl dications was performed recently by Boguslawski et al. [106]. The study included both the T- (Fig. 17a) and diamond-shaped (Fig. 17b) forms for the relevant spin multiplicities of (NpO₂)₂ⁿ⁺ (n = 2–4). The electronic spectra were predicted by SO-CASPT2 calculations.

For (NpO₂)₂²⁺, both structures were found as minima on the potential energy surface; for (NpO₂)₂³⁺, only the diamond-shaped form and only in solution, while none for (NpO₂)₂⁴⁺ similarly to (UO₂)₂⁴⁺ [96] (vide supra). The clusters were studied both in the gas and aqueous phases, in the latter phase using the COSMO solvation model as well as explicit first solvation shells (9H₂O for the T- and 8H₂O for the diamond-shaped forms). The two solvation models provided very similar geometries. The CCI bond distances were found to be considerably shorter in solution than in the isolated molecule.

The geometries of the diamond-shaped species differed slightly due to the different molecular charge (+3 vs +2). In agreement with the observation on uranyl CCIs [103] (vide supra), the increase of charge resulted in slight contraction of the intra-unit bond distances and slight increase of the inter-unit Np-O ones. Accordingly, the two Np atoms get slightly away from each other.

The SF-CASPT2 ground state of T-shaped (NpO₂)₂²⁺ proved to be the ⁵B₁ state while several low-lying states were obtained. For diamond-shaped (NpO₂)₂²⁺, similarly to the results in [105] (vide supra), the SF-CASPT2 calculations predicted a quasi-degeneracy of the lowest-lying quintet and triplet states. However, in disagreement with the reported preference of triplet in the SO ground state in [105], the SO-CASPT2 calculations of Łachmańska et al. predicted a quintet character of the SO ground state of both the isolated dimer and the (NpO₂)₂²⁺·8H₂O form [106]. For (NpO₂)₂³⁺ the quasi-degeneracy of two quartet states was obtained.

The limitations of the computational models for such difficult (to surroundings sensitive [107]) solvated chemical systems were shown by the computed positive binding energies at most theoretical levels and by the relative stabilities of the T- and diamond-shaped isomers contradicting the experimental observations. In contrast to the exclusively observed T-shaped structure in solution, the computed relaxed binding energies of (NpO₂)₂²⁺ with respect to the monomers predicted the preference of diamond-shaped isomers at all applied levels [105, 106]. Only a simplified model with four H₂O molecules in the first solvation shell predicted the preference of the T-shaped (NpO₂)₂²⁺ using the PBE0 and B3LYP hybrid functionals. This failure of the calculations was attributed to the lack of proper solvation modelling and an insufficient description of the active space and dynamic correlation in the multi-reference calculations.

Very recently, Feng et al. carried out a systematic study of isolated CCI homo- and heterodimers constructed from the monomers UO₂²⁺, UO₂⁺, NpO₂²⁺, NpO₂⁺, PuO₂⁺, and AmO₂⁺ [108]. The applied CCSD(T) level can be expected to give very accurate results for systems dominated by a single electron configuration. The T-shaped dimers satisfied this requirement, but most considered diamond-shaped dimers were too multireference to reliably use the CCSD(T) method. From the latter isomers, only (UO₂)₂²⁺ could be studied, and it proved to be thermodynamically more stable than the T-shaped (UO₂)₂²⁺ isomer by 41 kJ/mol.

Similarly to earlier results [105, 106], the CCI dimer ions were determined to be metastable, because due to the Coulomb repulsion their dissociations to the monomers were exothermic [108]. From the T-shaped dimers the largest stability was predicted for the ones when the acceptor had a +2 charge (An^VI actinyl) and the donor had a +1 charge (An^V actinyl). Dimers with both donor and acceptor An^VI were found to be unstable. The stability of CCI complexes decreased by the donor as UO₂⁺ > NpO₂⁺ > PuO₂⁺ > AmO₂⁺, and similarly by the acceptor as UO₂²⁺ > NpO₂²⁺ > PuO₂²⁺ > AmO₂²⁺. A natural bond orbital analysis confirmed that the stability of the CCI complexes was largely determined by charge transfer from the σ-type O lone pair of the donor to the empty An valence orbitals of the acceptor.

Large clusters observed in the gaseous phase

Large charged U oxide clusters were identified by their mass spectra, but hitherto no information on their molecular properties is available.

The first report was published on [(UO₂)₄O₃]⁻, [(UO₂)₄O₄]⁻, and [(UO₂)₄O₅]⁻ species obtained by electrospray ionization of uranyl citrate solutions followed by ion-molecule reactions in a 3D ion trap and detection by FT-ICR mass analyzer [109].

A later study of Marçalo et al. using laser ablation of solid UO₃ or (NH₄)₂U₂O₇ resulted in numerous uranium oxide anions with compositions ranging up to [U₁₄O₃₅]⁻as detected by FT-ICR mass spectrometry [36]. The cluster series [U_xO_3x]⁻ up to x = 6 could unambiguously be identified. For x > 5, a gradual enhancement of compositions [U_xO_3x-y]⁻ was observed converging towards [U_xO_2.5x]⁻ in the largest clusters. Collision-induced dissociation (CID) experiments using Ar as collision gas resulted in the loss of neutral UO₃ from [U₃O₉]⁻ and [U₄O₁₂]⁻, indicating that UO₃ constitutes the building block in these structures. The laser ablation of solid UO₃ produced also the cationic uranium oxide clusters [U_xO_n]⁺ with x = 2–9 and n = 3–24. With increasing cluster size the composition converged towards [U_xO_2.5x]⁺.

Conclusions

In the past decade, there has been a considerable progress in the field of high-valent actinides by detecting and characterizing their oxides in the gaseous phase. Sophisticated experimental methods like laser ablation, photoelectron spectroscopy, laser-induced electron detachment, electrospray ionization, 3D ion trap, and Fourier transform ion cyclotron resonance mass spectrometry facilitated the synthesis, observation, and analysis of some properties of such molecules. At the same time, advanced quantum chemical techniques delivered significant information on the structure, bonding, stability, and spectroscopic properties.

One of the main questions is the oxidation state, which was probed in oxides up to AnO₆ and in clusters containing up to AnO₄ moieties. Beyond the neutral oxide molecules the studies covered ionic species too, partly because they are better suited for investigations by experiment (by methods coupled with mass spectrometry) and partly because the charge could stabilize structures with higher oxidation state and result in different molecular properties. The highest stable oxidation state found up to know is VII in NpO₄⁻ and PuO₄⁻. The lighter actinides are characterized from this point of view by Th^IV, Pa^V, and U^VI, while the heavier ones by Am^V and from Cm as An^III, in agreement with the considerable stabilization of the 5f subshell. An exception in the second half of the row is No, where the advantageous f¹⁴ configuration leads to No^II.

Small molecular clusters are interesting because they appear in solution and are the building blocks of solid structures. The new theoretical studies contributed to the understanding of the structure and An-O-An bonding in these species, and uncovered the role of solvent for their stabilization. The largest clusters detected in the gaseous phase were the [U₉O₂₄]⁺ cations. The modelling of such large molecules with reliable quantum chemical methods can be one of the tasks of future research.