Molecular oxides of high-valent actinides

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 AnOx (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 req u i r e m e n t s i n h a n d l i n g r a d i o a c t i v e m a t e r i a l s . 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 [AnO 2 ] + and [AnO 2 ] 2+ 2. Neutral and ionic AnO 3 3. Neutral and ionic AnO 4 4. Neutral and ionic AnO 5 5. Neutral and ionic AnO 6 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 AnO 2 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 [AnO 2 ] + and [AnO 2 ] 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 AnO 2 + 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 η 2 -O 2 . The high stability of [Cm(η 2 -O 2 )] + is in agreement with the 5f 7 configuration of Cm III . In the triangular structures Cm, Bk, Cf, and Lr appeared as An III peroxides with a formal charge distribution of [An 3+ (O 2 2− )] + while Es, Fm, Md, and No as An II superoxides with a formal charge distribution of [An 2+ (O 2 − )] + . 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 LrO 2 + species is non-actinyl and is bent with a bond angle of 107°. Dau et al. reported in this paper also the first preparation and observation of BkO 2 + and CfO 2 + 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 5f 7 configuration. Somewhat unexpected was, however, the comparable stability of Bk V . The increasing stability of the [An(η 2 -O 2 )] + 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 AnO 2 2+ 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.
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(η 2 -O 2 )] 2+ superoxide C 2v structure. The other six actinides prefer oxidation state II in [An(η 1 -O 2 )] 2+ containing a physisorbed O 2 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 f 14 [17] and for the [O=An=O] 2+ structures from B3LYP [18] calculations. The experimental dissociation energy values for BkO 2 + and CfO 2 + could be determined only as lower limits (indicated by the arrows)

Neutral and ionic AnO 3
The three characteristic isomers of AnO 3 are presented in Fig.  4, while selected computed geometrical data are compared in Table 1. was studied by photoelectron spectroscopy in combination with DFT and CCSD(T) calculations [19]. Photoinduced electron loss of ThO 3 − resulted in neutral ThO 3 . 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 ThO 3 can be derived by a side-on (η 2 ) attachment of ThO to an O 2 molecule (Fig. 4c). The trioxide Tshaped form with C 2v symmetry ( Fig. 4a) was calculated to be higher in energy by 51 kJ/mol. In contrast, the ground-state ThO 3 − molecule proved to have a T-shaped structure, and the η 2 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 ThO 3 Fig. 3 AnO 2 2+ relative energies from spin-orbit-free CCSD(T) calculations [18]  Bond distances are given in angstroms, bond angles in degrees a Structures from Fig. 4 b The abbreviations of basis sets A, B, and C mean relativistic small-core pseudopotential, all-electron, and relativistic large-core pseudopotential, respectively c O 1 AnO 2 bond angle in the peroxide and superoxide structures UO 3 and UO 3 − The neutral UO 3 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 U 16 O 3 . Experiments using mixture of 16 O and 18 O 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-2electron σ and six 2-center-2-electron π U-O bonds [32]. Already early quantum chemical calculations on UO 3 using Hartree-Fock (HF) theory and relativistic large-core pseudopotentials [29] predicted the 1 A 1 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 UO 3 were investigated by multireference CASPT2 calculations [34] confirming the 1 A 1 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 UO 3 − 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 UO 3 and (NH 4 ) 2 U 2 O 7 upon laser ablation [36]. In recent laser vaporization experiments of Su et al., UO 3 − 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 UO 3 . Combined with Franck-Condon simulations, the electron affinity of UO 3 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 UO 3 (850 ± 30 cm −1 ). Five low-lying excited states with geometries similar to that of UO 3 − were observed and vertical detachment energies between 3.2 and 6.3 eV were determined. Regarding neutral UO 3 , 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 UO 3 − anion include the DFT one by Zaitsevskii for evaluation of the adiabatic electron affinity of UO 3 [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 O 1 -U-O 1 bond angle (cf. Table 1). The geometry features were confirmed by the DFT calculations of Su et al. [32]. The electronic structure of UO 3 − is similar to that of UO 3 , the main difference being the single occupation of a 5f-based B 2 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 B 2 MO [32].

NpO 3
The only information on the geometry and electronic structure of NpO 3 comes from a CASPT2 study of the ground and lowlying excited electronic states [34]. The calculations resulted in a C 2v ground-state geometry (Fig. 4a, Table 1 A detection of the PuO 3 molecule was reported from a mass spectrometric analysis of the sublimation products of solid PuO 2 [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 PuO 3 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 1 A 1g state of PuO 3 [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 7 B 1 ground electronic state with an Y-shaped C 2v structure (Fig. 4a) [39]. Two-component relativistic DFT calculations on triplet PuO 3 predicted a T-shaped structure [40,41] with geometrical parameters in good agreement with those reported by Straka et al. [38] for the 1 A 1g state (cf. Table 1). The 3 B 2 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 PuO 3 (most complex from the five AnO 3 , where An = U-Cm [34]) with several low-lying excited electronic states. An extensive mixing was shown between the SF ground 3 B 2 and first excited 3 A 2 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 PuO 3 + [44,45] Gao et al. reported a 6 B 2 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 PuO 3 molecule (vide supra), an independent confirmation of the data on PuO 3 + would be desirable. DFT results on PuO 3 − 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.

AmO 3
The geometry and bond dissociation energy of AmO 3 were predicted by two-component relativistic DFT calculations without providing details on the electronic structure [41]. CASPT2 calculations predicted the SF ground state of Tshaped ( Fig. 4a) AmO 3 being a sextet 6 B 2 , 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).

CmO 3
The CmO 3 molecule was indirectly inferred from a thermochromatographic measurement [47]. No molecular data are available for CmO 3 from experiment. Two-component relativistic DFT calculations [48] provided the first molecular data on CmO 3 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 CmO 3 was investigated by CASPT2 calculations. The lowest-energy SF state showed a 7 A 2 character, this state forming nearly exclusively the lowest-energy SO state [34]. Compared with other AnO 3 molecules (An = U-Am), the neighboring (quintet and nonet) spin multiplicities appeared here at the lowest energies: the quintet 5 B 2 was the major component in the first SO excited state at 28.5 kJ/mol, while the nonet 9 B 1 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].

BkO 3 , CfO 3
These trioxides were investigated by Zaitsevskii by relativistic SO-PBE0 calculations [49] reporting the structures and dissociation enthalpies. For BkO 3 the T-shaped structure (Fig. 4a), for CfO 3 the oxosuperoxide isomer ( Fig. 4c) was predicted to be the most stable.

Comparison of some properties of AnO 3 molecules
This comparative analysis is facilitated by systematic calculations on AnO 3 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 PuO 3 -CfO 3 using relativistic SO-PBE0 calculations [49]. The oxoperoxide isomer (Fig. 4b) has a formal charge distribution of (AnO) 2+ (O 2 ) 2− in agreement with the oxidation state An IV . The oxosuperoxide isomer ( Fig. 4c) with one unpaired electron localized on the O 2 fragment has a formal charge distribution of (AnO) + (O 2 ) − , corresponding to oxidation state An III .
The relative stabilities were assessed by the ΔH o 0 enthalpies of dissociation to AnO 2 + ½O 2 . Figure 5 shows the variation of the ΔH o 0 enthalpies from Pu to Cf. The oxoperoxide form had the highest energy from the three isomers and, due to the positive ΔH o 0 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.
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 V O 3 with respect to its neighbors Cm V O 3 and Cf V O 3 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 5f 7 ground state of the Cf 5+ ion), which can destabilize the T-shaped structure.
Trends in the geometrical parameters of T-shaped AnO 3 (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-O 1 bond distances, the increase of the An-O 2 bond distances, and the increase of the O 1 AnO 1 bond angles from U to Am (in agreement with CASPT2 data on UO 3 -CmO 3 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-O 2 bond distance (around 1.84 Å in the lighter U, Np, and Pu trioxides and around 2.1 Å in the heavier AnO 3 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-O 2 bond and the formal charge of O 2 a pentavalent character of Am and Cm was suggested [41,49] in these trioxides. The considerably longer Am-O 2 bond with respect to the analogous Pu-O 2 one is in agreement with the by ca. 80 kJ/mol smaller bond dissociation energy of the Am-O 2 bond [41], supporting its considerably weaker character.
The above noted long An-O 2 bonds in heavier AnO 3 (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 VI O 3 and Am V O 3 by ca. 1 e and the parallel increase of the unpaired 5f population by ca. 2 e (Fig. 7).
A detailed analysis of the valence molecular orbitals in [34] showed a gradually increasing number of unpaired nonbonding 5f electrons from UO 3 to PuO 3 (from 0 to 2, respectively). In contrast, in T-shaped AmO 3 and CmO 3 the lowestenergy states were composed of four and five non-bonding unpaired 5f electrons, respectively, and a singly populated B 2 bonding π orbital between the An and O 2 atoms. This replaced the analogous, but doubly occupied, B 2 π orbital in the U/Np/Pu trioxides, explaining the longer Am-O 2 and Cm-O 2 bonds.

Neutral and anionic AnO 4
Gas-phase experimental reports were published for neutral UO 4   5f unpaired 5f pair Fig. 7 Effective populations of the 5f atomic subshells. Data from [50] interesting isomers as depicted in Fig. 8. From them, the η 2 -O 2 -coordinated structure in Fig. 8a  . From the various considered isomers, the lowest-energy one proved to be the structure consisting of a bent protactinyl and an η 2 -coordinated O 2 (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. UO 4 was also produced in laser-induced electron detachment measurements on UO 4 − by Su et al. [32] (vide infra). The experiments resulted in the electron affinity of 3.60 ± 0.03 eV for UO 4 . The U-O symmetric stretching frequency of UO 4 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 1 A 1 ground electronic state of UO 4 having an η 2 -O 2 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 O 2 2− character of the η 2 -ligand, contradicting the previously suggested [27] superoxo nature of the ground electronic state. A superoxo UO 4 structure was obtained for a high-lying excited electronic state [32].
Anionic UO 4 − 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 UO 3 [53,54]. In this structure, the radical electron is delocalized between the two "equatorial" oxygen atoms resulting in slightly larger U-O 2 vs U-O 1 bond distances (cf.  Table 2. From them, the C 2 (distorted S 4 ) 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 UO 4 2− (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 UO 4 2− , NpO 4 − , and PuO 4 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 UO 4 2− and the preference of U VI over U III oxide. The D 4h and C 2v isomers proved to be low-energy structures. ) 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 O 2 (π*) orbital in the equatorial plane, was favored by 46 kJ/mol over the (UO 2 + )(η 1 -O 2 ) C s isomer (Fig. 8f). The calculated enthalpy and Gibbs-free energy for O 2 -addition to UO 2 + were − 52 and − 20 kJ/mol, respectively [61]. UO 4 + 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 O 2 [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 UO 4 + Ar 2 complexes with an IR-   [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 NpO 4 − 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 NpO 4 − (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 5f 0 configuration, i.e., to Np VII .  [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) (Fig. 8f) [66,67] on the basis of gas thermochromatographic measurements of volatile oxidation products of Pu. The suggested composition (Pu VIII O 4 ) of the detected species with unusually low deposition temperature was based on the similar deposition zones of well-known octavalent transition metal oxides, OsO 4 and RuO 4 , supposing an analogous tetrahedral structure [68] for PuO 4 . However, the formation of PuO 4 could not be confirmed in a similar independent experiment [69]. The detection of Pu VIII O 4 was questioned also by Zaitsevskii et al. [41] who obtained a non-tetrahedral structure for PuO 4 by DFT calculations (vide infra).
The formation of PuO 4 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 PuO 4 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 PuO 4 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 PuO 2 and PuO 3 . Accordingly, this singlet planar PuO 4 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 PuO 4 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 PuO 4 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.
Huang et al. performed DFT, MP2, CCSD(T), and SO-CASPT2 calculations on possible structural isomers of PuO 4 providing details also on the electronic structure and spectroscopic properties [57]. From the two minima found on the potential energy surface, the quintet PuO 2 (O 2 ) (Fig. 8a) was found to be superior to singlet PuO 4 (Fig. 8e)  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 UO 4 2− , NpO 4 − , and PuO 4 molecules: the singlet T d isomer, being the ground-state structure of UO 4 2− , became a gradually destabilized transition state for NpO 4 − and PuO 4 . The singlet D 4h isomer, being the ground-state structure of NpO 4 − , was found to be a low-energy isomer for UO 4 2− and PuO 4 . The stability of the quintet C 2v isomer increased gradually from UO 4 2− towards PuO 4 , corresponding to the ground-state structure of the latter molecule. These results further supported the preference of Pu V over Pu VIII oxide. Zaitsevskii (Fig. 8a, e, g), corresponding to this stability order. The reported comparison with the analogous AmO 4 and CmO 4 isomers is presented below in the "AmO 4 and CmO 4 " section.
The D 4h and C 2v isomers of PuO 4 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 n F 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 PuF 8 to PuF 6 + F 2 was found to be considerably exothermic (ΔE = −377 kJ/mol without thermal corrections). A subsequent comparative study on the highest oxidation states in selected MO 4 molecules (M = Fe, Ru, Os, Hs, Sm, Pu) [76] revealed the inferiority of f-elements to heavy d-elements. The Ru VIII O 4 , Os VIII O 4 , and Hs VIII O 4 oxides are stabilized by closed-shell electronic structures having empty metal d 0 valence shells bonded to O 2− ligands. In contrast, the light d-and the f-elements prefer partial occupation of their valance shells. Accordingly, Pu prefers the 5f 3 configuration and thus the superoxide (Pu V O 2 + )(η 2 -O 2 − ) 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 PuO 4 was estimated in the PBE0 study of PuO 4 − by Gibson et al. [46], vide infra. In the Supporting Information of [46], the relative energies and structures of six (singlet, triplet, quintet) PuO 4 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 PuO 4 − was reported recently [46]. It was synthesized by the gas-phase reaction of PuO 2 (C 2 O 4 ) − with O 2 in an ion trap, detected subsequently by mass spectrometry. The slow rate of water addition suggested the high stability of Pu VII O 4 − 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 PuO 4 − (Fig. 8e) 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.

AmO 4 and CmO 4
Experimental information on AmO 4 is not available hitherto. A n a s s u m e d d e t e c t i o n o f C m V I I I O 4 i n a g a s thermochromatographic study was reported in [77]. Because this report was based on an analogous experience with PuO 4 , the reliability was strongly questioned [72]. The first theoretical study of AmO 4 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, AmO 4 was found to be thermodynamically unstable and should spontaneously decay to AmO 2 and molecular O 2 . From the studied two minimum structures, AmO 2 (η 2 -O 2 ) superoxide and planar AmO 4 (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 PuO 4 , AmO 4 , and CmO 4 isomers [74]. Three isomers were considered: the planar tetroxide AnO 4 (Fig. 8e) 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 AnO 4 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 CmO 4 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 Cm 3+ (η 2 -O 2 2− )(η 2 -O 2 − ) 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 Pu 4+ (η 2 -O 2 2− ) 2 structure with C 2v symmetry. The study supported the gradually decreasing stabilities and An oxidation states for the three actinides.
Zaitsevskii and Schwarz investigated also the reaction of AnO 2 (O 2 ) (An=Pu, Am, Cm) molecules with O 2 and concluded that they can exothermally bind a second O 2 [74]. For more details of the AnO 2 (O 2 ) 2 molecules, see the "Neutral and ionic AnO 6 " section. . The structure was a square-based pyramid with close to C 2 symmetry (Fig.  10d). The data (computed energies, structures, vibrational frequencies) of the triplet and singlet states were given in the Supporting Information without discussion. UO 5 − was prepared by reaction of laser vaporized uranium disk and O 2 in He carrier gas and investigated using photoelectron spectroscopy and quantum chemical calculations [32]. In electron detachment experiments on UO 5 − , the neutral UO 5 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 UO 3 < UO 4 < UO 5 row in good agreement with spin-orbit-coupled CCSD(T) energy calculations.
The structures of UO 5 species were elucidated by B3LYP calculations [32]. Neutral UO 5 can be derived from UO 3 by η 1 -or η 2 -coordination of an O 2 molecule in the equatorial plane. The η 1 U-O 3 bond in the triplet global minimum structure (Fig. 10a)  ) isomer with η 2 -coordinated O 2 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 UO 5 − predicted similar structures to those of the neutral UO 5 molecule [32]. However, the CCSD(T) energy order of the η 1 -and η 2 -isomers (Fig. 10a, b) was interchanged, where the η 1 -O 2 isomer was computed to be higher in energy by 71 kJ/mol. In the 2 A″ ground state, the unpaired electron occupies a molecular orbital of O(2p) character in the η 2 -O 2 moiety. Su et al. performed also a comparative bonding analysis of several UO x (x = 3-6) isomers [32]. In UO 3 and in the η 2 -and η 1 -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 UO 3 − 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 O 2 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 UO 5 − in the Supplementary Information of [21] without dis-cussion in the text. The optimized structure of both spin states was a square-based pyramid (Fig. 10d), differing from the η 1and η 2 -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 PuO 5 − 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 UO 5− 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-O 2 bond in the sextet, indicating a reduction of the Pu oxidation state.

Neutral and ionic AnO 6
Hexacoordinated U is a frequent structural motif in solid U VI oxides, formally being UO 6 6− . The molecular hexakis-oxo UO 6 6− 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 UO 6 6− 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 UO 4 2− and, particularly, to UO 2 2+ 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.
The octahedral isomer of neutral UO 6 ( Fig. 11a)   Bond distances are given in angstroms, bond angles in degrees. For the definition of atoms, see Fig. 10 a Basis set A means relativistic small-core pseudopotential.
(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 1 A 1g octahedral isomer lying very high (ca. 540 kJ/mol) in energy compared to the 3 B 2 uranyl peroxide form, U VI O 2 (η 2 -O 2 ) 2 (Fig. 11b) [79]. Similar peroxide motifs exist in several uranium minerals [80]. Other high-energy isomers include the species 3 B 3u UO 4 (η 2 -O 2 ) and 1 A 1 U(η 2 -O 2 ) 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 O 2 were assigned to UO 2 (O 2 ) x species by Zhou et al. [27]. UO 6 + ions were produced in a supersonic molecular beam by laser vaporization of uranium in Ar containing a few percent of O 2 [62]. In the obtained UO 6 + Ar 2 gas-phase complex, due to the very weak effect of Ar atoms, the molecular parameters approximate well those of the isolated UO 6 + ion. The The enthalpies of formation of AnO 2 (η 2 -O 2 ) 2 (An=Pu, Am, Cm) molecules (Fig. 11b) from AnO 2 (η 2 -O 2 ) 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 metalorganic compounds, Th IV O x polyhedra were found with 4 ≤ x ≤ 12 [81], while U VI O 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 U 2 O n (n = 1-6) and U 3 O 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    [79] (a-d, UO 6 ) and [62] (e, UO 6 + ) obtained by SO-PW91/B and PBE/A calculations, respectively 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, UO 2 and UO 3 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 U 2 O n (n = 5-6) and trimer U 3 O 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.
All the found most stable dimer structures have at least two U-O-U bridges [33]. The lowest-energy structure of U 2 O 5 has C 2 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 U 2 O 6 [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 UO 3 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 UO 4 species. These changes, however, had marginal effect on the U-O bond distances (cf. Fig. 13).
The lowest-energy U 3 O 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 U 3 O 7 (slightly deformed from C 3 symmetry), each U atom has one terminal oxo group (Fig. 14a), in the triple-bridged U 3 O 9 with C 2v symmetry each U atom is involved in quasilinear O-U-O moieties (Fig. 14c), while in the four-bridged asymmetric U 3 O 8 , 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 a b  13 Characteristic structures of An 2 O 6 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) 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 U 3 O 7 , 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 U 3 O 7 and U 3 O 8 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 solidphase 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.    [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 AnO 3 and AnO 4 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 AnO 2 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 Pu 2 O 6 and Am 2 O 6 agreed with the global minimum structure of U 2 O 6 ( 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 PuO 3 by two Pu-O formal single bonds in the dimer confirmed that the hexavalent character of Pu is retained in Pu 2 O 6 . 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 PuAmO 6 resembled those of Pu 2 O 6 and Am 2 O 6 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 Pu 2 O 6 , Am 2 O 6 , and Bk 2 O 6 [49]. While for Pu 2 O 6 the calculated enthalpy of dissociation to monomers supported the global minimum character of the above shown D 2h isomer [40,41], for Am 2 O 6 and Bk 2 O 6 , a new C 2v structure (Fig. 13b) was found to be more stable. This isomer has an η 2 -O 2 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 Pu 2 O x (x = 1-8) molecules using the same computational techniques like in their earlier U 2 O x (x = 1-6) paper [33], vide supra. Beyond several lowenergy 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 Pu 2 O 6 , Pu 2 O 7 , Pu 2 O 8 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 Pu 2 O 6 and Pu 2 O 8 .
The ground-state structure of Pu 2 O 5 [88] agreed in character with that of the low-energy U 2 O 5 isomer in Fig. 12b from [33]. A triple-bridged structure, most stable for U 2 O 5 (cf. Fig.  12a), was not found for Pu 2 O 5 . Instead, several high-energy ones were reported which contain an O 2 moiety.
For Pu 2 O 6 , 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 Pu 2 O 6 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 Pu 2 O 7 , 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 AnO 4 + AnO 3 moieties by bonding of two AnO 4 oxygens to An in the equatorial plane of AnO 3 . Zaitsevskii et al. considered only the latter local minimum structure for both Pu 2 O 7 [40,41], Am 2 O 7 and the mixed PuAmO 7 [41]. On the basis of the high energy of the Pu 2 O 7 local minimum (vide supra), this structure may not correspond to the ground-state global minimum form of Am 2 O 7 and PuAmO 7 either. Zaitsevskii et al. found Pu 2 O 7 to have a remarkable stability [40,41], that of Am 2 O 7 was somewhat lower [41].
For Pu 2 O 8 , the HSE06 calculations predicted a doublebridged structure close to C 2h symmetry consisting of two PuO 2 (O 2 ) moieties (Fig. 16a) [88] as most stable. The bonding is analogous to the one observed in the Pu 2 O 7 ground state, where the bridging oxygen is part of a superoxo moiety. The isomer consisting of two facing PuO 4 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 PuO 4 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 Am 2 O 8 could not be found in the literature. For the PuAmO 8 heterodimer a structure with facing PuO 4 and AmO 4 moieties (Fig. 16b) was reported, pointing out its very low stability [41]. The structure in Fig. 16a was not probed for PuAmO 8 . 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 AnO 2 n+ ions (mainly UO 2 + and NpO 2 + ) 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.
An early quasirelativistic calculation of the (UO 2 ) 2 2+ 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 diamondshaped structure (Fig. 17b) was subjected to a partial optimization (distances and angles between two constrained UO 2 + 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. , 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 (UO 2 ) 2 4+ 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 (UO 2 ) 2 2+ , doublet (UO 2 ) 2 3+ , and singlet (UO 2 ) 2

4+
. 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 UO 2 2+ and UO 2 + 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) Fig. 17 The a T-(C 2v ) and b diamond-shaped (C 2h ) structures of (AnO 2 ) 2 n+ CCI dimers. An atoms are depicted in cyan, O in red calculations. The neptunyl moieties proved to have 5f 2 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 (NpO 2 ) 2 2+ 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 H 2 O 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)   Bond distances are given in angstroms, bond angles in degrees. The third column (M) gives the spin multiplicities. For the definition of atoms, see Fig. 17 a The abbreviations of basis sets A, B, and C mean relativistic small-core pseudopotential, all-electron, and relativistic large-core pseudopotential, respectively b Constrained at the value of the monomer c Aqueous phase using the COSMO solvation model studied both in the gas and aqueous phases, in the latter phase using the COSMO solvation model as well as explicit first solvation shells (9H 2 O for the T-and 8H 2 O 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 interunit Np-O ones. Accordingly, the two Np atoms get slightly away from each other.
The SF-CASPT2 ground state of T-shaped (NpO 2 ) 2 2+ proved to be the 5 B 1 state while several low-lying states were obtained. For diamond-shaped (NpO 2 ) 2

2+
, 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 (NpO 2 ) 2 2+ ·8H 2 O form [106]. For (NpO 2 ) 2 3+ the quasidegeneracy 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 diamondshaped isomers contradicting the experimental observations. In contrast to the exclusively observed T-shaped structure in solution, the computed relaxed binding energies of (NpO 2 ) 2 2+ with respect to the monomers predicted the preference of diamondshaped isomers at all applied levels [105,106]. Only a simplified model with four H 2 O molecules in the first solvation shell predicted the preference of the T-shaped (NpO 2 ) 2 2+ 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 UO 2 2+ , UO 2 + , NpO 2 2+ , NpO 2 + , PuO 2 + , and AmO 2 + [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 (UO 2 ) 2 2+ could be studied, and it proved to be thermodynamically more stable than the Tshaped (UO 2 ) 2 2+ 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 UO 2 + > NpO 2 + > PuO 2 + > AmO 2 + , and similarly by the acceptor as UO 2 2+ > NpO 2 2+ > PuO 2 2+ > AmO 2

2+
. 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

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 AnO 6 and in clusters containing up to AnO 4 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 NpO 4 − and PuO 4 − . 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 f 14 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 [U 9 O 24 ] + cations. The modelling of such large molecules with reliable quantum chemical methods can be one of the tasks of future research.

Compliance with ethical standards
Conflict of interest The author declares that there is no conflict of interest.
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