Relativistic density functional study on uranium(IV) and thorium(IV) oxide clusters of zonohedral geometry.

Free and ligated oxide clusters of thorium(IV) and uranium(IV) were studied with density functional theory using all-electron scalar relativistic method, as well as energy-consistent relativistic f-in-core pseudopotentials. The main driving force for the cluster formation is the sintering of the dioxoactinide moieties, which is more favorable for thorium(IV) than for uranium(IV) because, for the latter, a penalty for bending of the uranyl(IV) is to be paid. We assumed that the rhombic structural motif that exists already in the (AnO(2))(2) dimer could be a guide to explaining the preference for the existing An(6)O(8)-type clusters. On the basis of this, we have theoretically explored the possibility of the existence of similar (zonohedric) polyhedral actinide oxide clusters and found that the next possible cluster would be of An(12)O(20) stoicheometry. We have predicted by our DFT computations that the corresponding zonohedral clusters would be minima on the potential energy surface. The alternating An-O rhombic structural motif also offers a possible explanation of the existence and stoichiometry of the only nonfluorite cluster thus far, the An(12)O(20), which is nonzonohedral, nonconvex, but still a rhombic polyhedron. Our relativistic all electron DFT computations of both free cationic and ligated clusters predict that preparation of the larger clusters is not forbidden thermodynamically. We have also found that for the uranium(IV), oxide dimer and hexamer clusters are antiferromagnetic, broken spin singlet in their ground state, while ligated [U(6)O(8)] clusters prefer an all high-spin electronic configuration.

Theoretical study of the reduction of uranium(VI) aquo complexes on titania particles and by alcohols.

To provide insights into the adsorption and photoreduction of uranium(VI) on TiO(2), we have studied the structural and electronic properties of uranium(VI) aquo complexes adsorbed on stoichiometric and defected TiO(2) surfaces and nanoparticles. Plane wave calculations with the pure PBE density functional and the PBE+U approach were used to study U(VI) complexes on a periodic rutile (110) slab. In addition, a nanoparticulate Ti(38)O(76) cluster was used to simulate anatase nanoparticles. The electronic structures of the adsorbed U(VI) complexes indicate that the photoreduction process is a consequence of the photocatalytic properties of TiO(2). The reduction of the adsorbed complexes can only occur if the energy of the incident photon exceeds the semiconductor band gap. The gap states induced by single or neighboring hydrogen atoms and oxygen vacancies at the rutile (110) surface cannot reduce adsorbed U(VI) complexes as the unoccupied 5f  orbitals are found deeper in the conduction band. In the absence of a solid substrate, photoreduction proceeds by abstraction of a hydrogen atom from water or organic molecules present in solution. Photoreduction by chlorophenol results in lower product yield than reduction by aliphatic alcohols. This is because the triplet uranyl-chlorophenol complex is much more stable than similar complexes formed with methanol and ethanol. In the case of water, the hydroxyl photoproduct easily re-oxidizes the pentavalent species formed. In addition, it is easier for the triplet uranyl-water complex to decompose to the photoreactants.

Oxidative nucleophilic substitution of hydrogen in the sapphyrin dioxouranium(VI) complex: a relativistic DFT study.

A potentially trianionic expanded porphyrin ligand, sapphyrin does not form a 1:1 complex with the uranyl cation. However, in the presence of methanol, a complex of uranyl and meso-methoxy-substituted iso-sapphyrin is formed [Burrel et al. J. Chem. Soc., Chem. Commun. 1991, 24, 1710]. Here we performed a relativistic DFT study on the thermodynamics and the possible mechanism of the reaction. Our results have shown that (1) the reason for the failure of sapphyrin to stabilize its 1:1 uranyl complex is the highly basic character of the trianionic form of ligand that is hard to achieve in solution, (2) a driving force for the reaction lies in the better affinity of the methanol-substituted (and isomerized) ligand dianion to the uranyl cation, compared with the unsubstituted sapphyrin dianion, and (3) for the single-stage synchronous methanol addition pathways explored in this work, there is a path corresponding to noninnocent uranium behavior, via a neutral, triplet U(IV) intermediate complex. However, if the solvation effects were taken into account, this pathway would be unfavorable compared with singlet U(VI) pathways involving anionic intermediate complexes. The later pathway can be described as classical oxidative nucleophilic substitution of hydrogen in an aromatic system.

Binuclear uranium(VI) complexes with a "pacman" expanded porphyrin: computational evidence for highly unusual bis-actinyl structures.

On the basis of uranyl complexes reacting with a polypyrrolic ligand (H(4)L), we explored structures and reaction energies of a series of new binuclear uranium(VI) complexes using relativistic density functional theory. Full geometry optimizations on [(UO(2))(2)(L)], in which two uranyl groups were initially placed into the pacman ligand cavity, led to two minimum-energy structures. These complexes with cation-cation interactions (CCI) exhibit unusual coordination modes of uranyls: one is a T-shaped (T) skeleton formed by two linear uranyls {O(exo)=U(2)=O(endo)-->U(1)(=O(exo))(2)}, and another is a butterfly-like (B) unit with one linear uranyl coordinating side-by-side to a second cis-uranyl. The CCI in T was confirmed by the calculated longest distance and lowest stretching vibrational frequency of U(2)=O(endo) among the four U=O bonds. Isomer B is more stable than T, for which experimental tetrameric analogues are known. The formation of B and T complexes from the mononuclear [(UO(2))(H(2)L)(thf)] (M) was found to be endothermic. The further protonation and dehydration of B and T are thermodynamically favorable. As a possible product, we have found a trianglelike binuclear uranium(VI) complex having a O=U=O=U=O unit.

Theoretical actinide molecular science.

Interest in the chemistry of the early actinide elements (notably uranium through americium) usually results either from the nuclear waste problem or the unique chemistry of these elements that result from 5f contributions to bonding. Computational actinide chemistry provides one useful tool for studying these processes. Theoretical actinide chemistry is challenging because three principal axes of approximation have to be optimized. These are the model chemistry (the choice of approximate electron-electron correlation method and basis sets), the approximate relativistic method, and a method for modeling solvent (condensed phase) effects. In this Account, we arrange these approximations in a three-dimensional diagram, implying that they are relatively independent of each other. A fourth level of approximation concerns the choice of suitable models for situations too complex to treat in their entirety. We discuss test cases for each of these approximations. Gas-phase data for uranium fluorides and oxofluorides such as UF(6) and UO(2)F(2) show that GGA functionals provide accurate geometries and frequencies while hybrid density functional theory (DFT) functionals are superior for energetics. MP2 is seen to be somewhat erratic for this set of compounds, and CCSD(T) gives the most accurate results. Three different relativistic methods, small-core effective core potentials (SC-ECP), ZORA, and all-electron scalar, provide comparable results. The older large-core ECP (LC-ECP) approach is consistently worse and should not be used. We confirmed these conclusions through studies of the actinyl aquo complexes [AnO(2)(OH(2))(5)](n+), (An = U, Np, or Pu and n = 1 or 2) that are also used to test solvation models. As long as the first coordination sphere of the metal is included explicitly, continuum solvation models are reliable, and we found no clear advantage for the (costly) explicit treatment of the second coordination sphere. Spin-orbit effects must be included to reproduce the correct trend in An(VI)/An(V) reduction potentials. We propose a multistep mechanism for the experimentally observed oxygen exchange of UO(2)(2+) cations in highly alkaline solutions present in tank wastes. This process involves an equilibrium between [UO(2)(OH)(4)](2-) and [UO(2)(OH)(5)](3-), followed by formation of the stable [UO(3)(OH)(3)](3-) intermediate that forms from [UO(2)(OH)(5)](3-) through intramolecular water elimination. The [UO(3)(OH)(3)](3-) intermediate facilitates oxygen exchange through proton shuttling. We explain the experimentally observed stabilization of the pentavalent oxidation state of actinyl ions by macrocyclic ligands (such as 18-crown-6) as an effect of solvation: the large macrocycle screens the positive charge of the ion from the polarizable solvent. Alkyl-substituted isoamethyrin complexes are bent despite being aromatic because of steric factors, rather than fit/misfit criteria regarding the actinyl ion. By application of an efficient DFT code, actinide molecules with more than 100 atoms can now be studied routinely. "Real" chemical questions can be answered as long as we take great care to apply methods that are accurate with respect to the three axes of approximation described above. While the exclusive focus of this Account has been on the early actinide elements, these conclusions also apply elsewhere in the periodic table.

Stability of Hydrocarbons of the Polyhedrane Family Containing Bridged CH Groups: A Case of Failure of the Colle-Salvetti Correlation Density Functionals.

DFT-computed energies of polyhedric hydrocarbons, such as dodecahedrane C20H20, its smaller analogs C16H16 and C12H12, and the larger C24H24, estimated in comparison with corresponding isomeric hydrocarbons, vary widely with the choice of the density functional. In particular, large discrepancies were observed with the functionals that are based on the B88 (as well as G96, B86) exchange and the LYP (as well as OP) correlation parts. The problem is not related to the presence of the smaller cyclopropane rings in the C12H12 polyhedrane, for its hydrogenated products do show similar errors; moreover, the larger dodecahedrane that is free from the Bayer strain shows a similar trend. DFT-D corrections that are very useful in fixing long- and medium-range correlation issues with GGA DFT do not help in this case either. We show that these errors stem from the B88 (G96, B86) exchange functionals and are not compensated by Colle-Salvetti-based GGA correlation functionals such as LYP, OP, TCA, etc. However, they can be corrected by the PBE correlation functional based on the PW92 uniform electron gas (UEG) parametrization. Range-separated hybrids (Iikura and Hirao's LC-BOP, LC-BLYP) perform much better than the parent GGAs. Comparisons of polyhedranes with a well-studied system of similar size, the set of CnHn cyclophanes, reveal a completely different performance for the latter-for instance, RHF results are the poorest, and LC-type functionals do not give any improvement, but dispersion-corrected BLYP-D performs very well. We conclude that, while for polyhedranes medium-range delocalization errors from exchange dominate, for cyclophanes, the correlation/overlap-dispersion interactions are more important. The OPTX exchange functional shows significantly lower errors compared to B88 and G96; its combinations like OLYP and especially KT3 perform well for both test sets. The OPTX-based double hybrid, O2PLYP, also outperforms the corresponding B88-based B2PLYP functional for polyhedranes. Our computations also suggest that the (CH)16 and (CH)24 polyhedranes could be possible synthetic targets.

Performance of the Empirical Dispersion Corrections to Density Functional Theory: Thermodynamics of Hydrocarbon Isomerizations and Olefin Monomer Insertion Reactions.

Most of the commonly used approximate density functionals have systematic errors in the description of the stability of hydrocarbons. This poses a challenge for the realistic modeling of reactions involving hydrocarbons, such as olefin polymerization. Practical remedies have been proposed, including the application to usual black-box DFT of additional empirical correction CR(-6) terms for the van der Waals interaction (termed DFT-D), or introducing additional pseudopotentials that introduce some medium-to-long-range attraction (C-Pot). In this Article, we use the DFT-D scheme as realized in our BOptimize package to evaluate the performance of a range of commonly used DFT functionals (combinations of xPBE, B88, OPTX with LYP and cPBE GGAs and hybrids) for the modeling of the thermodynamics of reactions of the growth of common polyolefins. We also review and reproduce some of the previously done benchmarks in the area: alkane branching and relative stability of C12H12 and C10H16 isomers. In addition to the common DFT methods, computations with correlated wave function methods (MP2) and the new functionals B97-D and M06-L were performed. The performance of the special density functionals B97-D and M06-L is, in general, similar to the best DFT-D corrected regular functionals (BPBE-D and PBE-D). The results show that (1) the DFT-D correction is sufficient to describe alkane branching, but its performance depends on the parametrization; (2) inclusion of the correction is essential for a proper description of the thermodynamics of reactions of polymer growth; and (3) not all approximate density functionals perform effectively for the description of hydrocarbons even with the correction. The C-Pot method for the B3LYP functional shows quantitatively correct results for our test cases. The enthalpies of hydrocarbon reactions were analyzed in terms of the repulsion characteristics of a given DFT method. PBE is the least repulsive, while OLYP is the most. However, there are cases where the failure of a DFT method cannot be correlated with its repulsive character. A striking example is the performance of B3LYP and BLYP for caged molecules with small carbocycles, such as the [D3d]-octahedrane. The stability of [D3d]-octahedrane is underestimated by the B3LYP, BLYP, and B97-D functionals, but not by DFT methods that contain either B88 exchange or LYP correlation functionals separately. While DFT-D cannot amend the performance of the former functionals for the octahedrane, C-Pot for B3LYP does.

Modeling K+ and Ag+ complexation by thiacalix[4]arene amides using DFT: the role of intramolecular hydrogen bonding.

Complexation of methyl-glycine-amide functionalized thiacalix[4]arene with K(+) and Ag(+) has been studied using density functional theory (DFT) in the gas phase. To account for the conformational possibilities of the ligand, the free ligand and its potassium complexes were subjected to global minima searches on the molecular mechanics (MM) level of theory with the OPLS (optimized potentials for liquid simulations) force field. For the free ligand, the order of the energies and geometries of the ligand conformers is in agreement between MM and DFT; however, the position of K(+) in the ligand's cavity was predicted differently by these methods. Hydrogen bonding of amide hydrogens in the ligands' podand arms was found to take place predominantly with the ether oxygens of the same arm rather than the other arms' carbonyls. According to DFT calculations, the silver cation preferred to coordinate with one sulfur bridge and three carbonyl groups, whereas potassium cation favored interaction with the four carbonyl oxygens of the podand amide arms. Neither cation preferred the N-mode of coordination. For all obtained conformers, intramolecular hydrogen bonds disfavor complexation, increasing the preorganizational energy to be paid.

Theoretical study of the oxygen exchange in uranyl hydroxide. An old riddle solved?

A multistep mechanism for the experimentally observed oxygen exchange [Inorg. Chem. 1999, 38, 1456] of UO2(2+) cations in highly alkaline solutions is suggested and probed computationally. It involves an equilibrium between [UO2(OH)4](2-) and [UO2(OH)5](3-), followed by formation of the stable [UO3(OH)3 x H2O](3-) intermediate that forms from [UO2(OH)5](3-) through intramolecular water elimination. The [UO3(OH)3 x H2O](3-) intermediate facilitates oxygen exchange through proton shuttling, retaining trans-uranyl structures throughout, without formation of the cis-uranyl intermediates proposed earliar. Alternative cis-uranyl pathways have been explored but were found to have activation energies that are too high. Relativistic density functional theory (DFT) has been applied to obtain geometries and vibrational frequencies of the different species (reactants, intermediates, transition states, products) and to calculate reaction paths. Two different relativistic methods were used: a scalar four-component all-electron relativistic method and the zeroeth-order regular approximation. Calculations were conducted for both gas phase and condensed phase, the latter treated using the COSMO continuum model. An activation energy of 12.5 kcal/mol is found in solution for the rate-determining step, the reaction of changing the four-coordinated uranyl hydroxide to the five-coordinated one. This compares favorably to the experimental value of 9.8 +/- 0.7 kcal/mol. Activation energies of 7.8 and 5.1 kcal/mol are found for the hydrogen transfer between equatorial and axial oxygens through a water molecule in [UO3(OH)3 x H2O](3-) in the gas phase and condensed phase, respectively. Contrary to previously proposed mechanisms that resulted in high activation barriers, we find energies that are low enough to facilitate the reaction at room temperature. For the activation energies, two approximate DFT methods, B3LYP and PBE, are compared. The differences in activation energies are only about 1-2 kcal/mol for these methods.

Tetramerization of 3-methyl-cyclopropene-3-carbonitrile: a novel CN-alder-ene reaction.

At elevated temperatures 3-methyl-cyclopropene-3-carbonitrile 1 was found to tetramerize giving compound 2 (3-methyl-2,3-bis(2-t-methyl-2-c-cyanocyclopropyl)-1-(2-t-methyl-2-c,3-c-dicyanocyclopropyl)-cyclopropene) in good yields. This is the first example of Alder-ene type oligomerization of a 3,3-disubstituted cyclopropene. On the basis of the product geometry and stereoselective character of the reaction, a mechanism of formation of 2 involving CN-Alder-ene reaction was proposed. DFT modeling of the mechanism has shown that the CN-Alder-ene reaction is possible as a stepwise process involving a biradical intermediate.

The role of peripheral alkyl substituents: a theoretical study of substituted and unsubstituted uranyl isoamethyrin complexes.

Relativistic density functional theory has been applied to the uranyl(VI) and uranyl(V) complexes of unsubstituted (1) and dodeca-alkyl-substituted (2) isoamethyrin (hexaphyrin(1.0.1.0.0.0)). The experimentally observed bent conformation in the uranyl(VI) complex of 2 (Sessler, J. L. et al. Angew. Chem., Int. Ed. 2001, 40, 591) is reproduced accurately by the calculations. It is entirely due to the external alkyl substitutents; the unsubstituted complexes of 1 are planar. Complex geometry and stability are seen to be the result of two competing factors; aromatic stabilization favors a planar conformation of the macrocycle whereas the bending affords a much better fit between the cavity and the uranyl cation. The uranyl(VI) complex of 2 is more stable than that of 1 as a result; the trend is reversed for the larger uranyl(V) cation. An energy decomposition analysis shows that the differences between U(VI) and U(V) originate in the different capabilities of these cations for covalent and/or polarization interactions with the ligands rather than in sterical factors.

Crown ether inclusion complexes of the early actinide elements, [AnO2(18-crown-6)]n+, An = U, Np, Pu and n = 1, 2: a relativistic density functional study.

The title compounds, [AnO2(18-crown-6)]n+, An = U, Np, and Pu and n = 1 and 2, as well as the related (experimentally observed) complex [UO2(dicyclohexyl-18-crown-6)]2+ are studied using relativistic density functional theory (DFT). Different relativistic methods (large-core and small-core effective core potentials, all-electron scalar four-component) and two flavors of approximate DFT (B3LYP and PBE) are used. Calculated bond lengths agree well with the available experimental data for the NpV complex, while larger differences for the UVI complexes appear to be related to the large uncertainties in the experimental data. The axial AnO bonds are found to be weaker and longer than in the corresponding penta-aquo complexes, though still of partial triple-bond character. The AnO bond lengths and strengths decrease along the actinide series, consistent with the actinide contraction. Gas-phase binding energies calculated for the penta-aquo complexes and crown-ether complexes of the actinides studied, as well as ligand-exchange energies, show that there is no intrinsic preference, or "better fit", for actinyl(V) cations as compared to actinyl(VI) ones. Rather, the ability of NpO2+ (NpV) to form in-cavity 18-crown-6 complexes in water, which is impossible for UO22+, is traced to solvation effects in polar solvents. Thus, the experimentally observed stabilization of the pentavalent oxidation state as compared to the hexavalent one is due to the effective screening of the charge provided by the macrocycle, and this leads to destabilization of the AnVI crown complexes relative to their AnV counterparts.

A density functional study of the various forms of UN4O12 containing uranyl nitrate.

In this paper we report the computational results of a density functional study of 73 UN4O12 isomers containing uranyl nitrate, UO2(NO3)2, as a component. The isomers are grouped into three categories and 19 types. Forty-four isomers of 14 types are dinitrogen tetroxide adducts of uranyl nitrate, UO2(NO3)2.N2O4, 22 are nitrosonium salt adducts of uranyl nitrate, NO+UO2(NO3)3-, NO+UO2(NO3)2O(NO2)-, NO+UO2(NO3)2(ONOO)-, or (NO+)2UO2(NO3)2O22-, and 7 are bis(nitrogen dioxide) adducts of uranyl nitrate, UO2(NO3)2.2NO2. The 22 most stable isomers in solution, representing the 20 most stable gas-phase isomers, were selected for analysis. Of these selected structures only two categories and six types were represented. Structures, frequencies, gas-phase and solution energetics, atomic charges, dipole moments, and the bonding within the N2O4 unit and between NO+ and UO2(NO3)3- components have been analyzed in detail. On the basis of relative Gibbs free energy calculations five isomers (the N2O4 adducts a1, a2, and a3 and the nitrosonium salts b1 and b2) were identified as strong candidates to exist and possibly predominate in the gas phase, with a1 and a2 being the strongest candidates. Similarly, four isomers (a6, a5, a8, and a1, all of them N2O4 adducts) were identified as strong candidates to exist and possibly predominate in a nonaqueous solution of nitromethane/dinitrogen tetroxide. Of these, a6 was determined to be the most likely candidate to predominate in solution. The possibility of dissociation in solution has been addressed briefly. In addition, computational evidence for the existence of four new N2O4 isomers 20, 22, 27, and 28 in both the gas and the solution phases is presented for the first time.

A comparative relativistic DFT and ab initio study on the structure and thermodynamics of the oxofluorides of uranium(IV), (V) and (VI).

All the possible uranium(VI, V, IV) oxides, fluorides and oxofluorides were studied theoretically by using density functional theory (DFT) in the generalised gradient approximation (GGA), and three different relativistic methods (all-electron scalar four component Dyall RESC method (AE), relativistic small-core ECPs, and zeroth order regular approximation ZORA). In order to test different correlation methods, for the two former relativistic methods hybrid DFT, and, for the AE method, MP2 molecular orbital calculations were performed as well. Single-point AE-CCSD(T) energies were calculated on MP2 geometries as well. Energies of the uranium(VI) and (V) oxofluorides dissociation, uranium(VI) fluoride hydrolysis and oxofluoride disproportionation were calculated and compared against the available experimental thermochemical data. AE-CCSD(T) energies were the closest to the experiment. For GGA DFT methods, all the relativistic methods used yield similar results. For thermochemistry, the best quantitative agreement with the experimental and CCSD(T) values for both U=O and U-F bond strengths was obtained with hybrid DFT methods, provided that a reliable basis set was used. Both the GGA DFT and MP2 MO methods show overbinding of these bonds; moreover, this overbinding was found to be not uniform but strongly dependent on the coordination environment of the uranium atom in each case. U=O vibrational frequencies given by hybrid DFT, however, are systematically overestimated, and are better reproduced by GGA DFT; MP2 values usually fall in-between. Reaction enthalpies, U=O frequencies and complex geometries given by the PBE, MPBE, BPBE, BLYP and OLYP GGA functionals are quite similar, with OLYP performing slightly better than the others but still not as good as hybrid DFT. The geometries of the molecules are found to be influenced by the following factors: the inverse transinfluence (ITI) of the oxygen ligand and, for U(V), and U(IV), the Jahn-Teller distortion.

Relativistic density functional theory study of dioxoactinide(VI) and -(V) complexation with alaskaphyrin and related Schiff-base macrocyclic ligands.

Formation of complexes of alaskaphyrin 1, bi-pyen 2 and bi-tpmd 3 ligands with actinyl ions AnO2(n+), An = U, Np, Pu and n = 1, 2, was studied using density functional theory (DFT) within the scalar relativistic four-component approximation. The alaskaphyrin complexes of the uranyl are predicted to have a bent conformation, in contrast to the experimentally available X-ray data. This deviation is likely due to crystal packing effects. Apart from these conformational differences, calculated geometry parameters and vibrational frequencies are in agreement with the available experimental data. The character of bonding in the complexes is investigated using bond order analysis and extended transition states (ETS) energy decomposition. Metal-to-ligand bonds can be described as primarily ionic although substantial charge transfer is observed as well. Based on ETS analysis, it is shown that steric and/or fit/misfit requirements of actinyl cations to the ligand cavities, among the studied complexes, are the most favorable for the bi-pyen ligand 2, because its flexibility allows for optimal metal-to-donor-atom distances. Planarity of the equatorial coordination sphere of the actinide atom is found to be less important than the ability of a ligand to provide optimal uranium-to-nitrogen bond lengths. Experimental differences in demetalation rates between similar alaskaphyrin, bi-pyen and bi-tpmd uranyl complexes are explained as a result of easier protonation of the Schiff-base nitrogen of the latter. Reduction potentials calculated for the uranium complexes show a good agreement with the experiment, both in relative and in absolute terms.

Density functional studies of actinyl aquo complexes studied using small-core effective core potentials and a scalar four-component relativistic method.

The title compounds, [AnO(2)(H(2)O)(5)](n)(+), n = 1 or 2 and An = U, Np, and Pu, are studied using relativistic density functional theory (DFT). Three rather different relativistic methods are used, small-core effective core potentials (SC-ECP), a scalar four-component all-electron relativistic method, and the zeroeth-order regular approximation. The methods provide similar results for a variety of properties, giving confidence in their accuracy. Spin-orbit and multiplet corrections to the An(VI)/An(V) reduction potential are added in an approximate fashion but are found to be essential. Bulk solvation effects are modeled with continuum solvation models (CPCM, COSMO). These models are tested by comparing explicit (cluster), continuum, and mixed cluster/continuum solvation models as applied to various properties. The continuum solvation models are shown to accurately account for the effects of the solvent, provided that at least the first coordination sphere is included. Reoptimizing the structures in the presence of the bulk solvent is seen to be important for the equatorial bond lengths but less relevant for energetics. Explicit inclusion of waters in the second coordination sphere has a modest influence on the energetics. For the first time, free energies of solvation are calculated for all six [AnO(2)(H(2)O)(5)](n)(+) species. The calculated numbers are within the experimental error margins, and the experimental trend is reproduced correctly. By comparison of different relativistic methods, it is shown that an accurate relativistic description leads to marked improvements over the older large-core ECP (LC-ECP) method for bond lengths, vibrational frequencies, and, in particular, the An(VI)/An(V) reduction potential. Two approximate DFT methods are compared, B3LYP, a hybrid DFT method, and PBE, a generalized gradient approximation. Either method yields An(VI)/An(V) reduction potentials of comparable quality. Overall, the experimental reduction potentials are accurately reproduced by the calculations.