Correlation consistent basis sets for actinides. II. The atoms Ac and Np–Lr

Extraction of uranyl from spent nuclear fuel wastewater via complexation-a local vibrational mode study

CONTEXT

The efficient extraction of uranyl from spent nuclear fuel wastewater for subsequent reprocessing and reuse is an essential effort toward minimization of long-lived radioactive waste. N-substituted amides and Schiff base ligands are propitious candidates, where extraction occurs via complexation with the uranyl moiety. In this study, we extensively probed chemical bonding in various uranyl complexes, utilizing the local vibrational modes theory alongside QTAIM and NBO analyses. We focused on (i) the assessment of the equatorial O-U and N-U bonding, including the question of chelation, and (ii) how the strength of the axial U = O bonds of the uranyl moiety changes upon complexation. Our results reveal that the strength of the equatorial uranium-ligand interactions correlates with their covalent character and with charge donation from O and N lone pairs into the vacant uranium orbitals. We also found an inverse relationship between the covalent character of the equatorial ligand bonds and the strength of the axial uranium-oxygen bond. In summary, our study provides valuable data for a strategic modulation of N-substituted amide and Schiff base ligands towards the maximization of uranyl extraction.

METHOD

Quantum chemistry calculations were performed under the PBE0 level of theory, paired with the relativistic NESCau Hamiltonian, currently implemented in Cologne2020 (interfaced with Gaussian16). Wave functions were expanded in the cc-pwCVTZ-X2C basis set for uranium and Dunning's cc-pVTZ for the remaining atoms. For the bonding properties, we utilized the package LModeA in the local modes analyses, AIMALL in the QTAIM calculations, and NBO 7.0 for the NBO analyses.

Economical quasi-Newton unitary optimization of electronic orbitals

We present an efficient quasi-Newton orbital solver optimized to reduce the number of gradient evaluations and other computational steps of comparable cost. The solver optimizes orthogonal orbitals by sequences of unitary rotations generated by the (preconditioned) limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm equipped with trust-region step restriction. The low-rank structure of the L-BFGS inverse Hessian is exploited when solving the trust-region problem. The efficiency of the proposed "Quasi-Newton Unitary Optimization with Trust-Region" (QUOTR) solver is compared to that of the standard Roothaan-Hall approach accelerated by the Direct Inversion of Iterative Subspace (DIIS), and other exact and approximate Newton solvers for mean-field (Hartree-Fock and Kohn-Sham) problems.

Bonding and Magnetic Trends in the [AnIII(DPA)3]3- Series Compared to the Ln(III) and An(IV) Analogues

The crystal field parameters are determined from first-principles calculations in the [AnIII(DPA)3]3- series, completing previous work on the [LnIII(DPA)3]3- and [AnIV(DPA)3]2- series. The crystal field strength parameter follows the Ln(III) < An(III) < An(IV) trend. The parameters deduced at the orbital level decrease along the series, while J-mixing strongly impacts the many-electron parameters, especially for the Pu(III) complex. We further compile the available data for the three series. In some aspects, An(III) complexes are closer to Ln(III) than to An(IV) complexes with regard to the geometrical structure and bonding descriptors. At the beginning of the series, up to Pu(III), there is a quantitative departure from the free ion, especially for the Pa(III) complex. The magnetic properties of the actinides keep the trends of the lanthanides; in particular, the axial magnetic susceptibility follows Bleaney's theory qualitatively.

Coupled Cluster Study of the Heats of Formation of UF6 and the Uranium Oxyhalides, UO2X2 (X = F, Cl, Br, I, and At)

The atomization enthalpies of the U(VI) species UF6 and the uranium oxyhalides UO2X2 (X = F, Cl, Br, I, and At) were calculated using a composite relativistic Feller-Peterson-Dixon (FPD) approach based on scalar relativistic DKH3-CCSD(T) with extrapolations to the CBS limit. The inherent multideterminant nature of the U atom was mitigated by utilizing the singly charged atomic cation in all calculations with correction back to the neutral asymptote via the accurate ionization energy of the U atom. The effects of SO coupling were recovered using full 4-component CCSD(T) with contributions due to the Gaunt Hamiltonian calculated using Dirac-Hartree-Fock. The final atomization enthalpy for UF6 (752.2 kcal/mol) was within 2.5 kcal/mol of the experimental value, but unfortunately the latter carries a ±2.4 kcal/mol uncertainty that is predominantly due to the experimental uncertainty in the formation enthalpy of the U atom. The analogous value for UO2F2 (607.6 kcal/mol) was in nearly exact agreement with the experiment, but the latter has a stated experimental uncertainty of ±4.3 kcal/mol. The FPD atomization enthalpy for UO2Cl2 (540.4 kcal/mol) was within the experimental error limit of ±5.5 kcal/mol. FPD atomization energies for the non-U-containing molecules (used for reaction enthalpies) H2O and HX (X = F, Cl, Br, I, and At) were within at most 0.3 kcal/mol of their experimental values where available. The FPD atomization enthalpies, together with FPD reaction enthalpies for two different reactions, were used to determine heats of formation for all species of this work, with estimated uncertainties of ±4 kcal/mol. The calculated heat of formation for UF6 (-511.0 kcal/mol) is within 2.5 kcal/mol of the accurately known (±0.45 kcal/mol) experimental value.

Hydrolysis Reactions of the High Oxidation State Dimers Th2O4, Pa2O5, U2O6, and Np2O6. A Computational Study

The energetics of the hydrolysis reactions for high oxidation states of the dimeric actinide species Th2IVO4, Pa2VO5, and U2VIO6 were calculated at the CCSD(T) level and those for triplet Np2VIO6 at the B3LYP level. Hydrolysis is initiated by the formation of a Lewis acid/base adduct with H2O (physisorbed product), followed by a proton transfer to form a dihydroxide molecule (chemisorbed product); this process was repeated until the initial actinide oxide is fully hydrolyzed. For Th2O4, hydrolysis (chemisorption) by the initial and subsequent H2O molecules prefers proton transfer to terminal oxo groups before the bridge oxo groups. The overall Th2O4 hydration pathway is exothermic with chemisorbed products preferred over the physisorption products, and the fully hydrolyzed Th2(OH)8 can form exothermically. Hydrolysis of Pa2O5 forms isomers of similar energies with no initial preference for bridge or terminal hydroxy groups. The most exothermic hydrolysis product for Pa is Pa2O(OH)8 and the most stable species is Pa2O(OH)8(H2O). Hydrolysis of U2O6 and Np2O6 with strong [O═An═O]2+ actinyl groups occurs first at the bridging oxygens rather than at the terminal oxo groups. The U2O6 and Np2O6 pathways predict hydrated products to be more favored than hydrolyzed products, as more H2O molecules are added. The stability of the U and Np clusters is predicted to decrease with increasing number of hydroxyl groups. The most stable species on the hydration reaction coordinate for U and Np is An2O3(OH)6(H2O).

On the potentially transformative role of auxiliary-field quantum Monte Carlo in quantum chemistry: A highly accurate method for transition metals and beyond

Approximate solutions to the ab initio electronic structure problem have been a focus of theoretical and computational chemistry research for much of the past century, with the goal of predicting relevant energy differences to within "chemical accuracy" (1 kcal/mol). For small organic molecules, or in general, for weakly correlated main group chemistry, a hierarchy of single-reference wave function methods has been rigorously established, spanning perturbation theory and the coupled cluster (CC) formalism. For these systems, CC with singles, doubles, and perturbative triples is known to achieve chemical accuracy, albeit at O(N⁷) computational cost. In addition, a hierarchy of density functional approximations of increasing formal sophistication, known as Jacob's ladder, has been shown to systematically reduce average errors over large datasets representing weakly correlated chemistry. However, the accuracy of such computational models is less clear in the increasingly important frontiers of chemical space including transition metals and f-block compounds, in which strong correlation can play an important role in reactivity. A stochastic method, phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC), has been shown to be capable of producing chemically accurate predictions even for challenging molecular systems beyond the main group, with relatively low O(N³ - N⁴) cost and near-perfect parallel efficiency. Herein, we present our perspectives on the past, present, and future of the ph-AFQMC method. We focus on its potential in transition metal quantum chemistry to be a highly accurate, systematically improvable method that can reliably probe strongly correlated systems in biology and chemical catalysis and provide reference thermochemical values (for future development of density functionals or interatomic potentials) when experiments are either noisy or absent. Finally, we discuss the present limitations of the method and where we expect near-term development to be most fruitful.

Energetic and Electronic Properties of NpH0/+/- and PuH0/+/

High-level correlated molecular orbital theory calculations have been performed to predict the thermodynamic and electronic properties of diatomic NpH^0/+/- and PuH^0/+/-. The excited states up to ∼10,000 cm^-1 were predicted for these molecules at the multireference SO-CASPT2 level. The inclusion of spin-orbit effects is fundamental to predict the low-lying state ordering. NpH is predicted to have a ⁵Π₀ ground state, and PuH has a ⁶Π_1/2 ground state at the SO-CASPT2 level. The adiabatic electron affinities (AEAs) and ionization energies (IEs) of NpH and PuH were calculated to be 0.389 and 6.156 and 0.396 and 6.296 eV, respectively, using the Feller-Peterson-Dixon approach. The AEA increases going from AcH (0.425 eV) to ThH (0.820 eV) and decreases from ThH to PuH. The IEs of Pa-Np hydrides are close to ∼6.2 eV followed by an increase of 0.14 eV to PuH (6.296 eV). The An-H bond dissociation energy (BDE) decreases from 276.4 (AcH) to 107.1 (PuH) kJ/mol; the BDE(NpH) is ∼80 kJ/mol higher than that of PuH. Natural bond orbital calculations show that the bond character for these molecules is mainly ionic, An⁺H^-. The additional electron in NpH^- and PuH^- populates the 6d orbital, and NpH⁺ and PuH⁺ are formed by the removal of a 7s electron. The current work in conjunction with prior work on the AcH to UH in different charge states provides insights into how these properties change across the actinide series.

Prediction of the structures and heats of formation of MO2, MO3, and M2O5 for M = V, Nb, Ta, Pa

Structures for the mono-, di-, and tri-bridge isomers of M₂O₅ as well as those for the MO₂ and MO₃ fragments for M = V, Nb, Ta, and Pa were optimized at the density functional theory (DFT) level. Single point CCSD(T) calculations extrapolated to the complete basis set (CBS) limit at the DFT geometries were used to predict the energetics. The lowest energy dimer isomer was the di-bridge for M = V and Nb and the tri-bridge for M = Ta and Pa. The di-bridge isomers were predicted to be composed of MO₂⁺ and MO₃^- fragments, whereas the mono- and tri-bridge are two MO₂⁺ fragments linked by an O^2-. The heats of formation of M₂O₅ dimers, as well as MO₂ and MO₃ neutral and ionic species were predicted using the Feller-Peterson-Dixon (FPD) approach. The heats of formation of the MF₅ species were calculated to provide additional benchmarks. Dimerization energies to form the M₂O₅ dimers are predicted to become more negative going down group 5 and range from -29 to -45 kcal mol^-1. The ionization energies (IEs) for VO₂ and TaO₂ are essentially the same at 8.75 eV whereas the IEs for NbO₂ and PaO₂ are 8.10 and 6.25 eV, respectively. The predicted adiabatic electron affinities (AEAs) range from 3.75 eV to 4.45 eV for the MO₃ species and vertical detachment energies from 4.21 to 4.59 eV for MO₃^-. The calculated MO bond dissociation energies increase from 143 kcal mol^-1 for M = V to ∼170 kcal mol^-1 for M = Nb and Ta to ∼200 kcal mol^-1 for M = Pa. The M-O bond dissociation energies are all similar ranging from 97 to 107 kcal mol^-1. Natural bond analysis provided insights into the types of chemical bonds in terms of their ionic character. Pa₂O₅ is predicted to behave like an actinyl species dominated by the interactions of approximately linear PaO₂⁺ groups.

Theoretical Investigation of Single-Molecule-Magnet Behavior in Mononuclear Dysprosium and Californium Complexes

Early-actinide-based (U, Np, and Pu) single-molecule magnets (SMMs) have yet to show magnetic properties similar to those of highly anisotropic lanthanide-based ones. However, there are not many studies exploring the late-actinides (more than half-filled f shells) as potential candidates for SMM applications. We computationally explored the electronic structure and magnetic properties of a hypothetical Cf(III) complex isostructural to the experimentally synthesized Dy(dbm)₃(bpy) complex (bpy = 2,2'-bipyridine; dbm = dibenzoylmethanoate) via multireference methods and compared them to those of the Dy(III) analogue. This study shows that the Cf(III) complex can behave as a SMM and has a greater magnetic susceptibility compared to other experimentally and computationally studied early-actinide-based (U, Np, and Pu) magnetic complexes. However, Cf spontaneously undergoes α-decay and converts to Cm. Thus, we also explored the isostructural Cm(III)-based complex. The computed magnetic susceptibility and g-tensor values show that the Cm(III) complex has poor SMM behavior in comparison to both the Dy(III) and Cf(III) complexes, suggesting that the performance of Cf(III)-based magnets may be affected by α-decay and can explain the poor performance of experimentally studied Cf(III)-based molecular magnets in the literature. Further, this study suggests that the ligand field is dominant in Cf(III), which helps to increase the magnetization blocking barrier by nearly 3 times that of its 4f congener.

Multireference Wavefunction-Based Investigation of the Ground and Excited States of LrF and LrO

Complete active space self-consistent field (CASSCF) and multireference configuration interaction with Davidson correction (MRCI+Q) calculations have been carried out for lawrencium fluoride (LrF) and lawrencium oxide (LrO) molecules, detailing 19 and 20 electronic states for LrF and LrO, respectively. For LrF, two dissociation channels were considered, Lr(2P)+F(2P) and Lr(2D)+F(2P). However, due to the more complex electronic manifold of LrO, three dissociation channels were computed: Lr(2P)+O(3P), Lr(2D)+O(3P), and Lr(2P)+O(1D). In addition, equilibrium bond lengths, harmonic vibrational frequencies ωe, anharmonicity constants ωeχe, ΔG1/2 values, and excitation energies Te for the ground and several excited electronic states were calculated for both molecules, for the first time. Bond dissociation energies (BDEs) were calculated for LrF and LrO using several different levels of theory: unrestricted coupled-cluster with single, double, and perturbative triple excitations (UCCSD(T)), density functional theory (B3LYP, TPSS, M06-L, and PBE), and the correlation-consistent composite approach developed for f-elements (f-ccCA).

Population analysis and the effects of Gaussian basis set quality and quantum mechanical approach: main group through heavy element species

Atomic charge and its distribution across molecules provide important insight into chemical behavior. Though there are many studies on various routes for the determination of atomic charge, there are few studies that examine the broader impact of basis set and quantum method used over many types of population analysis methods across the periodic table. Largely, such a study of population analysis has focused on main-group species. In this work, atomic charges were calculated using several population analysis methods including orbital-based methods (Mulliken, Löwdin, and Natural Population Analysis), volume-based methods (Atoms-in-Molecules (AIM) and Hirshfeld), and potential derived charges (CHELP, CHELPG, and Merz-Kollman). The impact of basis set and quantum mechanical method choices upon population analysis has been considered. The basis sets utilized include Pople (6-21G**, 6-31G**, 6-311G**) and Dunning (cc-pVnZ, aug-cc-pVnZ; n = D, T, Q, 5) basis sets for main group molecules. For the transition metal and heavy element species examined, relativistic forms of the correlation consistent basis sets were used. This is the first time the cc-pVnZ-DK3 and cc-pwCVnZ-DK3 basis sets have been examined with respect to their behavior across all levels of basis sets for atomic charges for an actinide. The quantum methods chosen include two density functional (PBE0 and B3LYP), Hartree-Fock, and second-order Møller-Plesset perturbation theory (MP2) approaches.

ZORA Gaussian basis sets for Fr, Ra, and Ac

Segmented all-electron basis sets of double and triple zeta valence qualities plus polarization functions (DZP and TZP) for the elements Fr, Ra, and Ac to be used with the zeroth-order regular approximation (ZORA) were presented. These sets were constructed from the reoptimization of the contraction coefficients of the corresponding non-relativistic basis sets. In order to adequately describe electrons distant from the atomic nuclei, these sets were augmented with diffuse functions and were, respectively, designated as ADZP-ZORA and ATZP-ZORA. At the ZORA-B3LYP theory level, the relativistic sets were employed to calculate ionization energies of Fr, Ra, and Ac as well as bond lengths, dissociation energies, harmonic vibrational frequencies, and static mean dipole polarizabilities of some diatomics. Comparing with benchmark theoretical results and with experimental data available in the literature, it can be verified that our basis sets are able to produce reliable and accurate results. Evaluation of the performances of ZORA and second-order Douglas-Kroll-Hess Hamiltonians was performed.

Periodic Trends within Actinyl(VI) Nitrates and Their Structures, Vibrational Spectra, and Electronic Properties

A series of actinyl(VI) nitrate salts of the form MAnO₂(NO₃)₃, where M = NH₄⁺ K⁺, Rb⁺, Cs⁺, and Me₄N⁺ and AnO₂²⁺ = U, Np, Pu, and AnO₂(NO₃)₂(H₂O)₂·H₂O, and the uranyl tetranitrates M₂UO₂(NO₃)₄ have been synthesized from aqueous solution and their structures determined using single-crystal X-ray diffraction. Together, these complexes represent an isostructural series of actinide complexes among the salts crystallized with the same charge-compensating cation and have been studied using vibrational spectroscopy including Raman and Fourier-transform infrared. Periodic trends in both the structural properties of these complexes and their vibrational spectra are presented and discussed, in particular the invariant nature of the O≡An≡O asymmetric stretching frequencies observed across the actinyl series. Electronic structure calculations were performed at a variety of levels of theory to aid in the interpretation of the vibrational data and to correlate trends in the data with the underlying electronic properties of these molecules.

Protactinium and Actinium Monohydrides: A Theoretical Study on Their Spectroscopic and Thermodynamic Properties

Spectroscopic and thermodynamics properties including bond dissociation energies (BDEs), adiabatic electron affinities (AEAs), and ionization energies (IEs) have been predicted for AcH and PaH using the Feller-Peterson-Dixon composite approach. Comparisons with previous studies on ThH and UH were performed to identify possible trends in the actinide series. Multireference CASPT2 calculations were used to predict the spin-orbit effects and obtain potential energy curves for the low-lying Ω states around the equilibrium distance as well as the vertical detachment energies (VDEs) from AcH^- and PaH^- to excited states of the neutral species. The calculated AEA for AnH (An = Ac, Th, Pa, U) showed that the AEA increases from AcH (0.425 eV) to ThH (0.820 eV) and decreases to PaH (0.781 eV) and to UH (0.457 eV), whereas the IE values are 5.887 eV (AcH), 6.181 eV (ThH), 6.204 eV (PaH), and 6.182 eV (UH). The ground state of AcH, AcH^-, PaH, and PaH^- are predicted to be¹Σ⁺₀,²Π_3/2, ³H₄, and ⁴I_9/2, respectively. The BDEs for AcH and PaH are 276.4 and 237.2 kJ/mol, and those for AcH^- and PaH^- are 242.8 and 239.8 kJ/mol, respectively. The natural bond analysis shows a significant ionic character, An⁺H^-, in the bonding of the neutral hydrides.

Ab Initio Composite Approaches for Heavy Element Energetics: Ionization Potentials for the Actinide Series of Elements

The first, second, and third gas-phase ionization potentials have been determined for the actinide series of elements using an ab initio composite scalar and fully relativistic approach, employing the coupled cluster with single, double, and perturbative triple excitations (CCSD(T)) and Dirac Hartree-Fock (DHF) methods, extrapolated to the complete basis set (CBS) limit. The impact of electron correlation and basis set choice within this framework are examined. Additionally, the first three ionization potentials were obtained using an ab initio heavy element correlation-consistent Composite Approach (here referred to as α-ccCA). This is the first utilization of a ccCA for actinide species.

Uranium: The Nuclear Fuel Cycle and Beyond

This review summarizes the recent developments regarding the use of uranium as nuclear fuel, including recycling and health aspects, elucidated from a chemical point of view, i.e., emphasizing the rich uranium coordination chemistry, which has also raised interest in using uranium compounds in synthesis and catalysis. A number of novel uranium coordination features are addressed, such the emerging number of U(II) complexes and uranium nitride complexes as a promising class of materials for more efficient and safer nuclear fuels. The current discussion about uranium triple bonds is addressed by quantum chemical investigations using local vibrational mode force constants as quantitative bond strength descriptors based on vibrational spectroscopy. The local mode analysis of selected uranium nitrides, N≡U≡N, U≡N, N≡U=NH and N≡U=O, could confirm and quantify, for the first time, that these molecules exhibit a UN triple bond as hypothesized in the literature. We hope that this review will inspire the community interested in uranium chemistry and will serve as an incubator for fruitful collaborations between theory and experimentation in exploring the wealth of uranium chemistry.

Molecular Properties of Thorium Hydrides: Electron Affinities and Thermochemistry

High-level electronic structure calculations of the ground and low-lying energy electronic states for ThH_x and ThH_x^- for x = 2-5 are reported and compared to available anion photoelectron detachment experiments. The adiabatic electron affinities (EAs) are predicted to be 0.82, 0.88, 0.51, and 2.36 eV for x = 2 to 5, respectively, at the Feller-Peterson-Dixon (FPD) level. The vertical detachment energies (VDEs) are predicted to be 0.84, 0.88, 0.81, and 4.38 eV for x = 2-5, respectively. The corresponding experimental VDEs are 0.871 eV for x = 2, 0.88 eV for x = 3, and 4.09 eV for x = 5. As for ThH, there is a significant spin-orbit (SO) correction for the EA of ThH₂, and this correction decreases substantially for x > 2. The observed ThH₂^- photoelectron spectrum has many transitions as predicted at the CASPT2-SO level. The FPD bond dissociation energies (BDEs) increase from 67 to 75 kcal/mol for x = 2 to x = 4 at the FPD level. The BDE for ThH₅ is much lower as it is a complex of H₂ with ThH₃. The hydride affinities for x = 2 to 4 are all comparable and near 70 kcal/mol. A natural bond orbital analysis is consistent with a significant Th⁺-H^- ionic contribution to the Th-H bonds. There is very little participation of the 5f orbitals in the bonding and the valence electrons on the Th are dominated by 7s and 6d for the neutrals and anions except for ThH₂^- where there is a significant contribution from the 7p.

Bond Dissociation Energies Reveal the Participation of d Electrons in f-Element Halide Bonding

Bond dissociation energies (BDEs) reported in the literature for lanthanide monofluorides and lanthanide monochlorides LnX, where X = F or Cl, exhibit substantial irregular variations across the Ln series. It is demonstrated here that correlations of these variations with reported experimentally based atomic energies to prepare the Ln constituent for bonding reveal the nature of the bonding. Whereas some molecular characteristics are well understood in the context of highly ionic bonding, with LnX considered to be (Ln⁺)(X^-), some significant variations in BDEs are not well rationalized simply by ionization to convert Ln to Ln⁺ for bonding. Focusing here on lanthanide monofluorides LnF, a consideration of alternative Ln preparation schemes shows that a particularly good rationalization of BDEs is obtained by invoking the participation of a lanthanide 5d electron in bonding. This 5d participation could be in ionic (Ln⁺)(F^-) via π-donation from F^- 2p to empty Ln⁺ 5d orbitals or in covalent π-bonded Ln:F via polarization from Ln 5d to F 2p, with these ionic and polar covalent perspectives ultimately being equivalent. The inference of lanthanide 5d involvement suggests that the valence 4f and 6s electrons do not effectively participate in some key aspects of the bonding, presumably due to poor spatial overlap with F 2p orbitals. An extension to actinide monofluorides, AnF, assumes analogous ionic or polar covalent bonding involving a valence 6d electron and results in predictions for BDEs that include a general decrease from left to right across the series, except for a distinctive local minimum at AmF. Determining the BDE for AmF would serve to evaluate the predictions and the underlying assumption of 6d bonding. The BDE assessments/predictions for neutral monofluorides, LnF and AnF, are also applied to cationic LnF⁺ and AnF⁺, and it is noted that the approach can be directly extended to f-element monochlorides, monobromides, and monoiodides.

Covalency of Trivalent Actinide Ions with Different Donor Ligands: Do Density Functional and Multiconfigurational Wavefunction Calculations Corroborate the Observed "Breaks"?

A comprehensive ab initio study of periodic actinide-ligand bonding trends for trivalent actinides is performed. Relativistic density functional theory (DFT) and complete active-space (CAS) self-consistent field wavefunction calculations are used to dissect the chemical bonding in the [AnCl₆]^3-, [An(CN)₆]^3-, [An(NCS)₆]^3-, [An(S₂PMe₂)₃], [An(DPA)₃]^3-, and [An(HOPO)]^- series of actinide (An = U-Es) complexes. Except for some differences for the early actinide complexes with DPA, bond orders and excess 5f-shell populations from donation bonding show qualitatively similar trends in 5f ⁿ active-space CAS vs DFT calculations. The influence of spin-orbit coupling on donation bonding is small for the tested systems. Along the actinide series, chemically soft vs chemically harder ligands exhibit clear differences in bonding trends. There are pronounced changes in the 5f populations when moving from Pu to Am or Cm, which correlate with previously noted "breaks" in chemical trends. Bonding involving 5f becomes very weak beyond Cm/Bk. We propose that Cm(III) is a borderline case among the trivalent actinides that can be meaningfully considered to be involved in ground-state 5f covalent bonding.

Improving the theoretical description of Ln(III)/An(III) separation with phosphinic acid ligands: a benchmarking study of structure and selectivity

The efficient separation of trivalent lanthanides from minor actinides with soft-donor ligands, while showing experimental promise, has theorists continuing to search for suitable approaches for describing and interpreting selectivity. To remedy this, we employ several computational methods in describing the structure of model M(H₂PX₂)₃ complexes, with M = Eu and Am, and X = O, S, Se, and Te, and predicting the selectivity of model phosphinic acid ligands in Eu(III)/Am(III) separation. After first establishing a set of MP2 and CCSD(T)-DKH3 results as benchmarks, we evaluate several density functionals and descriptions of valence shells for their accuracy with respect to metal-ligand bonding and selectivity. We find that commonly employed functionals with a 0-27% range of exact exchange used with small-core effective core potentials or with an explicit treatment of the relativistic effects (DKH2) incorrectly predict a decrease in the metal-ligand bond distance in going from Eu(III) to Am(III) and completely fail to track a selectivity trend, even giving a wrong sign for some or all ligands. Surprisingly, when these functionals are used in conjunction with an f-in-core description of metal ions, the correct trend in selectivity is recovered, though Am-X distances are overestimated in relation to Eu-X. Functionals with high components of exact exchange (50%) and double-hybrid functionals are reasonably aligned with benchmark results, pointing to the problems of DFT with small exact exchange fractions to handle f-electrons. Natural bond orbital analyses reveal that these poorly performing functionals disproportionately overpopulate outer f orbitals in the model complexes. We anticipate that recommendations resulting from this work will lead to more accurate theoretical descriptions of lanthanide/actinide selectivity with soft-donor chalcogen-based ligands in the future.

Considering Density Functional Approaches for Actinide Species: The An66 Molecule Set

The importance of spin-orbit effects on the predictions of energetic properties of actinide compounds has been considered for 18 different density functionals, comparing the spin-orbit and non-spin-orbit ("standard") forms of density functional theory (DFT). A set of enthalpies of formation for 66 small actinide (Th-Am) compounds-the An66 set, for which experimental data are available-have been investigated. The set includes actinide halides, oxides, and oxohalides in the general form AnO_mX_n, where n = 0-6, m = 0-3, and X = F, Cl, Br, or I. The impact of basis set choice was investigated, and to help account for the impact of relativity, the Stuttgart general and segmented contracted atomic natural orbital (ANO) basis sets paired with small core relativistic effective core potentials (RECP) as well as all-electron calculations utilizing the third-order Douglas-Kroll-Hess were considered.

Guided Ion Beam Studies of the Thorium Monocarbonyl Cation Bond Dissociation Energy and Theoretical Unveiling of Different Isomers of [Th,O,C]+ and Their Rearrangement Mechanism

Threshold collision-induced dissociation (TCID) of the thorium monocarbonyl cation, ThCO⁺, with xenon is performed using a guided ion beam tandem mass spectrometer. The only product observed is Th⁺ resulting from loss of the CO ligand. Analysis of the kinetic energy-dependent cross sections for this CID reaction yields the first experimental determination of the bond dissociation energy (BDE) of Th⁺-CO at 0 K as 0.94 ± 0.06 eV. Calculated BDEs at the CCSD(T) level of theory with cc-pVXZ (X = T and Q) basis sets and a complete basis set (CBS) extrapolation are in good agreement with the experimental result. The Feller-Peterson-Dixon composite coupled-cluster methodology was also applied on both ThCO⁺ and ThCO, with contributions up to CCSDT(Q) and a four-component treatment of spin-orbit coupling effects. The final 0 K Th⁺-CO BDE of 0.94 ± 0.04 eV is in excellent agreement with the current experimental result. The ionization energy of ThCO, as well as the atomization energies and heats of formation for both ThCO and ThCO⁺, is reported at this same level of theory. Complete potential energy profiles of both quartet and doublet spin are also constructed to elucidate the mechanism for the formation and interconversion of different isomers of [Th,O,C]⁺. Chemical bonding patterns in low-lying states of ThCO⁺ and potential energy curves for ThCO⁺ dissociation are also investigated.

Hydrolysis of Small Oxo/Hydroxo Molecules Containing High Oxidation State Actinides (Th, Pa, U, Np, Pu): A Computational Study

The energetics of hydrolysis reactions for high oxidation states of oxo/hydroxo monomeric actinide species (Th^IVO₂, Pa^IVO₂, U^IVO₂, Pa^VO₂(OH), U^VO₂(OH), U^VIO₃, Np^VIO₃, Np^VIIO₃(OH), and Pu^VIIO₃(OH)) were calculated at the CCSD(T) level. The first step is the formation of a Lewis acid/base adduct with H₂O (hydration), followed by a proton transfer to form a dihydroxide molecule (hydrolysis); this process is repeated until all oxo groups are hydrolyzed. The physisorption (hydration) for each H₂O addition was predicted to be exothermic, ca. -20 kcal/mol. The hydrolysis products are preferred energetically over the hydration products for the +IV and +V oxidation states. The compounds with An^VI are a turning point in terms of favoring hydration over hydrolysis. For An^VIIO₃(OH), hydration products are preferred, and only two waters can bind; the complete hydrolysis process is now endothermic, and the oxidation state for the An in An(OH)₇ is +VI with two OH groups each having one-half an electron. The natural bond order charges and the reaction energies provide insights into the nature of the hydrolysis/hydration processes. The actinide charges and bond ionicity generally decrease across the period. The ionic character decreases as the oxidation state and coordination number increase so that covalency increases moving to the right in the actinide period.

The electron affinity of the uranium atom

The results of a combined experimental and computational study of the uranium atom are presented with the aim of determining its electron affinity. Experimentally, the electron affinity of uranium was measured via negative ion photoelectron spectroscopy of the uranium atomic anion, U^-. Computationally, the electron affinities of both thorium and uranium were calculated by conducting relativistic coupled-cluster and multi-reference configuration interaction calculations. The experimentally determined value of the electron affinity of the uranium atom was determined to be 0.309 ± 0.025 eV. The computationally predicted electron affinity of uranium based on composite coupled cluster calculations and full four-component spin-orbit coupling was found to be 0.232 eV. Predominately due to a better convergence of the coupled cluster sequence for Th and Th^-, the final calculated electron affinity of Th, 0.565 eV, was in much better agreement with the accurate experimental value of 0.608 eV. In both cases, the ground state of the anion corresponds to electron attachment to the 6d orbital.

Coupled Cluster Studies of Platinum-Actinide Interactions. Thermochemistry of PtAnOn+ (n = 0-2 and An = U, Np, Pu)

Accurate Pt-An bond dissociation enthalpies (BDEs) for PtAnOⁿ⁺ (An = U, Np, Pu and n = 0-2) and the corresponding enthalpies for the Pt + OAnOⁿ⁺ substitution reactions have been studied for the first time using an accurate composite coupled cluster approach. Analogous O-AnOⁿ⁺ bond dissociation enthalpies are also presented. To make the study possible, new correlation consistent basis sets optimized using the all-electron third-order Douglas-Kroll-Hess (DKH3) scalar relativistic Hamiltonian are developed and reported for Pt and Au, with accompanying benchmark calculations of their atomic ionization potentials to demonstrate the effectiveness of the new basis sets. For the charged PtAnOⁿ⁺ species (n = 1, 2), a low-spin state (LSS) for which the Pt-An σ bond is doubly occupied is studied together with a high-spin state (HSS) obtained by unpairing the σ bond orbital and placing one electron into the An 5f shell. The relative energies of the two spin states have been compared and qualitatively assessed via natural population and natural bond analyses. The enthalpies for the Pt substitution reactions, i.e., Pt + OAnOⁿ⁺ → PtAnOⁿ⁺ + O, are calculated to range from about 14-62 kcal/mol, and the Pt-AnOⁿ⁺ bond dissociation enthalpies range from about 78-149 kcal/mol for the ground electronic states. For the PtAnO⁺ species, the LSSs were all predicted to be the ground state, whereas the PtAnO²⁺ molecules all favored the HSSs. The prediction for PtUO²⁺ is consistent with previous theoretical findings. The natural bond orbital analyses indicate a triple bond between An and O, with a double to quadruple bond between the An and Pt.

Norm-Conserving Pseudopotentials and Basis Sets to Explore Actinide Chemistry in Complex Environments

We have developed a new set of norm-conserving pseudopotentials and companion Gaussian basis sets for the actinide (An) series (Ac-Lr) using the Goedecker, Teter, and Hutter (GTH) formalism with the Perdew, Burke, and Ernzerhof (PBE) exchange-correlation functional of generalized gradient approximation. To test the accuracy and reliability of the newly parameterized An-GTH pseudopotentials and basis sets, a variety of benchmarks on actinide-containing molecules were carried out and compared to all-electron and available experimental results. The new pseudopotentials include both medium- ([Xe]4f¹⁴) and large-core ([Xe]4f¹⁴5d¹⁰) options that successfully reproduce the structures and energetics, particularly redox processes. The medium-core size set, in particular, reproduces all-electron calculations over multiple oxidation states from 0 to VII, whereas the large-core set is suitable only for the early series elements and low oxidation states. The underlying reason for these transferability issues is discussed in detail. This work fills a critical void in the literature for studying the chemistry of 5f-block elements in the condensed phase.

Efficient Four-Component Dirac-Coulomb-Gaunt Hartree-Fock in the Pauli Spinor Representation

Four-component Dirac-Hartree-Fock is an accurate mean-field method for treating molecular systems where relativistic effects are important. However, the computational cost and complexity of the two-electron interaction make this method less common, even though we can consider the Dirac-Hartree-Fock Hamiltonian the "ground truth" of the electronic structure, barring explicit quantum electrodynamical effects. Being able to calculate these effects is then vital to the design of lower scaling methods for accurate predictions in computational spectroscopy and properties of heavy element complexes that must include relativistic effects for even qualitative accuracy. In this work, we present a Pauli quaternion formalism of maximal component and spin separation for computing the Dirac-Coulomb-Gaunt Hartree-Fock ground state, with a minimal floating point operation count algorithm. This approach also allows one to explicitly separate different spin physics from the two-body interactions, such as spin-free, spin-orbit, and spin-spin contributions. Additionally, we use this formalism to examine relativistic trends in the periodic table and analyze the basis set dependence of atomic gold and gold dimer systems.

Electron-Nucleus Hyperfine Coupling Calculated from Restricted Active Space Wavefunctions and an Exact Two-Component Hamiltonian

Exact two-component (X2C) relativistic nuclear hyperfine magnetic field operators were incorporated in X2C ab initio wavefunction calculations at the multireference restricted active space (RAS) level for calculations of nuclear hyperfine magnetic properties. Spin-orbit coupling was treated via RAS state interaction (SO-RASSI). The method was tested by calculations of electron-nucleus hyperfine coupling constants. The approach, implemented in the OpenMolcas program, overcomes a major limitation of a previous SO-RASSI implementation for hyperfine coupling that relied on nonrelativistic hyperfine operators [J. Chem. Theor. Comput. 2015, 11, 538-549] and therefore had limited applicability. Results from calculations on systems with light and heavy main group elements, transition metals, lanthanides, and one actinide complex demonstrate reasonably good agreement with experimental data, where available, as long as the active space can generate sufficient spin polarization.

The Molpro quantum chemistry package

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework.

Spectroscopic and theoretical studies of UN and UN. J Chem Phys 2020;152:094302. [PMID: 33480743 DOI: 10.1063/1.5144299]

The low-energy electronic states of UN and UN⁺ have been examined using high-level electronic structure calculations and two-color photoionization techniques. The experimental measurements provided an accurate ionization energy for UN (IE = 50 802 ± 5 cm^-1). Spectra for UN⁺ yielded ro-vibrational constants and established that the ground state has the electronic angular momentum projection Ω = 4. Ab initio calculations were carried out using the spin-orbit state interacting approach with the complete active space second-order perturbation theory method. A series of correlation consistent basis sets were used in conjunction with small-core relativistic pseudopotentials on U to extrapolate to the complete basis set limits. The results for UN correctly obtained an Ω = 3.5 ground state and demonstrated a high density of configurationally related excited states with closely similar ro-vibrational constants. Similar results were obtained for UN⁺, with reduced complexity owing to the smaller number of outer-shell electrons. The calculated IE for UN was in excellent agreement with the measured value. Improved values for the dissociation energies of UN and UN⁺, as well as their heats of formation, were obtained using the Feller-Peterson-Dixon composite thermochemistry method, including corrections up through coupled cluster singles, doubles, triples and quadruples. An analysis of the ab initio results from the perspective of the ligand field theory shows that the patterns of electronic states for both UN and UN⁺ can be understood in terms of the underlying energy level structure of the atomic metal ion.

Guided Ion Beam and Quantum Chemical Investigation of the Thermochemistry of Thorium Dioxide Cations: Thermodynamic Evidence for Participation of f Orbitals in Bonding

Kinetic energy dependent reactions of ThO⁺ with O₂ are studied using a guided ion beam tandem mass spectrometer. The formation of ThO₂⁺ in the reaction of ThO⁺ with O₂ is observed to be slightly endothermic and also exhibits two obvious features in the cross section. These kinetic energy dependent cross sections were modeled to determine a 0 K bond dissociation energy of D₀(OTh⁺-O) = 4.94 ± 0.06 eV. This value is slightly larger but within experimental uncertainty of less precise previously reported experimental values. The higher energy feature in the ThO₂⁺ cross section was also analyzed and suggests formation of an excited state of the product ion lying 3.1 ± 0.2 eV above the ground state. Additionally, the thermochemistry of ThO₂⁺ was explored by quantum chemical calculations, including a full Feller-Peterson-Dixon (FPD) composite approach with correlation contributions up to CCSDT(Q) and four-component spin-orbit corrections, as well as more approximate CCSD(T) calculations including semiempirical estimates of spin-orbit energy contributions. The FPD approach predicts D₀(OTh⁺-O) = 4.87 ± 0.04 eV, in good agreement with the experimental value. Analogous FPD results for ThO⁺, ThO, and ThO₂ are also presented, including ionization energies for both ThO and ThO₂. The ThO₂⁺ bond energy is larger than those of its transition metal congeners, TiO₂⁺ and ZrO₂⁺, which can be attributed partially to an actinide contraction, but also to contributions from the participation of f orbitals on thorium that are unavailable to the transition metal systems.

Actinyl cation–cation interactions in the gas phase: an accurate thermochemical study

Accurate coupled cluster calculations of actinyl cation–cation interactions suggest significant gas phase kinetic stabilities that correlate well with known species in condensed phases.

Structural Characteristics, Population Analysis, and Binding Energies of [An(NO3)]2+ (with An = Ac to Lr)

Efficient predictive capabilities are essential for the actinide series since regulatory constraints for radioactive work, associated costs needed for specialized facilities, and the short half-lives of many actinides present great challenges in laboratory settings. Improved predictive accuracy is advantageous for numerous applications including the optimization and design of separation agents for nuclear fuel and waste. One limitation of calculations in support of these applications is that the large variations observed from predictions obtained with currently available methods can make comparisons across studies uncertain. Benchmarking currently available computational methodologies is essential to establish reliable practices across the community to guarantee an accurate physical description of the systems studied. To understand the performance of a variety of common theoretical methods, a systematic analysis of differences observed in the prediction of structural characteristics, electron withdrawing effects, and binding energies of [An(NO₃)]²⁺ (with An = Ac to Lr) in gas and aqueous phases is reported. Population analysis obtained with Mulliken and Löwdin reflect a large dependence on the level of theory of choice, whereas those obtained with natural bond orbital show larger consistency across methodologies. Predicted stability across the actinide series calculated with coupled cluster with perturbative doubles and triples at the triple ζ level is equivalent to the one obtained when extrapolated to the complete basis set limit. The ground state of [Fm(NO₃)]²⁺ and [Md(NO₃)]²⁺ is predicted to have an electronic structure corresponding to An III state in gas and An IV in aqueous phase, whereas the ground state of [An(NO₃)]²⁺ (with An = Ac to Es, Lr) presents an electronic structure corresponding to An IV in the gas and aqueous phase. The compounds studied with No in gas and aqueous phase present a preferred No III state, and the Lr compounds did not follow trends predicted for the rest of the actinide series, as previously observed in studies regarding its unusual electronic structure relative to its position in the periodic table.

Exploring the potential energy surface of small lead clusters using the gradient embedded genetic algorithm and an adequate treatment of relativistic effects

Theoretical inclusion of relativistic effects (scalar and spin–orbit) play a crucial role to assure an adequate structural assignment on lead clusters.