Covalency in actinide(iv) hexachlorides in relation to the chlorine K-edge X-ray absorption structure

Bonding and Interactions in UO22+ for Ground and Core Excited States: Extracting Chemistry from Molecular Orbital Calculations

Theoretical analyses of actinyls are necessary in order to understand and correctly interpret the chemical and physical properties of these molecules. Here, wave functions of Uranyl, UO22+, are considered for the ground state and for the core excited states where an electron is promoted from the U 3d5/2 shell into a low-lying unoccupied orbital that is U 5f antibonding with the ligand, O, orbitals. A focus is on the application of novel theoretical methods to the analysis of these wave functions so that measurements, especially with X-ray absorption, can be related to the UO22+ chemical bonding. The bond covalency is examined with these theoretical methods. The study includes how the covalent character is different for the ground and excited configurations and how this character changes as the U-O distance is changed. Furthermore, analyses are mode of how many-body effects may modify excitation energies and X-ray adsorption intensities. This includes determining the extent to which a single configuration provides a satisfactory model for the UO22+ wave functions. Two distinct types of many-body effects are considered. One involves the angular momentum coupling of the open shell electrons in the excited states to yield correct multiplets. The second adds excitations from shells that are bonding into the antibonding open shell space. These excitations are essential to properly describe the X-ray adsorption. While these many-body effects must be taken into account, their importance and their role can be explained and understood using orbitals and orbital occupations.

Understanding covalency in molecular f-block compounds from the synergy of spectroscopy and quantum chemistry

One of the most intensely studied areas of f-block chemistry is the nature of the bonds between the f-element and another species, and in particular the role played by covalency. Computational quantum chemical methods have been at the forefront of this research for decades and have a particularly valuable role, given the radioactivity of the actinide series. The very strong agreement that has recently emerged between theory and the results of a range of spectroscopic techniques not only facilitates deeper insight into the experimental data, but it also provides confidence in the conclusions from the computational studies. These synergies are shining new light on the nature of the f element-other element bond.

Determination of Uranium Central-Field Covalency with 3d4f Resonant Inelastic X-ray Scattering

Understanding the nature of metal-ligand bonding is a major challenge in actinide chemistry. We present a new experimental strategy for addressing this challenge using actinide 3d4f resonant inelastic X-ray scattering (RIXS). Through a systematic study of uranium(IV) halide complexes, [UX6]2-, where X = F, Cl, or Br, we identify RIXS spectral satellites with relative energies and intensities that relate to the extent of uranium-ligand bond covalency. By analyzing the spectra in combination with ligand field density functional theory we find that the sensitivity of the satellites to the nature of metal-ligand bonding is due to the reduction of 5f interelectron repulsion and 4f-5f spin-exchange, caused by metal-ligand orbital mixing and the degree of 5f radial expansion, known as central-field covalency. Thus, this study furthers electronic structure quantification that can be obtained from 3d4f RIXS, demonstrating it as a technique for estimating actinide-ligand covalency.

Quantifying Covalency and Environmental Effects in RASSCF-Simulated O K-Edge XANES of Uranyl

A RASSCF approach to simulate the O K-edge XANES spectra of uranyl is employed, utilizing three models that progressively improve the representation of the local crystal environment. Simulations successfully reproduce the observed three-peak profile of the experimental spectrum and confirm peak assignments made by Denning. The [UO2Cl4]2- model offers the best agreement with experiment, with peak positions (to within 1 eV) and relative peak separations accurately reproduced. Establishing a direct link between a specific electronic transition and peak intensity is complicated, as a large number of possible transitions can contribute to the overall peak profile. Furthermore, a relationship between oxygen character in the antibonding orbital and the strength of the transition breaks down when using a variety of orbital composition approaches at larger excitation energy. Covalency analysis of the U-O bond in both the ground- and excited-state reveals a dependence on the crystal environment. Orbital composition analysis reveals an underestimation of the uranium contribution to ground-state bonding orbitals when probing O K-edge core-excited states, regardless of the uranyl model employed. However, improving the environmental model provides core-excited state electronic structures that are better representative of that of the ground-state, validating their use in the determination of covalency and bonding.

On the origin of low-valent uranium oxidation state

The significant interest in actinide bonding has recently focused on novel compounds with exotic oxidation states. However, the difficulty in obtaining relevant high-quality experimental data, particularly for low-valent actinide compounds, prevents a deeper understanding of 5f systems. Here we show X-ray absorption near-edge structure (XANES) measurements in the high-energy resolution fluorescence detection (HERFD) mode at the uranium M4 edge for the UIII and UIV halides, namely UX3 and UX4 (X = F, Cl, Br, I). The spectral shapes of these two series exhibit clear differences, which we explain using electronic structure calculations of the 3d-4f resonant inelastic X-ray scattering (RIXS) process. To understand the changes observed, we implemented crystal field models with ab initio derived parameters and investigated the effect of reducing different contributions to the electron-electron interactions involved in the RIXS process. Our analysis shows that the electron-electron interactions weaken as the ligand changes from I to F, indicative of a decrease in ionicity both along and between the UX3 and UX4 halide series.

Relativistic Quantum Chemical Investigation of Actinide Covalency Measured by Electron Paramagnetic Resonance Spectroscopy

We investigate actinide covalency effects in two [AnCptt3] (An = Th, U) complexes recently studied with pulsed electron paramagnetic resonance spectroscopy, using the Hyperion package to obtain relativistic hyperfine coupling constants from relativistic multiconfigurational wave functions. 1H and 13C HYSCORE simulations using the computed parameters show excellent agreement with the experimental data, highlighting the accuracy of modern relativistic ab initio methods. The extent of covalency indicated from the calculations on [ThCptt3] is in agreement with the original report based on traditional spectral fitting methods, while the covalency in [UCptt3] is found to be previously overestimated. The latter is due to the paramagnetic spin-orbit effect that arises naturally in a relativistic theory of hyperfine coupling and yet was not accounted for in the original study, thus highlighting the necessity of relativistic approaches for the interpretation of magnetic resonance data pertaining to actinides.

Progress in Nonaqueous Molecular Uranium Chemistry: Where to Next?

There is long-standing interest in nonaqueous uranium chemistry because of fundamental questions about uranium's variable chemical bonding and the similarities of this pseudo-Group 6 element to its congener d-block elements molybdenum and tungsten. To provide historical context, with reference to a conference presentation slide presented around 1988 that advanced a defining collection of top targets, and the challenge, for synthetic actinide chemistry to realize in isolable complexes under normal experimental conditions, this Viewpoint surveys progress against those targets, including (i) CO and related π-acid ligand complexes, (ii) alkylidenes, carbynes, and carbidos, (iii) imidos and terminal nitrides, (iv) homoleptic polyalkyls, -alkoxides, and -aryloxides, (v) uranium-uranium bonds, and (vi) examples of topics that can be regarded as branching out in parallel from the leading targets. Having summarized advances from the past four decades, opportunities to build on that progress, and hence possible future directions for the field, are highlighted. The wealth and diversity of uranium chemistry that is described emphasizes the importance of ligand-metal complementarity in developing exciting new chemistry that builds our knowledge and understanding of elements in a relativistic regime.

Contemporary Assessment of Energy Degeneracy in Orbital Mixing with Tetravalent f-Block Compounds

The f block is a comparatively understudied group of elements that find applications in many areas. Continued development of technologies involving the lanthanides (Ln) and actinides (An) requires a better fundamental understanding of their chemistry. Specifically, characterizing the electronic structure of the f elements presents a significant challenge due to the spatially core-like but energetically valence-like nature of the f orbitals. This duality led f-block scientists to hypothesize for decades that f-block chemistry is dominated by ionic metal-ligand interactions with little covalency because canonical covalent interactions require both spatial orbital overlap and orbital energy degeneracy. Recent studies on An compounds have suggested that An ions can engage in appreciable orbital mixing between An 5f and ligand orbitals, which was attributed to "energy-degeneracy-driven covalency". This model of bonding has since been a topic of debate because different computational methods have yielded results that support and refute the energy-degeneracy-driven covalency model. In this Viewpoint, literatures concerning the metal- and ligand-edge X-ray absorption near-edge structure (XANES) of five tetravalent f-block systems─MO2 (M = Ln, An), LnF4, MCl62-, and [Ln(NP(pip)3)4]─are compiled and discussed to explore metal-ligand bonding in f-block compounds through experimental metrics. Based on spectral assignments from a variety of theoretical models, covalency is seen to decrease from CeO2 and PrO2 to TbO2 through weaker ligand-to-metal charge-transfer (LMCT) interactions, while these LMCT interactions are not observed in the trivalent Ln sesquixodes until Yb. In comparison, while XANES characterization of AnO2 compounds is scarce, computational modeling of available X-ray absorption spectra suggests that covalency among AnO2 reaches a maximum between Am and Cm. Moreover, a decrease in covalency is observed upon changing ligands while maintaining an isostructural coordination environment from CeO2 to CeF4. These results could allude to the importance of orbital energy degeneracy in f-block bonding, but there are a variety of data gaps and conflicting results from different modeling techniques that need to be addressed before broad conclusions can be drawn.

Overdestabilization vs Overstabilization in the Theoretical Analysis of f-Orbital Covalency

The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin-orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl6]3- and [Ce(IV)Cl6]2- complexes show that time-dependent density functional theory with approximate exchange-correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

31P Nuclear Magnetic Resonance Spectroscopy as a Probe of Thorium-Phosphorus Bond Covalency: Correlating Phosphorus Chemical Shift to Metal-Phosphorus Bond Order

We report the use of solution and solid-state 31P Nuclear Magnetic Resonance (NMR) spectroscopy combined with Density Functional Theory calculations to benchmark the covalency of actinide-phosphorus bonds, thus introducing 31P NMR spectroscopy to the investigation of molecular f-element chemical bond covalency. The 31P NMR data for [Th(PH2)(TrenTIPS)] (1, TrenTIPS = {N(CH2CH2NSiPri3)3}3-), [Th(PH)(TrenTIPS)][Na(12C4)2] (2, 12C4 = 12-crown-4 ether), [{Th(TrenTIPS)}2(μ-PH)] (3), and [{Th(TrenTIPS)}2(μ-P)][Na(12C4)2] (4) demonstrate a chemical shift anisotropy (CSA) ordering of (μ-P)3- > (═PH)2- > (μ-PH)2- > (-PH2)1- and for 4 the largest CSA for any bridging phosphido unit. The B3LYP functional with 50% Hartree-Fock mixing produced spin-orbit δiso values that closely match the experimental data, providing experimentally benchmarked quantification of the nature and extent of covalency in the Th-P linkages in 1-4 via Natural Bond Orbital and Natural Localized Molecular Orbital analyses. Shielding analysis revealed that the 31P δiso values are essentially only due to the nature of the Th-P bonds in 1-4, with largely invariant diamagnetic but variable paramagnetic and spin-orbit shieldings that reflect the Th-P bond multiplicities and s-orbital mediated transmission of spin-orbit effects from Th to P. This study has permitted correlation of Th-P δiso values to Mayer bond orders, revealing qualitative correlations generally, but which should be examined with respect to specific ancillary ligand families rather than generally to be quantitative, reflecting that 31P δiso values are a very sensitive reporter due to phosphorus being a soft donor that responds to the rest of the ligand field much more than stronger, harder donors like nitrogen.

Bounding [AnO2]2+ (An = U, Np) covalency by simulated O K-edge and An M-edge X-ray absorption near-edge spectroscopy

Restricted active space simulations are shown to accurately reproduce and characterise both O K-edge and U M4,5-edge spectra of uranyl in excellent agreement with experimental peak positions and are extended to the Np analogue. Analysis of bonding orbital composition in the ground and O K-edge core-excited states demonstrates that metal contribution is underestimated in the latter. In contrast, An M4/5-edge core-excited states produce bonding orbital compositions significantly more representative of those in the ground state. Quantum Theory of Atoms in Molecules analysis is employed to explain the discrepancy between K- and M-edge data and demonstrates that the location of the core-hole impacts the pattern of electron localisation in core-excited states. An apparent contradiction to this behaviour in neptunyl is rationalised in terms interelectronic repulsion between the unpaired 5f electron and the excited core-electron.

Core Excitations of Uranyl in Cs2UO2Cl4 from Relativistic Embedded Damped Response Time-Dependent Density Functional Theory Calculations

X-ray spectroscopies, by their high selectivity and sensitivity to the chemical environment around the atoms probed, provide significant insights into the electronic structures of molecules and materials. Interpreting experimental results requires reliable theoretical models, accounting for environmental, relativistic, electron correlation, and orbital relaxation effects in a balanced manner. In this work, we present a protocol for the simulation of core excited spectra with damped response time-dependent density functional theory based on the Dirac-Coulomb Hamiltonian (4c-DR-TD-DFT), in which environmental effects are accounted for through the frozen density embedding (FDE) method. We showcase this approach for the uranium M4- and L3-edges and oxygen K-edge of the uranyl tetrachloride (UO2Cl42-) unit as found in a host Cs2UO2Cl4 crystal. We have found that the 4c-DR-TD-DFT simulations yield excitation spectra that very closely match the experiment for the uranium M4-edge and the oxygen K-edge, with good agreement for the broad experimental spectra for the L3-edge. By decomposing the complex polarizability in terms of its components, we have been able to correlate our results with angle-resolved spectra. We have observed that for all edges, but in particular the uranium M4-edge, an embedded model in which the chloride ligands are replaced by an embedding potential reproduces rather well the spectral profile obtained for UO2Cl42-. Our results underscore the importance of the equatorial ligands to simulating core spectra at both uranium and oxygen edges.

Periodic Trends in the Stabilization of Actinyls in Their Higher Oxidation States Using Pyrrophen Ligands

Owing to the prominent existence and unique chemistry of actinyls, their complexation with suitable ligands is of significant interest. The complexation of high-valent actinyl moieties (An = U, Np, Pu and Am) with the acyclic sal-porphyrin analogue called "pyrrophen" (L₍₁₎) and its dimethyl derivative (L₍₂₎) with four nitrogen and two oxygen donor atoms was studied using relativistic density functional theory. Based on the periodic trends, the [U^VO₂-L₍₁₎/L₍₂₎]^1- complexes show shorter bond lengths and higher bond orders that increase across the series of pentavalent actinyl complexes mainly due to the localization of the 5f orbitals. Among the hexavalent complexes, the [U^VIO₂-L₍₁₎/L₍₂₎] complexes have the shortest bonds. Following the uranyl complex, due to the plutonium turn, the [Am^VIO₂-L₍₁₎/L₍₂₎] complexes exhibit comparable properties with those of the former. Charge analysis suggests the complexation to be facilitated through ligand-to-metal charge transfer (LMCT) mainly through σ donation. Thermodynamic feasibility of complexation was modeled using hydrated actinyl moieties in aqueous medium and was found to be spontaneous. The dimethylated pyrrophen (L₍₂₎) shows higher magnitudes of thermodynamic parameters indicating increased feasibility compared to the unsubstituted ligand (L₍₁₎). Energy decomposition analysis (EDA) along with extended transition-state-natural orbitals for chemical valence theory (ETS-NOCV) analysis shows that the dominant electrostatic contributions decrease across the series and are counteracted by Pauli repulsion. Slight but considerable covalency is provided to hexavalent actinyl complexes by orbital contributions; this was confirmed by molecular orbital (MO) analysis that suggests strong covalency in americyl (VI) complexes. In addition to the pentavalent and hexavalent actinyl moieties, heptavalent actinyl species of neptunyl, plutonyl, and americyl were studied. Beyond the influence of the charges, the geometric and electronic properties point to the stabilization of neptunyl (VII) in the pyrrophen ligand environment, while the others shift to a lower (+VI) and relatively stable OS on complexation.

Evaluating f-Orbital Participation in the UV═E Multiple Bonds of [U(E)(NR2)3] (E = O, NSiMe3, NAd; R = SiMe3)

The reaction of 1 equiv of 1-azidoadamantane with [U^III(NR₂)₃] (R = SiMe₃) in Et₂O results in the formation of [U^V(NR₂)₃(NAd)] (1, Ad = 1-adamantyl) in good yields. The electronic structure of 1, as well as those of the related U(V) complexes, [U^V(NR₂)₃(NSiMe₃)] (2) and [U^V(NR₂)₃(O)] (3), were analyzed with EPR spectroscopy, SQUID magnetometry, NIR-visible spectroscopy, and crystal field modeling. This analysis revealed that, within this series of complexes, the steric bulk of the E^2- (E═O, NR) ligand is the most important factor in determining the electronic structure. In particular, the increasing steric bulk of this ligand, on moving from O^2- to [NAd]^2-, results in increasing U═E distances and E-U-N_amide angles. These changes have two principal effects on the resulting electronic structure: (1) the increasing U═E distances decreases the energy of the f_σ orbital, which is primarily σ* with respect to the U═E bond, and (2) the increasing E-U-N_amide angles increases the energy of f_δ, due to increasing antibonding interactions with the amide ligands. As a result of the latter change, the electronic ground state for complexes 1 and 2 is primarily f_φ in character, whereas the ground state for complex 3 is primarily f_δ.

On the highest oxidation states of the actinoids in AnO4 molecules (An = Ac - Cm): A DMRG-CASSCF study

Actinoid tetroxide molecules AnO₄ (An = Ac - Cm) are investigated with the ab initio density matrix renormalization group (DMRG) approach. Natural orbital shapes are used to read out the oxidation state (OS) of the f-elements, and the atomic orbital energies and radii are used to explain the trends. The highest OSs reveal a "volcano"-type variation: For An = Ac - Np, the OSs are equal to the number of available valence electrons, that is, Ac^III , Th^IV , Pa^V , U^VI , and Np^VII . Starting with plutonium as the turning point, the highest OSs in the most stable AnO₄ isomers then decrease as Pu^V , Am^V , and Cm^III , indicating that the 5f-electrons are hard to be fully oxidized off from Pu onward. The variations are related to the actinoid contraction and to the 5f-covalency characteristics. Combined with previous work on OSs, we review their general trends throughout the periodic table, providing fundamental understanding of OS-relevant phenomena.

Aqueous Speciation of Tetravalent Actinides in the Presence of Chloride and Nitrate Ligands

Speciation of hexachloride tetravalent uranium, neptunium, and plutonium species in aqueous media has been investigated using density functional theory in the presence of inner sphere ligands such as chloride, nitrate, and solvent molecules. All possible structures with the formula [An^IV(Cl)_x(H₂O)_y(NO₃)_z]^4-x-z (An = U, Np, and Pu; x = 0-6, y = 0-8, and z = 0-6) were considered to explore the speciation chemical space of each actinide. The nature of the mixed-ligand complexes present in solution is controlled by the concentration of free ligands in solution. A low chloride concentration is suitable to drive the speciation away from the highly thermodynamically stable hexachloride species. Furthermore, the formation of dimeric species can proceed through both olation and oxolation mechanisms. Oxolation is preferred for monomers that contain fewer water ligands, while olation becomes favorable for complexes with more water ligands.