Assessing Covalency in Cerium and Uranium Hexachlorides: A Correlated Wavefunction and Density Functional Theory Study

Cerium Photocatalyst in Action: Structural Dynamics in the Presence of Substrate Visualized via Time-Resolved X-ray Liquidography

[Ce(III)Cl6]3-, with its earth-abundant metal element, is a promising photocatalyst facilitating carbon-halogen bond activation. Still, the structure of the reaction intermediate has yet to be explored. Here, we applied time-resolved X-ray liquidography (TRXL), which allows for direct observation of the structural details of reaction intermediates, to investigate the photocatalytic reaction of [Ce(III)Cl6]3-. Structural analysis of the TRXL data revealed that the excited state of [Ce(III)Cl6]3- has Ce-Cl bonds that are shorter than those of the ground state and that the Ce-Cl bond further contracts upon oxidation. In addition, this study represents the first application of TRXL to both photocatalyst-only and photocatalyst-and-substrate samples, providing insights into the substrate's influence on the photocatalyst's reaction dynamics. This study demonstrates the capability of TRXL in elucidating the reaction dynamics of photocatalysts under various conditions and highlights the importance of experimental determination of the structures of reaction intermediates to advance our understanding of photocatalytic mechanisms.

Deciphering the Role of Symmetry and Ligand Field in Designing Three-Coordinate Uranium and Plutonium Single-Molecule Magnets

Actinide single-molecule magnets (SMMs) have gained paramount interest in molecular magnetism as they offer a larger barrier height of magnetization (U_eff) reversal compared to the lanthanide analogue, thanks to their greater metal-ligand covalency. However, the reported actinide SMMs to date yield a relatively smaller U_eff as there is no established design principle to enhance U_eff values. To address this issue, we have employed ab initio CASSCF/CASPT2/NEVPT2 calculations to study a series of three-coordinate U³⁺ and Pu³⁺ SMMs. To begin with, we have studied two experimentally characterized U³⁺ ion-field-induced SMMs, namely, planar [U{N(SiMe₂^tBu)₂}₃] (1) and pyramidal [U{N(SiMe₃)₂}₃] (2) complexes reported earlier. Both the complexes were found to stabilize m_J = |±1/2⟩ as the ground state with a very strong quantum tunneling of magnetization (QTM), rendering them unsuitable for SMMs. Our calculations reveal that in the pyramidal geometry (such as in 2), the energy of the 5f²6d¹ state is lowered compared to the planar geometry (as in 1), resulting in a slightly better SMM characteristic in the former. To unravel the effect of symmetry in magnetic properties, ab initio calculations were performed on two reported T-shaped complexes [U(NSiⁱPr₂)₂(I)] (3) and [U(NHAr^iPr6)₂I] (4, Ar^iPr6 = 2,6-(2,4,6-iPr₃C₆H₂)₂C₆H₃). Quite interestingly, m_J = |±9/2⟩ is found to be the ground state for both the complexes with a blocking barrier exceeding 900 cm^-1. Furthermore, to decipher the effect of the transuranic element in magnetic anisotropy, ab initio calculations were extended to the Pu analogue of 2, [Pu{N(SiMe₃)₂}₃] (5), which yields a record-breaking blocking barrier of ∼1933 cm^-1. Among the three-coordinate geometries studied, the pyramidal geometry was found to offer substantial magnetic anisotropy for Pu³⁺ ions, while a T-shaped geometry is best suited for U³⁺ ions. While the chosen theoretical protocols' overestimation of barrier height cannot be avoided, these values are still several orders of magnitude larger than the U_eff values reported for any actinide SMMs and unveil a design principle for superior three-coordinate actinide-based SMMs.

Covalency in Actinide(IV) Hexachlorides in Relation to Chlorine K­-Edge X­-ray Absorption Structure

Chlorine K-edge X-ray absorption near edge structure (XANES) in actinide^IV hexachlorides, [AnCl₆]²⁻ (An = Th–Pu), is calculated with relativistic multiconfiguration wavefunction theory (WFT). Of particular focus is a 3-peak feature emerging from U toward Pu, and its assignment in terms of donation bonding to the An 5f vs. 6d shells. With or without spin–orbit coupling, the calculated and previously measured XANES spectra are in excellent agreement with respect to relative peak positions, relative peak intensities, and peak assignments. Metal–ligand bonding analyses from WFT and Kohn–Sham theory (KST) predict comparable An 5f and 6d covalency from U to Np and Pu. Although some frontier molecular orbitals in the KST calculations display increasing An 5f–Cl 3p mixing from Th to Pu, because of energetic stabilization of 5f relative to the Cl 3p combinations of the matching symmetry, increasing hybridization is neither seen in the WFT natural orbitals, nor is it reflected in the calculated bond orders. The appearance of the pre-edge peaks from U to Pu and their relative intensities are rationalized simply by the energetic separation of transitions to 6d t_2gversus transitions to weakly-bonded and strongly stabilized a_2u, t_2u and t_1u orbitals with 5f character. The study highlights potential pitfalls when interpreting XANES spectra based on ground state Kohn–Sham molecular orbitals.

Chlorine K-edge XANES of An(iv) hexachlorides, calculated with multiconfiguration wavefunction theory, is interpreted in terms of similar metal–ligand covalency along the An = Th–Pu series.

A theoretical investigation of uranyl covalency via symmetry-preserving excited state structures

The structures of electronically excited states of uranyl are probed via density-based analysis to deepen understanding of uranium bonding.

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.

Near-infrared C-term MCD spectroscopy of octahedral uranium(V) complexes

C-term magnetic circular dichroism (MCD) spectroscopy is a powerful method for probing d-d and f-f transitions in paramagnetic metal complexes. However, this technique remains underdeveloped both experimentally and theoretically for studies of U(v) complexes of Oh symmetry, which have been of longstanding interest for probing electronic structure, bonding, and covalency in 5f systems. In this study, C-term NIR MCD of the Laporte forbidden f-f transitions of [UCl6]- and [UF6]- are reported, demonstrating the significant fine structure resolution possible with this technique including for the low energy Γ7 → Γ8 transitions in [UF6]-. The experimental NIR MCD studies were further extended to [U(OC6F5)6]-, [U(CH2SiMe3)6]-, and [U(NC(tBu)(Ph))6]- to evaluate the effects of ligand-type on the f-f MCD fine structure features. Theoretical calculations were conducted to determine the Laporte forbidden f-f transitions and their MCD intensity experimentally observed in the NIR spectra of the U(v) hexahalide complexes, via the inclusion of vibronic coupling, to better understand the underlying spectral fine structure features for these complexes. These spectra and simulations provide an important platform for the application of MCD spectroscopy to this widely studied class of U(v) complexes and identify areas for continued theoretical development.

Covalency in AnCl3 (An = Th-No)

The geometric and electronic structures of AnCl3 are studied computationally using scalar relativistic, hybrid density functional theory (PBE0). The An-Cl bond lengths generally decrease across the 5f series, although there is a slight lengthening from Fm-Cl to No-Cl as the metal ions display increasing M(ii) character. Covalency in the An-Cl bond is studied using a wide range of metrics drawn from the Natural Bond Orbital, Natural Resonance Theory and Quantum Theory of Atoms-in-Molecules (QTAIM) methods, including bond order, orbital composition, orbital overlap and electron density topology data. Most metrics agree that the later An-Cl bonds are less ionic than might be anticipated on the basis of trends in the first half of the series, due to energy degeneracy-driven covalency in the β spin manifold; for example, the An-Cl QTAIM delocalisation index (bond order) for MdCl3 (0.88) is almost exactly the same as for NpCl3 (0.89). By contrast, the ratio of the kinetic to potential energy densities at the An-Cl bond critical points indicates that ionicity increases across the series, suggesting that the delocalisation index measures both orbital overlap and energy degeneracy-based covalency, while the bond critical point metric gauges only the former. Recalculation of all the data using the generalised gradient approximation PBE functional finds larger energy degeneracy-driven covalency in the later actinides than using hybrid DFT. Hence, we find that conclusions concerning the covalency of the An-Cl bond are dependent not only on the metric used to evaluate it, but also on the underlying electronic structure method.

Structure and Characterization of an Americium Bis(O,O'-diethyl)dithiophosphate Complex

A facile synthesis of an americium complex with a sulfur-donor ligand has been developed, allowing characterization of americium bonding from multiple perspectives via several techniques. Reaction of ²⁴³Am with S₂P(OEt)₂^- yields the tetrakis complex [Am(S₂P(OEt)₂)₄]^- that can be crystallized as the tetraphenylarsonium salt. Structures obtained from single crystal X-ray diffraction show bond length discrepancies from the neodymium analogue consistent with the soft-donor bond enhancement common to actinides. Solid state optical spectroscopy confirms interaction of the ligand with 5f orbitals. ³¹P nuclear magnetic reflects the minor paramagnetism of Am(III). Computational investigations through CASSCF calculations, ligand-field density functional theory, and quantum chemical topological analysis allow a quantification of covalency or orbital interaction effects via total energy density and nephelauxetic parameters, both of which indicate greater covalency in the americium species than in the neodymium analogue or the americium aquo complex.

Series of Tetravalent Actinide Amidinates: Structure Determination and Bonding Analysis

Two series of isostructural tetravalent actinide amidinates [AnX((S)-PEBA)₃] (An = Th, U, Np; X = Cl, N₃) bearing the chiral (S,S)-N,N'-bis(1-phenylethyl)benzamidinate ((S)-PEBA) ligand have been synthesized and thoroughly characterized in solid and in solution. This study expands the already reported tetravalent neptunium complexes to the lighter actinides thorium and uranium. Furthermore, a rare Ce(IV) amidinate [CeCl((S)-PEBA)₃] was synthesized to compare its properties to those of the analogous tetravalent actinide complexes. All compounds were characterized in the solid state using single-crystal XRD and infrared spectroscopy and in solution using NMR spectroscopy. Quantum chemical bonding analysis including also the isostructural Pa and Pu complexes was used to characterize the covalent contributions to any bond involving the metal cation. Th shows the least covalent character throughout the series, even substantially smaller than for the Ce complex. For U, Np, and Pu, similar covalent bonding contributions are found, but a natural population analysis reveals different origins. The 6d participation is the highest for U and decreases afterward, whereas the 5f participation increases continuously from Pa to Pu.

Analysis of charge density in nonaaquagadolinium(III) trifluoromethanesulfonate - insight into GdIII-OH2 bonding

The experimental charge-density distribution in [Gd(H₂O)₉](CF₃SO₃)₃ has been analysed and compared with the theoretical density functional theory calculations. Although the Gd-OH₂ bonds are mainly ionic, a covalent contribution is detectable when inspecting both the topological parameters of these bonds and the natural bond orbital results. This contribution originates from small electron transfer from the lone pairs of oxygen atoms to empty 5d and 6s spin orbitals of Gd³⁺.

f-Orbital Mixing in the Octahedral f2 Compounds UX62- [X = F, Br, Cl, I] and PrCl63

Understanding how interactions between the f orbitals and ligand orbitals in lanthanide and actinide systems affect their physical properties is the central issue in f-element chemistry. A wide variety of approaches including both theoretical and experimental tools have been used to study these relationships. Among the most widely used tools has been crystal field theory (CFT), which bridges theory and experiment in that it is a model based largely on atomic theory that is parametrized using experimental data. Crystal field theory is quite accurate for the lanthanides, due in part to the highly contracted nature of the 4f orbitals. For actinides, crystal field theory is less accurate, potentially due to the treatment of orbital mixing. In CFT, orbital mixing is handled implicitly by allowing the electron repulsion parameters (Slater F^k parameters) and the spin-orbit coupling constant to vary. As a result, orbital mixing in CFT is isotropic in that the F^k parameters and the spin-orbit coupling constant affect all f orbitals equally. This approximation works well for the lanthanides due to the limited degree of orbital mixing in these complexes. In actinide complexes, the 5f orbitals have greater overlap with the ligand orbitals, and this approximation is less accurate than in the lanthanides. Here, we report a modification of CFT that includes the effect of orbital mixing on electron repulsion and spin-orbit coupling for each f orbital. The model is applied to the tetravalent uranium hexahalide dianions and PrCl₆^3- for which the energies of many low-lying excited states are known. The new model generally fits the data as well the traditional CFT although with fewer parameters. However, the new model does not fit the data better than the more complex CFT models of Faucher and co-workers. The results of the model show in detail how changes in overlap and orbital energies influence the energies of the bonding and antibonding orbitals.

Intra- and intermolecular interception of a photochemically generated terminal uranium nitride

The photochemically generated synthesis of a terminal uranium nitride species is here reported and an examination of its intra- and intermolecular chemistry is presented. Treatment of the U(iii) complex L^ArUI(DME) ((L^Ar)²⁻ = 2,2′′-bis(Dippanilide)-p-terphenyl; Dipp = 2,6-diisopropylphenyl) with LiNIm^Dipp ((NIm^Dipp)⁻ = 1,3-bis(Dipp)-imidazolin-2-iminato) generates the sterically congested 3N-coordinate compound L^ArU(NIm^Dipp) (1). Complex 1 reacts with 1 equiv. of Ph₃CN₃ to give the U(iv) azide L^ArU(N₃)(NIm^Dipp) (2). Structural analysis of 2 reveals inequivalent N_α–N_β > N_β–N_γ distances indicative of an activated azide moiety predisposed to N₂ loss. Room-temperature photolysis of benzene solutions of 2 affords the U(iv) amide (N-L^Ar)U(NIm^Dipp) (3) via intramolecular N-atom insertion into the benzylic C–H bond of a pendant isopropyl group of the (L^Ar)²⁻ ligand. The formation of 3 occurs as a result of the intramolecular interception of the intermediately generated, terminal uranium nitride (L^Ar)U(N)(NIm^Dipp) (3′). Evidence for the formation of 3′ is further bolstered by its intermolecular capture, accomplished by photolyzing solutions of 2 in the presence of an isocyanide or PMe₃ to give (L^Ar)U[NCN(C₆H₃Me₂)](NIm^Dipp) (5) and (N,C-L^Ar*)U(N Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> PMe₃)(NIm^Dipp) (6), respectively. These results expand upon the limited reactivity studies of terminal uranium–nitride moieties and provide new insights into their chemical properties.

Photolysis of the U(iv) azide L^ArU(NIm^Dipp) generates a reactive uranium nitride intermediate that can be intercepted by nucleophilic substrates – the first example of intermolecular chemistry of a rare photochemically generated uranium nitride.

Quantum chemical topology and natural bond orbital analysis of M–O covalency in M(OC6H5)4 (M = Ti, Zr, Hf, Ce, Th, Pa, U, Np)

V_XC(M,O): the exchange–correlation metric quantifies covalency between M and O atomic basins in M(OC₆H₅)₄ (M = Ti, Zr, Hf, Ce, Th, Pa, U, Np).

Computational analysis of M–O covalency in M(OC6H5)4 (M = Ti, Zr, Hf, Ce, Th, U)

Trends in covalency of structurally analogous d and f element compounds are explored over changes in the M–O bond distance.

Experimental and Theoretical Comparison of Transition-Metal and Actinide Tetravalent Schiff Base Coordination Complexes

A series of homoleptic tetravalent transition-metal and actinide Schiff-base coordination complexes, ML₂ {M = Zr, Hf, Th, U; L = N, N'-bis[(4,4'-diethylamino)salicylidene]-1,2-phenylenediamine}, have been synthesized that feature a rigid phenyl backbone. These complexes create the opportunity for comparing a series of complexes containing metal cations in the formal IV+ oxidation state by structural, spectroscopic, and theoretical analysis that also incorporate the previously reported Ce(IV) and Pu(IV) analogues. X-ray crystallographic analysis reveals that all complexes are isomorphous and feature a co-facial ligand geometry. TD-DFT and other quantum mechanical methods were used to explore bonding differences across between the complexes, and resulting calculated absorbance spectra for ML₂ are in good agreement with the experimental data. The computational results also suggest that U(IV) and Pu(IV) analogs have more covalent character in their bonding than found with the other metal cations reported here.

Ab Initio Study of Covalency in the Ground versus Core-Excited States and X-ray Absorption Spectra of Actinide Complexes

Relativistic multireference ab initio wave function calculations within the restricted active space (RAS) framework were performed to calculate metal and ligand X-ray absorption (XAS) near-edge spectroscopy (XANES) intensities for the metal M_4,5 edges of [PuO₂(H₂O)₅]²⁺, [An^VIO₂]²⁺ (An = U, Np, Pu), and [AmCl₆]^3- and the Cl K edge of the Am complex. The extent of An(5f)-ligand bonding was determined via natural localized molecular orbital analyses of the relevant spin-orbit coupled multireference states. The calculated spectra are in good agreement with experiments and allow a detailed assignment of the observed spectral features. The XANES M_4,5-edge spectra are representative of the actinide orbital covalency in the probed core-excited states, which may be different from the ground-state covalency. An assignment of ground-state An orbital covalency based on XAS spectra should therefore be made with caution.

Decomposition of d- and f-Shell Contributions to Uranium Bonding from the Quantum Theory of Atoms in Molecules: Application to Uranium and Uranyl Halides

The electronic structures of a series of uranium hexahalide and uranyl tetrahalide complexes were simulated at the density functional theoretical (DFT) level. The resulting electronic structures were analyzed using a novel application of the Quantum Theory of Atoms in Molecules (QTAIM) by exploiting the high symmetry of the complexes to determine 5f- and 6d-shell contributions to bonding via symmetry arguments. This analysis revealed fluoride ligation to result in strong bonds with a significant covalent character while ligation by chloride and bromide species resulted in more ionic interactions with little differentiation between the ligands. Fluoride ligands were also found to be most capable of perturbing an existing electronic structure. 5f contributions to overlap-driven covalency were found to be larger than 6d contributions for all interactions in all complexes studied while degeneracy-driven covalent contributions showed significantly greater variation. σ-contributions to degeneracy-driven covalency were found to be consistently larger than those of individual π-components while the total π-contribution was, in some cases, larger. Strong correlations were found between overlap-driven covalent bond contributions, U–O vibrational frequencies, and energetic stability, which indicates that overlap-driven covalency leads to bond stabilization in these complexes and that uranyl vibrational frequencies can be used to quantitatively probe equatorial bond covalency. For uranium hexahalides, degeneracy-driven covalency was found to anti-correlate with bond stability.

Pentavalent Curium, Berkelium, and Californium in Nitrate Complexes: Extending Actinide Chemistry and Oxidation States

Pentavalent actinyl nitrate complexes An^VO₂(NO₃)₂^- were produced by elimination of two NO₂ from An^III(NO₃)₄^- for An = Pu, Am, Cm, Bk, and Cf. Density functional theory (B3LYP) and relativistic multireference (CASPT2) calculations confirmed the AnO₂(NO₃)₂^- as An^VO₂⁺ actinyl moieties coordinated by nitrates. Computations of alternative An^IIIO₂(NO₃)₂^- and An^IVO₂(NO₃)₂^- revealed significantly higher energies. Previous computations for bare AnO₂⁺ indicated An^VO₂⁺ for An = Pu, Am, Cf, and Bk, but Cm^IIIO₂⁺: electron donation from nitrate ligands has here stabilized the first Cm^V complex, Cm^VO₂(NO₃)₂^-. Structural parameters and bonding analyses indicate increasing An-NO₃ bond covalency from Pu to Cf, in accordance with principles for actinide separations. Atomic ionization energies effectively predict relative stabilities of oxidation states; more reliable energies are needed for the actinides.

Quantification of f-element covalency through analysis of the electron density: insights from simulation

The electronic structure of f-element compounds is complex due to a combination of relativistic effects, strong electron correlation and weak crystal field environments. However, a quantitative understanding of bonding in these compounds is becoming increasingly technologically relevant. Recently, bonding interpretations based on analyses of the physically observable electronic density have gained popularity and, in this Feature Article, the utility of such density-based approaches is demonstrated. Application of Bader's Quantum Theory of Atoms in Molecules (QTAIM) is shown to elucidate many properties including bonding trends, orbital overlap and energy degeneracy-driven covalency, oxidation state identification and bond stability, demonstrating the increasingly important role that simulation and analysis play in the area of f-element bond characterisation.

Calculation of Dipole-Forbidden 5f Absorption Spectra of Uranium(V) Hexa-Halide Complexes

Restricted-active-space wave function calculations including spin-orbit coupling, in combination with Kohn-Sham density functional calculations of vibrational modes, were used to determine the vibronic and electronic absorption intensities of the near-infrared electric dipole-forbidden 5f-5f transitions of representative uranium(V) hexa-halide complex ions. The agreement with experimentally assigned vibronic and electronic transitions measured for powder or solution samples of salts of the complex ions is reasonable overall and excellent for the experimentally best-resolved E_5/2u → E_5/2u^' bands. The intensity of the vibronic transitions may be borrowed from ligand-to-metal charge-transfer excitations as well as 5f-to-6d metal-centered transitions. Magnetically allowed electronic transitions contribute to the two lower-frequency bands of the ligand-field spectrum.

Magnetic circular dichroism of UCl6− in the ligand-to-metal charge-transfer spectral region

We present a combined ab initio theoretical and experimental study of the magnetic circular dichroism (MCD) spectrum of the octahedral UCl₆⁻ complex ion in the UV-Vis spectral region.

Ligand size dependence of U–N and U–O bond character in a series of uranyl hexaphyrin complexes: quantum chemical simulation and density based analysis

A quantum chemical and density based analysis of bonding in uranyl hexaphyrin complexes, looking for trends in stability and covalency.

Assessing covalency in equatorial U–N bonds: density based measures of bonding in BTP and isoamethyrin complexes of uranyl

N-donor complexes of uranyl have been investigated with density-based analytical methods in order to quantify equatorial bond covalency and its effect on axial U–O_yl bonding.