The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes.

The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which generates a complex set of levels characterized by spin mixing. Although the model multispin Hamiltonian in the absence of local orbital momentum, , is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of HMS from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto HMS, thus validating it regardless of the exchange limit. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of HMS in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Furthermore, the strategy allows to question the use of the spin Hamiltonian approach by explicitly controlling the projection norms on the model space, which is showcased in the second complex where local orbital momentum could have occurred (distorted octahedra). Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak exchange limit.

Chemical design of electronic and magnetic energy scales of tetravalent praseodymium materials.

Lanthanides in the trivalent oxidation state are typically described using an ionic picture that leads to localized magnetic moments. The hierarchical energy scales associated with trivalent lanthanides produce desirable properties for e.g., molecular magnetism, quantum materials, and quantum transduction. Here, we show that this traditional ionic paradigm breaks down for praseodymium in the tetravalent oxidation state. Synthetic, spectroscopic, and theoretical tools deployed on several solid-state Pr4+-oxides uncover the unusual participation of 4f orbitals in bonding and the anomalous hybridization of the 4f1 configuration with ligand valence electrons, analogous to transition metals. The competition between crystal-field and spin-orbit-coupling interactions fundamentally transforms the spin-orbital magnetism of Pr4+, which departs from the Jeff = 1/2 limit and resembles that of high-valent actinides. Our results show that Pr4+ ions are in a class on their own, where the hierarchy of single-ion energy scales can be tailored to explore new correlated phenomena in quantum materials.

A charged diatomic triple-bonded U≡N species trapped in C82 fullerene cages.

Actinide diatomic molecules are ideal models to study elusive actinide multiple bonds, but most of these diatomic molecules have so far only been studied in solid inert gas matrices. Herein, we report a charged U≡N diatomic species captured in fullerene cages and stabilized by the U-fullerene coordination interaction. Two diatomic clusterfullerenes, viz. UN@Cs(6)-C82 and UN@C2(5)-C82, were successfully synthesized and characterized. Crystallographic analysis reveals U-N bond lengths of 1.760(7) and 1.760(20) Å in UN@Cs(6)-C82 and UN@C2(5)-C82. Moreover, U≡N was found to be immobilized and coordinated to the fullerene cages at 100 K but it rotates inside the cage at 273 K. Quantum-chemical calculations show a (UN)2+@(C82)2- electronic structure with formal +5 oxidation state (f1) of U and unambiguously demonstrate the presence of a U≡N bond in the clusterfullerenes. This study constitutes an approach to stabilize fundamentally important actinide multiply bonded species.

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

Chlorine K-edge X-ray absorption near edge structure (XANES) in actinideIV 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 t2g versus transitions to weakly-bonded and strongly stabilized a2u, t2u and t1u orbitals with 5f character. The study highlights potential pitfalls when interpreting XANES spectra based on ground state Kohn-Sham molecular orbitals.

X-ray absorption spectra of f-element complexes: insight from relativistic multiconfigurational wavefunction theory.

X-ray absorption near edge structure (XANES) spectroscopy, coupled with ab initio calculations, has emerged as the state-of-the-art tool for elucidating the metal-ligand bonding in f-element complexes. This highlight presents recent efforts in calculating XANES spectra of lanthanide and actinide compounds with relativistic multiconfiguration wavefunction approaches that account for differences in donation bonding in the ground state (GS) versus a core-excited state (ES), multiplet effects, and spin-orbit-coupling. With the GS and ES wavefunctions available, including spin-orbit effects, an arsenal of chemical bonding tools that are popular among chemists can be applied to rationalize the observed intensities in terms of covalent bonding.

Equatorial Electronic Structure in the Uranyl Ion: Cs2UO2Cl4 and Cs2UO2Br4.

Electric field gradient (EFG) tensors in the equatorial plane of the linear UO22+ ion have been measured by nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) experiments and computed by relativistic Kohn-Sham methods with and without environment embedding for Cs2UO2Cl4 and Cs2UO2Br4. This approach expands the possibilities for probing the electronic structure in uranyl complexes beyond the strongly covalent U-O bonds. The combined analyses find that one of the two largest principal EFG tensor components at the halogen sites points along the U-X bond (X = Cl, Br), and the second is parallel to the UO22+ ion; in Cs2UO2Cl4, the components are nearly equal in magnitude, whereas in Cs2UO2Br4, due to short-range bromide-cesium interactions, the equatorial component is dominant for one pair of Br sites and the axial component is larger for the second pair. The directions and relative magnitudes of the field gradient principal axes are found to be sensitive to the σ and π electron donation by the ligands and the model of the environment. Chlorine-35 NQR spectra of 235U-depleted and 235U-enriched Cs2UO2Cl4 exhibited no uranium-isotope-dependent shift, but the resonance of the depleted sample displayed a 58% broader line width.

Correction: Enhanced 5f-δ bonding in [U(C7H7)2]-: C K-edge XAS, magnetism, and ab initio calculations.

Correction for 'Enhanced 5f-δ bonding in [U(C7H7)2]-: C K-edge XAS, magnetism, and ab initio calculations' by Yusen Qiao et al., Chem. Commun., 2021, 57, 9562-9565, DOI: 10.1039/D1CC03414F.

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.

Enhanced 5f-δ bonding in [U(C7H7)2]-: C K-edge XAS, magnetism, and ab initio calculations.

5f covalency in [U(C7H7)2]- was probed with carbon K-edge X-ray absorption spectroscopy (XAS) and electronic structure theory. The results revealed U 5f orbital participation in δ-bonding in both the ground- and core-excited states; additional 5f ϕ-mixing is observed in the core-excited states. Comparisons with U(C8H8)2 show greater δ-covalency for [U(C7H7)2]-.

Probing Multiconfigurational States by Spectroscopy: The Cerium XAS L3 -edge Puzzle.

Invited for the cover of this issue are Prof. Jochen Autschbach and Dr. Dumitru-Claudiu Sergentu of State University of New York at Buffalo, and Dr. Corwin H. Booth of Lawrence Berkeley National Laboratory. The image depicts high-energy X-ray beams as lightnings probing Ce at the L3 edge in the iconic covalent-bonded Ce(C8 H8 )2 and in CeO2 . The mountain peaks in the background represent the double-peaked L3 edges. The peaks turn out to be intuitively interpreted in terms of localized orbitals and hence metal oxidation states. Read the full text of the article at 10.1002/chem.202100145.

Isolation and characterization of a covalent CeIV-Aryl complex with an anomalous 13C chemical shift.

The synthesis of bona fide organometallic CeIV complexes is a formidable challenge given the typically oxidizing properties of the CeIV cation and reducing tendencies of carbanions. Herein, we report a pair of compounds comprising a CeIV - Caryl bond [Li(THF)4][CeIV(κ2-ortho-oxa)(MBP)2] (3-THF) and [Li(DME)3][CeIV(κ2-ortho-oxa)(MBP)2] (3-DME), ortho-oxa = dihydro-dimethyl-2-[4-(trifluoromethyl)phenyl]-oxazolide, MBP2- = 2,2'-methylenebis(6-tert-butyl-4-methylphenolate), which exhibit CeIV - Caryl bond lengths of 2.571(7) - 2.5806(19) Å and strongly-deshielded, CeIV - Cipso 13C{1H} NMR resonances at 255.6 ppm. Computational analyses reveal the Ce contribution to the CeIV - Caryl bond of 3-THF is ~12%, indicating appreciable metal-ligand covalency. Computations also reproduce the characteristic 13C{1H} resonance, and show a strong influence from spin-orbit coupling (SOC) effects on the chemical shift. The results demonstrate that SOC-driven deshielding is present for CeIV - Cipso 13C{1H} resonances and not just for diamagnetic actinide compounds.

Probing Multiconfigurational States by Spectroscopy: The Cerium XAS L3 -edge Puzzle.

The Ce L3 edge XAS spectra of CeO2 and cerocene [Ce(C8 H8 )2 ] were calculated with relativistic ab-initio multireference wavefunction approaches capable of reproducing the observed spectra accurately. The study aims to resolve the decades-long puzzle regarding the relationship between the number and relative intensities of the XAS peaks and the 4f electron occupation in the ground state (GS) versus the core-excited states (ESs). CeO2 and cerocene exemplify the different roles of covalent bonding and wavefunction configurational composition in the observed intensity patterns. Good agreement is found between the calculated GS 4f-shell occupations and the value derived from XAS measurements using peak areas (nf ). The identity of the two-peaked Ce L3 edge is fully rationalized from the perspective of the relaxed wavefunctions for the GS and core ESs. The states underlying the different peaks differ from each other in a surprisingly simple way that can be associated with 4f1 vs. 4f0 sub-configurations. Furthermore, part of one of the cerocene spectral peaks is associated with 4f2 sub-configurations. The pattern therefore reveals excited states that can be interpreted in terms of Ce IV and III oxidation numbers, as long assumed, with Ce II states additionally appearing in the cerocene spectrum. While this work demonstrates the rough accuracy of the conventional approach to determining nf from Ce L3 -edge XAS, limitations are highlighted in terms of the ultimate accuracy of this approach and the potential of observing new types of excited states. The need to determine the sources of nf by calculations, is stressed.

Quantum chemical topology at the spin-orbit configuration interaction level: Application to astatine compounds.

We report a methodology that allows the investigation of the consequences of the spin-orbit coupling by means of the QTAIM and ELF topological analyses performed on top of relativistic and multiconfigurational wave functions. In practice, it relies on the "state-specific" natural orbitals (NOs; expressed in a Cartesian Gaussian-type orbital basis) and their occupation numbers (ONs) for the quantum state of interest, arising from a spin-orbit configuration interaction calculation. The ground states of astatine diatomic molecules (AtX with X = AtF) and trihalide anions (IAtI- , BrAtBr- , and IAtBr- ) are studied, at exact two-component relativistic coupled cluster geometries, revealing unusual topological properties as well as a significant role of the spin-orbit coupling on these. In essence, the presented methodology can also be applied to the ground and/or excited states of any compound, with controlled validity up to including elements with active 5d, 6p, and/or 5f shells, and potential limitations starting with active 6d, 7p, and/or 6f shells bearing strong spin-orbit couplings.

Compression of curium pyrrolidine-dithiocarbamate enhances covalency.

Curium is unique in the actinide series because its half-filled 5f 7 shell has lower energy than other 5f n configurations, rendering it both redox-inactive and resistant to forming chemical bonds that engage the 5f shell1-3. This is even more pronounced in gadolinium, curium's lanthanide analogue, owing to the contraction of the 4f orbitals with respect to the 5f orbitals4. However, at high pressures metallic curium undergoes a transition from localized to itinerant 5f electrons5. This transition is accompanied by a crystal structure dictated by the magnetic interactions between curium atoms5,6. Therefore, the question arises of whether the frontier metal orbitals in curium(III)-ligand interactions can also be modified by applying pressure, and thus be induced to form metal-ligand bonds with a degree of covalency. Here we report experimental and computational evidence for changes in the relative roles of the 5f/6d orbitals in curium-sulfur bonds in [Cm(pydtc)4]- (pydtc, pyrrolidinedithiocarbamate) at high pressures (up to 11 gigapascals). We compare these results to the spectra of [Nd(pydtc)4]- and of a Cm(III) mellitate that possesses only curium-oxygen bonds. Compared with the changes observed in the [Cm(pydtc)4]- spectra, we observe smaller changes in the f-f transitions in the [Nd(pydtc)4]- absorption spectrum and in the f-f emission spectrum of the Cm(III) mellitate upon pressurization, which are related to the smaller perturbation of the nature of their bonds. These results reveal that the metal orbital contributions to the curium-sulfur bonds are considerably enhanced at high pressures and that the 5f orbital involvement doubles between 0 and 11 gigapascal. Our work implies that covalency in actinides is complex even when dealing with the same ion, but it could guide the selection of ligands to study the effect of pressure on actinide compounds.

Modern quantum chemistry with [Open]Molcas.

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Probing the Electronic Structure of a Thorium Nitride Complex by Solid-State 15N NMR Spectroscopy.

The solid-state 15N NMR powder spectra of the thorium nitride complex, [K(18-crown-6)(THF)2][(R2N)3Th(µ-15N)Th(NR2)3] ([K][1-15N], R = SiMe3), and the thorium amide complex, [Th(NR2)3(15NH2)] (2-15N), were recorded. The spectrum for [K][1-15N] represents the first reported solid-state 15N NMR data for an actinide complex. The experimentally measured tensor spans are Ω = 847 ppm for [K][1-15N] and Ω = 237 ppm for 2-15N. Both shielding tensors exhibit axial symmetry, which for [K][1-15N] is consistent with a local rotational symmetry of its 15N-labeled nitride ligand. For 2-15N, the axial asymmetry can be rationalized by a quasi-free Th-NH2 bond rotation in the solid-state. Density functional theory calculations overestimate the tensor span somewhat for [K][1-15N], but provide isotropic shifts in good agreement with both the solid-state and solution values for both complexes. Natural localized molecular orbital analyses of the nuclear shielding reveal that the larger tensor span in [K][1-15N] vs 2-15N is primarily a consequence of more pronounced covalency of the σ(N-Th) bonds and large spin-orbit coupling due to significant Th 5f orbital contribution to those bonds, impacting the principal components of the shielding tensor perpendicular to the Th-N-Th axis. Overall, our analysis confirms the involvement of the 5f orbitals in Th-N multiple bonds and further demonstrates the value of solid-state NMR spectroscopy for interrogating actinide-ligand bonding.

The Exceptional Diversity of Homoleptic Uranium-Methyl Complexes.

Homoleptic σ-bonded uranium-alkyl complexes have been a synthetic target since the Manhattan Project. The current study describes the synthesis and characterization of several unprecedented uranium-methyl complexes. Amongst these complexes, the first example of a homoleptic uranium-alkyl dimer, [Li(THF)4 ]2 [U2 (CH3 )10 ], as well as a seven-coordinate uranium-methyl monomer, {Li(OEt2 )Li(OEt2 )2 UMe7 Li}n were both crystallographically identified. The diversity of complexes reported herein provides critical insight into the structural diversity, electronic structure and bonding in uranium-alkyl chemistry.

Ab Initio Analysis of Metal-Ligand Bonding in An(COT)2 with An=Th, U in Their Ground- and Core-Excited States.

Relativistic multireference ab initio wave function calculations with the restricted active space second-order perturbation theory (RASPT2) were performed on thorocene and uranocene to determine the actinide N4,5 -edge and carbon K-edge X-ray absorption near-edge structure (XANES) intensities and the metal-ligand orbital mixing in the ground state and core-excited states. Calculated spectral intensities show very good agreement with the experiments and therefore allow detailed and unambiguous assignment of the observed spectral features. φ-type covalent bonding or antibonding interactions are observed for thorocene in the core-excited states, though not in the ground state. This is because the molecular orbital of φ symmetry, which is the in-phase combination of the ligand Lφ and the Th 5fφ orbitals, can be populated with electrons in core-excited states, whereas it is essentially unoccupied in the ground state. For uranocene, the XANES spectra do not reveal much information beyond multiplet broadening, despite the presence of distinct peaks in the spectra. Every core-excited peak is best characterized by its own set of bond orbitals, as the excited state covalency is clearly different from the ground state covalency.

Diuranium(IV) Carbide Cluster U2C2 Stabilized Inside Fullerene Cages.

Novel actinide cluster fullerenes, U2C2@Ih(7)-C80 and U2C2@D3h(5)-C78, were synthesized and fully characterized by mass spectrometry, single-crystal X-ray crystallography, UV-vis-NIR, nuclear magnetic resonance spectroscopy (NMR), X-ray absorption spectroscopy (XAS), Raman spectroscopy, IR spectroscopy, as well as density functional and multireference wave function calculations. The encapsulated U2C2 is the first example of a uranium carbide cluster featuring two U centers bridged by a C≡C unit. The U-C bond distances in these U2C2 clusters are in the range between 2.130 and 2.421 Å. While the U2C2 cluster in U2C2@C80 adopts a butterfly-shaped geometry with a U-C2-U dihedral angle of 112.7° and a U-U distance of 3.855 Å, the U-U distance in U2C2@C78 is 4.164 Å and the resulting U-C2-U dihedral angle is increased to 149.1°. The combined experimental and quantum-chemical results suggest that the formal U oxidation state is +4 in the U2C2 cluster, and each U center transfers three electrons to the C2n cage and one electron to C2. Different from the strong U═C covalent bonding reported for U2C@C80, the U-C bonds in U2C2 are less covalent and predominantly ionic. The C-C triple bond is somewhat weaker than in HCCH, and the C-C π bonds undergo donation bonding with the U centers. This work demonstrates that the combination of the unique encapsulation effect of fullerene cages and the variable oxidation states of actinide elements can lead to the stabilization of novel actinide clusters, which are not accessible by conventional synthetic methods.