Benjamin E. Atkinson

The most fundamental and widely studied form of metal-ion complexation is hydration. Nevertheless, the hydration of the heaviest elements with experimentally accessible bulk properties, namely americium, curium, berkelium, and californium, remains a subject of ongoing debate. Herein, the solid-state series of nona-aqua complexes from uranium to californium is completed through the single-crystal structure characterization of [An(H2O)9](CF3SO3)3 (An3+ = Bk3+ and Cf3+) at 100 K. In addition, the largely unexplored solid-state octa-aqua series, [An(H2O)8](Hdtp)(dtp)·H2O (An3+ = Am3+, Cm3+, Bk3+ and Cf3+, H2dtp = 2,3-di(tetrazol-5-yl)pyrazine) is synthesized and comprehensively characterized to elucidate how variations in hydration manifest in electronic spectra and structural metrics. By combining crystallographic and spectroscopic data with ab initio multiconfigurational wave function calculations, we demonstrate that differences between the two hydration motifs give rise to distinct trends in bond lengths, spectral features, and crystal-field strengths. Although the average An–OH2 bond lengths decrease with similar slopes in both [An(H2O)8]3+ and [An(H2O)9]3+ from Am3+ to Cf3+, the trends in individual An–OH2 bond length contractions differ between the two series. Remarkably, the crystal-field splitting in the octa-aqua complexes can be up to twice that observed in the nona-aqua complexes.

Here, we investigate the magnetic exchange coupling and magnetic anisotropy of a Co(II)–Cu(II) complex using ab initio multiconfigurational calculations. This is one of the simplest cases of magnetic exchange coupling involving an orbitally degenerate metal center: a pseudo-octahedral 3d7 Co(II) ion and a spin-only 3d9 Cu(II) ion. Electronic structure calculations were performed using CASSCF and CASPT2/NEVPT2 methods, and the resulting electronic states were further analyzed via model Hamiltonians to extract physically meaningful parameters, including crystal field splitting, spin–orbit coupling, and exchange coupling. The CASPT2/NEVPT2 calculations improved the agreement with experiment compared to that of CASSCF by correcting the overestimation of ferromagnetic coupling. Our calculations highlight that spin–orbit exchange coupling (i.e., spin-other-orbit coupling) is just as important as spin–spin exchange coupling for an accurate description of exchange coupling.

Tau2 is a Python reimplementation and development of our code Tau, which calculates magnetic relaxation rates via the one-phonon (Orbach and direct) and two-phonon Raman-I mechanisms. It is substantially faster than Tau, by a factor of up to 12,000 times for Raman-I rates, and is more numerically accurate due to careful design of the integration grid. The most important optimization is that Raman rates are calculated via the calculation of a temperature-independent “Raman spectral density”, which avoids recalculation of the expensive sum over phonon pairs for each temperature. Tau2 takes advantage of just-in-time compilation with Numba to minimize the overheads of the interpreted Python language. The improved algorithm drastically reduces the cost of calculating magnetic relaxation rates, making the computational cost of routine rate calculations trivial, and allows for simulation of far larger spin systems, which would not previously have been feasible.

The chemistry of the classical uranium(III) complex [U(N″)₃] (N″ = {N(SiMe₃)₂}⁻) is well-developed; however, there have been surprisingly few studies of its reactivity toward N-heterocycles. Here, we report the separate reactions of [U(N″)₃] with pyrazine, 4-azido-pyridine, and the methylene transfer agent N-(9,10-dihydro-9,10-epiminoanthracen-11-yl)methanimine (C₁₄H₁₀N₂CH₂) to give the respective diuranium(IV) products [{U(N″)₃}₂(μ-NC₄H₄N-1κN,2κN′)] (1), [{U(N″)₃}₂(μ-NC₅H₄N-1κN,2κN′)] (2), and [{U(N″)₃}₂(μ-NC₁₄H₁₀N-1κN,2κN′)] (3). The solid-state structures of complexes 2 and 3 respectively revealed bent U–N═C angles of 167.6(5) and 155.3(4)°, short U–N bond lengths of 2.070(5) and 2.104(4) Å, and diagnostic C═N_ketimide distances of 1.297(7) and 1.364(7) Å. A combination of structural, spectroscopic, magnetic, and quantum-chemical calculations was required to confidently assign U(IV) ions exclusively in complexes 1–3 and to prove that 2 and 3 are ketimides rather than iminyls or nitrenes. Together, this study underscores the need for comprehensive analysis for the correct interpretation of the electronic structures of actinide complexes.

Tau2 is a Python reimplementation and development of our code Tau, which calculates magnetic relaxation rates via the one-phonon (Orbach and direct) and two-phonon Raman-I mechanisms. It is substantially faster than Tau, by a factor of up to 12000 times for Raman-I rates, and is more numerically accurate due to careful design of the integration grid. The most important optimisation is that Raman rates are calculated via the calculation of a temperature-independent “Raman spectral density”, which avoids recalculation of the expensive sum over phonon pairs for each temperature. Tau2 takes advantage of just-in-time compilation with Numba to minimise the overheads of the interpreted Python language. The improved algorithm drastically reduces the cost of calculating magnetic relaxation rates, making the computational cost of routine rate calculations trivial, and allows for simulation of far larger spin systems which would not previously have been feasible.

A sterically protected Pb( i ) radical exhibits clock-like enhancement of spin coherence, demonstrating how ligand control of the Pb 6p orbital tunes spin–orbit coupling and hyperfine interactions.

The development of technologies exploiting molecular spins, such as single-molecule magnets (SMMs) and molecular qubits, requires detailed knowledge of the microscopic spin-dynamics, which in turn relies on understanding the spin-phonon coupling. Building on our recent work, we perform ab initio calculations of the phonon modes, anharmonic phonon scattering and spin-phonon coupling in a molecular crystal of the dysprosocenium SMM [DyCpttt2][B(C6F5)4]. Spin-dynamics simulations give excellent agreement with experiment and provide further insight into the high-performance of the dysprosocenium class of SMMs. We find that strong phonon scattering in the (pseudo-)acoustic regime leads to very short phonon lifetimes, large phonon linewidths, and, consequently, slower spin relaxation.

Lanthanides have recently shown magnetic memory at both the atomic and molecular level. The temperatures at which single-molecule magnets (SMMs) show magnetic hysteresis only increased from 4 K to 14 K in nearly 25 years since the discovery of the first SMM in 1993. However, since 2017 energy barriers to magnetic reversal (Ueff) from 1237(28)-1631(25) cm–1 and open magnetic hysteresis loops between 40-80 K have often been delivered by molecules featuring rigid aromatic ligands in axial dysprosium cyclopentadienyl complexes and their derivatives. Here we report a dysprosium bis(amide)-alkene complex, [Dy{N(SiiPr3)[Si(iPr)2C(CH3)=CHCH3]}{N(SiiPr3)(SiiPr2Et)}][Al{OC(CF3)3}4] (1-Dy), which shows Ueff = 1843(11) cm–1 and slow closing of magnetic hysteresis loops up to 100 K. Calculations show that the record Ueff value of 1-Dy arises from the charge-dense bis(silyl)amide ligands, with a pendant alkene taking a structural role to enforce a large N–Dy–N angle while imposing only a weak equatorial interaction. This leads to molecular spin dynamics up to one hundred times slower than the current best SMMs above 100 K.

The paramagnetism of f-block ions has been exploited in chiral shift reagents and magnetic resonance imaging, but these applications tend to focus on ¹H NMR shifts as paramagnetic broadening makes less sensitive nuclei more difficult to study. Here we report a solution and solid-state (ss) ²⁹Si NMR study of an isostructural series of locally D _3h -symmetric early f-block metal(III) tris-hypersilanide complexes, [M{Si(SiMe₃)₃}₃(THF)₂] (1-M; M = La, Ce, Pr, Nd, U); 1-M were also characterized by single crystal and powder X-ray diffraction, EPR, ATR-IR, and UV-vis-NIR spectroscopies, SQUID magnetometry, and elemental analysis. Only one SiMe₃ signal was observed in the ²⁹Si ssNMR spectra of 1-M, while two SiMe₃ signals were seen in solution ²⁹Si NMR spectra of 1-La and 1-Ce. This is attributed to dynamic averaging of the SiMe₃ groups in 1-M in the solid state due to free rotation of the M-Si bonds and dissociation of THF from 1-M in solution to give the locally C _3v -symmetric complexes [M{Si(SiMe₃)₃}₃(THF) _n ] (n = 0 or 1), which show restricted rotation of M-Si bonds on the NMR time scale. Density functional theory and complete active space self-consistent field spin-orbit calculations were performed on 1-M and desolvated solution species to model paramagnetic NMR shifts. We find excellent agreement of experimental ²⁹Si NMR data for diamagnetic 1-La, suggesting n = 1 in solution and reasonable agreement of calculated paramagnetic shifts of SiMe₃ groups for 1-M (M = Pr and Nd); the NMR shifts for metal-bound ²⁹Si nuclei could only be reproduced for diamagnetic 1-La, showing the current limitations of pNMR calculations for larger nuclei.

Sequential reduction of a uranium-azide through all the nitride steps is revealed. Experimentally determined U–U coupling in the diuranium( iv )–dinitride is shown by ab initio calculations to stem from the nitride bridges, not U–U bonding.