The diffusionless Burgers-Bain phase transition from a hexagonal close-packed (hcp) arrangement to a cuboidal lattice (face-centered cubic, fcc, and body-centered cubic, bcc) is analyzed in great detail for LennardJones (LJ) solids. From the lattice vectors of an underlying bilattice smoothly connecting these phases, we are able to express the corresponding lattice sums for inverse power potentials in terms of fast converging Bessel function expansions, resulting in an efficient evaluation to computer accuracy for cohesive energies. From the kissing hard-sphere limit we derive exact analytical expressions for the lattice parameters varying along the minimum energy path of the phase transition. This simple model suggests that the Burgers-Bain transformation of a LJ solid requires a minimum of four lattice parameters, (a, alpha, beta, gamma = c/a), describing the change in the base lattice lengths a and c, the shear force acting on the hexagonal base plane through a parameter alpha, the sliding force of the middle layer in the original hexagonal packing arrangement through a single parameter beta, and the cuboidal transformation through a parameter gamma = c/a. This choice results in a smooth transformation through a two-step process: hcp -* fcc -* bcc. However, a further extension of the parameter space including an additional slide parameter for the middle layer, one suddenly observes a distinct symmetry-breaking effect along the hcp -* fcc transition path with a bifurcation point appearing joining the original Burgers with the Bain path of the bcc -* fcc cuboidal transition. Furthermore, for soft LJ potentials the bcc phase appears as a local minimum along the Burgers hcp -* fcc path with two transition states to either the hcp or fcc phase. The underlying topology of the Burgers-Bain phase transition also incorporates the rhombohedral distortion of the bcc phase, which is analyzed in detail. As a first application of our formalism, we discuss solid argon and compare the LJ results with variable-cell nudge elastic band optimizations using density functional theory. We find that the activation energy for the hcp -* fcc transformation is highly sensitive to the density functional applied, and that dispersion corrections are important as expected for weakly interacting systems.

Quantum systems with more than two levels - so-called qudits - offer increased computational density and reduced circuit complexity compared to qubit-based architectures, but achieving universal and scalable control remains challenging. We propose an all-optical scheme for universal qudit control in trapped neutral atoms in moderate to high magnetic fields, focusing on the fermionic isotope 173Yb (I = 5/2). The strong hyperfine interaction in the 3P1 manifold enables fast and selective Raman transitions between nuclear-spin states in the 1S0 ground-state manifold using a single linearly polarized laser. For each neighboring transition in the qudit manifold, we identify a magic polarization angle that enables coherent, state-selective control while suppressing off-resonant excitations, with operation frequencies exceeding 100 kHz. Combined with phase-shift operations, this provides universal control of the full single-qudit space. We further discuss compatible two-qudit gates based on the Rydberg blockade mechanism, completing a universal gate set, and analyze state-selective readout schemes compatible with the proposed protocol. Our results identify 173Yb as a promising platform for high-fidelity, all-optical qudit-based quantum information processing.

Among the possible types of magnetic dipole interactions in molecular systems, couplings between nuclear motion and the nuclear spin have probably received the least attention in molecular spectroscopy. Although very small in comparison to effects related to electron spin, this type of hyperfine interaction plays an important role in the NMR spectroscopy of molecular systems. While measurement and prediction of spin-rotation tensors are a common place, vibrationally induced effects still lack a comprehensive description. In this article we develop a generic, theoretical framework that is well embedded in modern electronic structure theory and inspired by the Breit-Pauli Hamiltonian for electronic interactions, distinguishing between nuclear spin-orbit and spin-other-orbit contributions. We show that the interaction of nuclear spins with pseudorotational excitations of highly symmetric molecules may lead to experimentally accessible hyperfine splittings in NMR spectra, triggered by infrared light.

Optical nuclear electric resonance (ONER) was recently proposed as a fast and robust single-qubit gate mechanism in Sr 87 . Here, we demonstrate through numerical simulations that ONER can be extended to single-qudit control, addressing multiple one-level hyperfine transitions within the ten-dimensional nuclear-spin manifold. We identify suitable operating regimes and show that ONER enables high-fidelity spin manipulations, with simulated π-gate fidelities exceeding 99.9%, while maintaining coherence under realistic parameter fluctuations. These results establish a proof of principle for optical qudit control in Sr 87 and delineate practical parameter ranges for future experiments, highlighting ONER as a promising pathway toward high-dimensional quantum information processing.

The precise control of nuclear spin states is crucial for a wide range of quantum technology applications. Here, we propose a fast and robust single-qubit gate in 87 Sr utilizing the concept of optical nuclear electric resonance (ONER). ONER exploits the interaction between the quadrupole moment of a nucleus and the electric field gradient generated by its electronic environment, enabling spin level transitions via amplitude-modulated laser light. We investigate the hyperfine structure of the 5s 2 1 S 0 → 5s5p 3 P 1 optical transition in neutral 87 Sr and identify the magnetic field strengths and laser parameters necessary to drive spin transitions between the m I = − 9 / 2 and m I = − 5 / 2 hyperfine levels in the ground state. Our simulations show that ONER could enable faster spin operations compared to the state-of-the-art oscillations in this ‘atomic qubit’. Moreover, we show that spin-flip operations exceeding 99.9% fidelity can be performed even in the presence of typical noise sources. These results pave the way for significant advances in nuclear spin control, opening new possibilities for quantum memories and other quantum technologies.

Although squaraine dyes are commonly praised as candidates for light-based applications, little is known about their excited state landscape beyond the low-energy visible light region. Our work aims for an improved understanding of the photophysical properties of squaraines at the example of N-isobutyl substituted anilino-squaraine (SQIB) by extending ground-state and excited-state absorption spectroscopy of the molecule into the ultraviolet up to 6.5 eV. In addition, we distinguish the relative transition dipole moments of the excited state absorption peaks with the help of transient absorption anisotropy experiments. To relate experimental features to specific states, we employ a set of ab initio methods including time-dependent density functional theory (TDDFT), the Bethe-Salpeter equation (BSE) and n-electron valence perturbation theory on top of a self-consistent complete active space (CASSCF/NEVPT2). Our assignment is complemented by vibronic simulations and a discussion of two-photon absorption measurements. Through this joint effort, we are able to provide a consistent picture of the optical behavior of SQIB across the visible and ultraviolet light regime, and assign a total of twelve electronically excited states to our experimental data.

Metal phthalocyanines, a highly versatile class of aromatic, planar, macrocyclic molecules with a chelated central metal ion, are topical objects of ongoing research and particularly interesting due to their magnetic properties. However, while the current focus lies almost exclusively on spin-Zeeman-related effects, the high symmetry of the molecule and its circular shape suggests the exploitation of light-induced excitation of 2-fold degenerate vibrational states in order to generate, switch, and manipulate magnetic fields at the nanoscale. The underlying mechanism is a molecular pseudorotation that can be triggered by infrared pulses and gives rise to a quantized, small, but controllable magnetic dipole moment. We investigate the optical stimulation of vibrationally induced molecular magnetism and estimate changes in the magnetic shielding constants for confirmation by future experiments.

A neural network-based method for advancing orbital-free density functional theory (OFDFT) is developed, which reaches DFT accuracy and maintains lower cost complexity.

Optical nuclear electric resonance (ONER), a recently proposed protocol for nuclear spin manipulation in atomic systems via short laser pulses with MHz repetition rate, exploits the coupling between the nuclear quadrupole moment of a suitable atom and the periodic modulations of the electric field gradient generated by an optically stimulated electronic excitation. In this theory paper, we extend the scope of ONER from atomic to molecular systems and show that molecular vibrations do not interfere with our protocol. Exploring the diatomic molecule LiNa as a first benchmark system, our investigation showcases the robustness with respect to molecular vibration, and the ability to address and manipulate each of the two nuclear spins independently, simply by adjusting the repetition rate of a pulsed laser. Our findings suggest that it might be possible to shift complicated spin manipulation tasks required for quantum computing into the time domain by pulse-duration encoded laser signals.

A homologous series of 4,7-bis(aryl) substituted benzothiadiazole (BTD) compounds, containing the helicenic derivatives bis([4]helicene), bis([5]helicene) and bis([6]helicene), have been prepared upon a double Suzuki coupling between 3,6-bis(pinacolyl-borane)-BTD and the corresponding bromo-aryl precursors. The single crystal X-ray structure of the bis([4]helicene) compound shows the existence of both helicities (M) and (P) on the same molecule. All the compounds of the series are highly emissive in solution, with quantum yields of the emission ranging from 50 to 91 %. The enantiopure compounds (M,M) and (P,P) for the BTD-bis([6]helicene) have been prepared from the corresponding enantiopure 2-bromo-[6]helicene precursors. Their chiroptical properties have been investigated in correlation with density functional theory (DFT) calculations, which allowed to confidently assign the absolute configuration of the helicene arms and to characterize the different electronic transitions, including the low energy charge transfer excitation from helicenes to BTD. The enantiomerically pure fluorophores (M,M)- and (P,P)-BTD-bis([6]helicene), which exist in solution as two main conformers, according to the DFT calculations, show CPL activity in solution, with glum factors of ≈1.7×10-3 at λem=525 nm, and also in the solid state, with glum factors of ≈1.2×10-3 in spite of the strong decrease of the quantum efficiency.

Homoleptic complexes [Fe(4bt)3](ClO4)2 (1), [Fe(2bt)3](ClO4)2 (2), and [Fe(3tpH)3](ClO4)2 (3) were obtained by a reaction between the Fe(II) precursor salt and the corresponding thiazole-based bidentate ligand (L = 4bt = 4,4'-bithiazole, 2bt = 2,2'-bithiazole, 3tpH = 3-(thiazol-2-yl)pyrazole). X-ray crystal structure determination revealed crystallization of solvent-free complex 1, a solvate 2·MeOH, and a co-crystal 3·2(3tpH). The crystal packing of all these complexes is dominated by one-dimensional interactions between the [Fe(L)3]2+ cations. These interactions are stronger in 2·MeOH and 3·2(3tpH), leading to cooperative and slightly hysteretic transitions between the high-spin and low-spin electronic configurations at ∼235 K and 159 K, respectively. In contrast, weaker intermolecular interactions in 1 result in a gradual spin crossover above 300 K, with the maximum fraction of the HS state ∼25% achieved at 400 K. Complexes 2 and 3·2(3tpH) exhibit light-induced excited spin state trapping (LIESST) under irradiation with white light or a 532 nm laser at 5 K. After the photoexcitation, the trapped metastable HS state relaxes to the ground LS state with the average relaxation temperature of 81 K and 68 K, respectively. Examination of the relaxation dynamics by optical absorption spectroscopy on a single crystal of 3·2(3tpH) revealed the sigmoidal shape of the relaxation curves at lower temperatures, attributed to cooperative effects, as well as a plateau at ∼10% of the HS fraction at intermediate temperatures, hinting at a more complex mechanism for the relaxation of the LIESST phase in this material.

The theoretical investigation of gas adsorption, storage, separation, diffusion, and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In this article, a new algorithm is presented, specifically developed for gas transport phenomena, which allows for a highly cost-effective determination of molecular potential energy surfaces. It is based on a symmetry-enhanced version of Gaussian process regression with embedded gradient information and employs an active learning strategy to keep the number of single point evaluations as low as possible. The performance of the algorithm is tested for a selection of gas sieving scenarios on porous, N-functionalized graphene and for the intermolecular interaction of CH4 and N2.

Nanoparticles with diameters in the range of a few nanometers, consisting of gold and vanadium oxide, are synthesized by sequential doping of cold helium droplets in a molecular beam apparatus and deposited on solid carbon substrates. After surface deposition, the samples are removed and various measurement techniques are applied to characterize the created particles: scanning transmission electron microscopy (STEM) at atomic resolution, temperature dependent STEM and TEM up to 650 °C, energy-dispersive X-ray spectroscopy (EDXS) and electron energy loss spectroscopy (EELS). In previous experiments we have shown that pure V2O5 nanoparticles can be generated by sublimation from the bulk and deposited without affecting their original stoichiometry. Interestingly, our follow-up attempts to create Au@V2O5 core@shell particles do not yield the expected encapsulated structure. Instead, Janus particles of Au and V2O5 with diameters between 10 and 20 nm are identified after deposition. At the interface of the Au and the V2O5 parts we observe an epitaxial-like growth of the vanadium oxide next to the Au structure. To test the temperature stability of these Janus-type particles, the samples are heated in situ during the STEM measurements from room temperature up to 650 °C, where a reduction from V2O5 to V2O3 is followed by a restructuring of the gold atoms to form a Wulff-shaped cluster layer. The temperature dependent dynamic interplay between gold and vanadium oxide in structures of only a few nanometer size is the central topic of this contribution to the Faraday Discussion.

Sub-nanometer metal clusters have special physical and chemical properties, significantly different from those of nanoparticles. However, there is a major concern about their thermal stability and susceptibility to oxidation. In situ X-ray Absorption spectroscopy and Near Ambient Pressure X-ray Photoelectron spectroscopy results reveal that supported Cu5 clusters are resistant to irreversible oxidation at least up to 773 K, even in the presence of 0.15 mbar of oxygen. These experimental findings can be formally described by a theoretical model which combines dispersion-corrected DFT and first principles thermochemistry revealing that most of the adsorbed O2 molecules are transformed into superoxo and peroxo species by an interplay of collective charge transfer within the network of Cu atoms and large amplitude "breathing" motions. A chemical phase diagram for Cu oxidation states of the Cu5 -oxygen system is presented, clearly different from the already known bulk and nano-structured chemistry of Cu.

Guest editors, Andreas W. Hauser, Martina Havenith, Markus Koch and Martin Sterrer, introduce this themed issue dedicated to Professor Wolfgang E. Ernst on the occasion of his 70th birthday.

Nuclear electric resonance (NER) spectroscopy is currently experiencing a revival as a tool for nuclear spin-based quantum computing. Compared to magnetic or electric fields, local electron density fluctuations caused by changes in the atomic environment provide a much higher spatial resolution for the addressing of nuclear spins in qubit registers or within a single molecule. In this article, we investigate the possibility of coherent spin control in atoms or molecules via nuclear quadrupole resonance from first principles. An abstract, time-dependent description is provided which entails and reflects on commonly applied approximations. This formalism is then used to propose a new method we refer to as `optical' nuclear electric resonance (ONER). It employs pulsed optical excitations in the UV-visible light spectrum to modulate the electric field gradient at the position of a specific nucleus of interest by periodic changes of the surrounding electron density. Possible realizations and limitations of ONER for atomically resolved spin manipulation are discussed and tested on ^9Be as an atomic benchmark system via electronic structure theory.

Bare clusters of five Cu atoms, synthesized electrochemically, display remarkable oxidation stability on highly oriented pyrolytic graphite. They exhibit reversible O2 adsorption, transitioning between various Cu oxidation states with changes in temperature and O2 pressure. In-situ XPS and XANES spectroscopy experiments, along with theoretical characterizations of Cu5–(O2)n complexes, provide direct evidence of the Cu5 clusters’ O2 stability. More information can be found in the Research Article by M. P. de Lara-Castells, F. G. Requejo, M. A. López-Quintela and co-workers (DOI: 10.1002/chem.202301517).

In fused donor-acceptor (D-A) ensembles, rapid charge recombination often occurs because the D and A units are spatially close and strongly coupled. To the best of our knowledge, a long-lived charge separated (CS) state is still elusive in such systems. The results presented here show that symmetric annulation of two tetrathiafulvalene (TTF) donors to a central tetraazapyrene (TAP) acceptor via two quinoxaline units leads to a CS state lifetime of a few ns. A detailed study of the electronic interactions between TTF and TAP units in the ground and excited states was performed and compared with the asymmetric counterpart by cyclic voltammetry, optical absorption and ultrafast transient absorption spectroscopy. The results demonstrate that the photoinduced asymmetric charge trapping between two TTFs significantly stabilizes the CS state, which is also verified theoretically.

Eyring theory provides a convenient approximation to the rate of a chemical reaction, as it uses only local information evaluated near extremal points of a given potential energy surface. However, in cases of pronounced anharmonicity and particularly low-lying vibrational frequencies, deviations from the correct reaction rate can become substantial. Molecular Dynamics simulations, on the other hand, are very costly at higher levels of theory, and of limited use since molecular reactions are `rare' events and hence statistically less accessible. In this article, we present an alternative description for problems of gas separation and storage via two-dimensional materials such as porous graphene or flat metal-organic frameworks. Taking geometric advantage of the typical problem setting, our method is based on a statistical analysis of molecular trajectories near the so-called `ridge', a hypersurface which divides the reaction volume into a reactant and a product side. It allows for more realistic predictions of permeabilities and selectivities, e.g. derived from density functional theory, but without the considerable costs of a full molecular dynamics simulation on the corresponding Born-Oppenheimer potential energy surface. We test our method on the example of methane separation from nitrogen and carbon dioxide via a graphdiyne membrane.

The ligand (2-[4-(2,1,3-benzothiadiazole)imino]methyl-phenol) HL1 containing the electron poor benzothia-diazole (BTD) unit, conveniently prepared by condensation of 4-amino-2,1,3-benzothiadiazole and salicylalde-hyde, has been structurally characterized by single crystal X-ray diffraction. Two energy minima have been determined, by DFT calculations, for HL1 and for its ortho-vanillin analogue HL2, corresponding either to the conformer observed in the solid state or to the chelating tridentate form. TD-DFT calculations have been per-formed on HL1 and HL2 in order to assign their experimental UV-visible absorption bands. Reaction of HL1 and HL2 with copper (II) hexafluoroacetylacetonate (hfac), zinc (II) hexafluoroacetylacetonate or zinc (II) acetate provided the neutral complexes [Cu(L1)(hfac)] (1), [Zn(L1)2] (2), [Cu(L2)2] (3) and [Zn(L2)2] (4) which were structurally characterized, with a focus on the coordination sphere of the metal centre and on the intermolecular interactions. The UV-visible absorption properties of the Zn(II) complexes 2 and 4 have been experimentally and theoretically investigated and compared to those of the ligands. Finally, the cryomagnetic study of 1 and 3 in the temperature range 2.0-295.0 K reveals a Curie-Weiss law behaviour with very weak intermolecular antiferro-magnetic interactions in the low temperature region.