Papers

Anharmonic intensities reveal vibrational coupling that band positions alone cannot determine. We derive explicit second-order infrared transition moments in curvilinear normal coordinates, including kinetic metric derivatives and transport through variational resonance polyads. The vibrational perturbation-to-second-order-then-diagonalization (VP2TD) treatment covers fundamentals, overtones, three-quantum transitions, and hot bands. A general computational platform combines Extended Symmetry-Adapted Local Coordinates (ESALCs), using Cartesian (ESALC-C) or internal (ESALC-I) primitives, with interchangeable quantum-chemical programs and parallel finite differences. Independent oscillator matrices verify the intensity equations; a molecular water check reproduces second-order amplitudes within $8.4\times10^{-8}$ atomic units. Comparisons with established tools reproduce a formaldehyde Fermi polyad within 0.163 cm$^{-1}$ and 0.061 km mol$^{-1}$ and water Raman activities within $10^{-7}$ Angstrom$^6$. For 29 matched formaldehyde rotational line pairs, the predicted hot-to-fundamental intensity ratio, using the measured lower-state energy, is consistent with the nuclear-spin-corrected median: the differences are 3.9% (ESALC-I) and 3.8% (ESALC-C), compared with a 15% uncertainty estimate for individual measured line intensities. Common analytic reference derivatives ensure identical harmonic observables, while internal coordinates reduce and localize intermode anharmonic couplings. Rotation-vibration constants extend the same tensor treatment. An integrated adiabatic discrete-variable representation treats large-amplitude motions, and finite-level partition functions provide anharmonic thermochemistry.

Embedding materials in optical cavities has emerged as a powerful strategy for controlling their physical properties. In this context, increasing attention has been devoted to the thermal Purcell effect, which describes how the radiative heat transfer between a material and its photonic environ- ment can be modified by the electromagnetic boundary conditions imposed by the cavity. Here, we investigate near-field effects in cavity-mediated radiative heat transfer in planar cavities composed of realistic, dissipative gold mirrors, extending previous work that considered ideal mirrors. We iden- tify the conditions under which near-field effects lead to a substantial enhancement of heat transfer between the material and a photonic thermal bath relative to free space, owing to the strong modi- fication of the photonic local density of states by evanescent modes within the cavity. In particular, we find that radiative heat flow can be enhanced by several orders of magnitude in cavities ranging from nanometer to micrometer scales, depending on the absorber frequency and dipole orientation. These findings suggest that near-field effects may be relevant to polariton chemistry experiments and other systems operating within this cavity length-scale regime. Our results add to the idea that cavities can modify material properties not only by engineering vacuum fluctuations in the strong light-matter coupling regime, but also by controlling radiative dissipation and heat transfer.

Nuclear quantum effects are essential for an accurate description of the hydrogen-bonded structure of liquid water, yet their spectroscopic signatures can be subtle and difficult to measure. Moreover, probing these effects in solution on femtosecond timescales (or below) is an open challenge that is pivotal for optical control of hydrogen bonds and ultrafast spectroscopy of proton transfer. Here, we combine path-integral molecular dynamics with real-time time-dependent density-functional theory to explore high-harmonic generation (HHG) in liquid water from first principles, rigorously accounting for quantum nuclear delocalisation. Relative to classical-nuclei simulations, quantum sampling suppresses the harmonic yield around certain harmonics by up to an order of magnitude, inducing local structural minima. By analysing the ab initio simulations and reproducing the key effects with a simplified model Hamiltonian, we trace the physical origins of the interference minima to the broadening of valence-band states induced by hydrogen-bond fluctuations, a mechanism expected to generalise to other hydrogen-bonded structures. Our work shows that nuclear quantum effects are indispensable for capturing ultrafast electronic dynamics in liquids, and demonstrates the power of liquid HHG spectroscopy for attosecond probing of nuclear fluctuations.

Densities and excess molar volumes ($V_{\text{m}}^{\text{E}}$) at (293.15 to 303.15) K and excess molar enthalpies ($H_{\text{m}}^{\text{E}}$) at 298.15 K are reported for the 2-butanol + 2,5-dioxahexane, or + 2,5,8-trioxanonane, or + 2,5,8,11-tetraoxadodecane, or + 2,5,8,11,14-pentaoxapentadecane systems at 95 kPa. Densities were measured using a densitometer Anton Paar DSA 5000, and excess enthalpies by means of a micro-calorimeter Tian-Calvet. $H_{\text{m}}^{\text{E}}$ and $V_{\text{m}}^{\text{E}}$ data are positive, indicating that interactions between like molecules are dominant and that the main contribution to $V_{\text{m}}^{\text{E}}$ is the interactional one. Our enthalpic data together with data from the literature have been used to evaluate the enthalpy of alcohol-glyme interactions, which are ranged between ($-$31 and $-$22) kJ mol$^{-1}$. From the comparison with $H_{\text{m}}^{\text{E}}$ results for glyme + heptane systems, and from the position of the investigated mixtures in the diagram $G_{\text{m}}^{\text{E}}$ (excess molar Gibbs energy) vs. $H_{\text{m}}^{\text{E}}$, it is shown that interactions are of dispersive type. 2-Alkanol + dipropyl ether (DPE), or + glyme systems have also been studied using the DISQUAC, UNIFAC (Dortmund) and ERAS models. According to ERAS results, physical interactions in glyme systems are dominant, while association effects are predominant in mixtures with DPE. The DISQUAC interaction parameters suggest that interactions related to the OH/O contacts are essentially dispersive. UNIFAC fails when representing thermodynamic properties of the studied solutions.

Reticular chemistry allows metal-organic frameworks (MOFs) to be designed from their building units, yet their synthesis remains constrained by sparse experimental data, noisy crystallization outcomes, and the absence of benchmarks for comparing active-learning strategies. While data-driven approaches such as Bayesian optimization (BO) can improve synthesis success rates, selecting appropriate optimizers beforehand for mapping MOF crystallization landscapes remains largely empirical. Here we present ActMOF, an experiment-grounded benchmark for comparing search strategies in aluminum-carboxylate MOF synthesis. ActMOF is emulated from experimentally measured microwave syntheses with each encoded condition assigned a crystallinity index calculated based on diffraction peak intensity and full width at half-maximum. By benchmarking policies guided by Gaussian processes (GP), tree ensembles and large language models (LLM), ActMOF placed the GP family among the leading policies for active learning in sparse synthesis landscapes. It then demonstrated transferability by guiding the microwave synthesis of six reticularly related aluminum MOFs. All six campaigns gave crystalline products within a fixed budget of 12 experiments each, and established a reusable testbed for AI-driven MOF synthesis.

A suite of tunable diode laser absorption spectroscopy (TDLAS) diagnostics targeting rovibrational states of nitric oxide (NO) in the mid-infrared (MIR) and electronic states of atomic oxygen (O) and nitrogen (N) in the near-IR (NIR) was combined with optical emission spectroscopy (OES) for overlapping wavelengths at the NASA Electric Arc Shock Tube (EAST) facility for three selected high-temperature air experiments. Absorption features were probed at rates up to 1 MHz to provide quantitative, time-resolved measurements of temperature and species number density profiles behind incident shocks, enabling comparisons to spatially-resolved emission measurements, with the two typically agreeing within their respective uncertainties. Inferred time-histories are further compared to incident shock simulations from two one-dimensional models - one leveraging the Park two-temperature rates and the other more recent rate values - as well as the Data Parallel Line Relaxation (DPLR) code. For the two low-velocity cases (3.81 and 3.98 km/s) in which NO is probed, inferred temperatures are typically well-captured by all three models, although the NO number densities show stronger variation, agreeing better for the model with updated NO formation and dissociation rates. Finally, one high-velocity case (7.03 km/s) demonstrates the simultaneous resolution of three O-atom and six N-atom electronic states, with all states showing a steady increase in number density over time - possibly due to shock trajectory effects. Together, this combined absorption and emission study demonstrates resolution of many states of nonequilibrium air species, while directly comparing ground- and excited-state populations via the combined diagnostic strategy.

Solid-state triplet-triplet annihilation upconversion offers a compelling route to harvest sub-bandgap photons to increase the efficiency of photovoltaics, but low sensitizer doping required to suppress non-radiative aggregation quenching severely restricts light absorption. Here, we present a dual-resonator planar silver microcavity housing a thermally co-evaporated rubrene:palladium phthalocyanine (PdPC) active layer designed to simultaneously enhance triplet-sensitizer absorption and out-couple upconverted emission. By aligning a dispersive cavity mode with the PdPC absorption peak at $32^\circ$, we achieve a 12-fold enhancement in absorptance at 665 nm. This absorption boost, combined with directional outcoupling through a second cavity mode, outweighs cavity-induced reabsorption losses to yield a 22-fold peak and 4.5-fold integrated enhancement in detected upconversion emission. Overall, this work highlights the potential of microcavity integration to substantially enhance solid-state upconversion performance across low-intensity optoelectronic applications.

Generating novel molecules with desired properties is a central challenge in drug discovery. Although foundational work focused on de novo generation, practical use cases require a more complex setting: conditioning on an initial seed molecule, optimizing multiple properties, and operating in data-sparse regimes. We introduce PairIT, a flexible training framework for autoregressive transformers over SMILES sequences that enables seeded generation by learning from pairs of structurally similar molecules. By leveraging matched pairs, the model learns to generate local, chemically meaningful edits that improve a property of the seed molecule. Prompt tokens extend this framework by specifying the target property, desired direction, and approximate magnitude of change. Multiple prompt tokens can be concatenated to enable multi-property optimization at inference time. For properties where pair supervision alone is insufficient, reinforcement learning post-training can further improve optimization, providing a tunable trade-off between proximity to the seed and the optimization objective. PairIT naturally supports pretraining on a large dataset and fine-tuning on a smaller dataset, which is critical for performance in data-sparse regimes. Surprisingly, we observe diminishing returns to the scale of the pretraining dataset. We demonstrate empirically on MoleculeNet and Therapeutics Data Commons datasets that, with appropriate paired-data curation, a standard transformer model of modest size (68M parameters) can achieve robust seeded molecular optimization in low-data regimes.

Circuit depth and measurement count are the main limitations for chemical applications of the leading variational quantum algorithms on quantum computers. We show that both resource requirements can be reduced by augmenting adaptive variational quantum algorithms with post-optimization corrective techniques. We focus on two such techniques—Hamiltonian-moment Krylov subspace diagonalization and the identity-augmented quantum self-consistent equation of motion (q-sc-EOM)—applied to optimized ADAPT-VQE states without further ansatz growth or nonlinear optimization. Across molecular systems studied with up to 20 qubits, first-order Krylov correction reduces the optimized iterations (and the corresponding number of adaptive layers) needed to reach the $1.6~\mathrm{m}E_h$ threshold by up to approximately sixfold, with a general trend toward larger reductions at higher determinant Rényi entropy. We also find measurement-cost reductions of up to approximately fortyfold using a suitable resource-cost model. Identity-augmented q-sc-EOM improves molecular potential-energy curves obtained from truncated ADAPT-VQE ansätze with limited expressivity and recovers accuracy from states produced by sampled operator ranking without additional gradient-based operator selection, providing an advantage when small pool gradients make selection measurement intensive. Together, these post-optimization corrections offer routes to improve energy accuracy and reduce adaptive circuit growth in quantum algorithms as quantum hardware advances.

The exact local exchange-energy density, obtained from the Slater potential of the Hartree-Fock exchange hole, is a central ingredient of Becke's B05 and B13 functionals and of many other local hybrids. It is usually evaluated in a Gaussian basis, so the local quantity retains a pointwise basis-set incompleteness error. We describe here a basis-set-free numerical code that solves the Kohn-Sham problem on real-space grids for atoms, diatomics, and polyatomics, and returns the exact local exchange-energy density together with the density, its derivatives, the kinetic-energy density, and the reverse Becke-Roussel hole quantities. Reconstructed from the published record of Becke's non-public NUMOL code, AXEL reproduces numerical atomic references through krypton, scalar-relativistic uranium orbital energies, and Becke's diatomic spectroscopic constants. We then extend the original local-density numerical framework to generalized-gradient and hybrid functionals. Comparisons with the independent adaptive-multiwavelet code MRChem give sub-millihartree agreement for Hartree-Fock and PBE0. The same calculations agree with large Gaussian-basis references to a similar level of accuracy. Atom-centred eXact Electronic Limit (AXEL) is intended as both a basis-set-free numerical reference and a platform for exchange-hole-based density-functional development.

Simulation-based Bayesian inference for Chemical Reaction Networks (CRNs) must simultaneously solve two computationally demanding problems: discriminating between overlapping reaction pathways and estimating reaction rate constants. Classical approaches, such as Sequential Monte Carlo ABC, rely on handcrafted summary statistics and scale poorly across large parameter spaces. To overcome this, we introduce a neural inference architecture. Our pipeline utilizes shared 1D-CNNs and a permutation-invariant Set Attention mechanism to learn low-dimensional summary statistics from variable-length, multi-experiment time-series data. These statistics simultaneously condition a model selection network to compute posterior model probabilities and model-specific conditional Invertible Neural Networks (cINNs) that estimate parameter posterior distributions. We demonstrate the practical utility of our approach on a real protodeboronation example, illustrating how it handles structural ambiguity and extracts kinetic parameters from competing catalyst deactivation pathways.

Engineered transport architectures can improve electrolyte distribution and active-material utilization in porous electrodes, yet their implementation remains limited by fabrication methods that compromise precision, throughput, active-material preservation, or scalability. Here, an integrated embossing-calendering method is introduced to pattern Prussian blue analog (PBA) porous electrodes with embedded, micro-interdigitated flow fields (e$\mu$-IDFFs) for electrochemical desalination. This non-subtractive, roll-to-roll compatible method forms channels by controlling plastic deformation while simultaneously calendering the electrode, preserving active material and reducing patterning time by 100-fold relative to mechanical milling. Indentation experiments and a closed-form model further show that embossing requires 15-fold less force than stamping, while electrode microstructures show local densification beneath embossed channels. PBA electrodes are embossed with novel e$\mu$-IDFFs that use continuous width-tapering with isometric flow paths that promote uniform electrolyte distribution, increase rate capability, and reduce polarization. Compared with e$\mu$-IDFFs patterned using less scalable means and non-isometric flow paths, these e$\mu$-IDFFs desalinate seawater-salinity feeds near to potable levels with 1.5-fold of its thermodynamic energy efficiency and water recovery. Brackish desalination benefits similarly. Tapered, isometric e$\mu$-IDFFs and the embossing method introduced to pattern them are readily translated other electrochemical energy storage and separations systems.

Fewest-switches surface hopping (FSSH) is a popular and versatile approach for performing dynamical simulations beyond the Born-Oppenheimer approximation, in which nonadiabatic effects are incorporated through stochastic hops of the active potential energy surface. However, the FSSH algorithm does not ensure that hops are completely consistent with the underlying electronic wavefunction dynamics. This can lead to significant errors as well as requiring small propagation time steps, which can significantly compromise the computational efficiency of the method. These problems are known to be particularly severe at so-called trivial crossings, for which the nonadiabatic coupling is entirely localized at the crossing point. Here, we solve the trivial-crossing problem by developing a fully-consistent hopping-probability formula, which generates attempted hops that match the time-evolution of the wavefunction across any size time step by construction. A state-tracking algorithm is also utilized to ensure that attempted hops are always accepted at trivial crossings. Through application to systems that contain extremely challenging trivial crossings, we demonstrate that this hopping scheme is capable of obtaining highly accurate results, even when large propagation time steps are used.

Rare events, such as crystal nucleation in mildly supercooled liquids, are characterized by waiting times that can be much longer than the timescale of the underlying microscopic dynamics. The mean first-passage time (MFPT) formalism [J. Wedekind and D. Reguera, J. Phys. Chem. B 112, 11060 (2008)] provides a route to reconstruct one-dimensional free-energy profiles from the MFPT and steady-state distribution measured along a reaction coordinate, but conventional implementations become inefficient for sufficiently high barriers because spontaneous crossings are rarely observed. We introduce a "top-start" extension that initiates trajectories near the barrier top and reconstructs the free-energy profile from their subsequent evolution away from the barrier toward lower-free-energy regions. We establish the equivalence between the top-start and two-region constructions using a Markov-chain transition-matrix formulation. We validate the method using one-dimensional random-walk simulations across low, medium, and high free-energy barriers, with transition-matrix calculations providing an exact benchmark for the corresponding discretized models. The top-start reconstruction remains accurate in the high-barrier regime where conventional MFPT sampling becomes prohibitively inefficient.

Chemical language models (CLMs) are pretrained on large corpora of molecules with the aim of learning representations that transfer to diverse downstream tasks. Here, we systematically study the effects of pretraining using a series of such CLMs across 64 molecular property prediction datasets. We find that the downstream gains of pretraining in CLMs do not scale and performance saturates below gradient-boosting baselines. Across the regimes evaluated, only supervised pretraining on traditional physico-chemical descriptors consistently improves downstream performance for the CLMs tested whereas some forms of pretraining result in models worse than a randomly initialized encoder. While models can resolve molecular structure well, they do so no better than a randomly initialized model, suggesting that, at best, CLMs learn descriptor-like properties in addition to low-level token statistics during pretraining, but surprisingly little chemistry beyond what classical molecular features already capture.

Cu-C materials and interfaces are central to diamond thermal management, metallization, graphene growth and carbon-coating technologies, but atomistic simulations across these applications require a potential that describes metallic Cu, diverse carbon bonding, heterogeneous Cu-C interactions and close atomic encounters. Here we develop NEP-CuC, a transferable neuroevolution potential trained on a dataset of 2,727 uniformly relabelled configurations selected from a heterogeneous Cu-C candidate pool. Disagreement within an ensemble of five independently trained models provides an internal indicator of model sensitivity. A Ziegler-Biersack-Littmark (ZBL) correction describes short-range nuclear repulsion, while a runtime D3(BJ) correction supplements dispersion-sensitive calculations. Tests on source-derived held-out and independent external datasets, together with structural, elastic, defect, interfacial, vibrational and finite-temperature transport benchmarks, establish broad but property-dependent physical fidelity across elemental Cu, diverse carbon environments and heterogeneous Cu-C configurations. Large-scale simulations of amorphous-carbon formation and orientation-dependent shock compression of Cu further test transferability under strongly non-equilibrium conditions. For Cu/diamond interfaces, the same potential describes deposition, annealing and tensile response: preparation history leaves persistent differences in interphase structure, while the mean peak nominal tensile stress at 500 K decreases from $12.35\pm0.71$ to $6.65\pm0.98$ GPa as the incident Cu energy during the initial deposition stage increases from 1 to 50 eV. NEP-CuC provides an atomistic framework for linking processing, interfacial structure and physical response across Cu-C systems, with direct relevance to Cu/diamond thermal-management interfaces, diamond metallization and non-equilibrium Cu-C processing.

Living supramolecular materials such as microtubules and actin filaments assemble and function in dynamic, heterogeneous environments, subject to chemical concentration gradients. Their rapid and precise response to such gradients—via aggregation, disassembly, or autonomous motion—underlies the fine spatiotemporal control typical of living systems. Reproducing such responsiveness in synthetic materials is a central challenge in materials science and requires a molecular-level understanding of how gradients couple to supramolecular structure and dynamics, which remains difficult to access experimentally. To this end, we combine implicit-solvent coarse-grained molecular dynamics (MD) with the constant chemical potential MD (C${\mu}$MD) technique to investigate, at molecular resolution, the coupling of two prototypical supramolecular polymer models with externally imposed ionic concentration gradients. Despite their contrasting responses to homogeneous ionic conditions, both systems undergo pronounced spatial reorganization under the gradient, generating regions of locally enhanced supramolecular activity that are inaccessible to homogeneous systems with the same overall content of self-assembling species. Crucially, the local supramolecular dynamics is largely determined by the local concentrations, consistent with the formation of local quasi-equilibria: this direct connection between spatial composition and supramolecular activity emerges as a common governing principle across the two models. These findings shed light on the spatially complex supramolecular response that can be triggered by chemical gradients, and show how a single gradient simulation can encode this response across a continuous range of local chemical environments, thus providing a general strategy to investigate and design materials operating under spatially heterogeneous conditions.

Rydberg atoms occupy a central role in quantum science; their loosely bound outer electron gives rise to properties that enable quantum information processing1 or the formation of exotic molecular bonds2. Beyond these roles, they have been proposed as a neutral platform for the observation of quantum effects in collisions and reactions of the ionic core with neutral particles3, 4, a long-standing goal of ion-based chemistry and physics. However, all of the experimental results so far could be explained using a classical description of the internuclear motion5. Here we demonstrate cold collisions inside a Rydberg helium atom, achieved by merging helium Rydberg and ground-state helium beams and imaging individual scattering events. We resolve the fully quantum-coherent motion and observe matter-wave diffraction and tunnelling-driven shape resonances down to collision energies of 90 mK. In the case of identical helium nuclei, we demonstrate a new regime of identical-particle Mott interference6, where quantum statistics begin to govern the total scattering cross section. For distinct isotopes, we show the breakdown of the Born-Oppenheimer approximation and benchmark parameter-free, state-of-the-art theory. We directly measure the helium isotope ionization-energy difference to be 15.0 +/- 0.1 K. Our experiments establish Rydberg atoms as a platform for the direct observation of quantum dynamics with a general class of ions, atoms and molecules.

State-to-state rate coefficients for inelastic molecular collisions are essential inputs for non-local thermodynamic equilibrium radiative transfer models, yet their computation using quantum scattering methods is prohibitive for large molecules and highly excited rotational states. We investigate the ability of artificial neural networks to extend existing datasets of collisional excitation rate coefficients without performing additional scattering calculations. A multilayer perceptron model was trained using molecular quantum numbers, level energies, energy gaps, and kinetic temperature as descriptors, and optimized on logarithmic rate coefficients. The model was tested on diverse collision systems ranging from simple diatomic molecules (CO, SiO) to open-shell species (SO), small asymmetric tops (H$_2$O, SO$_2$), and complex organic molecules (benzonitrile and vinyl cyanide) colliding with H$_2$ molecules or He atoms. Extrapolations were performed toward higher rotational levels, higher temperatures, and combinations of both. For most systems, predictions of rate coefficients involving previously unseen rotational states yielded mean error factors between 1.1 and 1.5, with the dominant rate coefficients generally reproduced more accurately than weaker transitions. Temperature extrapolations proved particularly successful, while combined extrapolations in temperature and rotational levels remained accurate to within a factor of two in most cases. The prediction quality depends on the interplay between dataset size, temperature range, molecular complexity, and the presence of clear collisional propensity rules. Overall, the approach demonstrates that machine learning can provide a practical route to extending collisional datasets for astrophysical applications, especially for large molecules for which additional quantum-scattering calculations are computationally demanding.

Large-area molecular junctions combining photochromic and redox-active functionalities provide an attractive platform for controlling charge transport by light. In this work, we study Au/DAEVIO/Ti/Au molecular junctions incorporated with electro-grafted layers of diarylethene-viologen with thicknesses of 12-16 nm. In the initial OFF state, the junctions exhibit low current densities and strong rectification, with a rectification ratio of 300 at 1V. Temperature-dependent measurements reveal a thermally assisted contribution at higher temperatures and a much weaker temperature dependence below 160-180K, consistent with multistep charge transport through molecular and/or interfacial states rather than direct coherent tunneling across the entire molecular layer. Under continuous in situ 385 nm irradiation, the electrical response is strongly and asymmetrically modified. The current density at +1V increases by a factor of 200, while the negative-bias current is only weakly modified, reducing the rectification ratio from 300 to 2. Illumination also produces a nonzero short-circuit current density of + 0.006mA cm-2 and an open-circuit voltage of -0.45V. These results indicate that irradiation simultaneously modifies molecular charge transport and generates a measurable photoelectric response. This behavior is consistent with light-induced changes in electronic coupling associated with DAE photocyclization, combined with photoinduced charge generation and field-dependent charge separation involving the redox-active viologen units and asymmetric electrode interfaces.

Crystallisation of calcium carbonate (CaCO$_3$) in aqueous solutions is essential for carbon dioxide sequestration and the sustainable production of calcium carbonate materials, which are widely used in industry and increasingly explored for novel applications. While crystallisation is often analysed within the framework of classical nucleation theory, CaCO$_3$ and other ionic crystals often form through amorphous precursor phases, motivating the need for alternative descriptions. In this work, we investigate the relationship between the formation of the first CaCO$_3$ coordination sphere, a fundamental unit of local ordering, and ionic aggregation using two complementary simulation approaches: on-the-fly probability-enhanced sampling (OPES) and asynchronous and infinite-swap replica exchange transition interface sampling ($\infty$RETIS). OPES was used to explore free-energy landscapes, whereas $\infty$RETIS was used to determine reaction kinetics. We studied systems at two levels of supersaturation, between which the formation of the first coordination sphere exhibited distinct kinetic behaviour. These differences were found to be linked to concentration-dependent ionic aggregation. At lower concentration, aggregation remains limited, whereas higher concentration promotes extensive spinodal-like aggregation. For both concentrations, the first coordination sphere forms within the pre-formed clusters through one of two distinct pathways: either within a cluster close to the minimum size required for its formation, or within larger amorphous aggregates whose size and structure depend on concentration. The coexistence of these pathways at both levels of supersaturation reveals the multifaceted nature of early-stage CaCO$_3$ crystallisation and highlights the importance of differentiating ionic aggregation and organisation.

The growing availability of quantum-mechanical (QM) datasets offers new opportunities to investigate structure-property and property-property relationships in drug-like molecules using data-driven methods. However, interactive tools that integrate molecular visualization, statistical analysis of QM properties, clustering, and machine learning (ML) remain limited, despite their value in facilitating dataset exploration and interpretation. To address this gap, we introduce QUPEX (QUantum Property EXplorer), an open-source Streamlit-based framework for the interactive exploration of QM property spaces in molecular systems. As a demonstration, we apply QUPEX to a subset of the QM7-X dataset comprising 41,537 equilibrium molecular structures containing up to seven non-hydrogen atoms (C, N, O, S, and Cl) and their 24 associated QM properties. In addition to property-space analysis, QUPEX incorporates an XGBoost regression pipeline for predicting PBE0 dipole moments from tight-binding-derived electronic descriptors, together with model evaluation and SHAP-based interpretability functionality. By combining interactive molecular visualization, data analysis, and predictive modeling, QUPEX provides an accessible and extensible environment for investigating molecular datasets and identifying patterns in their structural and electronic properties. These capabilities can support the exploration of chemical space and inform the rational design of drug-like molecules with targeted QM properties.

Although machine learning potentials (MLPs) generalize across configurational and chemical compound spaces, their accuracy is commonly believed to be limited by their training methods, with improvements beyond this limit achieved so far only by refitting to experimental observables. In this Perspective, we argue that MLPs can also be made more accurate than their training methods non-empirically by generalizing across a third space, that of quantum-chemical methods. We propose routes to method-transferable MLPs that predict at unseen methods, with working implementations in both density-functional and wavefunction-based theories showing that they can be more accurate than any of their training methods. Aiming beyond the accuracy of the training methods could also make universal MLPs more accurate than single-method models, even when the method-transferable MLPs remain less accurate than those QM methods. Method-transferable MLPs will shape the construction of training datasets and the evaluation of models, pushing the accuracy limits of chemical simulations.

Singlet–triplet gaps set the energy scale of the two-spin manifold in molecular quantum information materials, and such systems frequently carry diradical character: metal nanoclusters, metal–organic frameworks with radical linkers, and the nitrogen–vacancy center in diamond. Time-dependent density functional theory is the standard tool at this size but describes multireference systems poorly. A closed-shell reference is inadequate for a multiconfigurational ground state, and the adiabatic kernel excludes doubly excited configurations. The particle–particle random phase approximation (\pprpa{}) changes the particle number rather than the spin. Singlet and triplet states descend from one closed-shell reference, and double excitations enter on the same footing as single ones. Computational cost has confined \pprpa{} to small systems, and the two-electron integrals that drive it are factorized through an auxiliary basis. We develop \pprpa{}–as, which reduces that basis to a minimal set of atom-centered Gaussian shells whose exponents follow from free-atom radii and one global scaling factor. The approximation enters only the excited-state step, so both calculations proceed from the same self-consistent reference. We test molecules and clusters of up to 286 atoms, including heavy elements, and seven point defects in four periodic hosts, obtaining both multiplicities and their splitting without symmetry breaking or spin projection. We optimize the scaling factor and give guidance on choosing it. An order-of-magnitude smaller auxiliary basis delivers a speed-up of up to eightfold while staying within $0.03$~eV of conventional \pprpa{}, bringing diradical nanoclusters and periodic systems within reach.

We introduce STRUCTURES-P, a machine-learned all-electron orbital-free density functional for periodic CHNO systems. Electrostatics are evaluated analytically in an atom-centered Gaussian basis, while an equivariant network learns the kinetic and exchange-correlation energy from energies and gradients of non-ground-state densities. Minimizing the functional from a superposition of atomic densities recovers the Kohn-Sham ground state: on held-out crystals, the density error falls from 6.7% to 0.4% of the electron count and the energy error reaches 0.25 mHa per atom, half that of a same-architecture interatomic potential. A single functional can be trained for both isolated molecules and periodic systems, and the model generalizes to larger unit cells. It largely preserves relative-energy rankings and reproduces convex-hull vertices on the tested H-N composition slice. Together, these results demonstrate the viability of machine-learned all-electron orbital-free DFT for variational density optimization and energy evaluation in fixed-geometry solids.

We present a Python-based program that combines maximally localized Wannier functions-based first-principles electronic structure with the nonequilibrium Green's function formalism to enable efficient simulations of scanning tunneling microscopy (STM). The workflow builds upon standard density functional theory packages to construct compact transport Hamiltonians that preserve the properties of realistic materials. Superconductivity is incorporated via an effective pairing potential within the Nambu-spinor formalism, while coupling to the STM tip and substrate electrodes is treated using the wide-band limit approximation. Within this formulation, transport quantities such as current-voltage characteristics and differential conductance are evaluated in a closed analytical form. This avoids explicit numerical energy integrations and enables rapid spectroscopic calculations over broad parameter spaces. The framework provides a unified and computationally efficient approach for modeling superconducting hybrid nanostructures with spin-orbit coupling, magnetic textures, and spin polarization. Representative applications in spin chains, two-dimensional and molecular magnets on a superconductor demonstrate its robust capabilities for both simple model systems and realistic ab initio molecular structures relevant to modern STM experiments.

Density-functional tight binding has yet to yield a transferable description of vanadium oxides; for the standard second-order construction and the tested cells, we demonstrate that two of its approximations deviate by electron volts and offset each other in the band-index centroid separation between the V 3d and O 2p bands: the neutral two-centre reference omits electron-volt environmental terms, whereas the Mulliken charge model assigns the compact V 3d shell less than half of the self-consistent potential shift observed in PBE. Instead, we build a tight-binding model where the reference Hamiltonian derives from superposed neutral atoms, the full PBE exchange-correlation potential and frozen-core orthogonality, without adjustable terms, and where the orbital-resolved charge response employs three screening factors obtained from PBE linear response and an unscreened Coulomb range. Relative to the primary PAW reference, the plane-wave Harris-Foulkes energy differences of VO2 are matched by the reference energy at fixed geometry and the stated numerical settings, with signed deviations of +2.6 meV/atom for M1 relative to rutile (an energy difference of 92 meV/atom) and +6.2 and -5.2 meV/atom under 3% volume compression and expansion; the charge response reproduces 14 of 22 fitted and 5 of 8 held-out matched PBE responses within one tolerance, and 28 of the 30 within twice the tolerance, and in rutile the fitted first-radial V 3d shift is -4.39 eV, 0.47 eV more negative than PBE's -3.92 eV, whereas the tested DFTB2 charge model gives -1.53 eV. The convexity of the spinless model at fixed geometry prevents it from spontaneously differentiating symmetry-equivalent sites under the symmetries respected by its implemented operators and sampling, so within this model such differentiation in the Magnéli phases must arise from electron-lattice coupling or an explicit spin or correlation term.

The clean-energy transition is driving unprecedented demand for metals, whose extraction is among the largest industrial sources of carbon emissions. Molten-salt electrolysis offers a path toward carbon-free production of aluminum, iron, titanium, and critical metals. However, corrosive operating conditions and complex, multicomponent feedstocks make experimental development costly and challenging. Here, we introduce a first-principles framework for constructing electrochemical phase diagrams of multicomponent systems to accelerate electrode and electrolyte design and guide the selection of compatible materials and operating conditions for electrochemical cells. We derive a grand potential that generates these diagrams at scale, and supply free energies using first-principles data obtained through a fine-tuned foundation machine-learned interatomic potential. For silicon in molten CaCl$_2$, the construction not only recovers the experimental diagram when using the first-principles framework on a limited set of structures, but also predicts further domains when extended to a larger set of crystal structures. Finally, we demonstrate the predictive power of the approach by screening ten alkali and alkaline-earth halide electrolytes for aluminum electrowinning. Three thermodynamic criteria identify NaF, where cryolite emerges as the stable aluminum-bearing phase, recovering the chemistry that Hall and Héroult established empirically in 1886. The framework provides a first-principles basis for selecting compatible electrodes, electrolytes, and operating conditions toward low-carbon metal production from complex source materials.

Although weak at normal gravity, gas radiation sets the gravity at which a co-flowing hydrogen jet diffusion flame stops flickering. Flamelet-based simulations with unity Lewis numbers, which reproduce the flicker frequency measured by femtosecond coherent anti-Stokes Raman scattering within 4%, are combined with local stability analysis. At one tenth of normal gravity, the adiabatic flame flickers, the radiating flame does not, and switching the emission off restores flicker. Radiation acts through two mechanisms that do not weaken at reduced gravity. The hot outer layer loses buoyancy in proportion to the gas residence time, and a disturbance that displaces the flame also displaces its emission, which damps the disturbance on the lean flank (displaced-emission damping). Freezing the radiative source, which removes only its response to disturbances, slows the downstream recession of the oscillation more than tenfold. Both mechanisms slow the upstream spreading of disturbances. This spreading, competing with the co-flow, sets the onset location and the critical co-flow. Without radiation, the spreading speed scales with the square root of gravity; its radiative reduction does not. At reduced gravity, the flicker limit therefore becomes a straight line relating the square root of the co-flow Froude number to a radiation number, the ratio of buoyant to radiative time scales. The calibrated line places the critical gravity for the experimental co-flow at 0.13 times normal gravity, 2.6 times the adiabatic value. It correctly predicted whether two further flames keep flickering. Beyond the limit, transient wave packets can mimic flicker throughout a short drop-tower test.

Interpreting electron paramagnetic resonance (EPR) spectra commonly requires repeated forward simulation and optimization of spin Hamiltonian parameters. Established software provides mature simulation and fitting methods, but these calculations are not generally available as differentiable components within machine-learning workflows. We present TorchSpin, an open-source PyTorch framework that ports the organization and numerical conventions of EasySpin into a tensor-based computational environment. Representative calculations spanning continuous-wave EPR, ENDOR, pulse EPR, spin dynamics, trajectory simulation, and magnetometry closely reproduced corresponding EasySpin results. In matched benchmarks, TorchSpin CPU execution was faster than EasySpin for six of nine workloads although performance depended strongly on the calculation. We therefore focused on the capabilities enabled by automatic differentiation in PyTorch. In a Cu(II) powder-spectrum demonstration, feedback propagated through TorchSpin improved the quality of a supervised convolutional neural network (CNN) without using parameter labels during refinement. Models trained from randomly initialized CNNs using only noisy spectra and TorchSpin reconstruction loss achieved median similarities of $\geq$ 0.99. CNNs trained on TorchSpin-generated libraries also transferred without adaptation to independently generated EasySpin spectra with performance comparable to EasySpin-trained controls. Once trained, the CNN produced initial parameter estimates in approximately 1 ms per spectrum while a batch of 512 was processed in approximately 1.3 ms with GPU acceleration. TorchSpin therefore provides both a tested Python implementation of established EPR calculations and a differentiable physical layer for rapid learned inference, spectral refinement, and parameter-label-free training.