Papers

Small polarons, formed when excess electrons become localized through lattice distortions, play a critical role in charge transport, catalysis, and degradation processes in transition-metal (TM) oxides. Whether universal machine-learning interatomic potentials (uMLIPs), which lack explicit electronic degrees of freedom, can describe them remains unclear. Here, we investigate H-induced electron localization across a range of TM oxides using a geometric descriptor based on TM-O bond-length expansion (Z-score) to identify polaronic distortions. We find that uMLIPs exhibit varying degrees of electron localization, from delocalized states to metastable small polarons, with their behavior strongly dependent on the training data and treatment of electronic correlations. In particular, the absence of Hubbard U corrections for specific TM cations in the training data leads to electron delocalization, in contrast to DFT+U predictions. Although some uMLIPs reproduce polaron hopping barriers during coupled proton-polaron transfer, all of them fail to stabilize spatially separated polaron-donor configurations, instead favoring localization near the H dopant.

Analytic time-domain expressions for the elution-time density and its parameter derivatives were recently derived from a stochastic model of linear isocratic chromatography incorporating advective-diffusive transport, injection dispersion, and fast and slow retention mechanisms. A Gaussian approximation, justified asymptotically at high column-scale Péclet numbers, was adopted for the distribution of the combined mobile-phase and fast-retention time, while slow retention was incorporated through a series of Gaussian-Gamma convolutions. Here, the underlying normal-inverse-Gaussian density is approximated by a finite Gaussian mixture using an existing quadrature rule. The elution-time PDF is a weighted sum of series of the previously derived Gaussian-Gamma form. Its parameter derivatives are also obtained. Newly derived recurrences reduce the cost of evaluating the coefficients of that series and their derivatives from quadratic to linear in truncation order for a fixed number of mechanisms. Through a probabilistic analysis of the series coefficients, the required number of terms is found to be small enough for rapid evaluation under usual chromatographic conditions. A relative roundoff-error estimator is derived to quantify finite-precision loss in the inherited forward recurrence for Gaussian-Gamma convolutions. For the cancellation-prone regime, a backward reconstruction is developed, initialized from an exact ratio of consecutive Gaussian-Gamma terms expressed through parabolic-cylinder functions. A highly accurate approximation is derived for rapid evaluation of this ratio. Independent high-precision calculations confirm the high accuracy of the resulting double-precision evaluation in the tested numerical case.

Fast, high-fidelity molecular generation requires accurate chemical choices and efficient sampling. Chemical building blocks reduce graph size, but make each node a choice among tens of thousands of related identities. We introduce MIRRA (Molecular Identity Representation, Refresh and Assembly), a discrete flow-matching generator that learns from chemical knowledge and evaluates identity probabilities only when needed, while keeping every identity in its vocabulary available. Chemical features share information across related blocks, and learned identity corrections distinguish them in molecular context. By deciding which positions will refresh before computing their probabilities, the sampler avoids unused predictions while preserving each sampling transition. Against the strongest baselines in each task, MIRRA reduces chemical and graph distribution errors on ZINC250k by 29-31% and 53-60%, respectively, with generation up to 8.6 times faster. Property targeting yields an estimated 7.8-20.8 times more distinct novel hits per second. On a held-out polymer test set, MIRRA achieves 100% periodic validity with known chain topology, versus 57.0% for a polymer variational autoencoder. These results demonstrate fast, high-fidelity generation with the full chemical vocabulary available throughout sampling.

Most machine-learning interatomic potentials (MLIPs) are trained on gas-phase data, which limits their use for chemistry in solution. Here, we introduce AnySolv, a transferable implicit solvation potential that provides solvent-dependent energy and force corrections to existing gas-phase potentials without retraining them. It is trained on 1.4 million solvation energies and forces computed with density functional theory (DFT) and SMD in 36 solvents, spanning charged, open-shell, and transition-state structures. Because solvents are represented by continuous physical descriptors, AnySolv supports 179 solvents, including those absent from training. On external benchmarks, AnySolv reproduces DFT-SMD solvation energies to 2-4 meV mean absolute error at more than three orders of magnitude lower cost, and it matches the accuracy of DFT-SMD against experimental solvation free energies. This enables screening of the mechanisms of 120 nucleophilic aromatic substitution reactions in six phases as well as molecular dynamics simulations that reproduce the experimentally observed solvent-dependent conformational preferences of alanine dipeptide. By providing transferable solvation corrections to existing MLIPs, AnySolv enables scalable simulations of solvent-dependent chemical reactivity and molecular dynamics.

Molecular systems with optically addressable electron spins are emerging as versatile quantum sensing platforms, offering tunable qubit properties and molecular-scale spatial control. Owing to their longer lifetimes, coupled nuclear spins provide an attractive resource for enhancing sensing performance. For molecular spin systems, the ability to initialise, coherently control and readout nuclear spins at room temperature is crucial for realising such benefits. Here, we present the first optical detection of nuclear magnetic resonance and coherent nuclear spin control with a molecular system at room temperature. Specifically, we demonstrate optically detected Rabi oscillations of $^{14}$N nuclear spins in the photoexcited triplet state of the organic chromophore 6,13-diazapentacene. The strong hyperfine coupling between the electronic spin and $^{14}$N nuclei enhances the nuclear Rabi frequency, enabling fast coherent nuclear-spin rotations. This work lays the foundation for leveraging nuclear spins as memories for enhanced molecular-based quantum sensing.

Nitrite photochemistry in atmospheric aerosols and natural waters is a major source of hydroxyl radicals and reactive nitrogen oxides. Contrary to the prevailing view that in the environment aqueous nitrite photochemistry proceeds exclusively through photoexcitation followed by homolytic bond cleavage, we show that visible light directly ionizes aqueous nitrite in individual micron-sized droplets. Although the photoionization cross section is exceptionally small, this pathway is observable at the high photon flux densities accessible in single-droplet experiments. Molecular simulations reveal that this is because photoionization absorption has an exceptionally long wavelength tail due to the large solvent reorganization energy in aqueous solutions. Kinetic modeling of an aqueous-phase reaction mechanism quantitatively accounts for the observed chemistry and predicts the formation of nitrate, hydroxyl radicals, and solvated electrons. The overlap of the predicted broad photoionization continuum with the visible solar spectrum further suggests that visible-light photoionization is an overlooked source of nitrogen oxides, solvated electrons, and oxidants in atmospheric aerosols, snowpack, and natural waters. Under dilute conditions, where dissolved oxygen is the main sink for solvated electrons, photoionization is expected to be the dominant photochemical loss pathway for nitrite.

The nearly collinear configuration of highly stretched polymer chains before fracture motivates one-dimensional models. At fixed extension, stretching one bond redistributes length among the others, coupling rupture to the whole chain. In this work, I develop a framework for fracture-healing rates in periodic Morse chains, combining deterministic theories, equilibrium simulations and a quasi-deterministic approach using equilibrium fluxes and barrier-top trajectories. Constrained-partition calculations closely reproduce simulated populations and intact-state tensions. An intact-reservoir potential of mean force (PMF) supplies the first-fracture surface probability, while recrossing corrects the attempt flux without a rate-fitted prefactor. Independent rate tests identify an operational chain-length boundary for accurate two-state kinetics; failed-return durations decrease relative to population relaxation as chains grow. Kramers-Grote-Hynes (KGH), nonlinear reactive-flux and equilibrium rates show excellent agreement in this regime. KGH predicts rates away from coexistence and a chain-dependent local activation length dominated by the barrier response. Rates decrease approximately exponentially before declining more gently for longer chains: barrier growth dominates, additional fracture sites partly compensate, and transmission varies more weakly. Beyond coexistence, long chains can fracture practically irreversibly because healing becomes too rare to observe. Projected committor crossings, where the configuration-averaged probability of reaching the fractured core first is one half, lie near site-PMF maxima, although configurations at equal bond length retain different fracture probabilities. Multiple fractures remain negligible near coexistence through at least $N=50$. The framework could supply state-dependent rates to mesoscopic fracture models of polymer networks.

Liouville equation contains an excess coupling term in addition to the Poisson bracket. Neglecting this term yields the Poisson bracket mapping equation (PBME). We expand the mapping dependence of the density in Hermite functions about the Gaussian factor common to all physical mapping densities. In this basis, the excess coupling term acts purely as a raising operator and exactly cancels the raising contribution generated by the back–reaction force. Consequently, the exact dynamics does not generate higher Hermite orders and closes on a finite, sparse system of equations for the coefficient fields. Within the physical sector, these equations reduce to the subsystem quantum–classical Liouville equation. In contrast, the PBME retains the raising contribution of the force, modifying the back reaction within the physical sector while continuously generating higher Hermite orders. For Tully's dual avoided crossing model, direct propagation of the coefficient equations confirms this finite closure and agrees with independent solutions of the subsystem equation. Comparison with converged full quantum dynamics further shows that, across all regimes examined, the PBME is less accurate than the quantum–classical description for populations, coherences, and momentum distributions.

Halogen bonding in which a covalently bound fluorine acts as halogen-bond donor (F-bonding) is rare, and its open-shell variant with radical electron donors remains unexplored. We introduce SEFB-15 dataset (15 open-shell DF$\cdots$CH$_3$ complexes) exemplifying single-electron F-bonding (SEFB) and CSFB-14 dataset (14 closed-shell DF$\cdots$NH$_3$ complexes) representing closed-shell F-bonding (CSFB). Reference binding energies (BEs) at DF-RMP2-F12/CBS//DF-RMP2-F12/VDZ-F12 are validated against CCSD(T), CCSD(T)-F12b, W1-F12 and W2-F12 for selected systems (DF = F$_2$, NCF, CNF, NH$_3$F$^+$ and NH$_2$F$_2^+$), with MA%D of 4.5% (DF$\cdots$CH$_3$) and 3.4% (DF$\cdots$NH$_3$) against CCSD(T)-F12b/CBS//CCSD(T)-F12b/VDZ-F12. BEs from W1-F12 and W2-F12 are identical. Reference F-bond distances at DF-RMP2-F12/VDZ-F12 are validated against CCSD(T)-F12b, CCSD(T), CCSD, and DCSD for the same systems, with MA%D of 0.9% (SEFB) and 0.4% (CSFB) against CCSD(T)-F12b/VDZ-F12. M06-2X is recommended for closed-shell halogen bonding with heavier halogens but has never been assessed for open-shell F-bonding. M06-2X/AVTZ systematically overbinds all SEFB-15 complexes and underestimates their F-bond distances, with MA%Ds of 75.8% on BEs and 8.9% on F-bond distances. M06-2X predicts comparable BEs for F$_2\cdots$CH$_3$ and F$_2\cdots$NH$_3$, contrary to all ab initio results, an anomaly persisting across all 16 basis sets. Neither basis set nor BSSE correction resolves the overbinding. BSSE correction worsens BEs for DF$\cdots$NH$_3$ complexes. For CSFB-14, M06-2X/AVTZ yields MA%Ds of 16.0% for BEs and 3.3% for F-bond distances. M06-2X is reliable for CSFB but unreliable for SEFB regardless of basis set. Companion paper II reports performance of other Minnesota functionals and ab initio methods for these datasets.

Poorly soluble species can have mean populations below one in small systems such as nanopores. In this regime, the grand-potential minimum, which identifies the most probable particle number, differs from the ensemble-averaged solute loading. We use grand-canonical Wang-Landau sampling (GCWLS) to calculate the density of states $\Omega(N_\mathrm{A}, N_\mathrm{B})$ for a binary Lennard-Jones mixture of solute B in solvent A, both in bulk and in slit pores. One set of GCWLS simulations gives ensemble averages over a range of chemical potentials, whereas conventional grand-canonical Monte Carlo (GCMC) simulation requires a separate simulation at each state point. Independent GCMC simulations confirm the GCWLS ensemble averages. The solvent number distribution is nearly Gaussian, whereas the dilute solute distribution is skewed and Poisson-like. The most probable solute number therefore lies below the ensemble-averaged loading $\langle N_\mathrm{B}\rangle$ and is zero whenever $\langle N_\mathrm{B}\rangle<1$. Reading the solute loading from the grand-potential minimum underestimates it and can falsely indicate that no solute is present. Defining the oversolubility as $\mathcal{O}_\mathrm{B}=x_\mathrm{B}^{\mathrm{conf}}/x_\mathrm{B}^{\mathrm{bulk}}$, where $x_\mathrm{B}$ is the solute mole fraction, we find $\mathcal{O}_\mathrm{B}\approx12$ in a pore of 3.5 particle diameters width when both wall interactions are repulsive. Adding wall-solute attraction moderately raises it to $\approx13$, whereas wall-solvent attraction lowers it to $\approx3.4$. This comparison shows that the wall-solvent interaction controls most of the enhancement. As the pore widens, $\mathcal{O}_\mathrm{B}$ decreases toward unity. In bulk and in nanopores alike, the solubility of poorly soluble species should be obtained from ensemble averages rather than from grand-potential minima.

The restricted active space coupled cluster singles and doubles (RAS-CCSD) model, and its pilot implementation is detailed. The approach offers a simple, pragmatic way to formulate a coupled cluster theory for open-shell and multireference systems. For ground state energies, errors (compared to FCI) are shown to be similar to those of unrestricted (spin-orbital) CCSD. For excited states, the errors of RAS-CCSD are generally larger, and adaptations to the methodology are needed to achieve an approach which is balanced for both ground and excited states. However, unlike unrestricted CCSD, the approach is spin-adapted and can be used to add dynamical correlation to a multideterminantal reference state.

In molecules, electronic coherence typically decays within a few hundred femtoseconds, a timescale usually attributed to the environment. We show that it is set to a large extent by which coherences are excited: the molecule can host coherences that the bath barely sees, and optimal control can find and exploit them. Using gradient-based optimal control (GRAPE) with Redfield dynamics, we maximize the total vibronic coherence between the electronic ground and an optically bright electronic excited state in a three-state model with nonadiabatic features, in two regimes of low and high nonadiabatic mixing and for different system-bath coupling strengths. The Liouvillian spectrum reveals, in both regimes, a well-separated coherence mode with substantial ground-bright character that decays on a picosecond timescale. This mode is protected by mixing with the dark state, which brings the geometry of the optically accessible excited state close to that of the ground state and thus weakens its coupling to the bath. Without prior information, GRAPE finds this mode and keeps the photoexcited wave packet near the Franck-Condon region. At equal fluence, it increases the coherence at 800 fs by more than two orders of magnitude over a Gaussian pulse at the weakest coupling, and by many more at stronger coupling. The Liouvillian predicts the bath dependence of the long-lived coherence to within 1%, and a Gaussian pulse tuned to the mode frequency comes within 10% of the best pulse found. Beyond two-level and spin systems, our study puts forward the vibronic structure of molecules as a route to protected coherence subspaces, identifying a dark-state protection mechanism and a design criterion based on molecular parameters. These results lay the groundwork for our goal of using vibronic molecular systems as a resource for long-lived, controllable coherences in molecular quantum information science.

How charge rearranges within an electrode shapes the behavior of batteries, supercapacitors, and other electrochemical devices. Molecular simulations can capture this response by allowing the charge on each electrode atom to adjust to its surroundings, but repeatedly calculating these charges adds substantial computational cost. We present an open-source implementation of the constant-potential method in GROMACS that integrates these calculations into the program's optimized CPU and GPU routines. Comparisons with established codes validate the electrode charges, while charging, voltammetry, and impedance simulations demonstrate the response to changing electrical conditions. The implementation also supports electrodes that move or deform and models of finite metallic screening and electron spillover. In a pair of charged carbon nanotubes, allowing charge to move away from the facing surfaces reduces the repulsive force at contact by about half at an intermediate charge and keeps the pair bound where a uniform-charge model opens within the simulated time. These capabilities make the electrical response of electrodes accessible within GROMACS for studies of interfacial structure, charging dynamics, and electrode motion.

Accurate, robust, and efficient interatomic potentials are highly desirable for large-scale molecular dynamics simulations. Although machine-learning interatomic potentials can reproduce first-principles potential-energy surfaces with high accuracy, they typically incur higher computational costs than conventional empirical potentials and may be less reliable outside their training domains. We developed Tersoff-NN, a hybrid machine-learning potential for Si, which retains the analytical radial interactions and cutoff structure of the Tersoff potential while representing its environment-dependent bond-order factor using compact neural networks (NNs). Benchmarks for 32,768-atom systems show that Tersoff-NN is 4-12 times faster than the Behler-Parrinello-type NN potentials tested in this study. Tersoff-NN improves the short-range structure of liquid Si relative to the conventional Tersoff potential, closely reproduces the ab initio radial and angular distributions, and reproduces the equilibrium structure of diamond Si and qualitative energetic trends among several crystalline phases. Furthermore, melt-quench simulations reveal a disordered solid with predominantly four-coordinated, tetrahedral-like local environments. Additionally, characteristic reconstruction motifs are retained on Si surfaces despite their exclusion from the training dataset. A direct comparison with an alternative atom-centered bond-order NN highlights the critical role of physical constraints in ensuring dynamic stability. Despite exhibiting comparable validation errors, the selected triplet-based architecture remains stable, while an alternative model exhibits unphysical bond-order growth and atomic collapse. These results confirm that learning only the bond-order term improves the description of diverse Si environments while retaining substantial computational efficiency and enhancing dynamical stability.

Machine-learned interatomic potentials (MLIPs) accelerate molecular dynamics (MD) simulations by learning the energies and forces that govern atomic motion. Recent work has shown that relaxing physical inductive biases can improve computational efficiency and predictive accuracy, raising the question of whether energy-and-force matching alone is sufficient to ensure accurate sampling. We show that, for unconstrained hypothesis classes, the relationship between prediction error and sampling accuracy is exponentially ill-conditioned in dimension. In particular, prediction errors that decay exponentially with dimension can coexist with nearly maximal total variation distance between the learned and target distributions. We identify two failure mechanisms. The first is kinetic trapping, where relaxation to an accurate learned equilibrium requires exponentially long times, even when simulations are initialized from training configurations at which energies and forces are matched exactly. The second is equilibrium mismatch, where the learned stationary distribution itself remains far from the target. Under explicit assumptions, we show that equilibrium mismatch can persist even in local, symmetry-preserving models, where small per-atom errors coexist with a distributional discrepancy that approaches its maximum as system size increases. Finally, we establish global energy-control conditions that guarantee equilibrium accuracy and identify additional conditions required for rapid relaxation.

Accurately describing chemical bond breaking requires capturing strong/static electron correlation, a major challenge for single-reference self-consistent-field methods such as Hartree–Fock and Kohn–Sham density-functional theory (DFT). Fractional occupations substantially improve this situation, as demonstrated by information-density-matrix-functional theory (i-DMFT) and thermally-assisted-occupation DFT (TAO-DFT). Although useful, they are formulated within rather different theoretical frameworks, are somewhat semi-empirical, and their relationship remains unclear. Here we introduce finite-temperature adiabatic-connection reduced density-matrix functional theory (FT-AC-RDMFT), in which i-DMFT and TAO-DFT emerge as different reductions of a unified framework. The effective eigenvalue equation for natural orbitals and the Fermi–Dirac occupation numbers follow directly from the variational principle, while a thermal adiabatic connection relates the empirical entropy coefficient of i-DMFT to a characteristic temperature of the auxiliary non-interacting system. Within this framework, i-DMFT is the exact-exchange-based reduction, whereas TAO-DFT results when exact exchange is replaced by a density-based exchange-correlation functional. Numerical calculations confirm that i-DMFT, apart from a constant, coincides with the exact-exchange realization of the framework, and show that the improved dissociation behavior from finite-temperature occupations extends beyond exact exchange to hybrid and semilocal density functionals. For strongly correlated V2O3, finite-temperature occupations substantially reduce the severely overestimated non-magnetic LDA bulk modulus, bringing it close to experiment. These results establish FT-AC-RDMFT as a common theoretical foundation for finite-temperature occupation-based electronic-structure methods in molecular and solid-state systems.

Electron density is a fundamental quantity of electronic structure, yet most machine learning density models treat it solely as a reconstruction target and are developed separately from machine learning interatomic potentials. Here, we introduce a virtual-atom formulation within the DPA3 framework, in which density query points are represented as virtual nodes and processed by the same parameterized encoder used for real atoms. An asymmetric neighbor construction allows virtual atoms to receive information from nearby real atoms without altering the real-atom interaction graph. The resulting framework supports density, energy, and force prediction through task-specific readout heads. The proposed model achieves state-of-the-art density reconstruction accuracy on the Materials Project benchmark, matches the best reported performance on nickel-manganese-cobalt battery cathode materials, and is competitive with dedicated density models on QM9. When density labels are used jointly with energy and force supervision, the model improves in-domain accuracy, makes local environment information more accessible under linear probing, and reduces zero-shot force errors on larger QM40 molecules. Density-only checkpoints also provide useful initializations for downstream energy-force learning under the fixed fine-tuning protocol. Together, these results support electron density as a source of electronic-structure supervision for interatomic-potential representations.

We present the concept of quadrature-detected zero-to-ultralow-field nuclear magnetic resonance (QD ZULF NMR). Two orthogonal sensors, atomic optically pumped magnetometers, are used to separately detect components of oscillating sample magnetization, which are then combined into a quadrature signal. This approach enables the distinction of positive and negative resonance frequencies with respect to the laboratory frame—such that absolute signs of gyromagnetic ratios can be determined. In addition, QD ZULF NMR reduces peak density and overlap compared to ZULF NMR with single-axis detection, while providing richer information about nuclear-spin dynamics. As an illustration, we present experimental $J$-spectra for thermally polarized [$^{13}$C]-formic acid and [$^{13}$C]-methanol, compounds commonly used in ZULF NMR which represent XA and XA$_3$ spin systems, respectively. A theoretical framework describing QD ZULF NMR signals is provided.

Efficient and durable phosphors made from abundant elements underpin energy-saving solid-state lighting, near-infrared light sources for sensing, and X-ray and biomedical imaging. Co-doping is a standard route to brighter phosphors, yet the fate of the co-dopants is rarely established. We combine quantitative electron paramagnetic resonance (EPR) spin counting with photoluminescence, photoluminescence excitation, and X-ray-excited spectroscopy across two dilute Mn/Cr co-doping series of hydrothermally grown $\mathrm{ZnAl_2O_4}$ nanoparticles and show that the two ions can form an exchange-coupled, edge-sharing Cr–Mn defect complex, with $\mathrm{Mn^{2+/4+}}$ entering an octahedral site next to $\mathrm{Cr^{3+}}$. The octahedral Mn lifts the inversion symmetry of the $\mathrm{Cr^{3+}}$ site and strengthens its parity-forbidden absorption, enhancing the $\mathrm{Cr^{3+}}$ emission without energy transfer. The population of the defect complex follows the law of mass action, and above a threshold Mn concentration, Mn re-partitions into EPR-silent octahedral configurations that quench both emissions. Concentration optima in co-doped phosphors can thus reflect defect speciation, not only energy-transfer efficiency, which opens a structural design handle for brighter emitters.

Biomolecular processes, including protein folding, protein-protein association, and protein-DNA recognition, often occur on timescales beyond what individual atomistic molecular dynamics (MD) simulations can reach. To access these longer-timescale dynamics, practitioners commonly combine many parallelized, short trajectories into reduced kinetic models, such as Markov state models (MSMs), that describe how the biomolecules interconvert between a handful of biomolecular configurations (e.g., folded and unfolded states of a protein). Central to MSM construction is the assumption that, at sufficiently long time lags, these projected dynamics become memoryless, such that the future evolution of the system depends only on its current state. Yet, projecting high-dimensional biomolecular dynamics onto a small set of states necessarily discards information about unresolved degrees of freedom, including solvent reorganization, side-chain rearrangements, and intermediate configurations. Because these unresolved motions can continue to influence subsequent dynamics, the resulting dynamics retain memory that is absent from a Markovian description. Here, we present ugme, a modular, open-source Python package for constructing and validating generalized master equations (GME) models that explicitly account for these non-Markovian (memory) effects.

The luminescence of doped nanocrystals is usually optimised through the activator; here we show that the host cation ratio is an equally decisive, and largely overlooked, design variable. Mn-doped ZnGa$_2$O$_4$ nanocrystals (Mn:Zn = $4\times10^{-4}$) were grown hydrothermally at nominal Zn/Ga ratios between 0.30 and 0.75 (stoichiometric: 0.50) and post-annealed at 400–1100$^\circ$C, and the resulting composition–temperature matrix was mapped by X-ray- and UV-excited luminescence, EPR, Rietveld-refined X-ray diffraction, Raman spectroscopy and SEM. The as-grown crystals are phase-pure spinel at every composition and accommodate their off-stoichiometry internally as a point-defect inventory, reflected in a 0.4% variation of the lattice parameter; on annealing, the excess gallium is exsolved as $\beta$-Ga$_2$O$_3$ in amounts set by the solution composition. The Mn$^{2+}$ emission separates into two optima, near-stoichiometric crystals annealed at 400–600$^\circ$C and Zn-excess crystals annealed at 1100$^\circ$C, the latter being twice as bright under X-ray excitation. Under X-ray and 365~nm excitation the two optima are separated by a minimum at 800$^\circ$C that coincides with a collapse of the Mn$^{2+}$ EPR population and has no counterpart in the Raman linewidths, identifying transient, defect-compensated oxidation of the dopant rather than lattice degradation as its origin. The most Zn-rich composition shows neither Mn$^{2+}$ nor Mn$^{4+}$ emission at any annealing stage, whereas its trace Cr$^{3+}$ emission is strong, indicating that Mn is rejected already during growth. Solution stoichiometry therefore acts on two levels, dopant capture and native-defect inventory, while annealing controls dopant valence and lattice order. The brightest high-temperature phosphor is thus not the nominally stoichiometric one, but the composition whose excess is consumed on its way to stoichiometry.

We introduce the concept of spin migration, i.e. time-dependent spin density, and the absolute smallest example of molecular spintronics. We illustrate the concept by ab initio calculations of the coupled vibronic motion of the electrons and the nuclei in the argon dimer cation, in which the vibrational level spacing is similar to the spin–orbit splitting of the atomic argon cations. We find that the spin density varies on multiple time scales, given by the natural time scales of the electronic and nuclear wavepackets.

Machine-learning force fields (MLFFs) enable the calculation of transformation pathways in molecular crystals at a fraction of the computational cost of density functional theory (DFT). However, a good agreement in energies and structures does not necessarily imply an accurate description of vibrational properties, which are essential for characterizing transition states and determining free energies at finite temperatures. Herein, we assess the accuracy of system-specific SO3krates MLFFs trained on PBE+MBD reference data for describing vibrational properties of molecular crystal transformations. As examples, we consider a polymorph transition of 1,4-diiodobenzene and a single-crystal-to-single-crystal Diels-Alder reaction. The transition state structures obtained from solid-state nudged-elastic-band (NEB) calculations with the MLFFs exhibit a single imaginary $\Gamma$-point frequency associated with the respective transformation. Compared with PBE+MBD, the mean absolute errors of $\Gamma$-point vibrational frequencies and relative harmonic free energies at 300 K are about 3 cm$^{-1}$ and 1 kJ/mol, respectively. Furthermore, we compare for the Diels-Alder reaction a collective transformation pathway with a sequential one, in which individual diene-dienophile pairs react successively, and demonstrate that PBE0+MBD single-point corrections can significantly affect the predicted reaction energetics. These results demonstrate that system-specific MLFFs can reproduce not only the energies and forces but also the local curvature of the potential-energy surface with high accuracy, enabling reliable calculations of harmonic vibrational free energies, providing a basis for extending the studies of molecular crystal transformations to larger supercells.

Machine learning methods are increasingly used to predict chemical properties directly from the molecular structure to bypass the often prohibitive cost of quantum mechanical calculations. Recent work has shown that including the ground-state electron density as input to the machine learning model can improve accuracy in this setting. This work employs the recent surrogate functional framework originally developed for orbital-free density functional theory and extends it to predicting molecular properties. We show that passing the ground-state density as input to the model, while simultaneously enforcing it to be the minimum of the surrogate functional, surpasses state-of-the-art performance for six out of seven extensive properties of the QM9 dataset. Additionally, the approach shows improved generalization to larger molecules taken from the QM40 dataset. On all extensive properties of both datasets, our approach outperforms models that are informed by the ground-state density but do not enforce the surrogate functional constraints.

When investigating the performance of supercapacitors (SCs), it was found that they offer high-power density and long life but are limited in capacity and energy density. Water-in-salt electrolytes, i.e., 21___m lithium bis(trifluoromethanesulfonyl) imide (LiTFSI), offer a solution by expanding the electrochemical window compared to a diluted aqueous environment. While significant research has been dedicated to improving these electrolytes, the impact of carbon properties on energy storage remains relatively underexplored. This study investigated the influence of carbon structures, defects, and surface functional groups on supercapacitive performance in LiTFSI electrolytes. For this purpose, a series of carbon materials, including carbon nano-onions and porous conductive carbon black (ENSACO), were synthesized and systematically modified by oxidative and reductive thermal treatments. Our results indicated that higher specific surface area and active surface area improve the ion adsorption and capacitance, while specific oxygen functionalities, such as carboxylic and anhydride groups, were found to significantly enhance capacitance. Furthermore, crystallinity and graphitic characteristics play a role in capacitance, with smaller graphene domains and greater disorder promoting ion storage. The study demonstrates a direct correlation between carbon microstructure and electrochemical behavior, providing insights into the rational design of carbon electrodes in high-performance SCs.

We investigate the quantum dynamics of a single ion confined in a radio-frequency (RF) Paul trap in the presence of weak octupole-induced anharmonicity, as can occur in realistic ion-trap potential. The explicitly time-dependent quadrupole potential is treated in a reference-oscillator Fock basis, allowing the effects of the RF drive and the quartic correction to be resolved directly at the level of motional-state couplings. While the quadratic RF interaction generates $\Delta n=\pm2$ transitions and Gaussian squeezing, the quartic contribution opens additional $\Delta n=\pm4$ coupling pathways. Starting from the reference-oscillator vacuum, we show that the octupole interaction broadens the even-parity Fock-state distribution and enhances the phonon-number fluctuations more strongly than the mean occupation. At the same time, the RF-induced sub-vacuum quadrature squeezing remains robust, although its magnitude and orientation are modified by the quartic interaction. The number statistics and quadrature fluctuations therefore respond differently to the same nonlinear perturbation, reflecting the distinct roles of Fock-space redistribution and phase coherence. The resulting dynamics provide a quantum-mechanical characterization of weak octupole corrections beyond the ideal quadrupole approximation and clarify how realistic anharmonicities modify nonclassical trapped-ion motion. Importantly, the motional nonclassicality remains robust against the weak octupole perturbation, as evidenced by persistent sub-vacuum quadrature squeezing and Klyshko-inequality violation. These results characterize how realistic anharmonic corrections reshape trapped-ion motion beyond the ideal quadrupole approximation.

Simulating acid-base equilibria from first principles is a tremendous challenge, as it requires modeling bond-breaking events in a complex hydrogen-bonding environment. The quantum mechanical behavior of the protons is often important, complicating simulations even further. We show that by combining state-of-the-art machine-learning potentials, accelerated sampling of the dissociation process, and an efficient estimation of nuclear quantum corrections it is possible to reliably compute the dissociation constants of different species in water. We demonstrate the transferability of this workflow, applying it successfully to the autoionization of water and to the entire ladder of the aqueous dissociation of phosphoric acid. The definition of the dissociation constant, the choice of order parameters, sampling artifacts and finite-size effects, as well as quantum nuclear effects all play a non-trivial role in determining the outcome of the calculation, so that cutting corners is likely to introduce biases that can only be compensated by fortuitous cancellations of errors.

Neural-network variational Monte Carlo provides an accurate route to solving the electronic Schrödinger equation, but many neural wavefunctions are optimized for a single nuclear geometry, requiring separate calculations to map out a potential energy surface. We introduce NucleoNet, a nuclear-aware determinant ansatz in which electrons and nuclei form a unified particle set propagated through a shared electron–nucleus backbone that jointly evolves one-particle and two-particle representations. Nuclei carry learned representations that evolve alongside the electronic representations and condition orbital construction, while antisymmetry is imposed only by electronic determinants. On equilibrium small-molecule benchmarks, NucleoNet achieves accuracy comparable to established neural-wavefunction baselines with substantially fewer parameters. For each molecular system, a single model optimized jointly across geometries describes the N$_2$ dissociation curve, Li displacement in LiCN, and the ethane and formamide minimum-energy paths for bond dissociation. Sparse-geometry training generalizes to unseen geometries for N$_2$ and LiCN without further optimization, and N$_2$ ablations show that nuclear streams substantially improve this interpolation. These results show that a compact wavefunction with jointly evolved nuclear representations can describe the geometries of a molecular system with a single set of parameters.

Real-time time-dependent density functional theory (RT-TDDFT) has become a widely used first-principles method for studying excited-state and nonequilibrium electron dynamics. Hybrid exchange-correlation (XC) functionals, which incorporate a fraction of nonlocal exact exchange, are particularly important for accurately describing processes such as charge transfer and hot-carrier dynamics. However, the high computational cost which accompanies exact exchange, as required in hybrid XC functionals, has largely restricted RT-TDDFT simulations of condensed matter systems to using semi-local XC functionals. In this work, we present an all-electron implementation of exact exchange for RT-TDDFT based on numeric atom-centered orbitals, extending an efficient ground-state resolution-of-identity (RI) framework to the complex, time-dependent Hamiltonians required for real-time propagation. We validate the implementation against an established RI approach, for an isolated water molecule, finding exact agreement for both valence and core (K-edge) excitations. We also demonstrate the method on two extended periodic systems, crystalline silicon and silicon carbide. For silicon, the HSE06 spectrum reproduces previously reported real-time TDDFT results and agrees with experiment to within approximately 0.2~eV, consistent with plane-wave pseudopotential implementations. For silicon carbide, we compute valence and X-ray absorption spectra at the silicon $L$-edge and carbon $K$-edge. These results establish an efficient, all-electron route to hybrid-XC functional RT-TDDFT for both molecular and condensed matter systems.

Molecular spectra observed in the interstellar medium are commonly analyzed using non-local thermodynamic equilibrium models, which requires accurate state-to-state collisional rate coefficients. Close-coupling calculations become prohibitively expensive for transitions from highly excited rotational states, therefore available datasets are often truncated at low initial states and temperatures; and since each new system also requires an accurate ab initio potential energy surface, many detected molecules have no collisional data. We employ two machine learning strategies to predict rotational state-to-state rate coefficients of molecules included in the train set beyond the range of initial states and temperatures computed so far, and predicting those of a molecule absent from training and validation sets. Feed-forward neural networks are trained on state-to-state de-excitation rate coefficients of 24 linear molecules colliding with para-H2. Scheme 1 includes all systems in the train+validation set, with 70%, 80%, and 90% initial-state boundaries and a 90% temperature boundary. Scheme 2 is trained on 22 systems described only by transition and molecular properties, and predicts two excluded systems, CS and CF+, whose astrophysical impact is explored with non-LTE calculations. For the 90% boundary, Scheme 1 predicts 99.4% of the test transitions within a factor of 2, and no prediction deviates from the reference value by more than a factor of 4.7. This model was used to complete 18 datasets. Scheme 2 reproduces the rate coefficients of two excluded systems within a factor of 3 for more than 92% of their transitions. Both schemes provide near-instantaneous complements to close-coupling calculations: Scheme 1 extends the range of a molecule already included in the training set with high accuracy, while Scheme 2 gives a reasonable first estimate for a molecule that has not been studied.