Magnesium ions play an essential role in many biological processes but remain challenging to model in biomolecular simulations. Despite considerable scientific effort, classical force fields fail to simultaneously reproduce key structural, thermodynamic and kinetic solution properties, likely due to their inability to explicitly account for quantum many-body effects. Here, we develop and systematically benchmark MACE neural network potentials (NNPs) for aqueous MgCl$_2$ solutions trained on revPBE-D3/zd and revPBE0-D3/zd density functional theory reference data and assess their ability to reproduce a broad range of experimental solution properties including the structure of the first hydration shell, diffusion coefficient, activity derivative, water-exchange rate and mechanism as well as solvation free energy. Both NNPs accurately reproduce the octahedral structure of the first hydration shell, ion pairing properties and diffusion coefficients. Combining the NNPs with transition path sampling and other enhanced sampling techniques allows us to capture the rare event of water exchange in the first hydration shell of Mg$^{2+}$ revealing a dissociative exchange mechanism. Transition interface sampling yields exchange rates within one order of magnitude of experiment, representing a substantial improvement over classical dissociative force fields. In contrast, the NNP-derived solvation free energy significantly underestimates the experimental value, revealing a limitation of the present local NNP architectures for describing ion solvation thermodynamics. Our results demonstrate that DFT-trained NNPs can accurately describe Mg$^{2+}$ hydration structure, diffusion, ion pairing, and exchange kinetics, while highlighting the need for explicit long-range electrostatic treatments to achieve quantitative agreement with experimental ion solvation free energies.

The electronegativity equalization principle provides a simple framework to describe charge redistribution, yet its conventional formulation is limited to a first-order description based on chemical potential equalization. In this work, we introduce 'multi-equalization,' a generalized framework that extends this concept by incorporating higher-order responses within Conceptual Density Functional Theory. This approach represents molecules as sets of flexible electron density partitions, allowing different electronic descriptions (e.g., atomic densities or localized orbitals) to be treated within a unified formalism. We demonstrate that correlations between energy and density derivatives with respect to the number of electrons lead to the simultaneous equalization of multiple descriptors, including chemical hardness and Fukui indices. A constructive algorithm is introduced to determine the optimal density partitions satisfying these multi-equalization conditions. This scheme provides a consistent description of both global charge transfer and local reactivity, overcoming the intrinsic limitations of traditional electronegativity equalization models. Notably, the inclusion of density response functions enables local hardness equalization, introducing spatial resolution into reactivity descriptions. Under multi-equalization, local reactivity descriptors become constrained functionals of the global electron density. This framework establishes a deeper connection between charge equalization models and formal density functional theory, offering a theoretically grounded route toward improved predictions of molecular reactivity.

Strong light-matter and electron-phonon coupling generate ground states dressed by virtual bosonic excitations, making bare-state truncations and perturbative treatments unreliable in the ultrastrong-coupling regime. We introduce a nonperturbative variational ground-state framework based on a state-dependent polaron transformation, combined with a product-state ansatz and a second-order perturbative correction for residual matter-boson entanglement. We show that the optimized transformed frame becomes asymptotically decoupled at infinite coupling, because the leading linear coupling is canceled while off-diagonal matter transitions are suppressed by displaced-oscillator overlaps. The approach is asymptotically correct in both weak- and strong-coupling limits and remains accurate in the intermediate regime, where fixed polaron transformations are least reliable. Dicke-model benchmarks reproduce ground-state energies, fidelities, and the superradiant transition, with second-order energy errors below 0.2%. Holstein-model benchmarks yield errors below 0.5% and clarify how translational symmetry affects wave-function quality. This dressed-basis framework enables nonperturbative modeling of strongly coupled light-matter and electron-phonon systems.

The sub-Ohmic spin-boson model exhibits three distinct dynamical regimes in its spin population dynamics, classified as coherent, incoherent, and pseudo-coherent. Whether these regimes correspond to distinct spin-bath entanglement structures remains an open question. Here we address this using tree tensor network states with projector-splitting time evolution (TTN-TDVP-PS), scanning a broad grid in the sub-Ohmic $(s, α)$ plane. We find that the spin entanglement entropy $S_\mathrm{spin}(t)$ reaches a stationary plateau on a timescale shorter than the polarization relaxation, enabling construction of a stationary entropy landscape from the stationary value $S_\mathrm{stable}$. Within this scalar entropy landscape, the entropy ridge broadly follows the population-based phase boundary at small $s$, but does not reproduce the two-branch structure at large $s$. The ridge remains single-valued within the incoherent region rather than separately tracking both population-based transitions. The Bloch-sphere representation provides a geometric interpretation of this behavior. The entropy plateau corresponds to trajectories settling onto constant-radius shells, with the ridge marking the parameters of smallest stationary Bloch radius. Mode-resolved bath entanglement shows that low-frequency modes dominate the environmental entropy scale and that coherent dynamics enhance bath-mode correlations beyond direct spin--mode correlations. These results establish the stationary spin entanglement entropy as a physically informative observable that complements population-based classifications of dissipative quantum dynamics.

Quantum computers promise to solve the electronic structure problem for a large class of molecules. However, the performance of relevant quantum algorithms hinges on preparing initial states with substantial overlap with the target eigenvector. For classically challenging molecules with strong electron correlation, starting from multi-reference states, such as complete active space (CAS) wavefunctions is necessary. Unfortunately, the most advanced state preparation protocols applied to such states result in a gate complexity that scales exponentially with the active space size $d$. In fact, even encoding a CAS state classically is traditionally believed to be intractable for chemically relevant systems. Here, we draw insights from the recently introduced Quantum Paldus Transform (QPT) to show that there exists an efficient classical representation of CAS states and to design a new state preparation routine outperforming previous ones. The QPT represents a transformation from the Fock basis to a friendlier symmetry-adapted basis. Our main contribution consists in showing that CAS states expanded in this basis can efficiently be represented as a matrix product state (MPS) with a bond dimension scaling as $O(d^2)$. One can then efficiently load the MPS on a quantum computer and use the inverse QPT to transform the state to the Fock basis. Moreover, our method can easily be extended to the efficient preparation of CAS states in first quantisation with similar complexity. Crucially, we demonstrate that the complexity of both state preparation protocols only grows polynomially as $O(d^3)$ , which constitutes to the best of our knowledge an exponential improvement over the state of the art.

Velocity slip at the solid--fluid (SF) interface plays a key role in fluid transport at the nanoscale, and the SF friction coefficient has been extensively studied because it indicates the degree of slippage. Owing to the scale of this phenomenon, molecular dynamics (MD) simulations are commonly employed using two major approaches: the Green-Kubo integral method in equilibrium MD (EMD), and the direct calculation of friction force and slip velocity in non-equilibrium MD (NEMD) systems under shear. Regarding the latter, a strict definition of the slip velocity is missing due to the nonzero thickness of the boundary at the microscale, and the average velocity of the first adsorption layer or the velocity at the boundary obtained by extrapolation or interpolation is often used. In this study, we propose an alternative description of the slip velocity based on a thermal perspective from the two different scales, i.e., at the macroscale, frictional heat is defined as the product of the friction force and slip velocity, whereas at the microscale, it can be expressed as the sum of the works exerted on the fluid and solid by each other. By combining the two different scales, we defined the slip velocity based on the dissipation induced at the SF interface under shear, which avoids the arbitrariness in the slip velocity at the microscale.

We reconstruct unitary quantum dynamics from a minimal axiomatic foundation built on Hilbert-space observables and isospectral evolution. The only dynamical assumption is that physical time evolution is a continuous one-parameter flow of Hermitian observables that preserves their spectra, i.e. the possible outcomes of measurement. We show that this assumption is already sufficient to force the Lax form of quantum dynamics. The Heisenberg equation, the time-dependent and time-independent Schrödinger equations, conservation laws, and good quantum numbers then follow as theorems rather than postulates. In this formulation, Lax pair theory supplies the missing dynamical bridge between the measurement structure of a Hilbert space and standard quantum evolution: the Hamiltonian is not assumed, but emerges as the generator required for an isospectral observable flow.

Density-potential inversion for periodic systems within Moreau-Yosida-regularised density-functional theory is investigated, both theoretically and numerically. We develop the framework in a periodic homogeneous Sobolev space and use it to recover the exchange-correlation potential of Kohn-Sham theory through a limiting procedure. A key analytical ingredient is the proof of lower semicontinuity of the non-interacting kinetic-energy functional in the chosen topology. The proximal mapping, together with its algorithmic evaluation, plays a central role in the resulting inversion scheme. Numerical experiments illustrate the performance and properties of the method for both the Kohn-Sham and Gross-Pitaevskii equations.

Amorphous silicon (a-Si) is understood to be the canonical continuous random network material, ideally defined by fully fourfold coordination. Here, we show that a defect-free ('ideal') model of a-Si from machine-learning-driven molecular-dynamics simulations [L. A. M. Rosset et al., Nat. Commun. 16, 2360 (2025)], subsequently evaluated with hybrid-level density-functional theory computations, can accurately reproduce the experimentally observed electronic bandgap. We compare this model with one resulting from the Wooten-Winer-Weaire (WWW) bond-switching approach and with other recent approximants to ideal a-Si. More broadly, our work provides a platform for studies of band tails, optical properties, and transport in a-Si.

This study establishes a route to the Hartree--Fock (HF) limit for molecules and solids within the linearized augmented plane wave (LAPW) framework. We remove current limitations of the standard LAPW approach to nonlocal exchange by constructing radial basis functions and core orbitals consistently with the HF Hamiltonian. The presented method yields total energies of molecules and solids with a precision of a few $μ$Ha, and we use it to provide reference data for 14 semiconductors and insulators. For the systems considered in this study, the standard approach based on (semi)local potentials for constructing radial basis functions and core orbitals remains highly precise for practical relative energies, including molecular and solid-state formation energies and Si self-interstitial defect formation energies. More broadly, the results provide stringent all-electron benchmarks for basis-set and pseudopotential assessment, improve error control in hybrid-functional calculations within LAPW, and open the way to X-ray spectroscopy simulations within LAPW based directly on hybrid-functional core orbitals.

We develop a molecularly motivated description of the nonlinear index (NLI) in oscillatory shear deformation of entangled polymers. The central assumption is that the shear component of the tube-orientation tensor cannot grow without bound. Convective constraint release (CCR), chain stretch, and tube dilation progressively reduce the number and lifetime of orientational constraints, but the maximum shear alignment of a tube segment is geometrically limited by $S_{xy}\leq 1/2$. This motivates a constraint-limited orientation closure in which the NLI first grows approximately with strain amplitude and then approaches the limiting value $\mathrm{NLI}_{\max}=3$ asymptotically rather than through an artificial cutoff. The same framework yields a molecular expression for the characteristic half-saturation strain $γ_s$, defined by $\mathrm{NLI}(γ_s)=3/2$, in terms of the entanglement number, oscillation frequency, and a critical number of remaining orientational constraints. We further derive architecture-dependent expressions for the nonlinear onset strain $γ_c$ for linear, sparsely long-chain-branched, and more regularly branched polymers. The resulting framework provides a compact bridge between Fourier harmonic analysis, CCR-based tube dynamics, and the progressive loss of orientational memory in highly deformed entangled polymer liquids.

Predicting detailed atomistic structures of self-assembling systems remains a challenge for all-atom molecular dynamics simulations. Replica exchange with solute tempering (REST) has been used to study those systems by accelerating all monomers in a global and uniform manner. While such a global approach can in principle predict any morphology of the system, it has computational drawbacks such as inefficient replica traversal due to order-disorder transitions and the growing number of replicas with system size. To address these issues, here we propose an alternative, stepwise construction approach to modeling supramolecular polymers under the assumption of one-dimensional polymerization. Specifically, we generate polymer structures by adding new monomers one by one to the system and applying REST to the new monomers to find their optimal binding positions based on an energy-based scoring function. The monomer addition and enhanced sampling are repeated sequentially until a polymer of desired length is obtained. We test the above procedure using a model supramolecular polymer in explicit solvent, and show that it can generate a polymer structure with characteristic H-bonding patterns at reduced computational costs, while also improving the efficiency of replica traversal significantly. We thus expect that the sequential REST will be useful for modeling supramolecular polymers, particularly for cases where global REST simulations are too demanding computationally.

We demonstrate how the transport properties of molecular polaritons in optical cavities can be extracted from a microscopic modeling of pump-probe spectroscopy. Our approach combines a mean-field treatment of the light-matter Hamiltonian with a perturbative expansion of both light and matter components, along with spatial coarse-graining. This approach extends semiclassical cavity spectroscopy to multimode light-matter interactions, providing full access to spatially resolved transient spectra. By simulating a microscopy experiment with counter-propagating pump and probe pulses, we compute the differential transmission and show how molecular dephasing and persistent dark exciton populations drive sub-group-velocity transport of the root-mean-square displacement. We analyze transport across the polariton dispersion, showing how velocity renormalization correlates with excitonic weight, consistent with experimental observations, and further its dependence on the rate of molecular dephasing. Our results highlight the need to consider measured spectroscopic observables when characterizing transport in polaritonic systems.

Tetraphenylpyrazine (TPP) and 2,3,4,5-tetraphenyl-1H-pyrrole (TePP) are closely related heterocycles bearing four phenyl substituents, whose structural similarity makes them a useful pair for comparing how intramolecular flexibility influences excited-state relaxation and emission in the gas phase and in the solid state. TPP is a prototypical solid-state luminescence enhancement (SLE) emitter, exhibiting a markedly increased quantum yield upon molecular aggregation. In contrast, TePP displays similar quantum yields in solution and solid state, characteristic of dual-state emission (DSE). This behaviour indicates that intramolecular rotations are already significantly hindered in the isolated-molecule regime, consistent with our previous observations for TPP and other solid-state emitters (Hernández-Rodríguez et al., ChemPhysChem, 2024, 25, e202400563). To unravel the excited-state dynamics underlying this contrasting behaviour, we performed mixed quantum-classical trajectory simulations on a single molecule of TPP and TePP employing the surface-hopping method. Twelve singlet states were included at the TD-B3LYP-D3/def2-SVP level, which were previously benchmarked against coupled cluster methods. Simulated observables such as gas phase ultrafast electron diffraction (GUED) and time-resolved fluorescence (TR-FL) signals allow us to dissect the distinct deactivation pathways operating in both systems in the gas phase, while also providing mechanistic insight into how these pathways are expected to evolve in solution and solid-state environments.

The work functions of 7Li and 6Li metals have been measured as a function of temperature, by using photoionization of pure isolated metal nanoparticles in a beam. These data reveal a marked isotope effect in the temperature variation of these work functions. Furthermore, for both isotopes the curvature of this temperature variation is found to be significantly larger than may be ascribed purely to a change in the electron gas density. These findings enhance the characterization of lithium as a quantum material in which the interplay between electronic and ionic degrees of freedom is nontrivial, and call for a microscopic understanding beyond simple models. Additionally, the slope of the work function curves was observed to vanish in the low temperature limit, as had been predicted on the basis of the Third Law of thermodynamics.

We report the observation of charge-exchange collisions between trapped calcium monohydride molecular ions ($^{40}$CaH$^+$) and ultracold potassium atoms ($^{39}$K) in a hybrid ion-atom trap. The measured charge-exchange rate coefficient is significantly suppressed relative to the Langevin rate constant for the system. We use $\mathit{ab\ initio}$ quantum-chemical calculations to model the (CaH-K)$^+$ complex in the ground and excited electronic states and to identify possible charge-exchange mechanisms. Our calculations rule out a direct non-radiative charge-exchange reaction and instead point to a radiative mechanism, but do not quantitatively reproduce the measured rate, highlighting the need for a full-dimensional quantum dynamics treatment that includes vibrational motion and intermediate complex formation. Our work demonstrates that cold hybrid ion-atom platforms with molecular ions enable access to richer chemical complexity and collisional dynamics inaccessible in purely atomic systems.

This paper elaborates on the implications of the relationship between the Second and Third Laws and provides a comprehensive formal and historical justification for the logical redundancy of the Nernst heat theorem. By revisiting the Nernst-Einstein debate, the underlying hypotheses that lead to the traditional view of the Third Law as an independent postulate are examined. It is argued that the historical rejection of Nernst's proof -- motivated by Einstein's insistence on the practical non-performability of cycles at absolute zero -- overlooks the fact that a universal Second Law already precludes such cycles, rendering an independent Third Law an unnecessary complexity. Ultimately, the Nernst theorem is shown to be an essential consistency regulator rather than an independent physical discovery.

In this work we introduce an effective approach to quantize the electromagnetic response of plasmonic metallic nanostructures. Their shape is arbitrary and they feature a realistic description of the frequency-dependent metal dielectric function that is based on experimental data. The derived quantum modes correctly reproduce the linear response macroscopic polarization of the nanoparticle upon external drive according to classical macroscopic Maxwell equations in the quasistatic limit. We further investigate the coupling of these modes to a quantum-chemical molecular description. The presented methodology paves the way for accurate modeling of plexcitonic system, where strong plasmon-molecule coupling and/or strong-driving fields call for a quantized description of the plasmonic response.

We study energy minimization problems in quantum chemistry through the lens of computational algebraic geometry. We focus on minimizing the Rayleigh quotient of a Hamiltonian over a tensor train variety. The complex critical points of this problem approximate eigenstates of the quantum system, with the global minimum approximating the ground state. We call the number of critical points the Rayleigh-Ritz degree. We first study the Rayleigh-Ritz degree and introduce the Rayleigh-Ritz discriminant, which describes Hamiltonians that lead to a deficient number of critical points. We then specialize this framework to tensor train varieties: we identify instances when they are Segre products of projective spaces, report what we know about their defining ideals, and present a birational parametrization from products of Grassmannians. We use homotopy continuation to compute all critical points of this optimization problem over various tensor train and determinantal varieties. Finally, we use these results to benchmark state-of-the-art methods, the Alternating Linear Scheme and Density Matrix Renormalization Group.

The rapid decay of target signal strength with distance from the sensor presents a key challenge in nanoscale magnetic sensing with nitrogen-vacancy (NV) centers in diamond, limiting both sensitivity and spatial resolution. Here we introduce a strategy to overcome this limitation by using radical anions formed from rhodamine-derived dyes as reporter spins localized to the diamond surface. These radicals, generated through photoreduction, are optically identifiable and stable on timescales exceeding an hour. We experimentally demonstrate their coherent manipulation and detection using single, shallow NV centers for readout. We observe heterogeneity in the local magnetic environments of the photoactivated spins from site to site, likely due to variations in inter-radical couplings across our measurements. Looking forward, our approach enables correlative nanoscale magnetic and optical imaging, and opens new pathways toward single-molecule magnetic resonance studies.

We report the experimental super-resolution of pairs of point-like fluorescent sources using a modified image inversion interferometer microscope. The technique is inspired by recent developments in the application of quantum parameter estimation theory to semiclassical imaging problems. We find that the image inversion technique requires special polarization filtering to account for the dipolar nature of the emission. Using an azimuthal polarizer, we obtain improvements in the Fisher information of point-source separation by over an order of magnitude relative to direct imaging. Unlike established super-resolution fluorescence techniques, the method does not require sequential photoswitching/blinking of the fluorophores, and thus could facilitate significant speed-ups for certain biological imaging/tracking tasks.