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Semi-universal solution of the Thomas–Fermi equation for neutral jellium spheres
The Thomas–Fermi model of electronic structures provides a universal solution for neutral atoms. As a result, the energy of a neutral atom with nuclear charge Z is given as −0.7687Z7/3. Are there other systems where such universal solutions can be found? In this work, we look for an answer to this question and discover that for neutral jellium spheres, a semi-universal solution of the Thomas–Fermi equation exists; one parameter, f = N2/3rs, determines the properties of many neutral jellium spheres with different numbers of electrons (N) and bulk density parameters (rs). This parameter is connected to an earlier approximate analytical solution given in the context of simple metal clusters. The Thomas–Fermi energy of a neutral jellium sphere is found to be a simple function of f and N, of a form similar to that for atoms. Additional examples of semi-universal solutions are given by generalizing our method to other potentials. The present work, therefore, provides a motivation to explore whether such universal forms can be found in more accurate orbital-free density functional theories.
Relativistic strengthening of hydrogen bonds in bihalide anions: A four-component CCSD(T) study
In this study, we systematically investigate relativistic effects in bihalide anions [XHX]− (X = F, Cl, Br, I) using four-component coupled-cluster calculations based on the Dirac–Coulomb Hamiltonian at the CCSD(T) level. Relativistic contributions are quantified by comparing results obtained with the four-component Dirac–Coulomb and Lévy–Leblond Hamiltonians, both combined with a Gaussian nuclear charge distribution model. Relativistic effects are intrinsic to molecular systems and can, in principle, modify hydrogen-bond strengths alongside solvation, nuclear quantum effects, and nuclear dynamics. We identify two distinct regimes of relativistic behavior for bihalide anions with light (F, Cl) and heavy (Br, I) halogen nuclei. Relativistic effects lead to a measurable enhancement of hydrogen bonding as reflected in rovibrational constants (vibrational frequencies and rotational constants), equilibrium geometries, thermodynamic parameters, and the electron-density distribution, in contrast to the known trend of relativistic weakening of covalent bonding in the neutral hydrogen halides HX (X = F, Cl, Br, I). The maximum relativistic strengthening of the hydrogen bond is about 0.6–0.7 kcal/mol, while the relativistic localization of electron density in the internuclear region amounts to ∼0.1%–3.0%.
Statistical physics of the two-dimensional Coulomb liquid with ionic hard-core size
A self-consistent theory of bulk electrolytes incorporating electrostatic and hard-core interactions on an equal level is applied to the two-dimensional Coulomb liquid with finite ion size. The ionic pair distributions, the structure factors, and the thermodynamic functions of the formalism are compared with extensive Monte Carlo simulation results from the literature. At moderate salt densities, our computational approach can accurately describe the thermodynamics of two-dimensional solutions across weak to intermediate coupling strengths. The improved accuracy of the present theory with respect to continuum approaches stems mainly from its ability to account for the non-uniform screening of electrostatic interactions associated with the impenetrability of the charged hard disks by their ionic atmosphere. Due to the underestimation of the ionic clusters emerging in the dilute regime, the validity domain of our self-consistent formalism shrinks with the decrease of the salt density. As a result, our approach cannot reach the critical coupling domain where the conductor–insulator transition of two-dimensional charged hard disks occurs. This indicates that approaching the low-temperature dielectric phase via the present formalism will require extending the underlying self-consistent approximation at least to the next cumulant order.
Composite colloidal assembly by critical Casimir forces
We investigate the phase behavior of mixtures of two populations of colloidal particles dispersed in a binary solvent system near its critical composition. The surfaces of particles are chemically modified to elicit a specific solvent affinity for one of the solvents. In this way, fluid-mediated interactions, which involve the critical Casimir effect, become particle population specific. As a result, the colloidal mixture shows a complex crystallization behavior reminiscent of the crystallization of atomic alloys. We show that the exquisite temperature dependence and reversibility of the critical Casimir interaction allow sampling of the entire phase diagram of the binary system and can even be used to anneal the crystalline microstructure, analogous to temperature cycling in atomic alloy phases.
Ultraviolet photodissociation dynamics of D2S+: The S+-loss channel near the D-loss dissociation threshold
Photodissociation dynamics of deuterium sulfide cations (D2S+) via the A2A1 state were investigated using the time-sliced velocity map ion imaging technique. High-resolution images of S+(4S) from the S+-loss channel, D2(X1Σg+) + S+(4S), were acquired at five wavelengths near 320 nm. From the high-resolution images, we derived the total product kinetic energy releases, angular distributions, and rovibrational-state populations of the D2(X1Σg+) co-products. The product angular distributions are nearly isotropic across all photolysis wavelengths studied. While the available energy distributions in internal and translational energy show only weak variations, the internal state populations of products exhibit clear wavelength dependence. Based on MRCI+Q/aug-cc-pV5Z calculations, the energy correlation diagram of D2S+ was constructed. The excitation photon energies employed in this study lie near the dissociation threshold of the SD+(3Σ−) + D(2S) channel. The results reveal rich photofragmentation dynamics arising from complex non-adiabatic couplings among several electronic states. Multiple dissociation pathways, including possible roaming mechanisms, contribute to the formation of D2(X1Σg+) + S+(4S) products at the excitation energy near the dissociation threshold of the SD+(3Σ−) + D(2S) channel.
Aggregation dynamics of molybdenum-based precursors in rarefied carrier gas mixtures under sub-nucleation conditions
Precise control of fluid flow and chemical reactions under low-pressure conditions is critical for next-generation semiconductor manufacturing, where vapor-phase transport of precursor molecules governs the quality and reliability of thin-film deposition. Among emerging alternatives to conventional metals, transition metal-based compounds are gaining attention due to their favorable thermal and structural properties. In particular, molybdenum oxychloride molecules are being explored for their stability and compatibility with high-temperature processes. However, the behavior of these precursor gases in rarefied environments remains poorly understood, especially concerning spontaneous aggregation and its impact on uniformity and defect formation. This study investigates the aggregation dynamics of gas-phase molybdenum oxychloride species using atomistic simulations under varying thermodynamic conditions relevant to semiconductor processing. We explore the influence of temperature, pressure, molecular ratio, and initial density on the formation and dissociation of molecular clusters. To quantify aggregation behavior, we track the evolution of cluster size distributions and assess the likelihood and timescales of large-cluster formation. The analysis reveals that aggregation is favored at lower temperatures and higher densities, while larger clusters tend to dissociate rapidly under thermodynamically unfavorable conditions. The results indicate no persistent critical cluster size, but transient aggregation events may influence deposition outcomes. These findings provide new insights into the gas-phase behavior of transition metal precursors under low-pressure conditions and offer guidance for optimizing process parameters in vapor-phase fabrication techniques.
Ghost embedding bridging chemistry and one-body theories
Phenomenological rules play a central role in the design of chemical reactions and materials with targeted properties. Typically, these are formulated heuristically in terms of non-interacting orbitals and bands yet show remarkable accuracy in predicting the complex behavior of intrinsically interacting many-body systems. While their non-interacting formulation makes them easy to interpret, it potentially hinders the development of new rules for systems governed by strong correlations, such as transition-metal-based materials. In this work, we present a rigorous framework that allows bridging between fully interacting, even strongly correlated, systems and an effective one-body picture in terms of quasiparticles. Furthermore, we present a computational strategy to efficiently and accurately access the main components of such a description: the embedding approximation of the ghost Gutzwiller ansatz. We illustrate the capabilities of this quasiparticle formulation on the Woodward–Hoffmann rules and apply their reformulated version to toy “reactions,” which exemplify the main scenarios covered by them.
Spectral analysis of chemical fluctuations of biomolecules in living cells
Biomolecules suffering birth and death in living cells often exhibit non-exponential lifetime distributions. However, the chemical dynamics of these biomolecules cannot be described by conventional chemical kinetics or chemical master equations. Here, we present exact results for the mean, time correlation function, and power spectrum of the copy number of biomolecules in living cells, establishing their relationship to product creation dynamics and lifetime distributions. The correctness of these results is confirmed against accurate stochastic simulations. This work establishes the power spectrum of the copy number of biomolecules as a quantitative probe of their intracellular reaction dynamics.
Understanding the sign problem from an exact path integral Monte Carlo model of interacting harmonic fermions
This work shows that the recently discovered operator contraction identity for solving the discrete path integral of the harmonic oscillator can be applied equally to fermions in any dimension. This then yields an exactly solvable model for studying the sign problem where the path integral Monte Carlo energy at any time step for any number of fermions is known analytically or can be computed numerically. It is found that the sign problem is primarily a property of the free fermion propagator, but repulsive/attractive pairwise interactions can shift the sign problem to larger/smaller imaginary time but do not make it more severe than the non-interacting case. More surprisingly, one can prove analytically that the first closed-shell state in D dimension, with n = D + 1 fermions, has no sign problem at large imaginary time. Direct numerical simulations confirm that this is also true for higher closed-shell states in two and three dimensions. Fourth-order and newly found variable-bead algorithms are used to compute ground state energies of quantum dots with up to 110 electrons and are compared to results obtained by modern neural networks.
Hidden features in the OH-stretching spectra of amino acid decorated air–water interfaces
Chemical reactivity at the air–water interface is governed by the interfacial solvation of reactive species. For instance, during aqueous amino acid-based CO2 absorption, water reorganizes around the reactive sites and couples dynamically with reaction pathways, facilitating the reaction. In this context, surface-sensitive vibrational sum-frequency generation (vSFG) spectroscopy can probe the OH stretch vibrations of interfacial water and determine the solvation structures around reactants and products, thereby furthering our understanding of the role of interfacial solvation. However, vSFG spectra of the air–water interface in the presence of charged species can be remarkably complex; key species-bound local water structures with distinct orientations may be hidden beneath prominent vSFG peaks arising from water–water hydrogen bonds and remain difficult to resolve. Here, we measure and compute vSFG spectra of the water OH stretch at air–water interfaces decorated with amino acids in their zwitterionic and anionic forms, as well as equimolar mixtures of these forms with bicarbonate. The latter represents post-CO2-absorption conditions. We find that computing depth- and frequency-dependent spectral densities—decomposed into contributions from water molecules hydrogen-bonded exclusively to other water molecules, exclusively to amines, exclusively to carboxylates, or shared between these polar/charged groups—is indispensable for accurate interpretation of the vSFG spectra. Key findings include orientational flip-flop in water sub-layers, strong carboxylate-water H-bonding, and water orientational ordering extending into the bulk aqueous phase induced by anionic amino acids. This study provides a computational spectroscopic platform for improved understanding of interfacial solvation relevant to interfacial reactivity.
Frustrated supermolecules: The high-pressure phases of crystalline methane
Methane is the simplest hydrocarbon, yet it exhibits an extraordinarily complicated series of crystal phases. Notably, the non-plastic phases have large unit cells with nearly, but not quite, cubic symmetry. Furthermore, although non-polar molecules interact very weakly, their reorganization across phase transitions is very sluggish. Here, we demonstrate that these complex structures can be understood as a simple packing of near-spherical supermolecular clusters of methane molecules: the departure from cubic symmetry arising from the non-spherical nature of the molecules. We use molecular dynamics based on density functional theory calculations to simulate the finite-temperature crystal structures of methane, finding that the complex phase A is based around a 13-molecule regular icosahedron, with 8 additional molecules forming the 21-molecule unit cell. Similarly, phase B is based on a body-centered cubic (bcc) packing of 17-molecule Z16 polyhedra, with the remaining 12 molecules per cell in tetrahedral interstices. We demonstrate that the favored intermolecular separation depends sensitively on molecular orientation, leading to hindered rotation and suppressed entropy. The structures are determined by a trade-off between efficient packing and entropy.
From global flocking to local clustering: Interplay between velocity alignment and visual perception of active particles
While flocking together, living organisms follow their neighbors. The Vicsek model [T. Vicsek et al., Phys. Rev. Lett. 75, 1226 (1995)] for living systems, where individuals follow their neighbors within a spherically symmetric neighborhood with local velocity alignment rule in the presence of noise, provides a minimal framework to explore their collective dynamics. Associating limited vision angle to an individual provides a minimal description for cognitive perception. This breaks the spherical symmetry of its neighborhood and implements non-reciprocity within the interaction among themselves. Here, we show that in the low noise regime, with decreasing vision angle, the polar order parameter decreases from ≈1 to a much lower value, indicating a transition from a state with global coherent motion of large clusters to a state with small, locally ordered, fragmented clusters. These clusters can spontaneously merge and split among themselves hindering any significant large scale coherent motion in this state. However, we show that at small vision angles, even though the fragmentation restricts formation of larger sized clusters, particles exhibit strong short-range correlations within the small local clusters. In the high-noise regime, as the vision angle decreases, the local ordering observed for full vision angle (spherically symmetric neighborhood) gradually disappears, producing a homogeneous, disordered, steady state. Here, we probe the steady-state properties by analyzing the distributions and spatial correlations of velocities as well as their related fluctuations and also calculate the cluster size distributions for various sets of vision angle and noise strengths. The time evolution of these quantities helps in characterizing the emergence of the corresponding steady states.
Uncertainty quantification in stochastic simulations of nitrogen–carbon gas–surface interactions
This study investigates how uncertainty in the reaction rate parameters of an atomistic kinetic Monte Carlo (KMC) model propagates to model outputs, such as the defect growth rate in carbon materials used for thermal protection systems. A KMC model consisting of key processes between carbon and nitrogen is used to model defect growth caused by nitridation in graphene. Uncertainties in rate parameters of nitrogen adsorption, surface diffusion, and CN formation reactions were identified from density functional theory or other model calculations. These uncertainties result from variations in the model parameters of these methods and, thus, constitute epistemic uncertainties in the KMC model. The KMC model, along with the identified uncertainties, was used to perform a sensitivity analysis to quantify and study the influence of these uncertainties on the resulting defect growth rate uncertainty. The analysis revealed that the activation energy of CN formation contributed significantly higher uncertainties to the defect growth rate than other reaction rate parameters. This result is attributed to the strong limiting effect of CN formation on defect growth, as well as the greater propagation of uncertainty through activation energies rather than prefactor terms. In addition, uncertainty propagation was studied across temperature from 1700 to 2100 K. Results further demonstrated that a reaction’s uncertainty contribution strongly depends on its limiting effect, which varies with temperature. Together, these results highlight the factors influencing uncertainty propagation from key processes in carbon nitridation.
Physics-informed transfer learning via frontier orbital pretraining for prediction of polymer electronic properties
Accurate prediction of electronic properties, including bandgap, ionization energy (IE), and electron affinity (EA), is central to the design of polymer electronic materials but is hindered by the vast chemical space and the high cost of reliable reference data. Here, a frontier orbital-guided learning framework is proposed that integrates low-cost quantum chemical pretraining with transfer learning to enable efficient and physically consistent prediction of polymer electronic properties. The model is pretrained on GFN2-xTB-derived frontier orbital properties of polymer trimers and subsequently fine-tuned using limited highfidelity data to predict chain bandgap (bandgap-chain), bulk bandgap (bandgap-bulk), IE, and EA. The resulting models exhibit consistently high predictive accuracy across all target properties, with test-set mean absolute errors of 0.246 eV for bandgap-chain, 0.269 eV for bandgap-bulk, 0.169 eV for IE, and 0.136 eV for EA, corresponding to RMSE values below 0.360 eV, while maintaining strong correlation with reference data (R2 > 0.90) and preserving key physical behaviors, including chain-length scaling and inter-property consistency. Leveraging this framework, electronic properties of ∼12 × 106 polymer repeat units are predicted, enabling statistically robust fragment-level analysis in which the observed trends remain consistent with established physical intuition and known structure–property relationships. This work provides a scalable and data-efficient framework for machine learning-assisted screening and design of polymer electronic materials.
Higher order Magnus expansion for driven two-level quantum dynamics
We investigate the Magnus expansion for a generic time-dependent two-level system under single-axis driving. By virtue of the su(2) Lie algebra, the expansion is decomposed into a commutator-free form. To illustrate the usefulness of the gained expression, we then revisit the Landau–Zener–Stückelberg–Majorana model, with a focus on non-adiabatic transitions as well as the Stokes phase. In addition, the semiclassical Rabi model is systematically treated by determining the Floquet quasienergy up to different orders. We demonstrate how to employ suitable picture transformations as well as how to enforce the symmetry of the underlying model to guarantee convergence of the expansion as well as to achieve satisfactory agreement with the exact results. For both models that we studied, it turns out that a third order approximation yields results that are in next to perfect agreement with exact analytical ones. Surprisingly, in the case of the semiclassical Rabi model, even the second order Magnus approximation in the adiabatic picture produces almost exact results for a large parameter range.
Holistic simulation of iron–sulfur cluster electronic and physical structures with hybrid density functional approximation reduced density matrix functional theory
[Fe–S] clusters are privileged and highly conserved metallocofactors that perform a wide range of biological functions, including redox catalysis and small molecule activation. Their reactivity is largely owed to their manifold of energetically low-lying, near-degenerate d-orbitals, resulting in a highly multi-reference, or strongly correlated, electronic structure. This results in not only a large number of electronic degrees of freedom but also a delicate interplay with the geometric configuration of the cluster core. Due to the size and computational complexity of these clusters, their larger-scale simulation has traditionally been limited to single-reference density functional theory (DFT), which struggles to capture strong-correlation effects. This approach leads to significant uncertainties not only in the predicted electronic properties of the [Fe–S] cluster but also in their optimized geometries, resulting in limitations to the ability of simulations to serve as a predictive tool in [Fe–S] chemistry. In a step to overcome these limitations, we employ a methodology based on combining existing, traditional density functionals with a 1-electron reduced density matrix functional (DFA 1-RDMFT), which captures strong correlation effects via fractional orbital occupation, while retaining the low computational scaling of DFT. We apply this approach to both simulate the electronic structure and optimize the geometries of a set of site-differentiated [Fe4S4]+ clusters coordinated by a series of electronically diverse ligands, demonstrating the ability of DFA 1-RDMFT to capture the delicate interplay between the electronic and physical structures in [Fe4S4] clusters.
An argument why the spinterface model cannot explain the chirality induced spin selectivity effect
In the context of chirality induced spin selectivity effect, it has been argued that a chiral molecule when adsorbed on a metal facilitates the formation of a local spin moment at the interface between the metal and molecule, given a strong spin–orbit coupling in the metal. The possibility for such spin moment formation is analyzed in terms of general arguments and effective modeling of a pertinent setup. The conclusion from this analysis is that a strong spin–orbit coupling in the metal does not provide a sufficient mechanism to sustain a stabilized spin moment at the interface. It is, moreover, shown that an electron flux into or out of the molecule does not provide conditions for a spin moment formation, regardless of whether the flux is spin-polarized or not.
Estimating memory time within the frameworks of generalized quantum master equation and transfer tensor methods
Simulating long-time nonadiabatic dynamics in condensed-phase systems is computationally demanding due to the inherent non-Markovianity of the electronic reduced density matrix evolution. While the generalized quantum master equation (GQME) and transfer tensor method (TTM) allow for the reconstruction of long-time dynamics from short-time projection-free inputs, their accuracy hinges on the rigorous estimation of the memory time, a parameter often determined by heuristic trial-and-error. In this work, we establish a comprehensive framework for estimating memory time and benchmarking propagation accuracy using semiclassical and numerical exact inputs on both standard spin-boson models and general multistate harmonic models. We develop an error estimation scheme that reveals a characteristic three-stage decay pattern in the non-Markovian propagation error: an initial transient drop, an exponential decay, and a saturation plateau. This estimator serves as a critical diagnostic tool for GQME and TTM, successfully distinguishing between converged predictions and reliability failures in complex systems, such as the carotenoid–porphyrin–fullerene triad. These findings provide a robust, quantitative protocol for validating memory-kernel-based simulations of nonadiabatic dynamics.
<i>mrfmsim</i> : A modular, extendable, and readable simulation package for magnetic resonance force microscopy experiments
We present mrfmsim, an open-source Python package that facilitates the design, simulation, and analysis of magnetic resonance force microscopy (MRFM) experiments. MRFM is a scanning-probe technique that detects magnetic resonance from nanoscale ensembles of nuclear or electron spins with a force sensor. Because MRFM experiments are complex and operate at sensitivity limits, numerical simulation is essential for designing experiments and estimating per-spin sensitivity and imaging resolution from measured signals. In this paper, we highlight the challenges of developing MRFM simulations and show that software designed to simulate specific experiments only in a rapidly evolving experimental field can yield erroneous results. The mrfmsim package addresses these challenges by supporting post-definition customization without rewriting the internal model and by employing a plugin system for extending functionality. We show that the package’s modular, extendable, and readable architecture improves reproducibility and accelerates development.
An efficient hybrid spectral-compact difference scheme for rod–coil diblock copolymers in slit confinement
Self-consistent field theory simulations of rod–coil diblock copolymers in slit confinement present significant numerical challenges due to sharp density gradients near hard walls. To rigorously resolve these systems utilizing the Gaussian and wormlike chain models, a hybrid spectral-compact finite difference scheme is developed on a non-uniform Chebyshev–Gauss–Lobatto grid. Shen’s Chebyshev spectral method is employed for the flexible blocks. For the semiflexible blocks, a second-order upwind compact scheme together with an L-stable TR-BDF2 contour-stepping algorithm is adopted. This hybrid framework effectively suppresses spurious numerical oscillations. This unconditionally stable formulation strictly preserves propagator non-negativity and achieves up to a two-orders-of-magnitude speedup over uniform-grid implementations while maintaining linear spatial scaling. Simulations utilizing this advanced framework under neutral wall conditions reveal that the confining walls naturally induce preferential wetting of the semiflexible blocks at the impenetrable boundaries. As the incompressibility penalty increases, the compressible system progressively approaches the incompressible limit. For the selected physical parameters, decreasing the slit width induces a sequence of structural transitions from a smectic-C morphology with three internal periods (SC3) to morphologies with two and one internal periods (SC2 and SC1), and ultimately to a highly compressed smectic-P morphology (SP1). The equilibrium thickness of these confined structures deviates from exact integer multiples of the bulk spatial period. This deviation arises from the volume compensation associated with boundary depletion layers, together with adjustments in the molecular tilt angle and the degree of molecular interdigitation.