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Simulating quadrupolar NMR dynamics in solid electrolyte Li <b>10</b> GeP <b>2</b> S <b>12</b>
Quadrupolar solid-state nuclear magnetic resonance (NMR) spectroscopy is an excellent tool to trace lithium (Li) ion diffusion in solid electrolytes due to its sensitivity to dynamics over timescales from nanoseconds to seconds. However, the structural and dynamical complexity of battery materials limits the unambiguous interpretation of experimental data. Fast ionic motion can partially average experimentally observable quantities, leaving the underlying distribution of electric field gradients (EFGs) experimentally inaccessible and, therefore, the measured data hard to interpret. In contrast, atomic simulation approaches, while providing the structure–observable relationship, are often constrained to idealized models. Established methods such as density functional theory remain computationally expensive for realistic time and length scales. Here, we show how experimental complexity in the fast-ion conductor Li10GeP2S12 (LGPS) can be approached via a machine-learning (ML) assisted workflow. ML acceleration enables microsecond-scale molecular dynamics (MD) simulations and efficient predictions of EFG tensors via a tensorial model. By time averaging the EFG tensors from the MD trajectory, we compute the temperature dependence of 7Li NMR quadrupolar observables subject to motional narrowing. Our prediction of the quadrupolar coupling of 24 kHz for tetragonal LGPS is in excellent agreement with the experimental value of 23 kHz. Furthermore, we emulate a spin-alignment echo (SAE) experiment in silico and apply the inverse Laplace transform to extract correlation times for ionic motion of Li in different LGPS crystal structures. Finally, we assess whether SAE can differentiate inter-grain vs intra-grain ion dynamics via the orientational dependence of the EFG tensor.
Simultaneous optimization of assembly time and yield in programmable self-assembly
Rational design strategies for self-assembly require a detailed understanding of both the equilibrium state and the assembly kinetics. While the former is starting to be well understood, the latter remains a major theoretical challenge, especially in programmable systems and the so-called semi-addressable regime, where binding is often nondeterministic and the formation of off-target structures negatively influences the assembly. Here, we show that it is possible to simultaneously sculpt the assembly outcome and the assembly kinetics through the underexplored design space of binding energies and particle concentrations. By formulating the assembly process as a complex reaction network, we calculate and optimize the tradeoff between assembly speed and quality and show that parameter optimization can speed up assembly by many orders of magnitude without lowering the yield of the target structure. Although the exact speedup varies from design to design, we find the largest speedups for nondeterministic systems where unoptimized assembly is the slowest, sometimes even making them assemble faster than optimized, fully addressable designs. Therefore, these results not only solve a key challenge in semi-addressable self-assembly but further emphasize the utility of semi-addressability, where designs have the potential to be faster as well as cheaper (fewer particle species) and better (higher yield). More broadly, our results highlight the importance of parameter optimization in programmable self-assembly and provide practical tools for simultaneous optimization of kinetics and yield in a wide range of systems.
MD-BAX: A general-purpose Bayesian design framework for molecular dynamics simulations with input-dependent noise
Molecular dynamics (MD) simulations are a powerful tool for understanding complex molecular behavior, but exhaustively exploring the large space of input parameters can be computationally prohibitive, especially when the outcomes are noisy and/or expensive to evaluate. In this work, we introduce MD-Bayesian algorithm execution (BAX), a general-purpose, automated design framework that builds on BAX acquisition strategy to efficiently guide simulation campaigns toward learning meaningful features of the system. Unlike optimization-centric Bayesian optimization approaches, MD-BAX seeks to identify broader system properties (e.g., phase transition boundaries, level sets, and threshold crossings) by strategically selecting input/parameter settings based on uncertainty. To accurately represent the variability in simulation outcomes, MD-BAX incorporates a Gaussian process surrogate model with input-dependent noise, estimated directly from MD trajectory statistics at each simulation setting. This enables construction of reliable uncertainty estimates for guiding the next simulation. We demonstrate the approach on a case study involving coil-to-globule transitions in amphiphilic block copolymers, highlighting that explicitly including trajectory-derived noise improves uncertainty calibration and enables our framework to more efficiently map the relationship between polymer structure, solvent quality, and conformational behavior. MD-BAX represents a domain-informed specialization of the BAX framework for MD and is broadly applicable to molecular modeling problems where the goal is to infer key system behaviors from stochastic, trajectory-based simulation outputs rather than to locate a single optimal condition.
SHarmonic: A fast and accurate implementation of spherical harmonics for electronic-structure calculations
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian coordinates. This approach results in a code that is as precise as other implementations while being at least one order of magnitude more computationally efficient. The library can run on graphics processing units as well, achieving an additional order of magnitude in execution speed. This new implementation is simple to use and is provided under an open-source license; it can be readily used by other codes to avoid the error-prone and cumbersome implementation of the spherical harmonics.
Diffusion crossover of protein molecules: Two-step coarse-graining and oscillating memory
A consistent treatment of anomalous diffusion requires a microcosmic framework that captures the underlying couplings between the relevant degrees of freedom. To this end, we employ a two-step coarse-graining procedure, in which protein molecules are modeled as generalized Brownian particles interacting harmonically with their neighbors, while the latter are coupled to a thermal bath. Under this construction, the power-law memory kernel in the generalized Langevin equation can be approximated as a sum of several response functions of damped oscillators, revealing, in particular, oscillatory behavior on sub-picosecond timescales. When applied to diffusion of proteins, the model predicts that the protein molecules exhibit ballistic diffusion up to ∼0.3 ps and subdiffusion up to 100 ps. Owing to the limited measurement window and the initial velocity preparation, we find that the time-averaged mean-square displacement along the reaction coordinate displays an upward-tail behavior. Finally, we extend the Markovianized dynamics to the super-diffusive regime by introducing velocity-dependent coupling.
The connection between network structure and terminal relaxation of unentangled vitrimer melts: A dynamic cross-linked Gaussian-strand model study
Vitrimers are flowable cross-linked polymer networks that have drawn significant attention as a platform for developing novel polymer materials. Here, we utilize a dynamic cross-linked Gaussian-strand model to investigate network structure–viscoelasticity relationships for unentangled vitrimer melts. The terminal relaxation of model vitrimers depends on the number of dynamic linkages and the strand-length distribution. Because the short-term dynamics are coarse-grained, the stress relaxation modulus curves of the model vitrimers exhibit well-defined plateaus. This is consistent with experimental observations, as Rouse dynamics usually occurs far faster than the relaxation of networks in most cases. For uniform model vitrimers, the distribution of relaxation times moves toward longer times as the dynamic-linkage number increases, extending the spread and changing the shape of relaxation curves. The links between the longest relaxation time and zero-shear viscosity with the dynamic-linkage number are further examined. The ratio between the maximum loss modulus and plateau modulus is also affected by the dynamic-linkage number and strand-length distribution. The intrinsic exchange reaction kinetics and segmental mobility determine the topological reshuffle of model vitrimers. The temperature dependence of their terminal relaxation is also discussed in order to gain a better grasp of their characteristic viscoelasticity.
Ultrafast radiation chemistry of glycine in aqueous solution
Investigating the ultrafast dynamics of primary biological compounds is crucial for gaining insights into radiation damage. We computationally investigate the ionization-induced dynamics of glycine in an aqueous solution. By employing fewest-switches-surface hopping simulations, we specifically address ionization in different orbital levels of the glycine molecule as well as in water molecules in its solvation shell. Upon ionization, glycine undergoes rapid fragmentation on the Cα–C bond, resulting in the formation of CO2 and the methylamine (+H3NH2C⋅) radical. Our analysis shows that the solvation shell has little effect on the fragmentation dynamics. When ionized in water, or a deeper valence orbital of glycine, the system first relaxes to the ground state, involving the transfer of the valence hole between water and glycine. The associated redox reaction exemplifies the oxidizing power of H2O⋅+.
<tt>dynsight</tt> : An open Python platform for simulation and experimental trajectory data analysis
The study of complex many-body systems via analysis of the trajectories of the units that dynamically move and interact within them is a non-trivial task. The workflow for extracting meaningful information from the raw trajectory data is often composed of a series of interconnected steps, such as (i) identifying and tracking the constitutive objects/particles, resolving their trajectories (e.g., in experimental cases, where these are not automatically available as in typical molecular simulations); (ii) translating the trajectories into data that are easier to handle/analyze by using well-suited descriptors; and (iii) extracting meaningful information from such data. Each of these different tasks often requires non-negligible programming skills, the use of various types of representations or methods, and the availability/development of an interface between them. Despite the considerable potential that new tools contributed to each of these individual steps, their integration under a common framework would decrease the barrier to usage (especially by diverse communities of users), avoid fragmentation, and ultimately facilitate the development of new approaches in data analysis. To this end, here we introduce dynsight, an open Python platform that streamlines the extraction and analysis of time-series data from simulation or experimentally resolved trajectories. dynsight simplifies workflows, enhances accessibility, and facilitates time-series and trajectories data analysis, offering a useful tool for unraveling the dynamic complexity of a variety of systems (or signals) across different scales. dynsight is open source (github.com/GMPavanLab/dynsight) and can be easily installed using pip.
An interpretable molecular descriptor for machine learning predictions in atmospheric science
The study of aerosol formation and chemistry using machine learning is limited by the lack of molecular descriptors suited to atmospheric compounds. Interpretable models are particularly affected because they often rely on dictionary-based descriptors tied to specific molecular substructures, which currently fail to capture the full range of organic atmospheric compounds, including large, highly oxidized molecules common in the atmosphere. We introduce ATMOMACCS, an interpretable descriptor combining the 166 binary keys of the MACCS fingerprint with motifs inspired by the SIMPOL method for estimating saturation vapor pressures. We show that ATMOMACCS outperforms the RDKit topological fingerprint in kernel ridge regression models, improving predictions of saturation vapor pressures (7%, 8%, 29%, and 43% error reduction), equilibrium partition coefficients (5% and 9% error reduction), glass transition temperatures (22% error reduction), and enthalpies of vaporization (61% error reduction) on six datasets with atmospheric compounds. Feature analysis shows that saturation vapor pressure and partition coefficients are governed by carbon number and oxygen-related features, whereas other phase-transition properties (e.g., enthalpy of vaporization and glass transition temperature) depend on carbon–hydrogen bond types and the presence of heteroatoms other than oxygen. This highlights the generalizability of ATMOMACCS across different datasets and properties as an interpretable molecular descriptor.
Shedding light on reactive sulfur species coordination to metmyoglobin by QM–MM TD-DFT simulations
Understanding how sulfur-containing ligands modulate the structure, electronic configuration, and spectroscopy of ferric heme proteins is essential for interpreting their reactivity and assigning experimentally observed intermediates. Here, we investigated the spectroscopic properties of a series of ferric myoglobin species, MbFe(III)–X, being X = HS−, S2−, H2S2, HS2−, S22−, and OH−. We combined QM–MM molecular dynamics (treating the active site and the coordinated ligands as the QM region, with the rest of the protein and solvent treated classically) with the nuclear ensemble approach, in which we sampled configurations from the MD simulations and obtained the electronic spectra of the species using linear-response TD-DFT at the B3LYP/def2-TZVP level of theory. The simulated spectra reproduce the major experimental trends, providing strong support for assigning the sulfide-bound intermediate to MbFe(III)–HS−, explaining the near indistinguishability of MbFe(III)–HS2− and MbFe(III)–S22− spectra, and rationalizing the similarities between sulfide- and disulfide-derivatives absorption profiles. Taken together, our results demonstrate the importance of explicitly sampling nuclear configurations to account for dynamic fluctuations in the active sites of complex metalloproteins when modeling their electronic spectra. By incorporating this configurational heterogeneity, the resulting spectral predictions achieved a high level of reliability and showed close agreement with the experiments.
Nonadiabatic ImF instanton rate theory
Semiclassical instanton theory captures nuclear quantum effects, such as tunneling in chemical reactions. It was originally derived from two different starting points, the flux correlation function and the ImF premise. In pursuit of a nonadiabatic rate theory, a number of methods have been proposed—almost all based on the less rigorous ImF premise. Only recently, we introduced a nonadiabatic ring-polymer instanton rate theory in the rigorous flux-correlation function framework that successfully bridges from the Born–Oppenheimer to the golden-rule limit. Here, we examine the previous ImF-based attempts and conclude that they do not capture the two limits correctly. In particular, we will highlight how the last in a series of developments (called mean-field ring-polymer instanton theory) breaks down in the golden-rule limit. We develop a new nonadiabatic ImF rate theory to remedy the failings of previous attempts while taking inspiration from them. We analyze its behavior in the strong- and weak-coupling limits and also consider the crossover from deep tunneling to a high-temperature nonadiabatic rate theory. We test our new nonadiabatic ImF theory on a range of models, including asymmetric and multidimensional systems, and we show reliable results for the deep-tunneling regime but limitations for the related high-temperature rate theory. These findings are also relevant for the development of nonadiabatic ring-polymer molecular dynamics, where similar corrections have been previously proposed.
Branching ratios and mechanisms of the reactions of Ar+ with CH4 and C2H4 at cryogenic temperatures
Interest in interstellar noble gas chemistry has been stimulated by the recent detection of ArH+ and HeH+ in a variety of astrophysical environments ranging from diffuse clouds to supernova remnants. In this context, it seems timely to explore or revisit chemical reactions involving noble gas ions, such reactions being an efficient way to form noble gas bearing molecules in the interstellar medium. The reaction of Ar+ ions with methane, CH4, and ethylene, C2H4, at low temperatures, i.e., 24.1 and 71.6 K, was investigated in the laboratory with the help of a dedicated instrument combining a uniform supersonic flow reactor with a mass selective ion source. Computational flow dynamics and ion trajectory simulations were conducted to assess the thermalization of the ions in the flow. Ab initio and transition state theory calculations were employed to complement, at a microphysical scale, the interpretations derived from the macroscopic measurements of the Ar+ + CH4 and Ar+ + C2H4 reactions. The branching between the products is reasonably well explained by theoretical calculations.
Water hydration at high pressure in Fe3+, Ni2+, and Cu2+ solutions probed by EXAFS
We report the results of an EXAFS (extended x-ray absorption fine structure) study of Fe3+, Ni2+, and Cu2+ aqueous solutions under high pressures. EXAFS experiments were performed using synchrotron radiation at room temperature and up to pressures of about 1.2 GPa using a diamond anvil cell. Data analysis has been performed using advanced multiple-scattering simulations, and information about the evolution of the first hydration shell around the metal ions has been obtained. It is shown that Fe3+ and Ni2+ solutions retain a local octahedral structure up to the highest pressure, while Cu2+ solutions show a predominant distorted pyramidal fivefold structure with two oxygen distances. The first-neighbor metal–oxygen distances show a different behavior with pressure in the three solutions, being gradually shortened for Ni2+ solutions or elongated in Fe3+ solutions (by ∼−0.01 and ∼0.02 Å respectively), while in Cu2+ solutions, the difference between average equatorial and axial Cu–O distances is gradually reduced. The present results show that pressure does not act as a simple isotropic perturbation on ionic hydration, which is found to be dependent on the bonding mechanisms and ligand-field anisotropy of transition-metal ions.
State-to-state collision integrals and transport coefficients in oxygen mixtures
Accurate transport coefficients are critical for predicting aerothermal environments during high-speed flight and atmospheric reentry processes. This study calculates the vibrationally state-resolved transport collision integrals of O2–O and O2–O2 collision systems using the quasi-classical trajectory method based on high-accuracy ab initio potential energy surfaces within the state-to-state kinetic framework. A comprehensive state-resolved collision integral dataset for these systems is provided. The results demonstrate that vibrational excitation strongly influences collision integrals, rotational relaxation times, and transport coefficients, with effects becoming more pronounced at high temperatures. Collision integrals differ by up to 50% between ground and highly excited vibrational states, and state-resolved rotational relaxation times show substantial deviations from traditional Parker model predictions. Transport coefficients calculated for O2/O mixtures of varying composition indicate that, in molecule-dominated mixtures, traditional phenomenological models underestimate shear viscosity and thermal conductivity by 15%–25% above 10 000 K, while significantly overestimating bulk viscosity across the entire temperature range. The present quantitative analysis of vibrational-state effects on collision integrals and transport coefficients delineates the applicability limits of different phenomenological models and provides high-precision data for computational fluid dynamics simulations of high-speed flows.
Spectral finite-element formulation of the optimized effective potential method for atomic structure in the random phase approximation
We present a spectral finite-element formulation of the optimized effective potential (OEP) method for atomic structure calculations in the random phase approximation (RPA). In particular, we develop a finite-element framework that employs a polynomial mesh with element nodes placed according to the Chebyshev–Gauss–Lobatto scheme, high-order C0-continuous Lagrange polynomial basis functions, and Gauss–Legendre quadrature for spatial integration. We employ distinct polynomial degrees for the orbitals, Hartree potential, and RPA–OEP exchange–correlation potential. Through representative examples, we verify the accuracy of the developed framework, assess the fidelity of one-parameter double-hybrid functionals constructed with RPA correlation, and develop a machine-learned model for the RPA–OEP exchange–correlation potential at the level of the generalized gradient approximation, based on the kernel method and linear regression.
Correlation between the first-reaction time and the acquired boundary local time
We investigate the statistical correlation between the first-reaction time of a diffusing particle and its boundary local time accumulated until the reaction event. Since the reaction event occurs after multiple encounters of the particle with a partially reactive boundary, the boundary local time as a proxy for the number of such encounters is not independent of, but intrinsically linked to, the first-reaction time. We propose a universal theoretical framework to derive their joint probability density and, in particular, the correlation coefficient. To illustrate the dependence of these correlations on the boundary reactivity and shape, we obtain explicit analytical solutions for several basic domains. The analytical results are complemented by Monte Carlo simulations, which we employ to examine the role of interior obstacles on correlations in disordered media. Applications of these statistical results in chemical physics are discussed.
Concerted proton–electron transfer via vibration correlation function approach with effective anharmonicity: Beyond classical approximation with Duschinsky effects
Proton-coupled electron transfer reactions play a central role in natural and artificial energy conversion processes. The concerted type (CPET) offers unique kinetic advantages but remains challenging to model quantitatively within theoretical and computational frameworks, owing to the interplay of multiple quantum mechanical (QM) factors such as proton–electron nonadiabatic dynamics, anharmonic proton transfer (PT) potentials, and multimode vibronic coupling. When applied to CPET, standard simulation frameworks such as the Multistate Continuum (MSC) and Marcus–Levich–Jortner (MLJ) theories typically treat all solute vibrations other than the transferring-proton mode classically and neglect Duschinsky (mode-mixing) effects. Here, we present the vibration correlation function with effective anharmonicity (VCF-H) method, which extends the VCF formalism to systematically incorporate multidimensional vibronic coupling and Duschinsky transformations together with effective anharmonic corrections. Under a harmonic-potential setting, applications to gas-phase CPET model systems—specifically, the phenoxyl/phenol and thymine–acrylamide complexes—reveal that Duschinsky coupling between the transferring-proton motion and the donor–acceptor stretching mode, which is neglected in MSC/MLJ treatments, can play a major role and increase the predicted rate constants by several orders of magnitude. Furthermore, comparison across hierarchical approximations to VCF-H demonstrates that classical treatments of non-PT vibrational modes can substantially underestimate rate-constant predictions, whereas the fully QM description retained in VCF-H exerts a substantial influence on them. These results—currently limited to the gas phase—establish the VCF-H method as a streamlined and physically transparent framework for modeling CPET reactions, clarify its theoretical relationship to MSC/MLJ formulations, and highlight the critical role of multidimensional vibronic and Duschinsky effects in modeling CPET dynamics.
A bottom-up field-theoretic framework via hierarchical coarse-graining: Generalized mode theory
Multiscale simulations facilitate the efficient exploration of large spatiotemporal scales in chemical and physical systems, yet particle-based simulations become prohibitively expensive at time and length scales beyond the molecular level. Field-theoretic simulations offer an attractive alternative, but most existing formulations rely on top-down approximations and are not systematically connected to atomistic interactions. Here, we present a hierarchical bottom-up framework for constructing auxiliary field representations of molecular liquids directly from microscopic models. We introduce a hierarchical coarse-graining framework that constructs field-theoretic models directly from atomistic liquids. The method first maps atomistic interactions to coarse-grained center-of-mass potentials and regularizes short-range divergences through a perturbative expansion in reciprocal space. Building on the auxiliary field formulation developed in polymer field-theoretic simulations, we then generalize the Hubbard–Stratonovich transformation to arbitrary pair potentials by separating positive and negative Fourier modes and introducing two auxiliary fields. The resulting generalized mode theory extends bottom-up field-theoretic modeling beyond positive-definite kernels and is compatible with existing field-theoretic sampling strategies. By combining formal derivations with numerical regularization and mode-truncation procedures, this work provides the theoretical foundation for scalable, bottom-up field-theoretic simulations of molecular systems.
A fractional calculus framework for open quantum dynamics: From Liouville to Lindblad to memory kernels
Open quantum systems exhibit dynamics ranging from unitary evolution to irreversible dissipation. While the Gorini–Kossakowski–Sudarshan–Lindblad equation uniquely characterizes Markovian completely positive and trace-preserving (CPTP) evolution, many physical platforms display non-Markovian features such as algebraic relaxation and coherence backflow. Fractional calculus provides a natural way to model such long-memory behavior through power-law temporal kernels introduced by fractional time derivatives. Here, we develop a unified framework that embeds fractional master equations within the broader hierarchy of open-system formalisms. The fractional equation forms a structured subclass of memory-kernel models, reduces to the Lindblad form at unit order, and, through Bochner–Phillips subordination, admits a CPTP representation as an average over Lindblad semigroups. Its resolvent structure further connects fractional dynamics to established non-Markovian approaches, including Nakajima–Zwanzig kernels and hierarchical equations of motion, providing a compact surrogate for long-memory effects. This formulation positions fractional calculus as a rigorous and practical language for modeling non-Markovian quantum dynamics in chemical physics and physical chemistry, providing a CPTP-preserving, computationally efficient surrogate for structured condensed-phase environments where long-time memory and dissipation play a central role.
Representational power of selected neural network quantum states in second quantization
Neural network quantum states emerge as a promising tool for solving quantum many-body problems. However, its successes and limitations are still not well-understood, in particular for fermions with complex sign structures. Based on our recent work [Z. Wu et al., J. Chem. Theory Comput. 21, 10252–10262 (2025)], we generalize the restricted Boltzmann machine Ansatz to a more general class of states for fermions, which is formed by the product of neurons and, hence, will be referred to as neuron product states (NPS). NPS builds correlation in a very different way compared with the closely related correlator product states [H. J. Changlani et al., Phys. Rev. B 80, 245116 (2009)], which use full-rank local correlators. In contrast, each correlator in NPS contains long-range correlations across all the sites, with its representational power constrained by the simple function form. We prove that products of such simple nonlocal correlators can approximate any wavefunction arbitrarily well under certain mild conditions on the form of activation functions. In addition, we also provide elementary proofs for the universal approximation capabilities of feedforward neural networks and neural network backflow in second quantization. Together, these results provide a deeper insight into the neural network representation of many-body wavefunctions in second quantization.