Browse Articles

Theory of ion chemical potentials in heterogeneous electrolyte environments

Electrochemical applications, ranging from energy storage to electrocatalysis and separations, involve ions in heterogeneous environments such as electrode/electrolyte interfaces, material interphases, and confined spaces. These environments influence ion thermodynamics through their effect on chemical potentials and, consequently, on the driving forces relevant to ion transport and electrochemical processes. In addition, features in bulk electrolytes, such as different ion sizes and valence asymmetries, act as intrinsic heterogeneities in an otherwise homogeneous solution. Approaches for modeling ion chemical potentials are based either on statistical mechanics or phenomenological models for bulk solutions, where ion chemical potentials are treated as functions of local ion concentrations and mean-field electrostatics. As a result, heterogeneities that modify ion solvation energies and ion–ion correlations are often treated approximately or phenomenologically. In this work, we develop a statistical mechanical theory of ion chemical potentials formulated for heterogeneous electrolytes that explicitly accounts for ion sizes, short-range interactions, ion–ion correlations, and electrostatic solvation energies. To derive closure relations for the ion pair correlation functions, we introduce a perturbation scheme based on the ratio between the Bjerrum and Debye lengths. This approach enables the formulation of symmetrized pair correlation functions that account for steric effects and ion–ion correlations through the formalism of ion fluctuation potentials. We demonstrate the theory using the primitive model for a valence-asymmetric electrolyte with equal-sized ions in bulk electrolyte systems as controlled benchmark cases. For symmetric electrolytes, we recover the extended Debye–Hückel result, while valence asymmetries modify ion solvation. We close with a discussion of our work in the context of existing electrolyte theories.

Scaling laws and paradoxical metastable states in nanofilament entropic separation

Entropic forces play a fundamental role in nanoscale phenomena, from colloidal self-assembly to biomolecular disaggregation. Here, we develop an exact analytical theory and find general scaling laws for the entropic separation of tether-mediated nanofilament bundles, revealing that a single dimensionless parameter—the ratio of the excluded-volume radius to the tether length—dictates whether filaments are pushed apart or, contrary to the usual expectation, pulled together. This unexpected regime challenges the view that entropic forces invariably promote disaggregation, instead uncovering conditions under which the bundles can remain in attractive metastable states. Brownian dynamics simulations confirm this paradoxical effect, offering predictive insights for applications in biophysics, soft matter physics, and nanotechnology.

Quadrupole susceptibility automatic calculator in sum frequency generation spectroscopy incorporating magnetic contributions and refined local fields

While sum frequency generation (SFG) spectroscopy is known to have acute interface selectivity owing to the dipole approximation, it has been a long-standing concern to understand the contribution of higher-order polarizations and/or bulk. Motivated by recent advances in microscopic theory of SFG including quadrupole, this work reports our recent development of the calculation tool of quadrupole susceptibility, namely, QSAC. QSAC aims at evaluating relative intensity of surface/bulk and dipole/quadrupole contributions for an arbitrary molecule and vibrational mode, in combination of quantum chemical calculations and molecular dynamics simulations. The present QSAC fully takes account of the generalized quadrupole, including electric quadrupole and magnetic dipole, and the local field effects on these polarizations as well as the electric dipole. We applied it to methyl C–H stretching and carbonyl C=O stretching modes and thereby demonstrated the significantly improved performance of the QSAC program to evaluate the contribution of quadrupole. We found that the accurate treatment of local field gradient is important in evaluating the quadrupolar susceptibility of the interface χIQ and that the magnetic contribution is generally comparable with that of electric quadrupole and thus substantial in the quadrupolar susceptibilities. The revised QSAC provides a reasonably reliable estimate of the bulk contribution in SFG spectra.

Bootstrap embedding for interacting electrons in phonon coherent-state mean field

We develop a Fermi–Bose bootstrap embedding framework for the ground state of interacting electrons coupled to a phonon mean field. The method combines bootstrap embedding for correlated electrons with a self-consistent coherent-state mean-field treatment for phonons. This method models the interacting electron–phonon problem as a system of correlated electrons traveling in a self-consistently specified potential landscape, allowing for efficient treatment of large lattice systems. Convergence of the methods for fragment size and total system size is demonstrated for the one-dimensional Hubbard–Holstein model for up to 350 sites. Finite-size scaling is performed to extrapolate to the infinite system size. Benchmarking against the density matrix renormalization group for a small 8-site system at half- and quarter-filling shows an orders-of-magnitude runtime advantage. The comparison further reveals that the method performs best in regimes dominated by localization, such as the Mott insulating phase and the strong-coupling tiny polaron regime, where the local embedding ansatz is still valid. However, due to the mean-field treatment for phonons, we find limitations of our methods in the weakly coupled delocalized region and at the Peierls transition, where quantum phonon fluctuations and long-range kinetic correlations become substantial.

Isolating solvent–solute hydrogen bonding interactions via 2D IR solvation shell spectroscopy

The solvation shell around a solute is a fundamental feature of liquid-phase solutions, determining the behavior and properties of both the solute and the overall solution. Direct experimental measurements of the solvation shell properties are challenging due to the strong signals generated from the bulk solvent, which overwhelm the small contribution of the solvation shell. Here, we use ultrafast two dimensional infrared (2D IR) spectroscopy and intermolecular cross-peaks to isolate the IR absorption spectrum of methanol molecules in the solvation shell surrounding the solute N-methylacetamide. We demonstrate that the intermolecular coupling between the solvent and solute vibrations is indirectly mediated by a low-frequency hydrogen-bonding mode, suggesting an important mechanism for anharmonic coupling induced by hydrogen bonds. From the relative frequency shifts and cross-peak anisotropy, we find that methanol molecules surrounding N-methylacetamide form stronger and distinctly oriented hydrogen bonds than those in the bulk solvent. We also compare these results with the solvent spectra of the solute N,N-dimethylacetamide to investigate how solute structural changes alter the solvation shell and the contribution of N–H hydrogen bond donation. Our results are supported by molecular dynamics simulations, which provide detailed insights into the hydrogen-bonding distributions. Through these results, we demonstrate 2D solvation shell spectroscopy to be a valuable method for investigating solvation structures and dynamics without interference from the bulk solvent.

Pump–probe fluorescence lifetime imaging microscopy

Pump–probe spectroscopy is the most popular technique to resolve ultrafast photo-induced dynamics. Its fluorescence-detected variant connects it to fluorescence microscopy, for a combined spatial and temporal resolution in sensitive samples. In this work, we introduce fluorescence-detected pump–probe spectroscopy (F-PP) with fluorescence lifetime imaging microscopy (FLIM) detection, which we call pump–probe FLIM (PP-FLIM). Like FLIM, PP-FLIM images the time-resolved fluorescence decay in three spatial dimensions. At each voxel, furthermore, the full pump–probe spectrum is obtained, measuring spectrally resolved transient dynamics. We demonstrate the PP-FLIM principle on a microliter–volume mixture of two fluorescent dyes, oxonol VI and cresyl violet, whose transient spectra PP-FLIM disentangles by their fluorescence lifetime. We then showcase the high-resolution non-invasive ultrafast imaging by measuring individual chloroplasts within intact spinach leaves.

Accordion-like tuning of composite pulse dipolar recoupling in solid-state NMR

Solid-state nuclear magnetic resonance (NMR) spectroscopy, being an important analytical tool in materials science and structural biology, typically relies on magic-angle-spinning (MAS). Often, it is combined with dipolar recoupling to reintroduce effects from dipole–dipole coupling interactions for polarization transfer or for distance measurements. A large variety of dipolar recoupling methods have been presented over the past decades. However, most of them are heavily constrained to certain application regimes defined by the MAS frequency, the static magnetic field, radio frequency pulse power capabilities, and combinations with efficient 1H decoupling. In this work, we exploit recent findings in pulsed dynamic nuclear polarization and its combinations with MAS solid-state NMR to propose an accordion-like method for tuning periodic composite pulse dipolar recoupling sequences to different experimental conditions, thereby improving the experimental flexibility of dipolar recoupling experiments to adapt optimally to applications in chemistry, materials science, and structural biology.

Machine learning for biomolecular modeling

On the boroxol ring fraction in melt-quenched B2O3 glass: Insights from machine learning potentials

An atomistic structural model for melt-quenched B2O3 glass has eluded the simulation community so far. The difficulty lies in the abundance of six-membered boroxol rings—an intermediate-range order motif suggested by Raman and NMR spectroscopy—which is challenging to capture in atomistic molecular dynamics simulations. Here, we report the development of a density functional theory-accurate machine-learned potential and employ quench rates as low as 109 K/s to obtain B2O3 glasses with more than 30% of boron atoms in boroxol rings. Additionally, we show that the pressure, and consequently the boroxol fraction, in the deep potential molecular dynamics simulations critically depends on the range of the geometry descriptor used in the embedding neural network, and it converges beyond a value of 7 Å. The boroxol ring fraction increases with decreasing quench rate. Finally, amorphous B2O3 configurations display a minimum in energy at a boroxol fraction of 75%, remarkably close to the experimental estimate in B2O3 glass.

Effect of dynamics on anomalous thermal relaxations and information exchange

The Mpemba effect, an example of anomalous thermal relaxation, occurs when a system prepared at a higher temperature overtakes an identical system prepared at a lower temperature and cools down faster to the environment’s temperature. We explore the Mpemba effect within Markov jump processes on linear reaction networks and study the effect as a function of the relaxation dynamics. The dynamics are characterized by a load distribution factor introduced to modulate the transition rates in a manner that obeys detailed balance. We analytically diagonalize the dynamical generator of three-species unimolecular reactions and, through graphic exploration of parameters, identify the regimes in which the Mpemba effect occurs. In particular, we find that the regions of the strong variant of the Mpemba effect, known as the strong Mpemba effect, in cooling and heating are nonoverlapping and that there is, at most, a single strong Mpemba temperature. Furthermore, we demonstrate our findings using a Maxwell demon setup. In this context, we demonstrate that leveraging the strong Mpemba effect can lead to shorter cycles of the Maxwell demon device, thereby enhancing power output without compromising the stability of device operation or its efficiency.

Harnessing the charge-transfer-to-solvent state of aqueous triiodide: A strategy to mitigate I2 trapping and enhance hydrated electron yield

The charge-transfer-to-solvent (CTTS) states of aqueous halides serve as prototypical systems for probing electron-transfer dynamics. In the photogeneration of hydrated electrons [e−(aq)] from iodide ions [I−(aq)], the concomitant formation of I2 and I3− as primary byproducts severely limits the e−(aq) quantum yield. Although the formation of these byproducts has been extensively studied, the post-photoexcitation dynamics of I3−(aq), particularly the competition between molecular dissociation and electron ejection, remain unclear and warrant further investigation. In this paper, we employ time-dependent density functional theory calculations to confirm that the experimentally observed absorption peak at ∼5.5 eV originates from a CTTS state of I3−(aq). Furthermore, ab initio molecular dynamics simulations in excited states reveal that photoexcited I3−(aq) can generate a short-lived e−(aq) prior to dissociation. Crucially, the nascent I2 fragment efficiently traps the ejected electron via its low-lying σ* molecular orbital (MO). To overcome this bottleneck, we propose a strategic solution: introducing an electron-donating protic solvent (e.g., ethylene glycol). This approach simultaneously suppresses I3− formation and elevates the unoccupied MO energy level of I2, thereby mitigating its electron-trapping capability and ultimately enhancing the e−(aq) quantum yield from I−(aq). This work establishes a novel design principle, modulating solute MO energetics, for optimizing electron injection efficiency in liquid-phase systems.

Tuning fragility in sodium lead borate glasses: Unveiling the interplay between compositions, Stokes–Einstein breakdown, and dynamical heterogeneity

Viscosity is a critical determinant of a liquid’s ability to form a glass upon cooling from a high-temperature state. As glass-forming liquids are cooled, their viscosity, or equivalently the structural relaxation time, increases rapidly near the glass transition temperature, a universal hallmark of glasses. The temperature dependence of viscosity is characterized by fragility, which varies widely among glassy liquids: some show the Arrhenius temperature dependence of viscosity or relaxation time (“strong” liquids), while others exhibit super-Arrhenius behavior (“fragile” liquids). We performed extensive molecular dynamics simulations on a realistic glass-forming system, sodium–lead–borate (Na2O–PbO–B2O3), to investigate how increasing lead oxide (PbO) content at the expense of boron oxide (B2O3) influences viscosity and fragility. Our results show a transition from strong to fragile behavior with increasing PbO concentration, elucidating the role of chemical composition in driving this transition. We further examine the Stokes–Einstein (SE) relation, the Kohlrausch–Williams–Watts (KWW) stretch exponent (βkww), and dynamical heterogeneity across the strong-to-fragile spectrum. We find that SE violation becomes more pronounced with increasing fragility, while βkww decreases, indicating stronger deviation from exponential relaxation in fragile glasses. Interestingly, dynamical heterogeneity, characterized by the four-point susceptibility [χ4(t)] and the non-Gaussian parameter [α2(t)], is slightly enhanced in strong glasses despite weaker SE breakdown and higher βkww values. Furthermore, our results suggest that different local structural units play distinct roles in shaping dynamical heterogeneity in strong and fragile glasses. These findings underscore the intricate interplay between fragility, the Stokes–Einstein relation, and dynamical heterogeneity, while emphasizing the crucial role of glass composition in tuning viscosity in real glass-forming systems.

Systematically improved potential energy surfaces via sinNN models and sparse grid sampling

Accurate, global Potential Energy Surfaces (PESs) expressed in sum-of-products (SOP) form are a prerequisite for efficient high-dimensional quantum dynamics simulations using the multi-configuration time-dependent Hartree method. This work introduces a methodology for constructing such surfaces by combining hierarchical sparse grid sampling with a single-layer neural network using sinusoidal activation functions (sinNN). The sparse grid strategy provides a rigorous, unbiased discretization of the configuration space, enabling systematic improvement of the PES fidelity, where accuracy is strictly controlled by the refinement level, while successfully mitigating the curse of dimensionality. The sinNN fitting approach leverages a trigonometric factorization identity to maintain a compact SOP form, offering superior numerical stability compared to “standard” exponential-based networks for the molecular systems investigated. We validate this framework by refitting an analytical PES for nitrous acid (HONO). The flexibility of the sparse grid methodology is demonstrated through a dual-reference strategy, where grids centered on distinct isomers are merged to eliminate topological bias. This optimized sampling yields a global PES that reproduces fundamental vibrational transition energies for both trans- and cis-HONO with spectroscopic precision (<2.5 cm−1) and high data efficiency. Finally, the methodology is applied to fit potential energies computed via the AI-enhanced quantum mechanical method (AIQM2). The resulting AIQM2-based PES for HONO reproduces experimental vibrational frequencies with a root mean square deviation of ∼16 cm−1, a performance comparable to high-level ab initio methods. The robustness of the approach is further confirmed on larger molecules, formic acid (HCOOH) and carbamic acid (H2NCOOH), establishing the combination of sparse grid sampling and sinNN fitting as a powerful, automated tool for generating topologically sound, spectroscopic-quality potential energy surfaces.

Herzberg–Teller coupling in coherent multidimensional spectroscopy: Analytical response functions for multilevel systems

Coherent multidimensional spectroscopy enables detailed investigations of vibronic effects in molecular and solid-state systems. We present explicit analytical expressions for multidimensional nonlinear response functions in the presence of Herzberg–Teller (non-Condon) coupling, within the displaced harmonic oscillator model. The formulation applies to electronic systems with an arbitrary number N of electronic states and to response functions of arbitrary order M in the light–matter interaction. We show that Herzberg–Teller coupling introduces additional oscillatory factors in the time-domain response functions, leading, upon Fourier transformation, to replicas of the Franck–Condon multidimensional spectra shifted by integer multiples of the vibrational frequencies. The present results provide a general analytical framework for the interpretation of non-Condon effects in coherent multidimensional spectroscopies. A Python code that implements the present approach and simulates multidimensional spectra for N-level systems is available on GitHub.

GenSym: A tool for random symmetric structure generation and its application in crystal structure prediction software

Crystal structure prediction (CSP) methods have become essential tools in materials discovery. As the initial step in CSP, the quality of the generated structures critically determines efficiency. It has been increasingly recognized that incorporating symmetry during structure generation can significantly enhance efficiency, as most real materials crystallize in non-P1 symmetries. In this work, we present an open-source package for random symmetric structure generation under user-defined constraints. The program supports bulk, low-dimensional, and molecular crystal generation, with flexible control over parameters such as cell shape, bond length, conventional or primitive symmetry settings, Wyckoff position weighting, and density uniformity adjustment. Furthermore, it interfaces with prototype databases, enabling structure generation based on known prototypes. We demonstrate that its integration with CSP frameworks substantially improves search efficiency, offering strong potential for accelerating novel materials design and discovery.

Theoretical relationship between the macro-texture and micro-structure in dairy processing revealed by the multi-scale simulation of coupled map lattice

The theoretical relationship between the macroscopic textural quality and microscopic structural quality appearing in the phase inversion processes from fresh cream via whipped cream to butter is revealed by the multi-scale simulation of a coupled map lattice based on the mesoscopic elementary processes of the emulsion interfaces. Using the Young–Laplace equation, we derive the microscopic particle quantities of the size and density of air bubbles and butter grains in an emulsion from the macroscopic rheological quantities of the overrun and viscosity of the emulsion. In doing so, we focus on the size determined by the “tug-of-war” between air bubbles and butter grains via their cohesion pressures and on the density determined by the “costume transformation” of the emulsion molecular complexes (clad particles, e.g., butter grain-clad air bubbles) to their suitable size. Using the obtained microscopic particle quantities, we now propose a microscopic state diagram, the size-density plane, in addition to the previously proposed macroscopic state diagram, the viscosity-overrun plane. These state diagrams reveal that while the two well-known different phase inversion processes at high and low whipping temperatures appear as the two parallel processes of viscosity dominance and overrun dominance in the viscosity-overrun plane, they appear as the two orthogonal processes of isodensity/size dominance and isosize/density dominance in the size-density plane. This theoretical simulation result is significant for the quality design of butter because it demonstrates that differences in macroscopic textural quality can be easily controlled by differences in microscopic structural quality.

Analysis and sampling of molecular simulations with adversarial autoencoders

The design of good collective variables for analysis and the enhancement of sampling of molecular simulations is not a trivial task. It often relies on the knowledge of the system and the experience of the scientist. Machine learning and artificial neural networks can be used for this purpose. Here, we demonstrate for the first time the use of an adversarial autoencoder to design collective variables. Similar to other autoencoders, it encodes data into the latent space and decodes them back with minimal loss of information. Furthermore, it uses the “adversarial game” to control the distribution of the latent space. The coordinates of the latent space can be used as efficient collective variables for analysis and sampling enhancement. The method was applied to the alanine dipeptide trajectory and thermal unfolding trajectory of the tryptophan cage miniprotein. We demonstrate efficient visualization of the conformational space of both molecules. The latent space coordinates of the tryptophan cage were very efficient in accelerating its folding by metadynamics.

Atomic origins of electrochemical stability in acetate-based dual-cation water-in-salt electrolytes

A recent study reported a super-concentrated lithium–potassium acetate-based water-in-bisalt (WiBS) electrolyte. Notably, this system exhibits a high electrochemical stability window of ∼3 V despite the absence of a conventional solid electrolyte interphase. Intriguingly, vibrational spectroscopy revealed a systematic redshift of the O–D stretch of HOD in this electrolyte with increasing salt concentration, contradicting the idea that the enhanced electrochemical stability is positively correlated with the strength of the O–H bond. To explore the atomic factors determining such extended electrochemical stability of this WiBS, we investigate the molecular distributions and water reactivity at the electrified electrode–electrolyte interface using constant potential classical molecular dynamics simulations. By identifying truly interfacial molecules, we uncover a diminishing surface concentration of water molecules at the electrodes, which likely leads to a delayed onset of electrochemical processes. Furthermore, the reduced magnitude of the perturbing electric field along the reaction coordinates for electrochemical water splitting provides an atomic-level explanation for the enhanced electrochemical stability observed in this dual-cation system.

Empirical no-go principles for rigid three-point water models: A physically guided manifold of optimality

Rigid three-point water models are widely used in molecular simulations, yet they cannot simultaneously reproduce thermodynamic, dielectric, and dynamical properties. We show that these failures do not stem from incomplete parameter optimization, but from physical constraints that define the topology of the model parameter space. Treating the density anomaly as a master thermodynamic constraint, we find that viable geometries and electrostatics collapse onto a low-dimensional physical manifold governed by scaling relations. Within this framework, we identify two topological constraints, an empirical no-go principle, intrinsic to rigid three-point models with standard Lennard-Jones interactions. First, in the small-angle regime (θ ≲ 108°), matching the experimental dielectric constant requires molecular elongation that destabilizes the hydrogen-bond network and shifts the temperature of maximum density. Second, enforcing the density anomaly increases network rigidity, suppressing molecular mobility, and preventing agreement with the experimental self-diffusion coefficient. Together, these results define the fundamental limits of rigid three-point water models and recast their development as a constrained design problem rather than an empirical optimization task.

Polyelectrolyte complexation with biofunctionalized multivalent ions: Coarse-grained model and isothermal titration calorimetry experiment

Mixing polyelectrolytes and (oppositely charged) multivalent ions is a well-known technique used to produce nanoparticles (or nanogels) for various biomedical/biotechnological applications, such as drug, protein, or nucleic acid delivery. Quantitative prediction of the complexation process—in terms of polymer and ion properties and solution conditions—remains a challenge. The entropy associated with counterion release and the energy associated with polyelectrolyte–ion interactions are key mechanistic elements, and an important experimental development has been their isolation as distinct signatures within isothermal titration calorimetry (ITC) profiles. However, current models used to interpret ITC data generally neglect important electrostatic and polymer effects. We present here a theoretical model of the complexation process with an eye toward ITC, accounting for the long-range electrostatic energy plus translational entropy of the condensing/binding ions (i.e., Manning theory) and short-range non-electrostatic ion–polymer interactions (e.g., van der Waals, hydrogen bonding). We explore the influence of certain theoretical approximations and governing parameters on the predicted extent of ion condensation and test the model vs ITC experimental measurements of the biopolymer chitosan (and iron functionalized chitosan) complexing with the multivalent ionic nucleotides/nucleotide analogs adenosine, gemcitabine, and cytidine tri-phosphate. Excellent agreement is observed, and the resulting parameters provide important insight into polyelectrolyte–ion interactions. In particular, iron functionalization is seen not only to enhance the short-range ion–chitosan enthalpic attraction, but also to increase the associated entropic penalty.