Papers

We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy surfaces. Our main contribution is a multi-layer completeness theory. We show that $L$ layers of message passing on sparse, cutoff-based graphs achieve the same representational power as having access to the full $L$-hop neighborhood, provided the configurations are generic, satisfy an overlap condition and a connectivity condition. This provides the first rigorous justification for the common practice of using multi-layer message passing with a per-layer cutoff smaller than the physical interaction range, the setting used by virtually all practical graph neural network based machine-learned interatomic potentials. As immediate consequences, we show that both DPA3 and CHGNet architectures inherit universal approximation.

Machine learning interatomic potentials bridge the gap between quantum chemical precision and classical computational speed, enabling molecular dynamics simulations with first-principles accuracy. Their reliability is often improved through active learning, which iteratively expands the training set by identifying uncertain, out-of-distribution configurations. Existing uncertainty-quantification methods often involve a trade-off between computational cost and reliability, and generally cannot account for redundancy as an acquisition batch is assembled. Here, we introduce AdaptNTK, a single-model framework that measures uncertainty as a regularized Mahalanobis distance in empirical neural tangent kernel (NTK) feature space. With the NTK features fixed during acquisition, the uncertainty depends on the acquired configurations but not their reference labels. This allows the uncertainty to be updated recursively after each selection without retraining, reducing redundancy within an acquisition batch. On held-out rMD17 data, AdaptNTK achieves the highest mean correlations with force errors (Spearman 0.68, Pearson 0.71) and matches a three-member ensemble in error retention. In active learning experiments, AdaptNTK achieves the lowest force errors across rMD17 and Transition-1X, with particularly strong performance on transition-state configurations in Transition-1X. AdaptNTK provides a 2.6-fold speedup per Transition-1X cycle relative to the ensemble, providing efficient single-model uncertainty estimation with sequential updates for data-efficient active learning.

An overview is given about our efforts to speed up high-level computations of molec- ular energies and properties using Cholesky decomposition (CD). We describe the cor- responding developments in the CFOUR quantum-chemical package with a focus on (a) the use of CD in complete-active space self-consistent-field (CASSCF) and coupled- cluster (CC) computations, (b) the implementation of analytic CC gradients using CD, (c) the efficient calculation of magnetic properties (NMR shieldings and magnetizabili- ties) using CD when carried out with explicit magnetic-field dependent basis functions, i.e., the so-called gauge-including atomic orbitals (GIAOs), (d) the efficient computa- tion of CASSCF response properties using CD, (e) the use of CD in relativistic two- and four-component computations, as well as (f) computations for molecules in finite magnetic fields using GIAOs together with CD. An outlook on future developments concerning the CFOUR package is given.

Truncated Coulomb (TC) potentials reduce finite-size errors and accelerate thermodynamic-limit convergence in periodic Hartree–Fock (HF) calculations, but their use with Gaussian basis sets is complicated by the evaluation of electron repulsion integrals (ERIs), particularly for nonspherical truncation domains and all-electron calculations. We introduce the smoothed truncated Coulomb (sTC) potential as a systematically improvable approximation to a parent TC potential. A real-space Gaussian convolution smooths the sharp truncation boundary, and a single dimensionless parameter, $\eta$, controls the width of the smoothing window, which can be tightened to systematically approach the TC reference. The smoothing by sTC enables a dual-space algorithm for evaluating periodic Gaussian-basis ERIs that requires neither a large plane-wave basis nor new molecular integral kernels and is applicable to both pseudopotential and all-electron calculations, including the important Wigner–Seitz-cell truncation boundaries. Benchmarks spanning insulating, semiconducting, layered, metallic, and molecular-crystal systems show that sTC-based HF closely reproduces TC results in pseudopotential calculations and extends TC-quality calculations to all-electron settings. Across these systems, sTC substantially improves thermodynamic-limit convergence relative to the probe-charge Ewald method while remaining practical for all-electron calculations in which direct TC-based calculations are computationally challenging.

The kinetic Wulff construction predicts symmetric nonequilibrium shapes when crystallographically equivalent facets share a fixed growth rate. However, nanocrystals grow through finite facets whose nucleation barriers and ligand coverages depend on facet size. Here we develop a size-dependent kinetic construction and show that as a consequence infinitesimal seed asymmetries can be amplified into strongly asymmetric nanocrystal morphologies even when all symmetry-related facets obey the same microscopic growth law. Spatially heterogeneous nucleation rates and boundary limited growth generate facet growth velocities that depend on size, and deterministic shape evolution translates these local rates into global shape symmetry breaking. We illustrate the mechanism of persistent anisotropic growth on square and triangular lattices in two dimensions and on FCC seeds in three dimensions, where cuboctahedra can evolve toward rods or tetrahedra depending on which facet-area perturbations are amplified.

We study how colloidal inclusions modify the formation energy of dislocation pairs in lamellar block copolymer systems. Using a hybrid particle/Ginzburg–Landau model, we calculate defect formation energies by comparing defect-free and defect-containing states with and without embedded colloids. Finite-size scaling is used to obtain formation energies in the thermodynamic limit. The effect of colloid insertion depends strongly on particle sizes and surface patterning. Homogeneous particles increasingly stabilize dislocation pairs with increasing particle sizes. Particles larger than one lamellar domain preferentially occupy the dislocation cores, where they replace strained polymer rather than deforming defect-free lamellae. The magnitude of this stabilization depends on surface affinity. Balanced Janus particles instead increase the formation energy, because their competing surface preferences cannot be satisfied simultaneously near the curved core. Varying the patch ratio interpolates between these limits. Surface patterning has little effect for particles smaller than one lamellar domain but changes the formation energy by several tens of $k_BT$ for larger particles. These results provide quantitative guidelines for controlling topological defect stability in lamellar block copolymer systems.

Ultrafast electron diffraction (UED) provides direct information on changes in molecular structure following photoexcitation, but identifying the individual vibrational motions contributing to these dynamics remains challenging. Here, we introduce frequency-resolved UED, where Fourier transformation of the time-dependent difference pair distribution function ($\Delta$PDF) gives a two-dimensional frequency-distance representation of the structural dynamics. We apply this approach to allene and 1,2-butadiene following photoexcitation to the $S_1(\pi\pi^*)$ state at 200 nm, using electron scattering signals simulated from previously-published ab initio multiple spawning trajectories (S. P. Neville et al., J. Chem. Phys., 2016, 144, 014305). We identify C=C stretching and CCC bending motions and the internuclear distances over which they contribute, and separate overlapping CH$_2$ vibrational motions. By changing the pump-probe delay range used for the Fourier transform, we identify when specific frequency components contribute during the excited-state dynamics. Methyl substitution reduces the C=C stretching and CCC bending frequencies and introduces an additional frequency component in 1,2-butadiene during the first 90 fs. We further show the importance of sub-20-fs, and ultimately few-femtosecond, temporal resolution for retrieving these frequency components. Frequency-resolved UED therefore provides the vibrational frequencies, internuclear distances, and reaction times associated with photoinduced structural dynamics.

Thermal escape is governed by the Arrhenius law, where the mean escape time scales exponentially with the barrier height. We show that the non-Markovianity induced by time-delayed feedback in the confining force removes this exponential scaling. Beyond a threshold set by the curvature of the minimum, the delay destabilizes the well, and the thermal noise seeds an instability that is subsequently amplified deterministically to the boundary leading to slingshot escape trajectories. The escape time becomes logarithmic in the barrier, its fluctuations follow a Gumbel law, and an optimal delay enables escape faster than free diffusion. Our results propose time delay as a tunable and experimentally feasible control parameter for accelerating activated processes.

The Monte Carlo Projective Quantum Eigensolver (MC-PQE) was recently introduced as an alternative to hybrid algorithms like the variational quantum eigensolver (VQE). By using a quantum Monte Carlo-inspired scheme for energy estimation, MC\nobreakdash-PQE was found to decrease the required measurement cost relative to comparable conventional approaches. However, in the context of VQE, numerous techniques have been developed to reduce the measurement overhead by joint measurement of multiple observables. In this work, we extend these approaches to the asymmetric expectation values required in MC-PQE and assess the performance of different techniques for various molecular systems of up to 12 qubits. We find full commuting Pauli term grouping combined with tailored measurement allocation techniques leads to a 5-10$\times$ reduction in standard error for the same total number of quantum measurements. Conventional Hamiltonian grouped measurement outperforms tractable classical shadows tomography based techniques for the considered systems.

Atomic coordinates specify a structure, but they do not reveal how chemical connectivity across several length scales relates to atomic motion and configurational energy ordering. We formulate chemically directed persistent homology at four resolutions—complete networks, individual sites, spatial fields, and substitutional arrangements—while retaining the chemical identity and length scale of each connectivity feature. In ab initio molecular dynamics (AIMD) trajectories of $\delta$- and $\gamma$-CsPbI$_3$ at five temperatures spanning 500–700 K, the corner-sharing $\gamma$ network has a lower Pb–I restoring stiffness and permits larger iodide excursions, yet iodide positional correlations decay 2.27 times more slowly and Pb-network topology retains memory 1.63 times longer than in the edge-sharing $\delta$ phase. Local softness and loss of network memory are therefore distinct. At individual sites, rare $\gamma$-phase Pb environments with a $\delta$-like Cs-cage connectivity precede 0.17 $\mathring{\mathrm{A}}$ greater Pb displacement over the subsequent 0.5 ps. The same Pb-network coordinate resolves disruption of corner-sharing connectivity across a 2560-atom $\delta|\gamma$ boundary. In substituted CsPbI$_3$, compact dopant arrangements undergo greater cooperative host relaxation and lie lower in density-functional-theory (DFT) energy than dispersed arrangements of the same composition. SchNet and Allegro model families with comparable energy errors encode opposite ordering along this coordinate, and 61 of 247 supplied models with errors below 1 meV atom$^{-1}$ on separate test structures reverse the DFT relation. Because relative configurational energies set Boltzmann populations, chemical network topology links structure to physical response and tests whether learned energy models preserve DFT configurational ordering even when their average errors are small.

Full configuration interaction (FCI) provides exact electronic structure within a given atomic basis, but its computational cost grows exponentially with the number of spin orbitals. Selected configuration interaction (SCI) methods alleviate this limitation by retaining only the most important Slater determinants. However, the repeated identification of important determinants remains a major computational bottleneck. We present a quantum assisted selected configuration interaction (QASCI) method that combines SCI with graph based block diagonalization (GBBD) of FCI Hamiltonian. The GBBD method partitions FCI Hamiltonian into independent blocks, within which determinant selection problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO problems for selecting determinants to construct SCI space are iteratively solved using a fast annealing approach. We benchmark method on H8-H18 hydrogen chains and Li2S in STO3G basis. For Hn chains, chemical accuracy is achieved while retaining only a small fraction of Slater determinants, and this fraction decreases with increasing n, despite the exponential growth of the FCI Hilbert space. For Li2S, QASCI results remain within chemical accuracy while retaining substantially fewer determinants than the full FCI space. We apply QASCI to N2 using the 631G basis, considering both active orbital and full orbital treatments. The full orbital QASCI calculation, using 50000 determinants, yields a lower ground state energy than an FCI calculation within an active space comprising 12 spin orbitals and 12 electrons. These results demonstrate that the combination of QASCI and the GBBD approach can substantially reduce computational cost of determinant selection while maintaining the accuracy of FCI based electronic structure calculations, thereby enabling accurate calculations in larger orbital spaces.

In three-electrode electrochemical impedance spectroscopy (EIS), the impedance/capacitance response of the working electrode (WE) is measured relative to the reference electrode (RE), whereas the current required by potentiostatic control flows between the WE and the counter electrode (CE). Under classical three-electrode operation, the measured WE-RE response should therefore be independent of the properties of the electrode used as the CE, provided that conventional electrochemical and instrumental artifacts are negligible. Here, we test this expectation in cells containing nanostructured electrodes TiO2 + rGO and examine the results within a framework motivated by quantum discord to describe effective interelectrode correlations. We used dummy-cell measurements, a two-electrode bar-bar control, comparisons between Pt and bar CEs, a dummy circuit introduced into the CE branch, and CE ensemble comparisons to distinguish additive circuit behavior from CE-dependent behavior specific to the three-electrode configuration. In these experiments, the measured three-electrode capacitance response depends on CE, an effect that is not reproduced by the dummy-circuit controls examined. These findings identify a macroscopic CE-dependent capacitance response that departs from the tested classical expectation and is compatible with an effective interelectrode-correlation framework motivated by quantum discord, although the capacitance evidence alone does not constitute a direct measurement of quantum discord.

The chemical potentials of charged multi-component mixtures are central to electrolyte thermodynamics, but remain difficult to compute from atomistic simulations. The S0 method enables computing chemical potentials of mixtures from equilibrium molecular dynamics simulations. Here we extend the S0 method to charged mixtures by combining the composition-space framework developed in Part I: Neutral Multi-component Mixtures with a Coulombic treatment of the small-wavenumber limits of static structure factors. This approach separates thermodynamically relevant neutral composition fluctuations from forbidden macroscopic charge fluctuations, and further accounts for charge-neutrality constraints. We use the method to compute the chemical potentials of multiple-halide aqueous salt solutions, elucidating the ion-specific thermodynamic effects. We also calculate the mixing free energies of molten salt mixtures, demonstrating the importance of correctly describing long-wavelength electrostatic correlations.

Several next-generation fission reactor designs employ molten salts such as FLiBe (2LiF-BeF$_2$), with some concepts using fuel dissolved directly in the salt. During operation, fission products such as cesium will accumulate in the salt mixture, potentially leading to an evolution of the thermophysical properties underpinned by the atomic structure. To understand the structural perturbations in FLiBe with 5 mol% CsF, we conducted X-ray and neutron diffraction measurements, refined empirical potential structure refinement (EPSR) models against the experimental data, and compared the resulting structure with neural network molecular dynamics (NNMD) simulations. Comparisons of the EPSR and NNMD structures distinguishes features constrained by the scattering data from those that remain model dependent. The new Cs-bearing correlations account for the changes in the total structure factor and pair-distribution function, while the FLiBe correlations remain minimally altered. We find that Cs slightly disrupts the intermediate-range fluoroberyllate network, increasing the fraction of free fluorine ions, while the local coordination remains largely unchanged. The Cs ions within FLiBe cluster extensively, with BeF$_4^{2-}$ tetrahedra bridging neighboring cesium environments. In contrast to the minor structural perturbations in the liquid, the addition of 5 mol% CsF suppressed the formation of the crystalline Li2BeF4 phase at room temperature, with the phase appearing only above 180C upon heating. These experimentally constrained structural features provide a benchmark for atomistic models used to predict the behavior and properties of fission-product-containing FLiBe.

Vibrational spectroscopic probes can provide site-specific information on protein structure and dynamics. In this work, the possibility to relate protein motion with the vibrational response for –SCN, –N$_3$, and –SNO labels covalently linked to all alanine-residues in lysozyme is investigated. Depending on the position of the probe along the polypeptide chain, its local hydration, and the dynamics of its environment, the vibrational response can encode not only local fluctuations but also low-frequency, collective motions of the protein. The spectroscopic probes are described using machine-learning-based models for both bonded interactions, represented by reproducing-kernel models, and electrostatic interactions, represented by fluctuating minimally distributed charges. Spectroscopic dynamics are characterized through frequency fluctuation correlation functions (FFCFs). For many probe locations, the FFCFs contain a non-decaying component on the simulation time scale, indicating residual slow dynamics and incomplete sampling of the underlying conformational fluctuations. The magnitude of these static contributions is consistent with previous experimental observations, providing qualitative validation of the simulations. Overall, the results demonstrate that site-specific vibrational probes can report on dynamics extending beyond their immediate local environment and can, at suitable locations, provide information on collective protein motions.

We study the vibrational dynamics that is responsible for Li-NC <-> Li-CN isomerization reaction using the Lagrangian betweenness, a tool recently developed to identify dynamical bottlenecks in the context of oceanographic transport. Following the spirit of the betweenness-centrality metric, which efficiently identifies the nodes that act as bottlenecks in complex networks, the Lagrangian betweenness is similarly capable to identify bottlenecks in dynamical systems. On the one hand, in this paper we show the ability of the Lagrangian betweenness to identify transition states, which are short-lived states that are formed at the top of the energetic barrier that the system must surpass in order to transition the reaction from the (initial) reactants to the (final) products. On the other hand, we also demonstrate that the Lagrangian betweenness is also able to identify other dynamical bottlenecks, and phase-space invariant structures such as manifolds, chains of islands and invariant tori, which are also responsible for the intricate vibrational dynamics of the system.

Exciton–exciton-interaction pump–probe spectroscopy (EEI–PP) captures the fifth-order signal of light-matter interaction, directly probing exciton–exciton annihilation. This allows studying excitation energy transport even in extended, nearly isoenergetic landscapes. Although spectrally resolved fifth-order signals have already been explored in simplified cases, in larger systems only spectrally integrated signals have been analyzed. We present a microscopic theoretical description for spectrally resolved EEI–PP response with realistic lineshapes, revealing how single- and multi-exciton state structure shape the spectral features and dynamics. The description is applicable to large molecular systems such as squaraine polymers, facilitating a direct comparison with experimental spectra. By a decomposition of the total signal into individual excitation pathways, we demonstrate that the spectral resolution is needed to distinguish otherwise intertwined single- and multi-exciton dynamics, such as single-exciton relaxation and exciton–exciton annihilation.

The extreme persistence of per- and polyfluoroalkyl substances (PFAS) in the environment is rooted in their three-dimensional molecular conformation. The helical twist adopted by perfluoroalkyl chains due to hyperconjugation involving their recalcitrant C-F bonds governs their resistance to degradation, yet a quantitative, continuous metric for helicity has remained absent. Here we introduce a data-driven framework that quantifies backbone helicity using three statistical descriptors: void-state (binary occupancy) spatial autocorrelations, local backbone principal component analysis, and persistent homology. We further validate each statistical descriptor against geometric dihedral benchmarks and DFT-calculated Vibrational Circular Dichroism (VCD) spectra. The framework is initially established on a homologous series of perfluorocarboxylic acids (FC2 through FC16) and their hydrogenated analogues, then extended across perfluorosulfonic acids, fluorotelomer alcohols, polyfluoroalkyl hexanoic acid analogues, and longer-chain PFOA and PFOS analogues. Agreement between statistical, geometric, and spectroscopic definitions of helicity is established for PFCAs and extended to structurally distinct subfamilies, including PFOA analogues of varying fluorine content and perfluorosulfonic acids, demonstrating that the descriptors are robust to changes in headgroup chemistry and fluorine substitution pattern. The framework provides a chemistry-agnostic toolset for incorporating backbone conformation into predictive models of PFAS environmental fate and degradation reactivity.

The enumeration of chemical structures traditionally relies on graph- and group-theoretic techniques, including Pólya theory, in order to account for stereochemical symmetries. These methods require bespoke derivations and methods for each molecular family of interest, and quickly become very intricate for nontrivial classes. In this work, we demonstrate that analytic combinatorics provides a unifying, highly extensible, and relatively simple framework for enumeration problems. Using the symbolic method, we show that classical counting problems, such as the enumeration of acyclic alkanes and other hydrocarbon families, can be naturally solved via concise combinatorial specifications of the class of interest. We first demonstrate the simplicity of this approach by replicating existing results in this framework, requiring significantly less work than previously necessary, and then extend these ideas to more complex problems, counting broader classes of molecules accounting for both tetrahedral and E/Z stereoisomerism, counting the distribution of stereogenic units, and enumerating achiral and meso compounds. All results are made reproducible through CombOL, our open-source software package which automates the translation of combinatorial specifications into generating functions using the symbolic method, and performs both univariate and multivariate enumeration.

Solvent environments surrounding a solute can significantly alter its chemical properties. These changes become more prominent in electrolyte solutions, where mobile ions largely influence the solute through electrostatic interactions. A theoretical description of these ionic effects will benefit the design of chemistry performed in electrolyte solutions. As a result, the non-linear Poisson-Boltzmann equation (NLPBE) has emerged as an efficient implicit solvent model for electronic structure calculations to address such effects. However, the limited availability of NLPBE solvers for molecular electronic structure calculations greatly hinders theoretical investigation into the ionic effects. To improve accessibility of the NLPBE, we present libNLPBE, an open-source Python library, that solves the NLPBE for molecular systems in combination with density functional calculations, specifically to obtain electrostatic correction terms arising from the electrolyte solution environment for the Fock matrix. The library employs the density fitting (DF) approximation to efficiently calculate solute electrostatic potentials. Furthermore, we develop the modified Damped Inexact Newton Multigrid developed by Holst (mDINMH) method for solving the NLPBE. The mDINMH features a symmetric preconditioner for solving the Newton equation, which enables the use of robust multigrid methods designed for symmetric linear operators. In addition, an algebraic multigrid method has been incorporated into the mDINMH to support a broad range of grid points. We also present a GPU-accelerated version of libNLPBE to leverage parallelization efficiency of GPUs.

In the field of cavity quantum materials, vacuum fluctuations of optical cavities are used for modifying ground-state properties of quantum materials without external driving. Here, one example is the van der Waals (vdW)/dispersion interaction in layered 2D vdW materials, where non-additive long-range correlations can dominate the interlayer binding. While cavity-induced changes of such interactions have been predicted and described using ab initio methods for molecular systems, no efficient description exists yet for extended materials. In this Letter, we close this gap by introducing a periodic formulation of the photon many-body dispersion (pMBD) functional within quantum electrodynamical density-functional theory (QEDFT). Applying this method with efficient $\textbf{q}$-point sampling to bilayer hBN and graphene, we predict cavity-modified stacking, increased equilibrium interlayer distances, and softened layer breathing modes with increasing light-matter coupling strength. Our results establish cavity vacuum fluctuations as a tuning knob for the structural properties of vdW materials.

Molecular modeling of chemisorption with Monte Carlo requires the development of new trial moves to efficiently sample complex fluids such as water in Bronsted acid zeolites. Here, we develop a reaction volume bias (RxVB) Monte Carlo trial for modeling chemisorption by combining identity-switch and aggregation-volume-bias (AVB) moves. This method aims to promote the sampling of reactions by choosing reactive pairs that are within an arbitrarily specified reaction volume. The RxVB move achieves up to a 90-fold increase in accepted reaction events over unbiased moves in a single-site slit-pore model, corresponding to a 70-fold gain in statistical efficiency after accounting for computational overhead. But when the same move is applied to water in a Bronsted acid zeolite without orientational bias, there is no measurable speedup for a single MFI unit cell. We demonstrate a simple expression that predicts the maximum efficiency increase in the simplest case where selecting reactants that are near each other is the major sampling bottleneck. Dense water systems may require additional configuration-bias or orientational bias to improve sampling of the hydrogen bond network in order to increase acceptance. This new RxVB trial was made available with examples in the open-source Free Energy and Advanced Sampling Simulation Toolkit (FEASST) simulation package.

The algebraic diagrammatic construction (ADC) of the electronic self-energy is based on Moller-Plesset perturbation theory. Its vertices contain bare energy denominators that do not capture renormalization of Hartree-Fock excitations through excited-state correlations. As we show here, Epstein-Nesbet (EN) partitioning of the electronic Hamiltonian overcomes this deficiency at zero extra cost by introducing dressed denominators that resum to infinite order the diagonal elements of ladder diagrams described by the pair propagator in the particle-particle $T$-matrix approximation. Third-order ADC with EN-dressed denominators leads to an almost fourfold increase in accuracy compared to standard ADC(3) on a challenging benchmark set for IPs of closed-shell molecules, reaching an accuracy between EOM-CCSD and EOM-CCSDT. For open-shell systems, the gains in accuracy are more modest, but standard ADC is nevertheless outperformed.

At short times, interfacial tension depends on experimental geometry because surfactant transport to the interface depends on the mass-transfer conditions.A predictive description therefore requires more than a dynamic tension curve or a fitted adsorption constant: interfacial thermodynamics, diffusion, and adsorption kinetics must be identified separately. Here, we combine equilibrium and diffusion measurements with a microfluidic EDGE tensiometer that provides a nearly stationary interface and controlled micrometer-scale transport. Equilibrium properties and diffusion are determined independently, leaving adsorption kinetics as the key unknown. Dynamic tension is then calculated using a nonequilibrium thermodynamic description, without assuming instantaneous equilibrium between the adsorbed layer and the subsurface solution. For the nonionic surfactant C$_{10}$E$_{8}$, equilibrium thermodynamics and transport are independently constrained, and a single intrinsic adsorption rate constant describes several concentrations. We extend the framework to SDS by including electrostatic interactions and subsurface-concentration dynamics, capturing transient depletion and replenishment. Once thermodynamic, transport, and kinetic parameters are identified, the model predicts dynamic interfacial tension beyond the geometry and conditions used to determine them. The microfluidic EDGE tensiometer thus provides both a reliable short-time tensiometry method and a quantitative framework for identifying the physical mechanisms governing surfactant mass transfer at interfaces.

Assigning the lines of high-resolution molecular spectra to quantum states requires a Hamiltonian model and substantial expert intervention, so the spectra of larger molecules accumulate vast numbers of unassigned lines. Here we show that molecular energy levels can instead be reconstructed directly from the raw, unassigned transition frequencies, using graph theory alone with no model and no prior assignment. Our inverse graph construction exploits recurring frequency differences and four-cycle closures to assemble an energy-level network at kilohertz precision. The dense, broadband spectra this requires are produced by a cavity-enhanced spectrometer (SCALS) that scans continuously across tens of terahertz at kilohertz accuracy, combining broadband coverage, high sensitivity, and high precision in a single automated instrument. Applied to the water absorption spectrum in the range of 1537–1605~nm, 686 Lamb dips of water were obtained without assignments, and the method reconstructs 158 energy levels that are mostly two orders of magnitude more precise than the corresponding literature values. By removing the assignment barrier, this approach opens a route to exploratory precision spectroscopy of polyatomic molecules without a priori knowledge of transition frequencies.

Electronic-structure calculations require a finite representation of both the electronic wave functions and their Coulomb interaction. Conventional compact basis sets lead to a four-index interaction. Gausslet basis sets are one of a very small number of approaches that allow a much smaller two-index interaction, similar to a real-space grid, but with far fewer points. The continuing challenge in their development is reducing further the number of functions needed while maintaining high accuracy. Here we introduce projected q-shells (PQS), an improvement to the nested Cartesian gausslets of White and Lindsey. Their standard nesting construction divides a joining shell into disjoint faces, edges, and corners, reducing its polynomial completeness from order q to order q-2. PQS approximately restores the two lost orders. In terms of completeness, we prove that for an ideal, undistorted parent, the span of the PQS basis is equivalent to an overcomplete basis of overlapping patches. Coordinate distortions, which are always used in practice, harm this equivalence only slightly. The moment properties that allow two-index interactions also become inexact, even without distortion, but we show that the improvement in order more than makes up for this loss. For similar basis sizes, PQS gives smaller one-electron and interaction errors on small molecules, such as H2+, H2, and C2, than standard nesting. The improvement is largest for more compact bases with smaller q.

Phenacenes, in which benzene rings are fused in a zigzag manner, are chemically robust $\pi$-conjugated hydrocarbons of interest for organic electronic applications and superconductivity. However, quantitative electronic parameters of phenacene thin films remain limited compared with those of acenes. Here, we determine the ionization energies (IEs), electron affinities (EAs), band gaps, exciton binding energies, and polarization energies of orientation-controlled thin films of picene, [6]-phenacene, and [7]-phenacene using ultraviolet photoelectron spectroscopy and low-energy inverse photoelectron spectroscopy. The energy parameters depend only weakly on molecular size. In contrast, both IE and EA exhibit large orientation-dependent shifts of approximately 1 eV: lying films show IEs of 6.41-6.43 eV and EAs of 2.16-2.42 eV, whereas standing films show IEs of 5.44-5.67 eV and EAs of 1.36-1.53 eV. Nevertheless, the band gaps of approximately 4 eV and exciton binding energies of approximately 1 eV remain nearly independent of molecular size and orientation. Analysis of polarization energies shows that the induction term is nearly orientation independent, whereas the electrostatic term strongly depends on orientation and originates primarily from molecular quadrupole moments. These results identify molecular orientation as a key factor governing frontier energy levels in phenacene thin films.

Catalytic hydrogenation of $\text{CO}_2$ to formate on copper is a key elementary step for $\text{CO}_2$ utilization. Previous experimental and theoretical studies suggested an Eley-Rideal mechanism for this reaction, promoted by bending vibrational excitation, yet direct state resolved evidence remains lacking. Here, we present first-principles dynamical predictions for $\text{CO}_2$ hydrogenation on Cu(111) based on an accurate full-dimensional neural network potential energy surface. Our calculations near-quantitatively reproduce the measured reaction probabilities, including their nozzle-temperature and incidence-energy dependence. Our state-resolved results indicate that while vibrational excitation of the bending mode enhances reactivity, it alone cannot account for the observed reactivity increase with nozzle temperature. Instead, rotational excitation plays a dominant role, mainly attributable to the significant change in anisotropy of the molecular polar orientation as $\text{CO}_2$ accesses the transition state. This mode-specific insight reinforces the hidden role of rotation in surface reactivity, opening new avenues for state-selective control of $\text{CO}_2$ hydrogenation on heterogenous catalysts.

Designing molecular qubits requires controlling the spin-lattice relaxation pathways that fundamentally limit the coherence time. For spin-1/2 molecular qubits, significant discrepancies remain between theoretical predictions and experimental measurements of spin-phonon relaxation pathways, with theory often overestimating the role of low-frequency vibrational modes. Here, we present an alternative first-principles approach augmented with regularized regression that identifies spin-phonon relaxation pathways in an automated fashion without ad hoc mode selection. Applied to Cu porphyrins spin-1/2 molecular qubits, the method successfully reproduces experimental trends in relaxation times and predicts the curvature in the relaxation-vs-temperature profile. The g-tensor time series reveal distinct system-specific autocorrelation functions and spectral-density profiles despite the qubits' structural similarity. Further, regression between g-tensor time series and mode-projected vibrational-amplitude time series obtained from molecular dynamics yields linear and bilinear mode coupling contributions to each g-tensor component. Because the method is based on atomic displacements sampled directly from molecular dynamics, it naturally incorporates anharmonic effects and does not require the harmonic approximation. This framework puts forward a regression-driven, mode-resolved, and coupling-order-separated spin-phonon analysis as a general strategy for predicting and engineering longer-lived molecular qubits.

Machine learning interatomic potentials (MLIPs) have become emerging tools in molecular modeling and computational chemistry. By learning high-dimensional potential energy surfaces from quantum chemical data, MLIPs enable accurate and efficient predictions of structural, thermodynamic, and dynamical properties. However, such models have limitations in predictions of electronic properties and the effects of static electron correlation due to their lack of electronic structure information. This work presents OrbGNN, an electronic structure graph architecture analogous to molecular graph and MLIP frameworks, where pair-orbital interactions constitute the graph representation, while orbital entanglement encodes the connectivity between them. By embedding information derived from orbital correlation metrics directly into the graph topology, OrbGNN provides a compact representation of a molecule s orbital landscape and electron correlation patterns. Analysis of the behavior of the feature space in an orbital graph are shown to demonstrate model robustness. The model is evaluated for the dissociation of nitrogen and for a larger dataset of diatomic molecules. Finally, the OrbGNN model is applied to a set of octahedral iron(II) complexes to predict spin-state energy gaps.