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Δ-learning for transferable machine learning interatomic potentials
Machine-learning interatomic potentials (MLIPs) trained by directly learning the total interatomic interaction energies can suffer from limited transferability, unphysical behavior beyond a finite cutoff, and large errors for out-of-distribution geometries such as transition states and uncommon conformers. We evaluate Δ-learning (delta-learning) as a remedy by training an ANI-style high-dimensional neural network (HDNNP) potential as a correction to predict PBE0/aug-cc-pVTZ energies from a third-order tight-binding density functional theory (DFTB3) baseline model. On a held-out test set derived from the modified ANI-1x training set, the Δ-learning model (named ANIDFTB-Δ) achieves a mean absolute error (MAE) of 0.82 kcal/mol, while the HDNNP model (ANIPBE0-Direct) has an MAE of 2.01 kcal/mol. On selected GMTKN55 benchmarks, the Δ model systematically improves relative energies for conformers and tautomers and avoids catastrophic outliers on challenging structures. The good physical description of DFTB3 significantly reduces the error in proton-transfer transition states in the PX13 benchmark and intermolecular interactions in the DES370K dataset in comparison with reference target PBE0. The long-range electrostatics in DFTB3 also partially correct the long-range behavior of local descriptor MLIPs outside of their predetermined cutoff, reducing the MAE from 0.098 to 0.019 kcal/mol. The computational cost of this method is incrementally more expensive than DFTB3 alone, making it practical for extensive simulations of moderately sized systems, although the DFTB3 step makes the Δ model much more costly than a simple HDNNP alone.
Harmonic-oscillator-referenced ring-polymer molecular dynamics. II. Theoretical foundations of reference-modified dynamics and Gaussian reconstruction
The Paper I [H. Wang, J. Chem. Phys. 165, ■ (2026)] introduced harmonic-oscillator-referenced ring-polymer molecular dynamics (HO-RPMD) as a practical framework for approximately computing linear and nonlinear real-time quantum correlation functions. The present study develops the corresponding theoretical foundation in greater detail. The method is organized around three coordinated ingredients: exact harmonic-reference sampling in imaginary time, centroid-anchored real-time propagation, and Gaussian reconstruction of nonlinear observables from an anchored linear kernel together with sampled static information. We show that these elements are structurally linked. Once the quantum Boltzmann operator is represented by a harmonic reference kernel rather than by the primitive free-particle Trotter factorization, the centroid component of the real-time dynamical generator cannot generally be left unchanged without shifting the harmonic oscillation frequency. Likewise, beyond linear centroid observables, a direct nonlinear ring-polymer correlation function is no longer naturally protected from contamination by the internal fluctuation modes, and an explicit reconstruction step is therefore needed. We formulate these points at the operator, path integral, normal mode, and observable reconstruction levels and derive the finite-P reference distribution, the centroid-anchoring condition, and the Gaussian reconstruction logic. The resulting theory clarifies the relation of HO-RPMD to standard RPMD, centroid molecular dynamics, symmetrized/Wigner-type correlation-function formulations, and Gaussian moment-reconstruction ideas. It also makes clear that, beyond the harmonic limit, the natural practical nonlinear target of the present framework is the canonical hybrid correlation function, while nonlinear Kubo quantities remain primarily useful as harmonic benchmarks.
Publisher’s Note: “Reentrant phase transition in pH-responsive microgel suspensions” [J. Chem. Phys. 165, 024903 (2026)]
Living helices in fluctuating polymer chains: Cooperative nucleation and dynamics
Helical segments in polymer chains are often transient, finite, and dynamically evolving, yet their origin and stability remain incompletely understood. Here, we develop a minimal coarse-grained statistical-mechanical theory that explains how such “living helices” emerge in fluctuating polymer systems. Using a three-state model with cooperative interactions, we show that helix formation proceeds through a multistep nucleation mechanism. An initial constrained pre-nucleus forms first, followed by cooperative stabilization that promotes the growth of finite helical segments. The resulting free-energy landscape naturally favors marginally stable helices whose size is determined by a competition between cooperative gains and nonlinear penalties arising from stiffness, torsional strain, and solvent fluctuations. By formulating the dynamics as a stochastic process in segment size, we derive analytical expressions for both formation times and lifetimes within a mean first-passage framework. For representative parameters relevant to flexible polymers and peptide segments, the theory predicts characteristic timescales in the nanosecond to sub-microsecond range. These results provide a unified physical picture of “living helices” as finite, mobile, and fluctuating excitations and identify cooperativity and fluctuations as the key determinants of transient secondary structure in polymeric systems.
Publisher’s Note: “A microscopic theory of small-droplet adhesion on solid surfaces” [J. Chem. Phys. 165, 024707 (2026)]
Interfacial thermal conductance between a polyethylene glycol polymer chain and water: A molecular dynamics study
Understanding interfacial heat transfer between polymers and water is crucial for the design of biomaterials, drug delivery platforms, and nano-fluidic systems. In this study, we employed all-atom molecular dynamics (MD) simulations to quantify the interfacial thermal conductance between an infinitely diluted polyethylene glycol (PEG) 36-mer chain and explicit water over the temperature range of 280–350 K. To compare the conformational behavior of the PEG chain, we examined its radius of gyration and observed a temperature-dependent chain collapse consistent with previous coarse-grained models. By employing a transient non-equilibrium MD approach, we imposed temperature difference across the interface and analyzed the energy relaxation behavior to compute heat transfer across the polymer–water interfaces. Moreover, we investigate the impact of polymer conformation on heat transfer by considering modulations of the Lennard-Jones polymer/solvent interactions, different from the original PEG–water interactions. Our results demonstrate that both temperature and Lennard-Jones interfacial interaction strength influence interfacial thermal conductance, with temperature playing the dominant role. Structural factors such as chain conformation and interfacial area were found to mediate the effect of interfacial interaction. Additional analysis of the vibrational density of states and the mean square displacement reveal that vibrational coupling has minimal impact on thermal conductance across interfaces, whereas increased water thermal motion enhances energy transfer. These findings highlight the structural and dynamical origins of interfacial thermal conductance and provide atomistic insights into the tuning of interfacial heat transport in molecular systems through temperature and solvent interactions.
The transfer tensor method: An analytical study case
The transfer tensor method (TTM) is a versatile tool for analyzing and propagating general open quantum systems. It captures in a compact manner all memory effects in a non-Markovian system through a straightforward transformation of a set of dynamical maps. Transfer tensors (TTs) provide the exact convolutional propagator associated with a given time discretization over the past evolution of an open quantum system. Here we show that, for any finite time discretization, the memory kernel of the Nakajima–Zwanzig equation deviates from the exact TTs, although both converge in the continuous-time limit, as expected. We examine this behavior in the context of an analytically solvable model: a two-level atom resonant with a lossy cavity in the Jaynes–Cummings limit. The atomic dynamics separate into two decoupled subspaces—the coherence and the population difference. We derive exact expressions for the dynamical map, the TTs, and the memory kernel governing the coherence, and we relate them to their counterparts for the population difference. As a function of the ratio between the cavity loss rate and the atom-cavity coupling strength, we identify regions of enhanced non-Markovianity in which the dynamics can be described as fully Markovian for certain TTM time-step choices.
On intermolecular interactions in the Hamiltonian used in polaritonic chemistry
Experiments have shown that strong coupling between molecular excitations and a mode of a Fabry–Pérot cavity can significantly alter molecular properties, such as reaction rates and equilibrium constants. However, in spite of the large body of theoretical work, the mechanism behind this change is still not well understood. In order to make progress, we first take a step back and investigate the appropriateness of the Hamiltonian that most recent studies are based on. In particular, we investigate the dipole self-energy, which can be divided into self-terms and cross-terms. While the self-terms are an indispensable part of the Hamiltonian, the cross terms—which have received attention as they seem to mediate distance-independent interactions between all molecules in the cavity—are known to, under certain conditions, cancel exactly with the usually neglected intermolecular Coulombic interactions. In this study, we revisit how this cancellation comes about in free space and in a perfect cavity, clarifying that it can only be found when looking beyond the single-mode approximation and taking the full continuum of light modes into account. We also provide numerical evidence suggesting that this cancellation may extend to the case of an imperfect cavity and show how the situation changes for a more realistic cavity in the framework of macroscopic quantum electrodynamics. Finally, we discuss the implications of this cancellation for the single-mode Hamiltonian.
q-vSZPs: A polarized, adaptive minimal Gaussian basis set for the elements <i>Z</i> = 1–86 designed for efficient mean-field electronic structure calculations
We present q-vSZPs, a polarized, environment-adaptive minimal Gaussian basis set parameterized for elements Z = 1–86 (excluding lanthanides) and designed for efficient mean-field quantum-mechanical calculations on large molecular systems. Building on the previously introduced q-vSZP basis set, the number of primitive functions is substantially reduced while retaining the key feature of charge- and coordination-number-dependent contraction coefficients, which enable environment-dependent “breathing” of the atomic orbitals. The effective atomic charges required for the basis set setup are obtained from the bond-capacity electronegativity equilibration model (EEQBC), which accurately reproduces density functional theory (DFT)-level Hirshfeld charges at negligible computational cost. Comprehensive benchmarking on the GMTKN55 database demonstrates that q-vSZPs incurs only a moderate loss in accuracy relative to q-vSZP (WTMAD-2 increase of 2.9 kcal⋅mol−1), while substantially outperforming conventional non-adaptive minimal basis sets (MBs). For non-covalent interactions, the performance even surpasses that of the double-ζ def2-SVP basis set, owing to a substantially lower basis set superposition error as a consequence of the molecular optimization strategy. A non-adaptive variant using averaged charges and coordination numbers (qavg-vSZPs) is additionally provided as a drop-in minimal basis for any quantum-chemical program. For a representative 4108-atom system, q-vSZPs achieves a twofold reduction in both SCF wall time and memory consumption for DFT calculations relative to q-vSZP, placing it in the efficiency range of other MBs. The utility of q-vSZPs is further demonstrated through a mixed-basis application for the computation of the Raman spectrum of adenine in water.
Unbiased exploration of the transition region in ice nucleation using the <i>NpH</i> ensemble
In this work, we employ the isenthalpic–isobaric (NpH) ensemble to sample the transition region of ice nucleation without any external bias, thereby avoiding potentially artificial memory effects introduced by projections onto collective variables. Within this framework, we identify relevant degrees of freedom that expose the intrinsically non-Markovian nature of the largest nucleus size, indicating that it is not sufficient on its own to describe nucleation dynamics. The NpH ensemble leads to long-lived nuclei through the coupling between latent heat release or absorption and temperature fluctuations. As a result, nuclei persist over extended timescales and undergo a slow internal evolution, which we refer to as aging. A signature of this behavior is the emergence of hysteresis in the largest cluster size–temperature plane. To quantify these effects, we perform a structural analysis based on a high-dimensional set of descriptors, which we project onto a low-dimensional latent space using a neural network-based autoencoder. This approach reveals the existence of structurally distinct classes of nuclei with similar sizes and temperatures. Finally, we compare the nucleus sizes obtained with this approach with those from previous studies employing different methodologies, finding good agreement.
Para–ortho H2 conversion in collisions with NO: A surprising mechanism
Molecular hydrogen exists in two kinds, para-H2 and ortho-H2, which act as distinct molecules in many physical and chemical processes. Their interconversion is extremely slow but can be catalyzed by collisions with paramagnetic molecules such as O2 and NO. Temperature-dependent rate coefficients for para–ortho H2 conversion in gas-phase collisions with O2, NO, and NO2 were measured in 1933 in a beautiful series of experiments by Farkas and Sachsse [Z. Phys. Chem. B 23, 1–18 (1933)]. A complete and quantitative theoretical study of the conversion rate coefficients in collisions with O2 was published recently [X. Zhang et al., Nat. Sci. 1, e10002 (2021)]. The present paper describes a similar, although more difficult, study of para–ortho H2 conversion in collisions with NO. Not only does it yield conversion rate coefficients in good agreement with the experimental data, but it also explains the surprising finding that collisions with NO are substantially more effective in converting para-H2 into ortho-H2 than collisions with O2. It shows, moreover, that the effectivity of NO is caused by a completely unexpected mechanism: coupling with the transient magnetic dipole of NO generated by the transition of its excited spin–orbit state to the ground state in collisions in which para-H2 near-resonantly converts into ortho-H2.
Toward viable H2 storage in Ca decorated low-dimensional materials with insights from reference quantum Monte Carlo
Hydrogen technology is set to be a key energy alternative for mitigating pollution and reducing CO2 emissions. However, the current storage mechanism of hydrogen molecules in carbon fiber tanks detracts from the fuel economy of hydrogen in mobile applications, necessitating the development of alternative storage mechanisms. Adsorbing hydrogen in its molecular form (H2) under typical operating conditions of proton exchange membranes can potentially meet storage requirements. However, H2 is the smallest molecule with only two electrons and, therefore, it has very limited propensity to physisorb in a material within the binding energy window of −0.2 to −0.4 eV that is suitable for storage. Calcium atom decorators on graphene have previously shown promise for tunable H2 binding, but the system is thermodynamically unstable toward the formation of calcium hydride. Moreover, the absolute adsorption of H2 is challenging to predict accurately and is typically overestimated with van der Waals inclusive density functional approximations. In this work, we perform state-of-the-art fixed-node diffusion Monte Carlo alongside a selection of density functional approximations for two strategies of anchoring Ca: (i) Ca on boron-doped graphene and (ii) Ca inside carbon nanotubes. We predict reliable Ca and H2 binding energies and establish that Ca is anchored inside carbon nanotubes and on boron-doped graphene, while boosting the H2 adsorption energy. Importantly, the H2 adsorption energy is found to be improved by the anchoring strategies, with the energy inside a Ca decorated carbon nanotube reaching the viable storage window. The reference DMC binding energies provide much-needed benchmarks for developing data-driven methods and guiding experiment in the systematic design of hydrogen storage materials.
Exploring flat multi-minima potential energy surface by matrix isolation IR spectroscopy: Revisiting methanol–H2S complex
An extensive potential energy surface search of the methanol–H2S binary complex reveals four distinct conformers (two each of S–H⋯O and O–H⋯S H-bonded) within a small energy window (binding energies within −2.9 to −3.3 kcal mol−1). The four conformers are interconvertible via rotation along the C–O bond of methanol and the S–H bond of H2S, with very small rotational barriers (&lt;0.5 kcal mol−1). All four stable methanol–H2S complexes have been experimentally identified for the first time in cold and solid argon and nitrogen matrices via spectral signatures in νO−H and νS−H regions, while an earlier study in a molecular beam could identify only the global minimum structure. To further investigate matrix effects, quantum chemical calculations were carried out for the methanol–H2S complex embedded within an argon environment modeled as a face-centered cubic lattice, mimicking the solid matrix conditions. The rotational barriers were found to increase appreciably inside the model (&gt;1.5 kcal mol−1). Rate constants for conformational interconversions revealed that populations in local minima rapidly transfer to the global minimum at low temperatures, while the same become prohibitively slow inside the model. This prediction aligns well with the trapping of hitherto unidentified local minima conformers in a matrix environment.
Validating orbital-optimized linearized coupled-cluster theory for high-accuracy thermochemistry and spectroscopy of prototypical π-systems: Ethylene and its ions
High-level ab initio estimates for the equilibrium structure (rCC = 1.330 79 ± 0.000 31 Å, rCH = 1.080 75 ± 0.000 21 Å, and αCCH = 121.423° ± 0.023°), the adiabatic ionization energy (10.52 eV), and the 0 K proton affinity (673.2 kJ/mol) of ethylene were obtained via focal-point extrapolation of coupled cluster results to the basis set limit. This methodology also provided accurate equilibrium structures for the ethylene radical cation (ionized ethylene) and the ethenium cation (bridged protonated ethylene). An additive correction scheme allowed for the prediction of the vibrational spectrum of ethylene with a root-mean-square error of 2.4 cm−1. A systematic evaluation of popular wavefunction-based methods revealed that the recently implemented orbital-optimized linearized coupled cluster (OLCCD) method predicts the geometry and properties (the ionization potential, the proton affinity, and the fundamental frequencies) of ethylene significantly better than the orbital-optimized Møller–Plesset (OMP2 and OMP3) and the standard coupled cluster with singles and doubles methods. Notably, where coupled-cluster with single, double, and perturbative triple excitations analytic Hessians suffer from wavefunction instability issues along several normal modes, OLCCD yields superior vibrational anharmonicities, making it a robust alternative for challenging π-systems.
Infrared spectroscopy of H3+ and Hn+ ions in helium nanodroplets
This work reports the infrared laser spectroscopic study of the H3+ and Hn+ (n = 5, 6, 7, 9) ions in helium droplets. The ions were produced upon electron impact ionization of helium droplets and charge transfer to small hydrogen clusters formed within the He droplets. The spectrum of H3+ shows a well-resolved rotational structure, indicating a small (∼8%) decrease in the rotational constants as compared to the gas-phase values. This small change is rationalized in terms of the small anisotropy of the H3+ interaction potential with He atoms. However, it was found that the interaction with the helium environment has a profound effect on the spectrum of the fluxional H5+ ions. Whereas the previously measured gas-phase spectrum has well-separated bands, the spectrum of H5+ in helium droplets shows a broad spectrum extending over 2000 cm−1 containing some maxima with frequencies close to those of the gas phase. The bands of H7+ and H9+ due to vibrations of their H2 moieties were also observed near 4000 cm−1. The structure of these ions could be treated as an H3+ core solvated in H2 molecules and He atoms. The spectrum of larger Hn+ clusters is also reported.
The electron affinity and ionization potential of the solvated uranyl from the quantum embedding approach
The quantum embedding approach offers an efficient way for large-scale electronic-structure calculations, enabling reductions in computational cost while retaining high-level accuracy. This aspect is particularly crucial for the modeling of actinide solution systems. Here, we present a subsystem approach for predicting valence electron binding energies, including the electron affinity (EA) and the ionization potential (IP) of the solvated uranyl. This approach combines the equation-of-motion coupled cluster method for electron attachment/detachment and the mean-filed treatment via absolutely localized projection-based embedding scheme, using representative structures extracted from ab initio molecular dynamics simulations, together with our newly developed norm-conserving actinide pseudopotentials. Our results show that the EA of solvated uranyl can be well reproduced by using the quantum embedding approach, whereas the IP requires an expanded active high-level region because of its global character. Including the full first solvation shell yields a marked improvement for the IP. This work demonstrates that the accuracy of the embedding partition is determined not only by the apparent structural locality of the system but also by how spatially localized the electronic-structure property of interest is. We anticipate that the quantum embedding approach will provide an efficient route to reducing the computational cost of high-level quantum chemical calculations for complex actinide solution systems.
Isomer effects in orbital-resolved photoionization cross sections of C2H4O2: Role of continuum dynamics and shape resonances
We present ab initio calculations of total and orbital-resolved photoionization cross sections for the C2H4O2 isomers glycolaldehyde, acetic acid, and methyl formate from threshold up to 40 eV. The calculations were performed using the ePolyScat framework at the static-exchange (SE) and SE-plus-polarization levels. The total photoionization cross sections, obtained as the sum over all twelve valence orbitals, exhibit a similar overall energy dependence for all isomers, with systematic differences near the ionization threshold and in the region of the cross section maximum. In contrast, the orbital-resolved analysis reveals a pronounced isomer dependence. To justify the single-particle picture underlying the scattering calculations, electron propagator theory was employed; the calculated pole strengths for the outer-valence orbitals remain high (∼0.9), validating the use of Hartree–Fock initial states as adequate representations of the Dyson orbitals. The highest occupied molecular orbitals, dominated by nonbonding oxygen lone pairs, give rise to the largest cross sections. Pronounced shape resonances are observed in the HOMO channels in the 15.5–19.3 eV range, with positions and intensities strongly dependent on molecular structure. Partial-wave analysis shows that these features are primarily governed by the l = 4 component, with additional contributions from neighboring channels. These results demonstrate that, despite identical stoichiometry, differences in molecular structure lead to distinct continuum electron dynamics. The computed cross sections provide quantitative input for astrochemical models and provide insights into isomer-dependent behavior in UV-irradiated environments.
Canonically consistent quantum master equation for proton-transfer reactions
The canonically consistent quantum master equation (CCQME) method to treat system–bath dynamics is used to describe intramolecular proton transfer in the thioacetylacetone molecule (TAA, C5H8OS), modeled as an N-level quantum system coupled to a solvent. The solvent is represented as a harmonic bath (a continuum of oscillators) characterized by Ohmic–Drude spectral density. We benchmark the secularized population dynamics and steady-state populations predicted by CCQME against numerically exact hierarchical equations of motion (HEOM) theory and compare it to the corresponding secularized Redfield results. Our results reveal that Redfield dynamics deviates increasingly from the HEOM reference as the system–bath coupling strength grows. In contrast, for not too strong couplings, the secularized CCQME population dynamics remains consistent with HEOM over an extended system–bath coupling range and approaches the second-order mean force Gibbs state. A complementary non-secular calculation shows that retaining population–coherence coupling reveals limitations of the second-order treatment for coherence-sensitive observables.
Tracking water vapor homogeneous nucleation and droplet growth with spectroscopy and holography in a free expansion cloud chamber
We use a newly commissioned rapid expansion aerosol chamber facility to study the homogeneous nucleation of water vapor to form liquid droplets. We perform high-speed measurements to track the partitioning of water into vapor and droplets throughout the expansion process, including tunable diode laser absorption spectroscopy (TDLAS) to access the vapor concentration and in-line holography to track the size and concentration of nucleating droplets. We retrieve the peak saturation ratio achieved in each expansion from the TDLAS measurements in combination with adjusted thermocouple temperature readout. We monitor the number of nucleated droplets and their subsequent growth as a function of saturation ratio and observe the onset of homogeneous nucleation of water vapor occurring at a threshold saturation ratio near S = 5, in agreement with prior literature and classical nucleation theory. The trends we observe in average diameter and droplet concentration suggest that warm air pockets near the chamber walls inhomogeneously mix with cold air at the center of the chamber following expansion. Active forced mixing with fans yields more spatially uniform temperature readings across the chamber but also significantly broadens the droplet size distribution. Our results demonstrate the capability of TDLAS and holography techniques to track both water vapor and liquid water in the high saturation ratio environments necessary for the homogeneous nucleation of droplets. Our findings also reveal that droplet nucleation and growth dynamics are highly sensitive to turbulence.