Papers

Charge-equilibration models predict how electrons redistribute over a molecule more cheaply than quantum chemistry, and each begins from a table of atomic electronegativities and hardnesses. A recent table replaces ionization energies and electron affinities with one geometric quantity: each main-group atom's fractional distance to the noble gas closing its row. Holding geometries, electrostatic damping and the molecule list fixed, we compare it with spectroscopic values, with its own kernel refitted, and with a quadratic control, over a primary set of fifty-two molecules and ions at the B3LYP/def2-TZVP level. Two structural consequences follow from the table construction rather than the equalization solver. Atoms at equal fractional distance receive identical electronegativities, so the dipole moments of chlorine monofluoride, iodine monobromide and sulfur dioxide vanish exactly, and the measured $0.72$ debye $\mathrm{HF}/\mathrm{HCl}$ gap is lost. Because the first period is excluded, hydrogen retains its spectroscopic electronegativity above every geometric value, reversing $\mathrm{O{-}H}$, $\mathrm{N{-}H}$ and hydrogen-halide polarity. Fitted alike, geometric and quadratic kernels agree to $0.0022$ electron per atom, so predictions are set by the fitted energy scales, not the kernel shape. Resolving the electronegativity scale period by period restores correct polarity in all five polyatomic heavy-atom-hydrogen tests.

Neural-network quantum states (NNQSs) can represent many-electron wave functions without explicitly enumerating the determinant space, but their accuracy depends jointly on model size and variational-optimization effort. Here we characterize this dependence for a physics-conditioned autoregressive NNQS trained separately on two six-molecule source benchmarks. Across eight model sizes and five optimization milestones, we find that model size and optimization steps jointly shape the energy error. The capacity advantage of larger models becomes more apparent with sufficient optimization, while the returns from additional optimization vary with model size. We capture this coupling using an interaction scaling law and quantify the cumulative compute of each evaluated configuration. The resulting error-compute Pareto frontiers provide a practical decision rule for jointly selecting model size and optimization steps under a given compute budget within the evaluated range. Furthermore, we find that this beneficial scaling trend persists during fine-tuning on held-out N$_2$. Pretrained models show decreasing error with increasing model size, with a steeper reduction following pretraining on the Hard benchmark. Together, these results place autoregressive neural quantum states within the broader landscape of empirical neural scaling and open a quantitative route toward the systematic scaling of neural quantum solvers for ab initio quantum chemistry.

The LDA-1/2 method provides an efficient correction to semilocal density functional theory for improving ionization energies and band gaps, yet its application to molecular systems has remained limited. In this work, we present an all-electron finite-element implementation of LDA-1/2 within the NESSIE electronic-structure framework and apply it to the GW100 molecular benchmark set with systematically controllable numerical accuracy. The self-energy correction is constructed explicitly from neutral and half-ionized calculations for each molecule, avoiding the use of precomputed atomic correction potentials. The real-space finite-element formulation enables systematic convergence with respect to the discretization and provides a controlled assessment of LDA-1/2 performance. For the GW100 set, the present implementation yields a mean absolute error of 0.472 eV and a root-mean-square error of 0.645 eV relative to CCSD(T) reference ionization energies, substantially improving upon conventional LDA and the previously reported LAPW implementation of LDA-1/2, while achieving accuracy comparable to G0W0@PBE. Convergence tests show that third-order finite elements are sufficient to reach or approach chemical accuracy relative to higher-order calculations for the representative systems considered. The resulting corrected Hamiltonian also improves several lower lying valence states relative to LDA, although the improvement becomes less systematic away from the HOMO. This work provides accurate LDA-1/2 benchmark data for molecular systems and establishes a rigorous finite-element foundation for future molecular GW calculations.

Charge-transfer-to-solvent (CTTS) excitations provide a chemically central route to generating hydrated electrons and initiating redox chemistry in solution, yet the earliest stage of CTTS—the formation of the excited state itself—is usually treated as instantaneous. Here we present a time-domain perspective of how CTTS character builds up during core-level photoexcitation of an aqueous metal ion. Using time-dependent configuration interaction, we simulate the coherent evolution of a dense manifold of core-excited states and track the ultrafast flow of electronic charge from the initially localized site into solvent-supported final states. We find that the dynamics evolves from a few-state, oscillatory behavior to effectively irreversible delocalization, as the charge disperses among many coupled configurations, providing a microscopic mechanism for the early-time emergence of CTTS character. Our results offer a transparent real-time interpretation of what core-level spectroscopies and core-hole-clock-type measurements can probe in solutions, outlining experimental signatures for probing the build-up of CTTS states on the core-hole-lifetime timescale. Looking ahead, attosecond and sub-femtosecond X-ray pump–probe approaches at X-ray free-electron lasers provide a realistic route to directly time-resolve the core-excited CTTS wave packets in solution.

We present ElemCo.jl, an open-source Julia package for molecular electronic structure and properties calculations with a particular emphasis on Coupled Cluster and Distinguishable Cluster methods. The package provides a high-level, macro-based user interface which makes routine calculations accessible to users with no prior Julia experience. A newly developed visualizer, JLmol, assists in the graphical preparation of ElemCo.jl input files and displays results such as molecular orbitals. ElemCo.jl offers restricted closed-shell and unrestricted variants of state-of-the-art electron-correlation methods such as FCI, MP2, CCSD(T) as well as EOM-CCSD and the DC methods DCSD and DC-CCSDT. In addition to traditional approaches, ElemCo.jl provides recently developed methods that are currently unique to the package. These include tensor-decomposed implementations of DCSD and DC-CCSDT (SVD-DCSD and SVD-DC-CCSDT) as well as two-determinant and fixed-reference CC and DC methods. For excited-state calculations, ElemCo.jl also offers EOM-DCSD, which is benchmarked in this work against CC3 on the QUEST3 benchmark set, alongside EOM-CCSD. Furthermore, both ground and excited states, including those of multireference character, can be treated using CIPHI - an efficient selected Configuration Interaction (CI) approach employing a CIPSI/Heat-Bath-CI-based algorithm. Users can directly invoke internal functions from the input file, enabling them to test and compose new methods without the need to modify ElemCo.jl's source code. Also, ElemCo.jl can be readily interfaced with external quantum chemistry codes through the Fcidump format, for example as the high-level solver for transcorrelated Hamiltonians, periodic embedded fragments, etc. We provide a detailed overview of ElemCo.jl's methodological repertoire and discuss its technical details and implementation, performance, interfaces, and usage.

Entangled photons offer quantum correlations with no classical analogue. In entangled pair two-photon absorption (ETPA), absorption rate is predicted to scale linearly rather than quadratically with photon flux, promising molecular excitation at fluxes far below the classical threshold. Reported ETPA cross sections nevertheless vary widely across experiments, largely since the observable, the differential of the transmitted flux or weak fluorescence, is difficult to separate from scattering and linear losses. We present a method which uses Franson interference to study entangled two-photon absorption through delay-dependent coincidence measurements on dye molecules. Applying the method to Rhodamine 6G, we observe a small asymmetry in the Franson interference envelope and obtain a model-derived effective cross section of approximately 2.1 E(-21) centimeter squared for Rhodamine 6G. However, the estimated systematic uncertainty does not allow a definitive ETPA assignment. Instead, the experiment establishes a quantitative bound on the ETPA response and provides a background-free benchmark for future measurements.

The square of a sum of single-electron time reversals has been proposed as a conserved quantity with an integer eigenvalue spectrum for the many-electron Dirac-Coulomb Hamiltonian [Phys. Rev. A 94, 052104 (2016)], and its expectation value is in use as a diagnostic of Kramers contamination. This work identifies the operator behind the construction, a component of a pseudospin attached to the chosen Kramers pairs, whose angular-momentum algebra reproduces the reported spectrum and yields the eigenvectors in closed form. The label $k$ entering the proposed quantum number $-k^2$ is twice the magnitude of a pseudospin projection onto an axis fixed by the basis and changes when the Kramers pairs are rephased. The commutation with the Hamiltonian is unfounded, and the proposed quantum number does not stand.

Understanding the coupling between transport, chemical kinetics, and structural response within solid fuel combustion requires in situ measurements at high spatial resolution. To examine the dynamics of biomass pyrolysis, we optimize synchrotron X-ray micro-computed tomography ($\mu$CT), and conduct 3D particle-resolved simulations. A micro-focused heating cell with controlled heating and flow rate is employed, achieving temperatures of up to 1240 K and 3D imaging at 3.24 $\mu$m spatial and sub-minute temporal resolutions. The pyrolysis of three biomass materials at sample heating rates of 10-14 K/min are examined. The $\mu$CT measurements capture pore deformation, cracking, anisotropic shrinkage, and provide simultaneous thermogravimetric and thermovolumetric analyses to examine specific secondary pyrolysis pathways. Complementary 3D simulations considering detailed kinetics and structural response reproduce the key trends observed, and identify deficiencies in capturing simultaneous mass and volume losses during pyrolysis.

Many matrices in computational chemistry are neither sparse nor low-rank, making the design of low-scaling algorithms difficult. In this Perspective, we point out that many important matrices in computational chemistry, such as the Coulomb matrix, the electronic repulsion integral tensor, the density matrix, the localized molecular orbital (LMO) coefficient matrix, the Fock matrix, and the nuclear Hessian matrix share the same property: when their basis functions are suitably ordered, their off-diagonal blocks have low numerical ranks (despite that they as a whole have high numerical ranks). This property, termed off-diagonal low rank (ODLR), has been extensively studied in the mathematics community, but has surprisingly found very little use in computational chemistry. This Perspective reviews the existing mathematical literature on how to use the ODLR property of matrices to compactly store, as well as efficiently calculate or use them. Subsequently, we review the use of the ODLR property in computational chemistry, and point out possible future opportunities of devising new low-scaling methods for dense, full-rank matrices, exploiting the ODLR property. In particular, we prove for the first time that Fock matrices and LMO coefficient matrices satisfy the ODLR property, even if the system is gapless (in which case the matrices are dense). This paves the way to linear scaling electronic structure calculations of gapless systems at zero electronic temperature.

In swollen elastomers, elasticity can arrest macroscopic demixing between the polymer network and the solvent, producing stable domains of finite size. While previous theories have focused on isotropically swollen elastomers, anisotropy strongly influences the phase behavior of many related systems, such as gels and crosslinked polymer blends. Building on the approach developed in Part I of this two-part paper, we investigate the effects of two experimentally induced sources of anisotropy: uniaxial swelling and stiffness gradients. We show that uniaxial swelling can lead to the formation of stable lamellar microphases and modify phase behavior, while stiffness gradients can cause spatial variations in the characteristic microphase size.

Computing density-functional response properties requires contracting derivatives of the exchange–correlation (xc) energy with perturbed densities on a grid. While the xc functional's derivatives have long been available to high orders from libraries such as Libxc, the surrounding contraction layer - the chain rule that combines them with the grid-based basis-function and density data into the total xc contribution - has instead been hand-derived and hand-coded in every program, for every functional family, spin case, and property. We present libxckernel, a library that automatically generates this layer by symbolic differentiation. The xc functional's ingredients are expressed as sesquilinear forms in the density matrix, so the xc energy can be differentiated to any order while the functional derivatives remain opaque. The basis functions and the orbital coefficients may both be complex. The chain rule then produces any xc matrix element: Fock matrices, orbital Hessians, and response terms of any order. Terms sharing a pattern are collapsed for efficiency. Extensible plugins emit the expressions as NumPy Einstein sums, compiled C kernels with C++/Fortran interfaces, or host-program specific source code. libxckernel is free and open-source software under the BSD-3-Clause license, enabling rapid implementation of functionality missing from many electronic structure programs. We demonstrate it by extending Psi4 with meta-generalized gradient approximation (mGGA) response kernels for orbital stability analysis and time-dependent density-functional theory (TD-DFT), GGA and mGGA analytic nuclear Hessians, and exact quadrature grid response, and by extending GPAW with mGGA and triplet TD-DFT kernels and gradient-corrected kernels for periodic dielectric response.

Macroscopic hydrogen transport codes model material interfaces with local thermodynamic equilibrium (LTE), imposing continuity of chemical potential as a per-species constraint. Three assumptions hide in that condition: fast interfacial equilibration, a single exchange pathway between the two sides, and a carrier species known in advance on each side. The literature scrutinises the first, but the other two are the more consequential failures, and neither survives at a metal/molten-salt interface. We replace the constraint with reversible reaction channels at the interface that obey mass action, with detailed balance fixing each ratio of rate constants from the thermodynamic data that already parameterise LTE, and we implement the framework in festim. LTE is recovered as the fast-kinetics limit of a single channel, in both its Sieverts/Sieverts and its Sieverts/Henry form, so the framework generalises LTE and does not compete with it. A Damköhler number delimits validity within a channel, a branching ratio between channels. In a representative nickel/FLiBe system, hydrogen partitions kinetically between molecular and fluoride carriers. The apparent interfacial law then drifts between Sieverts and Henry with loading and salt redox state, and an LTE condition underestimates the steady permeating flux. The measured pressure exponent is set by the branching ratio, not by any fixed property of the salt; a redox sweep at fixed temperature should continuously shift it between 0.5 and 1. With two isotopes, two metal-side species feed five salt-side carriers, and a per-species LTE condition is ill-posed.

Enzymatic recycling of plastics is limited by the presence of semi-crystalline spherulites that are recalcitrant to enzymatic depolymerization. Depending on the quality of the waste stream and its treatment history, a large volume fraction of the material actually remains in form of connected clusters of such spherulites. We build on a recently published numeric method to predict the number, the connectivity, and the morphology of these clusters as an outcome of enzymatic degradation. When applied to PET waste, our method predicts that the resulting aggregates are loosely connected, "fluffy" structures with a high surface-to-volume ratio, accompanied by smaller clusters following a continuous size distribution. By providing a quantitative framework for understanding the microparticle production during the depolymerization, these findings should assist choosing a suitable downstream treatment, such as filtering or flocculation. This work could thus help to advance the enzymatic depolymerization technologies.

Core-valence double ionization electron spectra near the S2p, F1s and S1s edges of SF6 are presented, analyzed and compared with conventional valence photoelectron spectra and quantum chemical calculations. The core-valence spectra are energetically stretched out, revealing salient structures between 15 and 40 eV that are sufficiently separated for molecular orbital analysis. The spectra offer new insights into the electronic structure, showing that the core hole substantially rearranges the molecular orbital order. This effect can be traced to orbital localization and nodal structure, as well as to valence-to-core penetration. The singlet and triplet splittings of the dicationic states progressively decrease in all three core-valence spectra towards deeper core levels, with larger splittings for S2p than S1s, reflecting greater valence-to-core penetration and exchange interaction for S2p. By large, the MO interpretation holds in frozen or self-consistent-field representations, except for the inner parts of the F1s spectra, which require analysis in terms of MO breakdown effects. An intensity model for CV spectra is derived using an independent-channel approach, where primary core ionization is treated by dipolar coupling to a continuum and the valence electron is promoted to a second continuum through shake-off. Full spin coupling and spin selectivity between the discrete doubly ionized states and the two continuum electrons are maintained. The primary molecular photoelectron intensity is expressed as a weighted sum of atomic subshell cross sections using a one-center atomic orbital projection of the relevant molecular orbital. The calculated spectra agree well with experiment and allow detailed assignment. In particular, symmetry breaking at the F1s core-ionization site is identified and discussed.

The Dyson-algebraic diagrammatic construction (ADC) and the multi-channel Dyson equation (MCDE) formalisms explicitly leverage multi-particle channels to formulate correlated theories of the single-particle Green's function that produce positive semi-definite spectral functions by construction. While the MCDE is strictly rooted in the Dyson formalism, most ADC calculations are performed in the non-Dyson (nD) framework that decouples electron attachment and detachment sectors. We benchmark the Dyson-ADC(2)-X [that is equivalent to the (3,1)-MCDE] and ADC(3) approximations on a set of 58 ionization potentials of 23 small molecules for which near-full configuration interaction reference data exist. Comparison of Dyson- to nD-ADC(3) reveals deviations of the order of 0.1 eV between both methods, calling into question the reliability of the nD approximation. We show that Dyson-ADC gives similar accuracy for first IPs as for semi-valence and semi-core transitions. Finally, we also benchmark the screened (3,1)-MCDE that screens all ladder interactions, and show that it improves over its unscreened counterpart.

Equations of state accurately describe hard-sphere thermodynamics but are generally considered to fail under nanoscale confinement. We show that this failure is geometric rather than thermodynamic: a closed-form, parameter-free mapping from apparent to effective packing fraction restores the accuracy of the Carnahan-Starling equation of state and, with it, the entire analytical thermodynamic framework, including free energies, wall pressures, chemical potentials, and the large-cavity surface response. Applied to overlapping anchored hard-sphere droplets, a geometry inherent to biomolecular force generation, it yields unmixing free energies and full distance-dependent force profiles in quantitative agreement with simulations from the dilute regime to above the bulk freezing transition.

We developed a new mechanistic model for lithium and cobalt recovery during acidic-reductive leaching from LiCoO$_2$. The system considers HCl as an acid and H$_2$O$_2$ as a reducing agent. The model tracks conversion of LCO, the particle radius, the acid, H$_2$O$_2$, formation-dissolution dynamics of Co$_3$O$_4$ film, the film thickness, recovery of lithium and cobalt, and moles of O$_2$. We introduced the film passivation effects for reduced recovery in the absence of H$_2$O$_2$. We validated the model against the experimental data of recovered Li and Co reported in literature at three acid concentrations (0.5 M, 1.5 M, and 2.5 M) and four H$_2$O$_2$ concentrations (0%, 0.2%, 0.4%, and 0.6% (v/v)). The model works reasonably well at 0.5 M and 1.5 M HCl for the 0% and 0.6% concentrations of H$_2$O$_2$. At 2.5 M HCl, the model over-predicts the data in the presence of H$_2$O$_2$, while it works well at 0% H$_2$O$_2$. We suggest pathways for further improvements in the model. The comprehensive mechanistic modelling framework for the leaching with a full list of the equations, the parameters, and the variables, reported for the first time, can be extended to other cathode chemistries and acid-reductive leaching systems.

We present a self-consistent field framework for finite embedded quantum-chemical clusters with constant potential boundary conditions. The coupling is realized through an energy-independent self-energy commonly employed in quantum-transport calculations within the wide-band approximation. Starting from the corresponding non-equilibrium Green's function formalism, we derive an analytic expression for the one-particle density matrix update that can be incorporated into conventional Hartree–Fock and density functional theory. The resulting non-Hermitian self-consistent field equations are solved using adapted Pulay-type mixing schemes. Applications to a quasi-periodic hydrogen ring demonstrate that a finite fragment coupled through an optimized self-energy accurately reproduces the polarization response of the extended system, while calculations on a lithium cluster capture metallic charge transfer and fractional occupations under open-boundary conditions. The proposed framework establishes practical grand-canonical boundary conditions for finite quantum-chemical clusters and lays the methodological foundation for quantum embedding methods for electrochemical systems.

One-dimensional carbon wire materials are an interesting class of materials which have potentially useful applications in sub-nanoscale junction technology due to their unique quantum transport properties. In this work, we apply a non-equilibrium Green's function approach based on multiconfiguration pair-density functional theory (NEGF-MCPDFT). NEGF-MCPDFT is a wave-function-based non-periodic framework to study electron transport in systems exhibiting strong correlation. The advantage of this approach is multiconfigurational wave functions are used which offer enhanced abilities to describe strong electron correlation beyond single-determinant approaches. MC-PDFT necessitates the use of an active space, and a key step in such calculations is the determination of which orbitals to include. In application of this theory to carbon wire junctions of various lengths, we find that NEGF-MCPDFT is capable of reproducing trends from recent experimental results, and we use our findings to further the development of best practices in active space design for transport calculations of this type.

Raman spectroscopy is commonly reduced to molecular fingerprint sensing, neglecting Raman intensities. Atomic Raman intensity contributions trace Raman intensities back to their microscopic origin and act as local electronic structure descriptors; however, a both physical but intuitive framework is missing by now. Therefore, in this work, we combine the two main lines of decomposing Raman intensities: atomic Raman tensors and atomic Raman Intensity Densities (RIDs). The former are used to define atomic Raman intensities which quantify both the magnitude and the phase of each atom's contribution to the global Raman signal, demonstrating that weak Raman bands may arise from destructive interference of individually strong atomic contributions. The latter build on redefined atomic Raman Polarizability Densities, RPDs, and are defined in analogy to our atomic Raman intensities. They show how the motion of an individual atom modulates the polarizability of the entire molecule. Atomic RIDs thus show local interferences of different atomic contributions. They integrate to the atomic Raman intensities bridging the two main lines. Additional (atomic) Charge Density Differences (CDDs) extend the RIDs to electronic structure effects. Finally, we apply the methodology to experimental surface-enhanced Raman spectra of substituted 2-mercaptobenzothiazole derivatives and discuss substituent-induced Raman intensity changes. We show that such changes do not necessarily stem from globally altered polarizabilities but from changes in the relative phase of atomic contributions. However, this method is not limited to SERS but widely applicable to all kinds of Raman, SERS or picocavity TERS experiments offering a basis for atomically resolved investigations of molecular processes such as adsorption, catalysis, and chemical reactions

We used simulations of short single stranded DNA (ssDNA) homopolymers, based on the sequence dependent Three Interaction Site (TIS) model, to calculate the persistence length ($l_p$) in polyvalent cations. The TIS model accounts for stacking interactions and electrostatic interactions are treated using the Coulomb potential. We find that $l_p$ for $\mathrm{dT_{30}}$ (T is thymine) and $\mathrm{dA_{30}}$ (A is adenine) is quantitatively fit using $l_p = l_p^0 + \lambda \kappa^{-1}$ ($l_p^0$ is the bare persistence length, $\lambda$ is a dimensionless constant, and $\kappa$ is the inverse Debye length) in the divalent cations $\mathrm{Mg^{2+}}$ and $\mathrm{Ca^{2+}}$. The dependence of $l_p$ on $\kappa$ is surprising because it was derived for long flexible polyelectrolytes in which the charges interact via the Debye-Hückel potential. The $l_p^0$ values are 0.4 nm and 1.1 nm for polyT and polyA, respectively. Strikingly, $l_p$ is almost independent of the tetravalent spermine concentration. There is no clear theoretical explanation although simulations suggest that the number of spermine molecules that bind to the ssDNA saturates at a small value. A qualitative picture, based on the restrictions of access to the phosphate groups due to volume exclusion of the anisotropic structure of $\mathrm{Spm^{4+}}$, rationalizes the simulation results. The predicted dependence of $l_p$ in spermine awaits experimental test.

The topology of the electronic structure for an avoided crossing and a conical intersection (CI) is different and is characterized by the presence of the geometric phase in the electronic wavefunction in the latter. Using the linear Jahn-Teller model, we show that an avoided crossing can be created from the conical intersection while preserving the nontrivial topology of the latter by adding a Pauli $\sigma_y$ term to the Hamiltonian. Analogously to solid state systems, we derive a half-integer topological invariant as the integral of the Berry curvature over the CI nuclear branching space. We investigate the influence of electronic topology on chemical dynamics by conducting fewest-switches surface hopping simulations and find distinct hopping rates on identical eigensurfaces but with different topologies. Our work extends the influence of topology on molecular excited state dynamics beyond the Berry phase that can be practically realized through electron-nuclear and spin-orbit coupling.

The effects of pressure on the chemical sooting structure of equi-diffusive soot formation (SF) in a counterflow diffusion flame (CDF) are explored in a combined experimental and numerical study over pressures ranging from 1 bar to 6 bar. Experiments preserve the diffusive flame structure and carbon flux at increasing pressures and utilize measurements of soot concentrations, dispersion exponents and soot production rates. Numerical simulations are completed in OpenSMOKE++ with detailed \ce{C1}-\ce{C16} chemistry, lumped PAH consideration up to \ce{C160}, sectional soot model and tracking of the C/H ratio in particulates. Network-based tools are utilized to study the organization and evolution of carbon routing pathways. Results show that for equi-diffusive flames, soot concentration increases with residence time and pressure, whereas soot production rates are influenced only by pressure. Soot C/H ratio is observed to increase with pressure using numerical and experimental methods, but numerical solutions underestimate the increase in hydrogen abstraction reactions. The soot-forming network undergoes a percolation-like organization of its pathways before soot inception. The network then continues to grow by adding connections through its influential nodes. Acetylene is identified as a highly influential node in the carbon transfer graph, with its influence increasing with pressure.

Nucleation is a key rate-limiting process in phase transition and phase separation. Recent studies highlight a significant discrepancy between experimentally measured nucleation rates and theoretical predictions, particularly when dynamic structural reordering occurs along multi-step pathways. To bridge this gap, we develop a multi-shell model with a space-time-dependent order-parameter field to describe the reordering-nucleation process, where structural reorganization couples with the early growth of condensed clusters. Through stochastic simulations, we track the time-resolved evolution of heterogeneous structural order inside growing clusters. Path analysis of the first-passage problem in early-stage nucleation demonstrates that shifting the reordering rate alters the nucleation rate by several orders of magnitude. Furthermore, as the coupling strength increases, the relationship between the mean first-passage time and reordering susceptibility shifts from monotonic to non-monotonic, exhibiting a turnover effect. We quantitatively rationalize these behaviors with an effective nucleation barrier that accounts for non-equilibrium properties. Our findings elucidate the mechanisms behind multi-step nucleation and offer a predictive framework for future studies.

Intermolecular Coulombic decay (ICD) is a widely spread phenomenon in nature and laboratory in which the excess energy of a donor is utilized to ionize a nearby acceptor. If the excess energy is insufficiently large to enable ICD, two (or more) donors can collectively transfer their combined excess energy to ionize the acceptor. Experiments show that this collective ICD is, surprisingly, operative in gases. Recently, it has been demonstrated that standard ICD can efficiently take place at large distances between the donors and acceptors due to retardation. Here, we derive the theory of collective ICD including retardation. Quantum electrodynamics (QED) perturbation theory is used and it is shown that the theory can be substantially simplified and the process also made more amenable to interpretation by introducing two-body interaction potentials which include retardation. Explicit formulas for the rate of collective ICD are derived and interpreted by expressing the rate in terms of measurable quantities and geometric factors. It is demonstrated that the change of the permanent dipole moments of the species upon excitation is a relevant ingredient in collective ICD.

Absolute nuclear magnetic shielding constants and relative chemical shifts are second-derivative response properties that underpin the interpretation of Nuclear Magnetic Resonance (NMR) spectra and provide critical insights into the structural and electronic environments of diverse chemical systems. However, their accurate computation is often constrained by the need for method-specific, analytical response implementation, and therefore is particularly challenging for non-variational, correlated wavefunction methods where analytical second derivatives are frequently unavailable. Here we present a scalable framework that computes NMR shielding tensors through finite magnetic field differentiation of complex-valued, gauge-including atomic-orbital (GIAO) based self-consistent field (SCF) calculations. By combining hybrid MPI and OpenMP parallelization and resolution-of-identity (RI) approximation-based Coulomb (J) and Exchange (K) implementation and mixed numerical/analytical derivatives computational scheme, we achieve very good efficiency for hybrid density functional theory (DFT) NMR shielding, relative to existing state-of-the-art analytic implementations across realistic chemical systems of various sizes. Forward differentiation with optimal step sizes derived from rigorous error analysis retains favorable numerical errors much smaller than experimental uncertainty or intrinsic DFT errors. The results demonstrate that RI-accelerated finite magnetic field calculations can obtain DFT-level NMR shielding constants very precisely, providing a scalable foundation for extensions to more advanced quantum chemistry methods in future work.

Atomically precise gold nanoclusters are versatile for photocatalysis and energy conversion because their electronic structure stems from strong metal-ligand interactions. However, these interactions are mostly discussed statically, leaving dynamic reorganization of Au-ligand interfaces under photoexcitation unclear. We investigate rod-shaped [Au25(PPh3)10(SC2H5)5Cl2]2+ using ultrafast transient-grating spectroscopy, two-dimensional electronic spectroscopy, ab initio calculations, and hierarchical equations-of-motion simulations. The multidimensional spectra resolve multiple electronic relaxation pathways and a hierarchy of coherent structural motions, from localized Au-ligand distortions to collective framework vibrations. Wavelet analysis reveals that high-frequency Au-ligand vibrations emerge immediately after excitation, whereas low-frequency collective modes appear later through interstate vibronic coupling, indicating sequential redistribution of structural coherence. Simulations reproduce the nonlinear response and identify the microscopic vibronic couplings responsible. The results show that photoexcitation drives continuous ultrafast reorganization of the Au-ligand bonding network, transiently reshaping interfacial electronic structure before thermalization. This work establishes dynamic Au-ligand interfaces as the microscopic link between excited-state energy flow and photochemical function in atomically precise nanoclusters.

Chain scission is a key molecular process underlying damage and fracture in polymer networks. In this Letter, we develop a statistical-mechanical framework for predicting chain-scission kinetics while accounting for three-dimensional (3D) conformational fluctuations. Within transition-state theory, scission is formulated as a multichannel first-rupture problem, with bond-specific rates governed primarily by self-consistent potentials of mean force. In the freely jointed limit, the additional 3D configurational freedom enhances rupture relative to the collinear 1D reference. Finite bending stiffness introduces orientational correlations that can reverse this enhancement and, at high stiffness, reduce rupture rates by orders of magnitude. These correlations also make rupture bond-position dependent, with higher rates near the chain ends and a common interior rate. For sufficiently long chains, the interior contribution dominates, yielding linear scaling of the chain-scission rate with chain length. These molecularly resolved rates provide physically grounded inputs for future network-scale models of polymer damage and fracture.

Inspired by the chemical reaction network considered as the smallest system featuring a Hopf bifurcation and its reversible extension, we introduce an even more minimal reaction network that is thermodynamically consistent and exhibits autonomous oscillations under nonequilibrium driving. The model combines three features that are rarely realized simultaneously in compact oscillator networks: a chemically plausible structure restricted to uni- and bimolecular reactions, reversibility of such reactions, and analytical tractability. The system consists of three internal species coupled to two chemostatted species and still undergoes a supercritical Hopf bifurcation when a chemostat concentration is varied. To analyze the dynamics and thermodynamics near the onset of oscillations, we employ the mathematical technique of normal-form reduction, which allows obtaining a controlled irreversible approximation that preserves the leading phase-space structure of the full reversible network while enabling explicit calculations. This framework provides analytical access to the bifurcation structure and the leading contributions governing thermodynamic observables. Within this setting, we use the onset of oscillations to characterize the thermodynamic response of the system. In particular, we offer an analytical description of key thermodynamic quantities such as the semi-grand Gibbs free energy and the non-conservative work rate, which exhibit a kink-like discontinuity at the Hopf bifurcation. We thus provide an analytical description of a phenomenon previously characterized only through numerical simulations of more complex networks.

Kohn–Sham density functional theory (DFT) underpins electronic-structure simulations, but repeated orbital diagonalizations lead to cubic scaling, restricting quantum calculations to modest scales only. Eliminating these auxiliary orbitals while retaining Kohn–Sham accuracy is the central goal of orbital-free DFT, but both analytical and machine-learning methods have so far fallen short. Prior learning approaches either try to learn the variational kinetic-energy functionals, which are ill-conditioned, or directly predict the ground state, which extrapolate poorly to larger systems. Instead, we identify the Kohn–Sham map as the right learning target for orbital-free DFT. It maps a Kohn–Sham potential directly to the corresponding density and noninteracting kinetic energy, quantities otherwise obtained through an orbital diagonalization. Focusing on the density component in this work, a domain-invariant $\mathrm{SE}(3)$-equivariant Fourier neural operator learns to predict it from the potential as input on real-space grids, enabling stable quasi-linear scaling SCFs. Trained jointly on 8,504 molecules and solids, a single model generalizes to out-of-distribution organic molecules, insulators, and metals. For the first time, the same method converges SCFs across these systems without explicitly constructing Kohn–Sham orbitals, while reproducing densities, electronic spectra, and structural observables at Kohn–Sham DFT accuracy. Linear-scaling SCFs additionally allow converging magnesium dislocation densities containing up to 82,500 valence electrons on a single GPU.