We summarize a recent symposium on density functional theory for electronic structure in chemical applications and honor a key contributor, Axel Becke. The theory of electronic structure is entirely quantum mechanical and, in its original wave function form, runs into mathematical and numerical problems due to high spatial dimensionality, as each electron adds three new coordinates. The approximate reduction of dimensionality in the form of density functional theory (DFT) was first proposed in the mid-1920s but took 40 years to be verified as possible in principle. The development of increasingly accurate functionals, expressing the electronic energy in terms of the density of the electrons, was initially driven by the physics community, but after a series of innovations, including (i) going from local to non-local exchange-correlation energy functionals and (ii) partial retention of exact exchange in terms of wave functions, there was a breakthrough in the early 1990s, and leading quantum chemists accepted DFT. The resulting improved ability to solve chemical problems by computation was rewarded with a Nobel Prize to Walter Kohn and John Pople in 1998. Given the many controversies surrounding the introduction of DFT into chemistry, a symposium was held at the Royal Swedish Academy of Sciences on November 7 and 8, 2024, to look back at the barriers and breakthroughs and identify the key contributors and their advancements. Axel Becke played a major role in bringing DFT into chemistry. We record the unique breadth and depth of the discussions at the symposium and the role of Becke, whose life ended a year thereafter.

We present a practical formulation of harmonic-oscillator-referenced ring-polymer molecular dynamics (RPMD) for the calculation of linear and nonlinear real-time correlation functions under quantum statistical conditions. The method is formulated as a direct extension of standard RPMD but incorporates three coordinated modifications aimed at observables for which a direct ring-polymer average is either inconvenient or strongly contaminated by internal-mode artifacts. First, the imaginary-time distribution is built from an exact harmonic oscillator reference rather than the primitive free particle Trotter factorization so that the exact harmonic canonical variance is already recovered at a finite bead number. Second, the real-time dynamics is centroid-anchored, ensuring that the slow collective mode evolves on the physical timescale while the internal modes remain statistically organized by the reference quadratic form. Third, nonlinear observables are reconstructed from the anchored linear correlation and sampled static moments through a Gaussian moment reconstruction. In the present work, this reconstruction is used primarily for canonical/Wigner-type correlation functions, while a Kubo mixed-moment reconstruction is retained as a special harmonic benchmark. The resulting scheme preserves the familiar ring-polymer workflow, is straightforward to incorporate into existing RPMD implementations, and provides a practical route to higher moments such as x(0)x(t)3 and related mixed correlations. We present the working formulation, implementation strategy, and benchmark structure for harmonic, mildly anharmonic, and strongly anharmonic quartic model systems.

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.

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.

Time-slicing has emerged as a strategy for incorporating semiclassical propagation into real-time path integral formulation and recovering full quantum dynamics. A central step is the decomposition of a time-evolved wave function into a superposition of Gaussian wave packets (GWPs). Here, we introduce a quadrature-free variational framework for GWP decomposition, reformulating it as an optimization problem in which the GWP parameters are chosen to maximize the overlap with the time-evolving wave function. An autoencoder-decoder neural network is used for this optimization, with the representation being adaptively reoptimized during propagation. Each wave packet in this decomposition represents a localized patch of the underlying semiclassical manifold, while retaining full correlations between all degrees of freedom. This variational adaptive Gaussian decomposition (VAGD) approach yields a compact Gaussian expansion, providing a scalable route to time-sliced semiclassical quantum dynamics. While general, applying VAGD to facilitate time-slicing of thawed Gaussian dynamics allows a route to improving the semiclassical treatment to the full quantum mechanical result in a systematic manner.

NOPT is an ab initio package for calculations using Non-Orthogonal methods and multireference Perturbation Theory. It can be used both as a ready-to-use quantum chemistry program and as an open-source system for modifying existing methods and developing new ones. The key functionality includes restricted Hartree-Fock, configuration interaction with single excitations, complete active space self-consistent field, and several multireference perturbation theory (MRPT) methods. The MRPT module provides extended multiconfigurational quasi-degenerate perturbation theory (XMCQDPT2), multipartitioning perturbation theory (MPPT2), and a novel variant of uncontracted MRPT-CDAS-PT2. NOPT allows one to perform a complete computational workflow starting from a molecular geometry. It also contains an interface for using data calculated by other quantum chemistry programs. The implemented non-orthogonal methods are aimed at the fragment-based calculations with multireference wave functions. All the methods are implemented with the resolution of identity approximation to gain higher performance. We hope that this makes NOPT a useful tool for the calculations with both standard and novel methods of quantum chemistry.

We theoretically explore how microRNAs (miRNAs) can modulate the expression of ion channel proteins and the resulting cell membrane potentials in multicellular aggregates. To this end, we simulate the spatiotemporal regionalizations that characterize experimentally instructive bioelectrical states. Instead of focusing on a particular biological system, we consider a simple but illustrative biophysical model for the interplay between genetics and bioelectricity at the single-cell level. At the multicellular level, the assumed intercellular connectivity can establish spatiotemporal patterns of coupled bioelectrical and transcriptional states. The resulting distributed control exerts a significant influence on protein expression in multicellular aggregates, establishing instructive maps for development and regeneration. The system dynamics are simulated in spatially inhomogeneous aggregates under different miRNA production rates and intercellular connectivity. The results allow a qualitative understanding of the context-dependent effects observed when signaling biomolecules are spatially regionalized and transferred through intercellular junctions under the influence of multicellular electrical potentials.

Perovskite transition metal oxide membranes with exact chemical composition and ordered lattice structures facilitate atomic-level catalytic mechanisms in diverse electrochemical processes, thus aiding in the development and design of potential catalysts. Nevertheless, the puzzling ascendancy of spin in the oxygen evolution reaction (OER) process remains an enigma owing to the robust correlation between TM 4d and oxygen 2p orbitals. Herein, we employed SrRuO3 (SRO) with 4d electron states as a ferromagnetic catalyst for the OER, which were deposited onto the flexible mica substrates. By applying compressive or tensile stresses to the SRO film, the bipolar enhancement of OER activity was observed. At the potential of 1.8 V, the current density (j) of SRO enhanced by ∼34% or ∼44%, with a 0.2% compressive or tensile strain, respectively, attributing to the diminished chemisorption of Ru-O. In addition, it was found that j enhanced by ∼86% or ∼104% and the overpotential reduced by ∼20% or ∼26% at a 0.2% compressive or tensile strain with a 13 kOe in-plane (IP) magnetic field, respectively. Those were attributing to the enhancement of the double exchange effect and the concentration of O22- in SRO, thus promoting electron transfer and regulating the adsorption/desorption capacity of reaction intermediates, respectively. Moreover, the magnetohydrodynamic-induced bubble effect is one of the factors that enhance the electrocatalytic activity. This investigation offers experimental evidence to comprehend the regulation of spin degree and electronic state during OER, hence advancing the design and engineering of the flexible magnetoelectrochemistry catalysts with encouraging prospects.

Singlet fission (SF), which has applications in areas ranging from solar energy to quantum information, relies critically on transitions within a multi-spin manifold. These transitions are driven by fluctuations in the spin-spin exchange interaction, which have been linked to changes in nuclear geometry or exciton migration. While simple calculations have supported this mechanism, to date, limited efforts have been made to model realistic fluctuations, which are informed by the actual structure and properties of physical materials. In this paper, we develop a modular computational pipeline for calculating SF spin dynamics by way of electronic structural calculations, molecular dynamics, and numerical models of spin dynamics. The outputs of this pipeline aid in the interpretation of measured spin dynamics and allow us to place constraints on geometric fluctuations, which are consistent with these observations.

Based on previously reported high-accuracy electronic states of the ΛΣ presentation, we calculate the temperature-dependent photodissociation cross sections and rates of the NaS molecule in the ultraviolet region. The calculation includes transitions from the ground state X2Π to several excited electronic states, up to 12Δ. Particular attention is given to the nonadiabatic couplings between the 22Π-32Π and A2Σ+-22Σ+ states and their influence on the photodissociation dynamics. Spin-orbit coupling among the avoiding crossing electronic states and the ground state as well as the nonadiabatic couplings are incorporated through diabatic representation. Photodissociation cross sections obtained from the coupled channel calculations are compared with adiabatic results that include only spin-orbit coupling. The results show that nonadiabatic interactions significantly modify the cross sections near the avoided crossing regions and induce the pronounced Feshbach resonances. Using the local thermodynamic equilibrium cross sections, photodissociation rates of NaS are further evaluated under the standard interstellar radiation field and blackbody radiation fields. The rates show a relatively weak dependence on the molecular temperature. These results provide useful data for astrochemical modeling of NaS in ultraviolet radiation environments.

Fluids in nanopores are of importance for many engineering applications, including energy storage in supercapacitors, hydrocarbon recovery from unconventional sources, or water desalination. Thermodynamic properties of fluids confined in nanopores differ from the properties of the same fluids in bulk. Density functional theory (DFT) has been widely used for modeling the thermodynamics of confined fluids. However, it is rarely used for calculations of derivative thermodynamic properties. Here, we use a rather simple DFT model for argon based on the Percus-Yevick equation and show that with standard parameterization, it fails to predict derivative properties. However, a slight adjustment in parameters leads to quantitative predictions of isothermal compressibility and thermal expansion coefficient at a selected temperature. Using the adjusted parameterization, we performed the calculations of compressibility of argon confined in carbon slit pores of various sizes and demonstrated that the compressibility of argon in confinement is lower than that in bulk and is pore size dependent. We confirmed the DFT predictions using the Monte Carlo molecular simulations. In addition to isothermal compressibility, we calculated the thermal expansion coefficient of confined argon. Our calculations showed that it behaves similarly to compressibility-it is always lower than the bulk value and gradually increases for smaller pore sizes. For several selected pore sizes, we verified the DFT calculations by Monte Carlo simulations. Overall, our results suggest that the classical DFT can be utilized for calculations of derivative thermodynamic properties of confined fluids, which are computationally challenging to predict using molecular simulations.

Recently, nonequilibrium orbital angular momentum in low-dimensional systems has attracted renewed attention. Here, we introduce a minimal three-orbital tight-binding model for a single helical chain and show that chirality alone generates a momentum-dependent orbital-angular-momentum texture through Slater-Koster hybridization in the local basis (pr, pϕ, pz), without requiring atomic spin-orbit coupling. In the single-helix geometry, the radial orbital texture vanishes identically, while the azimuthal and longitudinal components remain finite and arise from the odd-in-momentum (pz, pr) and (pr, pϕ) sectors. As a result, the equilibrium average orbital texture vanishes by parity, although persistent-like orbital angular momentum currents may still exist and imply chirality-dependent end magnetization in a finite helix. Under an applied longitudinal electric field, the system develops a finite orbital Edelstein response, whereas the projected longitudinal orbital conductivity vanishes in the linear regime by parity. When spin degrees of freedom are included, the orbital texture acts as a source of spin polarization through orbital-to-spin transduction. Instead of being limited by the weak, natural spin-orbit coupling of individual atoms, the overall spin response is driven by the much stronger interactions of overlapping molecular orbitals, making it a stronger candidate for spin injection than the conventional spin Edelstein mechanism. These results identify chirality as the minimal microscopic ingredient for generating orbital angular momentum response in one-dimensional systems and support an orbital route to spin selectivity in chiral conductors.

The controllable application and property modulation of energetic materials is a long-standing challenge, as their macroscopic behavior fundamentally depends on structures formed by microscopic intermolecular interactions and the accompanying vibrational energy transfer (VET). Here, we present the regulatory capability of external electric fields (EEFs) toward intermolecular interactions and VET in energetic systems. First-principles structural studies confirm that EEFs applied parallel or antiparallel to the system dipole reshape binding properties by modulating intermolecular interaction contributions. Furthermore, first-principles molecular dynamics simulations reveal that fields aligned with the dipole promote vibrational energy accumulation on intermolecular N-N trigger bonds. This phenomenon, driven by field-induced reshaping of potential energy surfaces, is evidenced by short-time Fourier transform VET spectra of excited C-H vibrations. Our findings highlight that EEFs can manipulate intermolecular interactions by influencing molecular dipoles at the atomic level, thereby providing a potential feasible pathway for property modulation in energetic molecular systems.

Unbranched n-alkanes provide useful models for investigating how conformational complexity evolves with chain length. In this work, we examine the energy landscapes of n-C14H30 to n-C20H42 with a Δ-corrected transferable many-body permutationally invariant polynomial potential, explored with the Cambridge Energy Landscape software. Basin-hopping global optimization was used to identify low energy minima, and discrete path sampling was employed to construct kinetic transition networks connecting the conformational families. We find that the lowest energy family changes systematically with chain length: extended all-trans structures are most favorable for n-C14H30, hairpin structures are favored for n-C15H32 to n-C17H36, and a more compact folded conformation becomes the global minimum on the MB-PIP surface from n-C18H38 onward. Additional DLPNO-CCSD(T1)-F12 calculations suggest that the hairpin conformer is actually more stable for these longer chains, but the compact conformations are still relevant. Analysis of the pathways connecting representative minima reveals that interconversion proceeds through multistep paths that become increasingly complex with chain length. Disconnectivity graphs further reveal competing low energy funnels, indicating that increasing chain length reorganizes, not only relative stability, but also the underlying landscape. For n-C18H38, we further analyzed first-passage times and heat capacity signatures to characterize the kinetic and thermodynamic features of the multifunnel organization. Relaxation to the global minimum occurs over a broad range of timescales, and a low-temperature heat capacity feature arises from configurational redistribution among competing low energy minima and funnels. Overall, this study provides a detailed picture of how folding behavior, landscape organization, and the associated kinetics and thermodynamics evolve with chain length in n-alkanes.