Browse Articles

An exact approach for describing adsorption and catalysis of interacting species in lattice models

Lattice models provide a useful framework for studying the adsorption and catalysis of interacting species. For such systems, the mean-field and quasi-chemical approximations are widely used. At equilibrium, full enumeration of the grand-canonical partition function would allow for an exact solution to these problems. However, the combinatorial complexity confines this approach to small systems. In this work, we consider how large a lattice needs to be for full enumeration to yield a feasible solution for equilibrium systems. As representative applications, we consider adsorption isotherms and the rate of a catalytic bimolecular reaction for the case that the surface reaction is the rate-limiting step. In these applications, we show that full enumeration on appropriately chosen small lattices accurately reproduces the converged results of Monte Carlo simulations on much larger lattices. We find that the commonly employed mean-field approximation can be off by up to five orders of magnitude and the quasi-chemical approximation is also inaccurate, while results from full enumeration are exact and converged. Our results are promising for studies aiming to quantify surface phenomena from first principles. Moreover, the full enumeration approach can be extended to kinetics, making this approach feasible for both equilibrium and kinetic studies of surface phenomena.

Atomistic determination of bending rigidity in the HPV-16 capsid

The assembly of viral capsids emerges from local interactions between protein building blocks that collectively generate highly ordered shells with defined geometry and robust mechanical properties. However, a quantitative link between atomistic interactions and the macroscopic elastic parameters that determine capsid shape and rigidity has remained elusive. Here, we present an atomistic framework that bridges molecular interactions and continuum-scale mechanics in human papillomavirus type 16 (HPV-16). Using all-atom molecular dynamics simulations with umbrella sampling, we evaluate the potential of mean force governing angular deviations between neighboring L1 pentamers and extract both the preferred interaction angle and the associated bending modulus. We find a clear decoupling between spontaneous curvature of the capsid and bending rigidity. While the optimal interaction angle remains almost invariant across changes in pH and ionic strength, the bending modulus, which is an order of magnitude larger than any previous estimates, is strongly modulated by the electrostatic environment: protonation enhances angular stiffness at low ionic strength, whereas electrostatic screening suppresses this effect at higher salt concentrations. Our results identify inter-capsomer rigidity as a key determinant of capsid size and shape and provide a quantitative framework for linking specific protein–protein interactions to the emergent mechanical properties of self-assembled viral capsids.

60th birthday Carlos Vega Festschrift: Reality, dream or simulation?

Intrinsic structure and interfacial tension of the HDL/LDL water interface

The coexistence line between the high-density liquid (HDL) and the low-density liquid (LDL) phases of water lies in the supercooled, high pressure region of the phase diagram where water is metastable with respect to ice, relaxation is slow, and the low free-energy cost of forming interfaces between the HDL and LDL phases can lead to soft, fluctuating, and morphologically complex domains. These conditions make both the structure and the thermodynamics of the interface difficult to access not only experimentally but also in computer simulations. Here, we study explicit HDL-rich/LDL-rich coexistence in long simulations at constant temperature, volume, and number of water molecules in elongated cells that promote interface stability. Using a high 1:1:8 aspect ratio proved key to obtaining two stable planar interfaces that persist for the full simulation time of about 1.35 μs. These interfaces bound an HDL-rich slab containing transient LDL-rich droplets, while the surrounding LDL-rich phase contains a fluctuating population of ice-like crystallites. This complex morphology makes the pressure anisotropy inadequate for measuring the interfacial tension of the HDL/LDL boundary. An analysis based on capillary wave theory, including the intrinsic interfacial broadening, reveals instead a very soft boundary, with γ = 4.25 ± 0.25 mN/m. These results point to an HDL/LDL interface that is weak, structured, and easily distorted by the competing liquid and crystalline fluctuations present in this region of the phase diagram.

Förster resonance energy transfer, including transient coherent effects

We formulate the weak intramolecular coupling Förster resonance energy transfer theory in a form suitable for calculating the ultrafast non-linear response of molecular systems. This is done through a formally exact factorization of the time-dependent molecular statistical operator into the system and bath components. Combining this factorization with unperturbed environment evolution, we generalize the traditional Förster master equation for the state population probabilities into a complete master equation for the system’s reduced statistical operator. The traditional Förster theory applies in the limit where the intermolecular coupling is weak and the system–bath coupling is strong. Our derivation explicitly yields a time-nonlocal Förster-type master equation that remains valid even in the limit of vanishing system–bath coupling. The theory predicts a rapid initial coherent evolution of populations arising from a transient initial coherence-dependent term, which induces a “slippage” of the initial condition that persists during subsequent rate-controlled transfer. Comparison with exact numerical results confirms the clear improvement of the present generalization over earlier formulations of the Förster theory and delineates its range of validity.

Role of electron correlation on the adenine dimer interaction for non-equilibrium geometries: A benchmark quantum Monte Carlo study

The accurate description of non-covalent interactions is critical for understanding the structure, dynamics, and eventual function of biomolecules. The adenine dimer serves as a benchmark system for computational methods due to its role in nucleic acid structures and its rich conformational landscape. In this study, we employ benchmark diffusion quantum Monte Carlo (DMC) methods to investigate the relative energies and role of electron correlation on a set of adenine dimer conformations generated via a search of the potential energy landscape using the global optimizer algorithm. Relative DMC energies are compared against a wide range of density functional theory (DFT) approximation results. We find that although most of the DFT functionals perform well for low-energy structures, their accuracy varies significantly for higher-energy conformations, including stacked and T-shaped structures. A large fraction of the variation is due to the treatment of the van der Waals interaction. BLYP, B3LYP, and PBE0 significantly improve with added D4 dispersion, while the recent r2SCAN-D4 and ωB97M-V functionals show the least scatter and closest agreement with the DMC. These findings highlight the delicate nature of these interactions in biomolecular systems and provide guidance for simulations of their structure and dynamics and for the development of machine learned interatomic potentials.

Enhanced oxygen evolution reaction via the tunability of spin and electronic states in a flexible van der Waals membranous catalyst

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.

Evolution of the energy landscape for <i>n</i> -alkanes: <i>n</i> -C14H30 to <i>n</i> -C20H42

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.

Variational adaptive Gaussian decomposition: Scalable quadrature-free time-sliced thawed Gaussian dynamics

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: Quantum chemistry package for multireference perturbation theory calculations and its non-orthogonal extensions

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.

Density functional theory predictions of derivative thermodynamic properties of a confined fluid

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.

UV photodissociation rates and cross sections of the NaS molecule including diabatization and spin–orbit coupling

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.

Impact of the nuclear model and electron correlation on the parity-violation effects on the electric field gradient

In this work, the parity violation (PV) effects on the electric field gradient (EFG) at a four-component (4c) Density Functional Theory (DFT) level are presented. Such effects were studied previously [J. J. Aucar and A. F. Maldonado, Phys. Chem. Chem. Phys. 27, 7594 (2025)] at the Dirac–Hartree–Fock level in several chiral molecules. In the present study, we include electron-correlation effects at the DFT level with the PBE0 functional, as it was shown to give a good performance in the parity conserving (PC) part of the EFG as well as in the PC nuclear quadrupole coupling constant calculations. We study the basis-set convergence on the PV effects on EFG, improving the core region and adding s- and p-type tight functions to the nuclei under consideration. Finally, we also analyze nuclear-model effects, including a more realistic charge distribution of the nuclei under study through a relativistic point-coupling energy model, denoted as the DD-PCX nuclear model, and compare it with the widely used Gaussian charge distribution model. All these corrections improve the accuracy of calculations. Nuclear-model effects were found to be significant also for the PV effects in energy, and their impact must be studied for PV effects in other properties.

Modulating intermolecular interactions and vibrational energy transfer in energetic systems with external electric fields

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.

Harmonic-oscillator-referenced ring-polymer molecular dynamics. I. Practical computation of correlation functions

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.

Orbital angular momentum textures and currents in a discrete helix: Equilibrium and linear response

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.

Revisiting the electronic structure of PtO: Cryogenic photoelectron spectroscopy and relativistic insights

We investigate the electronic structure of PtO via cryogenic anion photoelectron spectroscopy combined with relativistic multireference calculations, clarifying long-standing ambiguities in the assignment of its low-lying electronic manifold. Vibrationally resolved spectra covering the low-lying states are obtained via 193 nm photodetachment and 400 nm velocity map imaging (VMI) of PtO− anions cooled to 13 K. The adiabatic and vertical detachment energies are measured to be 2.16 and 2.29 eV, respectively, in good agreement with relativistic SOC-NEVPT2 predictions within 0.12 eV. High-resolution VMI reveals a fine-structure splitting of 1008 ± 30 cm−1 in the X3Σ− ground state, quantitatively reproduced by SOC-NEVPT2 as a 959 cm−1 second-order spin–orbit splitting. The two components display nearly identical vibrational structure, confirmed by Franck–Condon simulations. At higher binding energy, an intense σ-detachment feature is observed at 3.27 eV, providing a decisive spectroscopic anchor for reassessing the electronic manifold. Together with theoretical results, this feature establishes that the band at 2.73 eV corresponds to the A1Δ singlet state rather than to a widely split 3Π-state manifold, as previously proposed. These results establish a revised, experimentally benchmarked electronic structure of PtO and demonstrate that cryogenic cooling combined with high-energy photodetachment is essential for resolving spin-orbit-coupled manifolds in heavy transition-metal oxides.

Bioelectrical regionalization of multicellular aggregates by microRNAs

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.

Singlet fission spin dynamics from molecular structure: A modular computational pipeline

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.

The rocky path of DFT into chemistry—Discussions at a symposium and reflections on a circular journey in honor of Axel Becke 1953–2025

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.