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The chemical reaction critical point exponent
The principle of critical point universality is thought to govern critical phenomena in systems as disparate as ferromagnets, pure fluids, and binary liquid mixtures exhibiting a miscibility gap ending in a critical point of solution. The goal of any critical point theory is to determine how a given thermophysical property of interest depends upon the reduced temperature, t=(T−Tc)/Tc, where T is the thermostat temperature, and Tc is the critical temperature. Two theoretical formulations are available. The Landau mean field theory ignores fluctuations in composition in the critical region, while the mathematically more complicated Ising model takes fluctuations into account. The Landau and Ising theories agree, however, that certain of the thermophysical properties, ω, diverge in the critical region according to ω ∝ t−x as t → 0, where the value of x depends upon the property. In the Landau model, x assumes rational values, whereas in the Ising model, x assumes irrational values. In the majority of cases, the Ising model has been in better agreement with the experiment. Binary liquid mixtures with immiscibility gaps ending in a critical point of solution can be used as solvents in order to determine the critical effect in the extent, ξ, of a chemical reaction. With ξc serving as the critical value of ξ, some consensus exists in support of ξ−ξc∝tx, as t → 0. Otherwise, speculation prevails as to the value of x. Consistent with the universality principle, we find that the critical effect in the extent of the reaction, such as the shape of the liquid–liquid coexistence curve in the critical region, has its basis in the failure of phase stability. Pursuing this analogy, we note that the exponent governing the temperature dependence of ξ is x = 1/2 in the Landau model, whereas it is x = 0.3265 in the Ising model. Thermodynamic theory is exploited to distinguish the Landau/Ising limiting law, ξ−ξc∝tx, which prevails in the critical region, from the van’t Hoff background, which applies at temperatures removed from critical. The resulting equations are converted to dimensionless form and compared with data from homogeneous and heterogeneous chemical equilibria involving binary liquid mixtures as solvents.
Activated electron transfer at zero reorganization energy induced by a fluctuating donor–acceptor coupling
We study analytically and numerically a rate model for donor-to-acceptor charge transfer in the case of a fluctuating donor–acceptor coupling and of zero reorganization energy. The model applies to situations where the donor and acceptor reorganization energies are very low such that there is no polaron formation and the donor-to-acceptor transition arises purely from dynamic disorder in the coupling. We consider both quantum and classical limits for the reaction coordinate that modulates the coupling and describe the adiabaticity parameter for charge-transfer induced by coupling fluctuations, analogous to the Landau–Zener parameter used in the case of transfer induced by energy-level fluctuations. Our purpose is to explore the magnitudes of the charge-transfer rate for realistic parameter values, the transition from non-adiabatic to adiabatic transfer, and the behavior of the rate as a function of the donor–acceptor energy gap and temperature. We find that the coupling-fluctuation mechanism can lead to fast rates. Furthermore, the energy-gap and temperature dependencies can differ from Marcus theory describing polaron transfer. Therefore, these dependencies may be used to identify experimentally whether charge transfer is induced by coupling fluctuations.
Resonances of recurrence time of monitored quantum walks
The recurrence time is the time a process first returns to its initial state. Using quantum walks on a graph, the recurrence time is defined through the stroboscopic monitoring of the arrival of the particle to a node of the system. When the time interval between repeated measurements is tuned in such a way that the eigenvalues of the unitary become degenerate, the mean recurrence time exhibits resonances. These resonances imply faster mean recurrence times, which were recorded on quantum computers. The resonance broadening is captured by a restart uncertainty relation [Yin et al., Proc. Natl. Acad. Sci. U.S.A. 122, e2402912121 (2025)]. To ensure a comprehensive analysis, we extend our investigation to include the impact of system size on the widened resonances, showing how the connectivity and energy spectrum structure of a system influence the restart uncertainty relation. Breaking the symmetry of the system, for example time-reversal symmetry breaking with a magnetic flux applied to a ring, removes the degeneracy of the eigenvalues of the unitary, hence modifying the mean recurrence time and the widening of the transitions, and this effect is studied in detail. The width of the resonances studied here is related to the finite time resolution of relevant experiments on quantum computers and to the restart paradigm.
The quantum origin of magnetic coupling in molecular crystals for spintronics
Organic-based magnetic materials have attracted significant attention in recent years, particularly in the domain of spintronics. However, in order to realize viable spintronic-based technologies, high temperature coupling is a necessity. Understanding the physical exchange mechanisms that underpin the observed ordering in magnetic materials provides an effective tool to engage with this issue. In this report, a decomposition methodology is adopted to analyze the coupling in two metal phthalocyanine systems—cobalt (II) phthalocyanine (CoPc) and copper (II) phthalocyanine (CuPc)—and to extract the contributing exchange interactions. A dimeric molecular geometry is used to approximate the periodic chain structure, and the exchange interactions between the two magnetic centers are examined. The results of the study offer a more comprehensive insight into the physical mechanism underlying the observed exchange interactions and reveal the relationship between the electronic configuration and emergent magnetic properties of each respective system. More specifically, the coupling in CoPc is shown to be attributable to a dominant kinetic exchange interaction arising from the single occupation of a dz2-derived a1g molecular orbital, while in CuPc, an indirect spin polarization mechanism is found to underpin the weak exchange interaction. This study, therefore, demonstrates the validity of applying the decomposition methodology to a dimeric system and highlights its importance as a powerful tool to investigate the physical nature of magnetic interactions in molecular magnets.
A promising statistical approach for studying the collisional excitation induced by CO: Application to the CS–CO system
The calculations of rate coefficients for the interpretation of molecular spectra are a recognized computationally expensive task. This is particularly true for media like comets, where the dominant species (CO, CO2, and H2O) have relatively high masses. Currently, no clear methodology exists to treat the collisional excitation of heavy species at low temperatures, thus limiting the number of collisional studies on such species. We present here a promising statistical approach to determine collisional rate coefficients of heavy systems as an alternative to fully quantum calculations when heavy projectiles such as CO are considered. This is illustrated through the determination of the first rate coefficients for the collisional excitation of CS induced by CO of cometary interest. The CS–CO rate coefficients were computed up to 30 K, and the accuracy of the data was assessed by comparison with rate coefficients computed using the fully quantum time-independent close-coupling approach restricted to the minimal partial wave J = 0. The excellent agreement between the two sets of data demonstrates that the proposed method can be both fast and reliable to study the collisional excitation of molecules induced by CO at low temperatures.
Temperature dependence in the NEXAFS spectra of protonated and deuterated <i>N</i>-hexacontane isotopologues
This paper examines the temperature dependence of the Near Edge X-ray Absorption Fine Structure (NEXAFS) spectra of protonated and deuterated n-hexacontane isotopologues. We observe a distinctive low-energy broadening in the characteristic C–H band with a change from cryogenic to ambient sample temperature. We model this temperature dependence with density functional theory simulations of the NEXAFS spectra, calculated for geometries obtained from ab initio molecular dynamics simulations. Our results show that thermally populated nuclear motion leads to peak broadening as the sample temperature increases but that this nuclear motion broadening has significant overlap with vibronic transitions. An improved understanding of thermal broadening mechanisms is essential for the use of NEXAFS spectroscopy for chemical microanalysis, particularly where cryogenic cooling is used to reduce radiation damage.
Angular distributions of single-photon and above-threshold detachment of sulfur hexafluoride anions in femtosecond laser fields
We experimentally investigate the photodetachment of sulfur hexafluoride anions (SF6−) in 400 nm 35 fs laser fields using a home-built mass-selective anion source combined with electron velocity map imaging (VMI). The electron kinetic energy and the photoelectron angular distributions (PADs) are obtained from the VMI measurements. In addition to the single-photon detachment, two-photon above-threshold detachment (ATD), which is induced by strong laser fields with peak intensity higher than &gt;1.0×1013W/cm2, is clearly identified for the first time. By fitting the measured PADs, the partial-wave distributions of the detached electron are achieved, resulting in the coefficiency of the s-orbital (p-orbital) of ∼68.1%(∼31.9%) in the mixed s–p molecular orbital of SF6−, which is in good agreement with the ab initio calculations. The ponderomotive shift in the ATD channel is investigated and different behaviors for the strong-field photodetachment comparing with that in weak laser fields are discussed. The present study adds to our knowledge on the photodeachment of the SF6− anion and sheds some light on the dynamics of the interaction of polyatomic molecular anions with ultrafast strong laser fields.
On the functional dependence of transition-potential coupled cluster
Orbital relaxation of the core region is a primary source of error in the computation of core ionization and core excitation energies. Recently, Transition-Potential Coupled Cluster (TP-CC) methods have been used to explicitly treat orbital relaxation using non-variational molecular orbitals determined by reoccupation of orbitals optimized for a fractional core occupation. The amount of fractional occupation is governed by parameter λ, and recommended values for accurate TP-CCSD and XTP-CCSD computations of carbon, nitrogen, oxygen, and fluorine K edges were previously determined. Herein, we explore the performance of several density functionals for generating the fractionally occupied orbitals used in TP-CCSD. These functionals include HF, BP86, BH&HLYP, B3LYP, M06-2X, and ωB97m-V. The fractionally occupied orbitals computed across the various functionals were subsequently employed as the initial orbitals for our TP-CCSD calculations of organic K-edge x-ray absorption and photoelectron spectra. Regardless of the functional used to generate the fractionally occupied orbitals, the TP-CCSD calculations yield accurate and comparable core ionization energies, core excitation energies, and oscillator strengths.
Escape rate of a charge carrier from a semiconducting polymer chain
Charge carriers in amorphous semiconducting polymers diffuse rapidly along the polymer chains, hopping less frequently to neighboring chains. The escape time required on average to hop to a neighboring chain affects the design of new polymers and determines the relative importance of other system parameters such as polymer rigidity or polymer molecular weight. We provide a general expression for the escape rate, which lends itself to a more simplified and transparent expression in the limit of vanishing reorganization energy. The escape rate appears to be more sensitive to disorder and temperature than the intra-chain transport. We show how the parameters required for the evaluation of this rate can be derived from a combination of classical and quantum chemical models already used to characterize semiconducting polymers, and we provide an illustration based on two realistic polymeric materials.
Cotunneling assisted nonequilibrium thermodynamics of a photosynthetic junction
We theoretically investigate a photosystem II-based reaction center modeled as a nonequilibrium quantum junction. We specifically focus on the electron–electron interactions that enable cotunneling events to be captured through quantum mechanical rates due to the inclusion of a negatively charged many-body state. Using a master equation framework with realistic spectral profiles, we analyze the cotunneling assisted current, power, and work. Amplification of the cotunneling assisted current and power occurs over a narrower bias range, reflecting a trade-off where a higher flux is compensated by a reduced work window. We further report that the cotunneling-enhanced thermodynamic variables, particularly within specific bias windows, depend on the interplay between cotunneling amplitudes, electron transition rates, and interaction energy. Both attractive and repulsive electronic interactions can enhance cotunneling, but this effect is sensitive to the energy balance between states and the tunneling strength asymmetries.
Charge transfer at air–water interfaces: A machine learning potential-based molecular dynamics study
Water at interfaces plays a crucial role in many natural processes and industrial applications. However, the relationship between water’s hydrogen bonding and charge transfer characteristics at these interfaces remains poorly understood. Here, we develop machine learning potentials at near density functional theory accuracy based on datasets generated with ab initio molecular dynamics simulations, enabling us to explore the structure and charge transfer at air–water interfaces. Our simulations reveal a non-uniform charge distribution along the interfacial normal direction: water molecules in the outermost layer in direct contact with the air tend to be positively charged, while those in a thin sub-interface layer are negatively charged. We further demonstrate that this uneven charge distribution arises from the donor–acceptor asymmetry of H-bonds among interfacial water molecules. These findings provide a detailed atomic-level insight into the charge transfer behaviors of water at interfaces.
Driven polymer translocation through a nanopore from a confining channel
We consider the dynamics of pore-driven polymer translocation through a nanopore to a two-dimensional semi-infinite space when the chain is initially confined and equilibrated in a narrow channel. To this end, we use Langevin dynamics (LD) simulations and iso-flux tension propagation (IFTP) theory to characterize local and global dynamics of the translocating chain. The dynamics of the process can be described by the IFTP theory in very good agreement with the LD simulations for all values of confinement in the channel. The theory reveals that for channels with a size comparable to or less than the end-to-end distance of the unconfined chain, in which the blob theory works, the scaling form of the translocation time depends on both the chain contour length and the channel width. Conversely, for a very narrow channel, the translocation time only depends on the chain contour length and is similar to that of a rod due to the absence of spatial chain fluctuations.
Rational design of dual-atom δ5-borophene catalysts for nitrogen reduction reaction via density functional theory and machine learning
Electrocatalytic nitrogen reduction reaction (NRR) for synthesizing ammonia (NH3) is a promising strategy for sustainable NH3 production. Identifying appropriate NRR electrocatalysts is crucial for enhancing the efficiency and selectivity. Here, we employed density functional theory (DFT) and machine learning (ML) to investigate the performance of dual-atom catalysts (DACs) supported on δ5-borophene (δ5-BP) for NRR. Through four-step screening process and full reaction pathway calculations, we evaluated 23 homonuclear catalysts (MM@δ5-BP) and 21 stable heteronuclear candidates (MM∗@δ5-BP). The TiTi@δ5-BP and ZrZr@δ5-BP exhibited superior NRR catalytic activity with a limiting potential (UL) of −0.60 V among MM@δ5-BP, while NbHf@δ5-BP showed the lowest UL (−0.48 V) in MM∗@δ5-BP. We also investigated the influence of applied potential on the NRR through grand canonical DFT calculations. By constructing feature dataset and applying XGBoost Regressor (XGBR) and Gradient Boosting Regressor (GBR) algorithms with SHAP analysis, we achieved good agreement between ML-predicted UL and DFT-calculated UL. Our finding highlights the bonding interaction between two nitrogen atoms during N2 adsorption as the most critical feature. This work integrates DFT and ML approach to gain deep insights into complex dual-site activation and NRR mechanisms and to pave the way for accelerating the rational design of efficient DACs.
Effect of electron–phonon interaction on thermoelectric properties of a DNA molecule
We investigate the thermoelectric properties of a DNA molecule situated between semi-infinite contacts, taking into account the effects of decoherence. To represent the DNA molecule, we use two models: the fishbone model and the ladder model. Our approach employs a tight-binding method that utilizes Green’s function technique, as well as real-space renormalization and polaron transformation methods. We calculate the transmission probability using the Landauer–Büttiker formalism and analyze the thermoelectric properties of the DNA molecular system. We calculate the electrical conductance, thermal conductance, the Seebeck coefficient, the figure of merit, and the Lorenz number, all while considering the effects of decoherence. This study provides insights into understanding inelastic effects in nanoscopic molecular systems.
Wavefunction-based simulations of 2D electronic spectroscopy of conjugated polymers: Signatures of exciton transport and coherent vibronic dynamics at finite temperature
Spectroscopic signatures of exciton transport and vibronic coupling in two-dimensional electronic spectroscopy (2DES) are studied for an oligothiophene chain as a minimal model for intra-chain exciton migration in poly-(3-hexylthiophene). Generalizing our previous approach [Brey et al., Faraday Discuss. 237, 148 (2022)], a first-principles parameterized Frenkel Hamiltonian is combined with a collective high-frequency lattice mode and a set of ring-torsional modes whose thermal fluctuations drive exciton migration. A wavefunction-based quantum–classical treatment is employed, where quantum Langevin friction via the Kostin equation acts on the collective lattice mode, while the torsional modes evolve under a classical Langevin equation at finite temperature. Single wavefunction realizations exhibit largely adiabatic, diffusive exciton motion across the 20-site lattice under periodic boundary conditions. 2DES spectra are computed using the equation-of-motion phase matching approach (EOM-PMA) within a wavefunction setting. In line with experimental observations, a pronounced vibronic fine structure is observed, which is modulated by spectral diffusion due to fluctuation-induced changes in the exciton extension and localization.
Self-alignment and anti-self-alignment suppress motility-induced phase separation in active systems
In this article, we investigate the impact of self-alignment and anti-self-alignment on collective phenomena in dense active matter. These mechanisms correspond to effective torques that align or anti-align a particle’s orientation with its velocity, as observed in active granular systems. In the context of motility-induced phase separation (MIPS)—a non-equilibrium coexistence between a dense clustered phase and a dilute homogeneous phase—both self- and anti-self-alignment are found to suppress clustering. In particular, increasing self-alignment strength first leads to flocking within the dense cluster and eventually to the emergence of a homogeneous flocking phase. In contrast, anti-self-alignment induces a freezing phenomenon, progressively reducing particle speed until MIPS is suppressed and a homogeneous phase is recovered. These results are supported by scaling arguments and are amenable to experimental verification in high-density active granular systems exhibiting self- or anti-self-alignment.
Predicting the morphology of cobalt, copper, and ruthenium on TaN for interconnect metal deposition
Downscaling of metal interconnects has become a bottleneck in the back-end-of-line processing of CMOS semiconductor devices. The conductivity of the commonly used Cu metal drastically reduces at nanoscale, limiting its use as the devices shrink, as the metal starts forming non-conductive islands. This has led to the requirement for new interconnect metals such as Co and Ru, as they have a much higher tendency to form conductive films with horizontal growth at nanoscale. Understanding how the morphology of interconnects depends on the metals’ atomistic properties and their interactions at diffusion barrier layers is necessary to continue the rapid development of interconnects. In this study, we have used first-principles density functional theory (DFT) relaxations, ab initio molecular dynamics, and neural network machine learning potentials (MLPs) to investigate how the morphology of Cu, Co, and Ru differs on TaN substrates. We investigate the binding of single metal atoms and four atom clusters to obtain the metals’ substrate binding energy and metal–metal interaction energies. The morphology of the metals was then investigated by 15 ps molecular dynamics simulations with DFT and 5 ns with MLPs using larger metal structures that can display 2D and 3D morphologies. Comparing the binding energies with the obtained morphology allows us to demonstrate how the balance of metal–substrate and metal–metal interactions determines the morphology, while the MLP simulations allow longer timescale processes to be included. These insights help in the development of morphology predictors, allowing a rapid method for screening new interconnect materials with targeted horizontal growth on substrates used in semiconductors.
Machine learning meets su(n) Lie algebra: Enhancing quantum dynamics learning with exact trace conservation
Machine learning has emerged as a promising tool for simulating quantum dissipative dynamics. However, existing methods often struggle to enforce key physical constraints, such as trace conservation, when modeling reduced density matrices (RDMs). While physics-informed neural networks (PINN) aim to address these challenges, they frequently fail to achieve full physical consistency. In this work, we introduce a novel approach that leverages the su(n) Lie algebra to represent RDMs as a combination of an identity matrix and n2 − 1 Hermitian, traceless, and orthogonal basis operators, where n is the system’s dimension. By learning only the coefficients associated with the operators, our framework inherently ensures exact trace conservation, as the traceless nature of the operators restricts the trace contribution solely to the identity matrix. This eliminates the need for explicit trace-preserving penalty terms in the loss function, simplifying optimization and improving learning efficiency. We validate our approach on two benchmark quantum systems: the spin-boson model and the Fenna–Matthews–Olson complex. By comparing the performance of four neural network architectures—purely data-driven physics-uninformed neural networks (PUNN), su(n) Lie algebra-based PUNN (su(n)-PUNN), traditional PINN, and su(n) Lie algebra-based PINN (su(n)-PINN)—we highlight the limitations of conventional methods and demonstrate the superior accuracy, robustness, and efficiency of our approach in learning quantum dissipative dynamics.
Electronic structure theory with molecular point group symmetries on quantum annealers
Quantum computation has the potential to revolutionize quantum chemistry through major speedups in computation times and an exponential reduction in computational resources. Here, we combine the symmetry-adapted Jordan–Wigner encoding based on the full Boolean symmetry group Z2k with our new implementation of the Xia–Bian–Kais (XBK) method for improving the efficiency of electronic structure theory calculations on quantum annealers, particularly by reducing the number of qubits needed to achieve the same accuracy. By providing a more extensive symmetry-adapted encoding (SAE) than previous work, we are able to simulate molecules larger than those previously reported that have been studied using methods developed for quantum annealers and without using an active space. We calculated the potential energy surfaces of H2, LiH, He2, H2O, O2, N2, Li2, F2, CO, BH3, NH3, and CH4, with the largest molecule in the STO-6G basis set requiring 16 qubits with our SAE, and compared them with full configuration interaction results. The application of SAE to the XBK method provides an exponential reduction in the size of the Hilbert space and scales well with the size of the problem. It does not introduce significant additional errors for even or large values of a key variational parameter that determines the number of ancilla qubits used in the XBK method’s Hamiltonian embedding, or for certain molecules such as He2 and H2O. We provide an explanation for this behavior and a recommendation on the usage of our method. In addition, we briefly discuss the potential of extracting electronic excited states from our method.
Extending the information-theoretic approach from the (one) electron density to the pair density
Within the framework of chemical reactivity theory, information-theoretic descriptors have predominantly focused on global and local measures, while nonlocal descriptors beyond Shannon entropy remain largely unexplored. By extending the information carrier from the one-electron density to the two-electron distribution function (pair density), this work introduces information-theoretic descriptors rooted in both one-electron and pair densities. This broadens the scope of the information-theoretic approach (ITA) and introduces new types of ITA descriptors, notably the joint, conditional, and mutual ITA quantities. To elucidate the interaction between electron correlation and localization, we compute and analyze a suite of ITA descriptors for one-electron and pair electrons, including the Shannon entropy, Fisher information, and Rényi entropy, for neutral atoms ranging from helium (He) to argon (Ar). The results demonstrate how the pair-density ITA enhances the interpretation of electronic correlations and its connection to spatial localization.