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Onsager’s real cavity model near solid interfaces
We develop an extended Onsager real-cavity framework to describe the Casimir–Polder interaction of small molecules dissolved in dielectric liquids near planar interfaces. By analytically resolving the geometry of the cavity opening, we derive closed-form expressions that capture the modification of the interaction as the molecule approaches a surface and connect smoothly to the asymptotic medium-assisted limit. Using experimentally established dielectric functions for water, propanol, and PTFE together with accurate molecular polarizabilities for O2 and N2, we compute the full distance-dependent potential for representative molecule–liquid–surface combinations. The results reveal how local-field screening, cavity geometry, and material response jointly determine both the magnitude and shape of the interaction, including the characteristic transition between open-cavity (z ≲ zC) and closed-cavity (z ≳ zC) regimes. Beyond providing quantitative predictions, the framework offers an analytically transparent decomposition of dispersion forces in liquids, enabling a direct identification of the underlying physical contributions and an efficient exploration of parameter dependencies across different systems. The approach thus provides a useful baseline for interpreting dispersion interactions in complex environments within a continuum, local-field corrected description.
Molecular electron transfer in optical cavities: From excitonic to vibronic polaritons
Strong coupling between molecular excitations and quantized electromagnetic fields in optical cavities provides a powerful means to control the physical and chemical properties of molecular systems. Here, we study electron transfer (ET) dynamics in cavity-coupled molecules using the numerically exact hierarchical equations of motion method, which captures nonperturbative and non-Markovian effects beyond standard perturbative theories. We identify distinct resonance and collective effects associated with polariton formation and show that the ET rate saturates in the strong-coupling regime, a feature not captured by perturbative approaches. We further extend the cavity-modified ET model by incorporating the nuclear-coordinate dependence of molecular electric dipole moments, which gives rise to a three-body interaction involving molecular electronic and vibrational degrees of freedom and cavity photons. This vibronic polariton formation leads to non-monotonic, oscillatory dependencies of the ET rate on the light–matter coupling strength and cavity frequency, which we attribute to quantum interference among multiple transfer pathways. These findings establish cavity-modified electron transfer as a multichannel quantum process governed by the interplay of electronic, vibrational, and photonic degrees of freedom.
A simple, physically intuitive alternative for fitting temperature-dependent kinetic data
A new “global Arrhenius” approach for fitting temperature-dependent data, inspired by a dynamical Maxwell relation, is introduced as an alternative to the widely used Vogel–Fulcher–Tammann (VFT) and Arrhenius equations. The proposed form is general and provides a thermodynamically motivated description of temperature dependence in which all the parameters have a clear physical interpretation. To illustrate its utility, it is applied to temperature-dependent kinetic data, including diffusion coefficients, viscosity, and solution conductivity for a series of molecular systems, where it produces fits of comparable quality relative to the VFT and Arrhenius equations. Importantly, the resulting parameters exhibit systematic trends with molecular characteristics, e.g., alkyl chain length, enabling a direct physical interpretation of the driving forces of dynamics in terms of underlying thermodynamic properties.
Dataset distillation for machine learning force field in phase transition regime
Machine learning force fields (MLFFs) have emerged as powerful data-driven tools for atomistic simulations, enabling large-scale and complex atomic systems to be simulated with accuracy comparable to that of ab initio methods. However, MLFFs often suffer from low training efficiency in the phase transition regime, where structural fluctuations are significantly elevated. To address this challenge, we propose a Central-Peripheral Distillation (CPD) algorithm for training dataset distillation. By strategically integrating representative samples with critical corner cases, the CPD algorithm ensures that the distilled dataset retains maximum structural diversity. We validated the efficacy of the CPD method on the liquid–liquid phase transition of dense hydrogen. Results show that, with the CPD approach, only 150 configurations are sufficient to train a MLFF that can fully reproduce the structural and dynamical properties of liquid hydrogen in the vicinity of its phase transition regime. This work paves the way for high-fidelity labeling of the MLFF training datasets, for instance, by adopting high-level ab initio calculations beyond the standard density functional theory, thereby enhancing the predictive accuracy of MLFFs.
Modeling the coincident three-ion momentum imaging of diiodomethane photodissociation on reduced-dimensional potential energy surfaces
We present an efficient theoretical model to simulate observables in the time-resolved coincident three-ion Coulomb explosion experiment of diiodomethane. The model employs two degrees of freedom to describe the C–I bond breaking and the CH2I rotation during photodissociation and three degrees of freedom to describe the coincident CH2++I2++I2+ fragmentation during the subsequent Coulomb explosion. By solving the equations of motion, the photodissociation pathways are obtained on two-dimensional potential energy surfaces of the valence excited states of the neutral molecule, and the asymptotic momenta of the three ionic fragments are determined on the three-dimensional ground-state potential energy surface of the fivefold-charged cation. The photodissociation pathways are consistent with previous ab initio molecular dynamics simulations and indicate a CH2I rotational period of ∼340 fs. The theoretical time-resolved kinetic energy release and the correlation between the kinetic energy release and the angle between the two I2+ momenta show good agreement with experimental signals in part, reflecting and confirming the static CH2I2 state and the CH2I + I dissociation channels.
Geometric diagnostics of scrambling-related sensitivity in a Bohmian preparation space
Out-of-time-ordered correlators (OTOCs) provide algebraic diagnostics of operator growth and scrambling-related sensitivity, while Lagrangian descriptors (LDs) provide trajectory-based geometric diagnostics of finite-time phase-space structure. This article develops a preparation-space LD construction for localized Gaussian quantum states and compares it with semiclassical stability structures entering OTOC calculations. Motivated by Bohmian mechanics, the numerical diagnostic uses wavepacket-center (WPC) trajectories from direct wavepacket propagation. Gaussian preparations are labeled by parameters (q0, p0) representing initial center and mean momentum. The LD is evaluated on the induced preparation-space map (q0,p0)↦(qc(t),pc(t))=(⟨q̂⟩t,⟨p̂⟩t), where ⟨⋅⟩t denotes expectation at time t. The inverted harmonic oscillator provides an exactly solvable benchmark: WPC dynamics coincide with classical hyperbolic flow, and the preparation-space Jacobian is the usual stability matrix. The nonquadratic double-well potential V(q) = q4 − 2q2 is treated by split-operator propagation. The classical LD resolves the separatrix skeleton sharply, whereas the quantum WPC LD produces a smoother, preparation-dependent sensitivity landscape organized relative to the classical separatrix. Finite-time sensitivity maps compare classical and WPC final-time maps, including the canonical derivative ∂qc(T)/∂q0 relevant to semiclassical OTOCs. These results support preparation-space LDs as geometric companion diagnostics for semiclassical OTOC sensitivity, clarifying that an LD is neither an OTOC nor a universal limit of one.
Thermal conductivity of aligned polymers with kinks
The thermal conductivity of aligned polymer molecules can be exceptionally high along the alignment direction due to energy transport through strong covalent bonds. At the same time, it is highly sensitive to molecular conformation, varying by orders of magnitude as a result of gauche kinks. Here, we theoretically investigate phonon transport in kinked polymers by numerically evaluating thermal conductivity and interpreting the results in terms of phonon scattering from randomly distributed kinks. For strongly aligned polymers with restricted deviations from a linear backbone, we find that heat transport becomes superdiffusive at long lengths, with thermal conductivity scaling as κ ∝ L1/3. At shorter lengths, thermal conductivity exhibits non-monotonic behavior: it increases at very short scales due to ballistic transport of almost all phonons, then decreases at intermediate lengths due to the Anderson localization of most phonon modes. These results are consistent with experiments and molecular dynamics simulations, and they elucidate the microscopic mechanisms governing heat transport in polymers.
State-resolved vibrational dynamics of Ar–Kr+
We report a state-resolved study of ultrafast vibrational dynamics in the singly ionized heteronuclear dimer Ar–Kr using a femtosecond pump–probe reaction microscope. A linearly polarized pump pulse initiates the dynamics by ionizing the neutral dimer and preparing a coherent superposition of vibrational states on multiple electronic potential energy surfaces of Ar–Kr+. A time-delayed, circularly polarized probe pulse then induces further ionization and dissociation, allowing the evolving nuclear motion to be mapped onto the time-dependent kinetic-energy-release spectra of the fragments. The resulting time- and KER-resolved measurements reveal vibrational revivals at characteristic delays, each serving as a spectroscopic signature of a specific electronic state and exhibiting agreement with numerical simulations. Fourier analysis of the delay-dependent spectra further extracts the vibrational beating frequencies, which are consistent with established spectroscopic constants.
Active Brownian particles in quenched matrices
Active particles convert stored energy into directed motion and can display complex emergent behavior arising from non-equilibrium effects. In many cases, e.g., living cells, the environment is complex and heterogeneous. In this work, we investigate a two-dimensional system of soft active Brownian particles (ABPs) in quenched matrices. The matrix induces a clustering of the particles even at low density and activity. However, the nature of clustering is different in regimes of low and high activity. For low activity (Peclet number less than 10), the number of clusters increases with increasing activity and the size of the clusters decreases. The opposite is true for high activity (Peclet number greater than 50). We perform a percolation analysis using a Voronoi construction where the connectedness of empty space depends on the activity. As expected, the percolation threshold is higher for active particles (compared to passive counterparts) because they can push through the matrix. For a fixed time slice, a fraction of particles satisfy all four diagnostic criteria consistent with genuine fractional Brownian motion (FBM), including scale-free velocity correlations. Analysis of long trajectories shows that single particles display FBM-like dynamics for some stretches. Such a behavior is absent for passive particles in a matrix and for active particles without a matrix and suggests a possible physical origin for the particle-to-particle variability observed in single-particle tracking experiments in cellular environments. Polydispersity in the matrix particle size has a quantitative but not qualitative effect on the properties of the ABPs.
Elucidating the synergetic interplay between average intermolecular coupling and coupling disorder in short-time exciton transfer
Exciton transport in molecular aggregates is a fundamental process governing the performance of organic optoelectronics and light-harvesting systems. While most theoretical studies have emphasized long-time transport behavior, recent advances in ultrafast spectroscopy have brought into focus the short-time regime, in which exciton motion remains ballistic on femtosecond-to-picosecond timescales. In this work, we develop an analytical framework for short-time exciton dynamics in a one-dimensional lattice subject to both on-site energetic (diagonal) disorder and intermolecular coupling (off-diagonal) fluctuations. Utilizing the reciprocal-space analysis, we derive closed-form expressions for the first and second spatial moments considering both localized excitation and moving Gaussian initial conditions. Our analytical and numerical results show that, while the long-time dynamics are influenced by diagonal disorder, the short-time ballistic expansion is governed primarily by off-diagonal disorder. Crucially, we reveal a synergistic interplay between the average intermolecular coupling and the off-diagonal coupling disorder strength, demonstrating that they contribute equivalently to short-time exciton transport. Moreover, we integrate this generic disorder model with a realistic molecular system within the framework of macroscopic quantum electrodynamics, thereby providing a theoretical foundation for characterizing and optimizing ultrafast energy flow of disordered molecular aggregates in complex dielectric media.
Electronic orbital response to static magnetic fields. II. A general theoretical method
As a part of an ongoing project devoted to the development of theoretical foundations and computational methods for treating systems in external electro-magnetic fields, we present a new method here for dealing with magnetic fields of arbitrary strength and for arbitrary systems. The method is based on leaving the commonly used Coulomb gauge and instead introducing an operator gauge. We show that this method avoids the obstacles related with using the Coulomb gauge in combination with GIAOs (gauge-invariant atomic orbitals) as basis functions, i.e., complicated matrix elements and oscillatory behavior for non-magnetic terms. Moreover, our approach shares many features with the “Modern Theory of Magnetization,” which is based on the operator, ∇⃗k. However, our approach is not restricted to periodic systems and avoids many complications involved in the application of ∇⃗k. Our method is applicable for any system and field strength, and it readily provides an answer to the question of whether there is a surface/shape contribution to intensive magnetic responses for large systems. Test calculations on H2+ using a homemade ab initio program developed for small systems, and a simplified model for large systems, give mutually consistent and complementary results in support of our suggested approach, but not in complete agreement with results of GIAO calculations. We present a detailed analysis of this finding.
Nonadiabatic dynamics starting from reactant and transition state in luminol chemiluminescence
The role of the starting configurations in nonadiabatic dynamics is investigated, and it is found for the first time that the dissociation times of the surface hopping trajectories initializing with the reactant are much greater than those starting from the transition state; however, the two sets of chemiexcitation yields are almost the same within standard errors in luminol chemiluminescence. The significant singlet chemiexcitation yield is explained by the difference between the number of S0 to S1 excitations and S1 to S0 de-excitations, and the negligible triplet can be explained similarly. The substantial singlet chemiexcitation yield obtained via the trajectory surface hopping method is attributed to the existence of the chemiexcitation region, through which the intrinsic reaction path does not pass.
Partial oxidation of methane to methanol is made possible with metal monoxide anions
Previous calculations have shown that certain transition metal monoxide anions have an advantage in catalyzing the partial oxidation of CH4 to CH3OH, viz., MO− + CH4 → M− + CH3OH, because their anionic metal centers interact only weakly with the methanol product, thus preventing its over-oxidation to formaldehyde. In this study, the oxidation of methane to methanol by NiO− was demonstrated experimentally by cryo-trapping the neutral reaction products onto a substrate and then characterizing the eluded product via temperature-programmed desorption. This work both vindicates the previous calculations and presents a proof-of-principle example. Concurrent calculations showed this reaction to selectively form methanol to the detriment of other products.
Neural network based molecular structure retrieval from Coulomb explosion imaging data
Determining the structure and following the structural evolution of molecules undergoing chemical reactions is one of the key goals of ultrafast molecular physics and chemistry. Recently, Coulomb explosion imaging has emerged as a promising technique for imaging the evolving structure of individual molecules in the gas phase. However, its practical application to structure determination is hampered by the lack of suitable algorithms for directly retrieving the molecular structure from the measured fragment-ion momentum data. Here, we propose a scheme to solve the underlying inverse problem by employing neural networks to infer the initial atomic positions from the final ion momenta on an event-by-event basis. Using this scheme, we retrieve the structure of several polyhalomethane isomers from simulated Coulomb explosion imaging data with an average per-atom position error of ∼0.1 atomic units, i.e., to within 5% of the typical bond lengths. This development paves the way for an automated structure retrieval from Coulomb explosion data one molecule at a time, making it ideally suitable for analyzing pump–probe experiments where several products are formed that need to be distinguished.
Shadow Hamiltonian in molecular dynamics simulations: Against a possible suggested misuse of its physical meaning
Symplectic integrators are largely employed in MD due to their long-term stability and near conservation of invariants. Their numerical robustness can be rationalized by the existence of a shadow HamiltonianHsh, exactly conserved by symplectic integrators and expressible as an asymptotic expansion with respect to the integration time steps δt around the physical Hamiltonian H. In this work, we suggest not attaching any physical meaning to Hsh, based on theoretical analysis and MD simulations of a standard LJ system using the velocity-Verlet algorithm. We do not intend to optimize symplectic algorithms. Instead, we claim that the existence of Hsh cannot provide better observables to estimate statistical properties. For that reason, we will also examine the behavior of trajectories integrated with large δt that are always exact integrations of their corresponding Hsh(δt). To these trajectories, of course, we do not attach a physical meaning. Note that the stability of the energy cannot be enough to guarantee accurate estimates of statistical properties. Although symplectic integrators yield, within numerical accuracy, exact trajectories of Hsh, thermodynamic quantities derived from Hsh deviate from the physical ones when δt is too large. Indeed, the conventional kinetic temperature of H is wrongly estimated for large δt, while “shadow” temperature becomes unphysical for the same large δt, despite its exact meaning for Hsh. We conclude that Hsh lacks physical relevance for large δt, and the only remedy to perform simulations by standard integrators, such as the velocity-Verlet, is to use a short enough δt, in which case the estimated physical properties coincide.
Spectral convergence of sum-of-Gaussians tensor neural networks for many-electron Schrödinger equation
An improved version of the sum-of-Gaussians tensor neural network (SOG-TNN) architecture is presented for solving the many-electron Schrödinger equation for one-dimensional soft-Coulomb systems. Model reduction techniques are introduced to reduce the number of tensor-factorized bases under the SOG approximation of the kernel. The Slater determinant ansatz is employed so that the antisymmetric property of the wave function can be strictly preserved. Numerical results show that the SOG-TNN achieves high accuracy with remarkably small basis sizes. Robust spectral convergence with respect to the basis size is also observed, consistently characterized by a mixed algebraic-exponential model for the error decay. These findings validate that the SOG-TNN architecture provides an ultra-efficient and low-rank representation of complex multi-electron wave functions, shedding light on high-fidelity quantum calculations in larger-scale many-electron systems.
Surface and mass fractals in patchy particle aggregation
The fractal study plays an important role in predicting the properties of materials and the underlying growth mechanisms in self-aggregating systems such as colloids and proteins, since such systems form highly irregular, scale-invariant structures. In this work, we performed a simulation study of the aggregation of spherical patchy particles interacting via four irreversible patches arranged in a square geometry along with an isotropic potential whose interaction strength can be varied. Structural analysis shows that at low isotropic strengths, hexagonal lattices form, whereas at higher isotropic strengths, cubic structures are more prominent locally. The slopes obtained from the calculation of the structure factor revealed the presence of both mass and surface fractals. This was independently confirmed by calculating the mass fractal dimension from the cluster size distribution and the surface fractals from the surface roughness measurements of the cluster, revealing that both mass and surface fractals are possible in irreversible patchy particle systems.
Orthogonally constrained CASSCF framework: Newton–Raphson orbital optimization and nuclear gradients
In a recent work [S. Yalouz and V. Robert, J. Chem. Theory Comput. 19, 1381 (2023)], we introduced the foundations of an orthogonally constrained complete active space self-consistent field (OC-CASSCF) framework that produces state-specific molecular orbitals for mutually orthogonal multiconfigurational electronic states. In the present study, we extend this approach by incorporating a Newton–Raphson orbital-optimization scheme, for which we derive the analytical expressions of the orbital gradient and Hessian. Furthermore, we outline a practical route toward the evaluation of analytical nuclear gradients, enabling geometry optimizations within the OC-CASSCF formalism. Benchmark calculations on the three lowest singlet states of LiH and H2O molecules demonstrate a systematic improvement as compared to conventional state-averaged CASSCF, even when using modestly sized active spaces.
Finite-bath open quantum systems: Exact dynamics
In this study, we introduce a method for deriving exact master equations from the dynamical map for finite open quantum systems coupled to (in)finite reservoirs, using the principle of minimal dissipation. The exact dynamics of the central spin model, which models a finite-bath open quantum system, is developed for two interaction types: Heisenberg and stochastic pure-dephasing interactions. The Heisenberg interaction yields a novel phase-covariant quantum channel in the strong-coupling regime, offering a new platform for studying a range of quantum information protocols. The stochastic pure-dephasing interaction provides the microscopic derivation of the paradigmatic non-Markovian random telegraph noise (RTN) channel, establishing its quantum foundation and offering insight into stochastic couplings. We derive the closed-form master equations for both models. As a demonstration, we explore the thermodynamic performance of these systems as quantum batteries. A direct relationship between quantum heat current and charging power is revealed, and RTN quantum batteries are shown to have advantages in charge storage.
A reduced-cost third-order algebraic diagrammatic construction method based on state-specific frozen natural orbitals: Application to the electron-attachment problem
We have developed a reduced-cost non-Dyson third-order algebraic diagrammatic construction theory for the electron-attachment problem based on state-specific frozen natural orbitals. Density fitting and truncated natural auxiliary functions were employed to enhance computational efficiency. The use of state-specific frozen natural orbitals significantly reduces the size of the virtual space and provides a notable speedup over the conventional EA-ADC(3) method with systematically controllable accuracy. A perturbative correction for the truncated natural orbitals significantly reduces the error in the calculated electron affinity values. The method also shows sufficient accuracy in the case of non-valence correlation-bound anions, where the local approximation-based methods fail. The efficiency of the method is demonstrated by performing an EA-ADC(3) calculation with more than 1300 basis functions.