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Two-dimensional IR–Raman spectroscopy of vibrational polaritons: Role of dipole surfaces
Nonlinear spectroscopy provides a unique perspective to understand time-resolved molecular dynamics under vibrational strong coupling (VSC). Herein, equilibrium–nonequilibrium cavity molecular dynamics simulations are performed to compute the two-dimensional (2D) infrared–infrared–Raman (IIR) spectroscopy of liquid water under VSC. In conventional computational chemistry practices, accurate molecular spectra are often constructed by using an advanced molecular dipole or polarizability model to post-process molecular dynamics trajectories evolved under a computationally efficient potential. By contrast, this work highlights the necessity of employing a consistent dipole surface model in both cavity molecular dynamics (CavMD) simulations and spectroscopic post-processing. While utilizing inconsistent dipole models only mildly influences the linear polariton spectrum, it severely distorts 2D spectra in wide frequency regions. With a consistent dipole–induced-dipole model, compared to the outside-cavity molecular 2D-IIR spectrum, the cavity 2D-IIR spectrum splits the OH stretch band to a pair of polariton branches only along the IR (not Raman) axis, while fading molecular signals at other frequency regions. This work provides the foundation for employing direct CavMD simulations to construct 2D spectra of realistic molecules under VSC.
Generalized Einstein relations between absorption and emission spectra in the electric-dipole approximation
Recently, Ryu et al. showed that two broadened bands connected by a set of four Einstein-coefficient spectra for stimulated and spontaneous single-photon transitions will obey detailed balance at equilibrium if the spectra satisfy generalized Einstein relations. Here, quantum mechanical expressions for Einstein-coefficient spectra are obtained in the electric-dipole approximation using an intramolecular Boltzmann distribution and the quantized field operators in isotropic, dispersive media of Nienhuis and Alkemade [Physica B+C 81, 181–188 (1976)]. These expressions suggest relationships between Einstein-coefficient spectra and dipole-strength spectra. The electrodynamic relationship between the spectral density for electromagnetic energy and the spectral density for the square of the electric field is developed and used to define dipole-strength spectra in terms of conditional transition probabilities per unit time. These rigorously relate dipole-strength spectra to Einstein-coefficient spectra, thus establishing quantum formulas for dipole-strength spectra and new generalized Einstein relations between dipole-strength spectra. For transitions between two bands, the dipole-strength spectra depend on a single total dipole strength but replace Einstein’s degeneracy ratio and transition frequency with a change in standard chemical potential and a single underlying lineshape that is manifested differently in the four spectra. At equilibrium, the relations specify the Stokes’ shift between forward and reverse transitions. The relationships between dipole-strength spectra, spontaneous emission spectral densities, and stimulated transition cross sections depend on the refractive index, the dielectric constant, and the local field, but not on the derivative of the refractive index. The broadband relationships reduce to known relationships for narrow spectra inside materials and for line spectra in vacuum.
A new Fe(IV) superoxide: The perferrate isomerization re-examined
The perferrate anion [FeVIIO4]−, the elusive iron analog of permanganate, has been extensively investigated, yet key questions remain unresolved concerning its stability with respect to isomerization. A previous computational work had been unable to reproduce the stability trend between the peroxide and perferrate: [FeVO2(η2-O2)]− > [FeVIIO4]−. Herein, the manifold of possible structures is revisited, for the first time, using an MRCISD+Q/x2c-TZVP//CASPT2(25,17)/ANO-RCC-VDZP level of theory. Computationally, we not only reproduce the correct stability trend but also find that the most stable species is a cyclometalated superoxide [FeIVO2(η2-O2)]− (6B1 ground state), perferrate being less stable by +29.2 kcal mol−1. In parallel, gas-phase ions of [FeO4]− stoichiometry were generated via an alternative electrospray ionization-based approach and probed by collision-induced dissociation mass spectrometry, providing complementary evidence for the presence of O–O motifs in the experimentally generated ions, in agreement with the computational results.
Thermodynamic properties of Lennard-Jones fluids residing in two to five spatial dimensions
The thermodynamic properties and the microscopic structure of Lennard-Jones fluids residing in two to five spatial dimensions are discussed. Complementing literature data for one to three dimensions, molecular dynamics simulations are conducted in four and five dimensions. Thermodynamic properties are sampled over wide temperature and density ranges and used to develop accurate Helmholtz energy equations of state that are also adequate near the critical point. The influence of the number of dimensions n on the critical point, vapor–liquid equilibrium, bulk properties, microscopic structure, and second virial coefficient is analyzed. The results show that with an increasing number of dimensions, there is a remarkable loss of structure and a strong expansion of the state region with a gas-like behavior. This is a consequence of the rise of the critical density (for n ≥ 3) that is accompanied by an almost exponential increase of the critical temperature. In addition, a clear reduction of criticality is observed with a rising number of dimensions. Moreover, the second virial coefficient is shifted to higher temperature values as the number of dimensions increases. Based on the power-law scaling behavior of the critical exponent β, a simple estimate of an upper critical dimension nc of Lennard-Jones fluids is given for the first time, roughly confirming the prediction of the Ising model, being nc = 4.
The low-field effect in radical pairs: A zero-field singlet–triplet basis picture
We present a new formulation of the low-field effect (LFE) in spin-correlated radical pairs based on a zero-field singlet–triplet basis for the isotropic spin Hamiltonian. The aim is to provide a description that is both formally rigorous and mechanistically transparent, especially in the regime of weak magnetic fields such as the geomagnetic field. For the standard model radical pair containing a single spin-12 nucleus, we show that the usual electron singlet–triplet basis obscures the distinct dynamical roles of the hyperfine and Zeeman interactions. In a zero-field S–T basis constructed from the angular-momentum structure of the zero-field Hamiltonian, by contrast, the mechanism separates cleanly: isotropic hyperfine coupling mixes singlet–doublet and triplet–doublet states, whereas the weak-field Zeeman interaction mixes triplet–quartet and triplet–doublet states without directly introducing an additional singlet–triplet coupling. The LFE is, therefore, revealed as a sequential process in which a weak field unlocks access from a triplet-only manifold to a singlet-accessible triplet manifold, from which hyperfine-driven singlet–triplet interconversion can occur. We then generalize this picture to radical pairs with arbitrary isotropic hyperfine structures by identifying maximal, interior, and, when present, minimal triplet-only manifolds in the zero-field spectrum. Finally, we introduce a practical blockwise triplet-only state recruitment measure for the triplet-only zero-field state space made singlet-accessible by a weak field and show how this quantity depends on hyperfine symmetry, including the effects of equivalent nuclei. The resulting framework provides both a simple physical picture of the LFE and a general route for estimating its structural upper bound for arbitrary radical pairs.
Intrinsic structural factors and solvent effects on excited-state dynamics and photophysical properties of BIDP derivatives with dual-ESIPT units
When multiple excited-state intramolecular proton transfer (ESIPT) units are incorporated into a molecule, the excited-state dynamics become more complex and sensitive to both intrinsic structure and solvent environment. However, a systematic understanding of how intrinsic and extrinsic factors regulate these dynamics remains unclear. Herein, quantum-chemical calculations were performed to elucidate the effects of the number of ESIPT units, coupling position, symmetry, and solvent polarity on the photochemical behavior and photophysical properties of BIDP derivatives with dual-ESIPT units. The results show that structural symmetry alteration can significantly change H-bond strength and ESIPT efficiency, compared with other intrinsic factors. Topological analysis of the electron localization function along proton-transfer channels offers mechanistic insights into the reduction in proton-transfer barriers for excited-state molecules with mirror-symmetric structures. The DLPNO-STEOM-CCSD method enables accurate assessment of energies in different electronic states for the keto tautomer. Furthermore, calculated radiative and nonradiative decay rate constants support that emission from keto-form BIDP derivatives exhibits anti-Kasha characteristics. In addition, high-polarity solvents impede the ESIPT process by preferentially stabilizing the more polar enol structures compared with the corresponding transition state structures. We expect that this theoretical work will provide valuable insights into the design and development of photochromic materials featuring dual ESIPT units.
Solvation of the Ra2+ ion in ammonia and water. A hybrid density functional theory Born–Oppenheimer molecular dynamics study
We present a comprehensive theoretical investigation of Ra(II) solvation in water and ammonia micro-solvation environments using hybrid density functional theory Born–Oppenheimer molecular dynamics simulations. While other alkaline earth dications (Mg2+–Ba2+) have been extensively studied, Ra2+ remains poorly characterized due to experimental challenges. Our simulations reveal that Ra2+ exhibits exceptional aqueous solvation dynamics, with a broad first hydration shell (2.7–3.8 Å) showing large temporal coordination number (CN) fluctuations between 9 and 12 and short-lived coordination states. The calculated average Ra–O distance (2.92 Å) and CN (10.9) are in good agreement with EXAFS experimental data. In the ammonia environment, Ra2+ displays a similar but better-defined solvation structure, with a dominant tenfold coordination, longer coordination lifetimes, and rapid NH3 exchange. Comparative analysis across group IIA cations shows systematic trends: increasing cation size (M2+) correlates with longer M2+–L distances and more extended solvation shells, while structural flexibility at 300 K increases dramatically from Mg2+ to Ra2+, with Ba2+ and Ra2+ showing the closest structural analogy, consistent with their similar crystal ionic radii. This work provides fundamental reference data for radium solution chemistry and presents possible implications of the observed solvation differences between water and ammonia for radiochemical separation strategies, as well as the ability of Ra2+ to mimic the coordination properties of Ca2+ in biochemical environments.
SITH: A quantum-chemical framework for predicting bond destabilization in stretched molecules
Mechanical forces can selectively destabilize chemical bonds of molecular systems, particularly in biological and synthetic polymers. While experimental and theoretical methods have advanced our understanding of mechanochemical processes, predicting where energy concentrates within a molecule remains a significant challenge. To address this, we introduce SITH (Splitting Intramolecular Tension due to stretcHing), a novel method that decomposes the total electronic energy change of a stretched molecule into the contributions from its internal degrees of freedom—such as bond lengths, angles, and dihedrals—using numerical integration of the work-energy theorem. Unlike previous approaches that rely on harmonic approximations, SITH provides high accuracy and robustness for studying the distribution of energies of stretched molecules up to a first bond cleavage. Although SITH uses 3N-6 degrees of freedom for the energy decomposition, we show that it can work even for ring structures like prolines. We apply SITH to a dataset of tripeptides and demonstrate that glycine and proline exhibit significantly different energy distributions in their Cα–C backbone bonds under tension: proline requires less energy to be elongated, making it more prone to rupture, while glycine has the opposite behavior. These findings reveal intrinsic differences in mechanochemical susceptibility across amino acids, offering more accurate predictions of bond rupture in proteins and other (bio)polymers. SITH thus provides a powerful, interpretable tool for understanding energy distribution at the quantum level, with possible applications in mechanochemistry and force field validation.
Analytic gradients and geometry optimization for orbital-optimized pair coupled cluster doubles
We introduce a reusable geometry-optimization engine in PyBEST for analytic, gradient-driven molecular structure optimization, with particular emphasis on orbital-optimized pair coupled-cluster doubles (OOpCCD/AP1roG). The engine interfaces PyBEST with the geomeTRIC optimizer, combining analytic electronic-structure gradients from PyBEST with the translation–rotation–internal coordinate (TRIC) framework, step control, and convergence machinery provided by geomeTRIC. Specificially, we present the first implementation of analytic OOpCCD nuclear gradients within a Lagrangian formalism. Our approach and implementation are generally applicable to any seniority-zero wavefunctions that feature orbital optimization and allow for the evaluation of response one- and two-particle reduced density matrices. Owing to the seniority-zero structure of pCCD and the orbital stationarity of the optimized reference, the resulting gradient equations are compact, minimizing the storage of the full two-particle reduced density matrix, and avoiding finite-difference differentiation of wavefunction parameters. Validation on representative closed-shell systems shows that the OOpCCD-based PyBEST–geomeTRIC workflow converges robustly and reproduces reference equilibrium geometries and energies within tight tolerances. Most importantly, OOpCCD produces structural parameters that deviate by ∼0.02 Å (0.01 Å) for bond lengths or less than 1° for bond angles from CCSD(F12c)(T*) (MP2) reference structures.
Constrained Møller–Plesset perturbation theory for charge transfer states
We propose a constrained Møller–Plesset second-order perturbation theory (CMP2) that incorporates electron correlation into the constrained Hartree–Fock (CHF) framework. In CMP2, the CHF solution is employed as the reference state, and a common Lagrange multiplier is introduced for both the zeroth-order and constraint Hamiltonians, enabling the inclusion of correlation effects with minimal modification to existing MP2 implementations. Two schemes are developed for determining the Lagrange multiplier: (i) CMP2-i (iterative), which iteratively updates the multiplier until the MP2 electron density satisfies the constraint, and (ii) CMP2-s (single-shot), which performs a single MP2 calculation using a CHF reference that satisfies the constraint at the Hartree–Fock level. The methods are applied to an intramolecular charge-transfer reaction of the 1,3-dinitrobenzene anion radical. CMP2-s significantly reduces computational cost while reproducing relative energy profiles comparable with CMP2-i. In addition, adiabatic energy profiles obtained with configuration interaction calculations based on CMP2 (CMP2-CI) are in good agreement with those from extended multistate complete active space second-order perturbation theory (XMS-CASPT2), demonstrating that the present approach provides a practical and efficient extension of constrained electronic structure methods to the post-Hartree–Fock level.
Binary colloidal mixtures in near-critical binary solvents
The phase behavior of a single type of colloid C suspended in near-critical solvents is known to be very rich. Motivated in part by recent experiments [Kodger et al., “Composite colloidal assembly by critical Casimir forces,” arXiv:2602.12431 (2026)], we consider a mixture of two colloidal types C1 and C2 in a binary solvent close to its demixing critical point. We extend a mean-field description of a lattice model, previously used to investigate systems with a single type of colloid in two dimensions, to the binary colloid case in three dimensions. The model treats the system as a full four-component mixture. For simplicity, we choose C1 and C2 to be hard spheres with the same radius but with different affinities for one species, B, of the AB binary solvent. We show that intricate interplay between C1–solvent and C2–solvent interactions as well as solvent–solvent interactions and hard sphere packing drive significant changes in the topology of the colloidal phase diagram when the relative volume fractions of the two different colloid types change. The behavior of the two lines of triple points is particularly interesting. Our results can provide some insight into the control of the self-assembly process for colloidal “alloys” mediated by a near-critical solvent and, therefore, controlled by temperature in a reversible manner.
Fermionic mean-field dynamics for spin systems beyond free fermions
We introduce the fermionized time-dependent Hartree–Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan–Wigner transformation. fTDHF is formally equivalent to exact dynamics in the case of free fermions and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size and linearly with the time steps. We benchmark fTDHF against exact dynamics on three separate spin-1/2 models, representing adiabatic preparation of states with long-range correlations, disorder-driven observation of many-body localization, and particle production in the Schwinger model. For each of these systems, fTDHF is shown to reproduce the qualitative dynamics generated by exact evolutions while maintaining a simple physical picture due to its mean-field nature.
How do diluent-aggregates interactions affect the structure of colloidal systems in solvent extraction?
The structure and dynamics of extractant-based aggregates strongly influence metal ion extraction and third-phase formation in liquid–liquid systems. Here, classical molecular dynamics simulations were used to study aggregates composed of Eu(NO3)3, water, and the extractants DMDOHEMA or DMDBTDMA in two linear n-alkanes, n-heptane, and n-dodecane. Micelle organization and solvent interactions were analyzed through radial distribution functions and potentials of mean force. Polar and apolar micellar radii were similar for both extractants, but diluent penetration into the apolar region was greater in n-dodecane than in n-heptane. Extractant chains generally wrapped around the polar core, with orientations primarily driven by entropy, except for DMDBTDMA in n-dodecane, where stronger diluent–extractant interactions were observed. Penetrating diluent molecules are oriented roughly perpendicular to the micelle, following the same behavior as the extractant chains. These results reveal that the apolar regions of the aggregates are highly dynamic, with chain motions becoming nearly isotropic beyond the polar core. Solvent molecules readily penetrate the micelle interior, challenging the conventional view of reverse micelles as rigid, star-like structures. Overall, this study demonstrates how the interplay between the extractant and diluent governs aggregate structure and dynamics, offering molecular-level insights into the factors controlling ion extraction and third-phase formation.
Efficient simulation of non-Markovian path integrals via imaginary time evolution of an effective Hamiltonian
Accurately simulating the non-Markovian dynamics of open quantum systems remains a significant challenge. While the recently proposed time-evolving matrix product operator (TEMPO) algorithm based on path integrals successfully circumvents the exponential scaling associated with memory length, its reliance on layer-by-layer tensor contractions and compressions leads to steep scaling with respect to the system Hilbert space dimension. In this work, we introduce the effective Hamiltonian-based TEMPO (EH-TEMPO) algorithm, which reformulates the calculation of the Feynman–Vernon influence functional as an imaginary time evolution governed by an effective Hamiltonian. We demonstrate that this effective Hamiltonian admits a highly compact matrix product operator representation, enabling substantial compression with negligible loss of accuracy. Combining a one-shot global evolution with a backward retrieval approach, EH-TEMPO significantly reduces algorithmic complexity and is naturally suited for GPU acceleration. We benchmark the method by simulating the energy transfer dynamics in the 7-site Fenna–Matthews–Olson complex model and 4-site perylene bisimide model. The results demonstrate that EH-TEMPO achieves numerically exact accuracy with superior efficiency, delivering speedups of up to 17.5× on GPU hardware compared to standard CPU implementations.
Perspective of Fermi’s golden rule and its generalizations in chemical physics
This perspective provides a succinct history of Fermi’s golden rule (FGR), an overview of its derivation, assumptions, and representative forms. Major applications of FGR, mostly in the field of chemical physics, are reviewed. These illustrate the broad applicability and success of FGR. Ambiguities and open issues encountered in practical applications of FGR are clarified. Recent advances in generalizations of FGR and computational methods for practical applications are addressed.
Erratum: “Thermal and chemical control of emission and excited-state dynamics in non-(TMS)3P-derived InP quantum dots” [J. Chem. Phys. 164, 144702 (2026)]
Semiflexible ring polymers on active motor beds: Nonequilibrium dynamics and conformations
A semiflexible ring polymer on a motor-protein bed exhibits activity- and processivity-dependent rotational and conformational dynamics that are not captured by linear-chain behavior. Using coarse-grained Langevin simulations with bending elasticity, excluded-volume interactions, and stochastic motor attachment, stepping, and detachment, we vary activity (Péclet number), motor processivity, and chain stiffness to map the nonequilibrium response. The mean-squared displacement shows crossover dynamics, with semiflexible rings displaying subdiffusive-to-diffusive behavior at low activity and an intermediate ballistic regime at higher activity, while increasing flexibility shifts the short-time response toward a Rouse-like limit. Diameter autocorrelations exhibit damped oscillations associated with coherent rotation; the rotational frequency increases with activity and processivity, whereas the decorrelation time is nonmonotonic at high processivity. Fourier mode analysis identifies competition between the radius (k = 0) and elliptic (k = 2) modes as the origin of the nonmonotonic asphericity.
Extended Lagrangian molecular dynamics on vibronic surfaces in the nuclear–electronic orbital framework
Proton transfer is central to many processes of chemical interest. The simulation of proton transfer dynamics requires the inclusion of nuclear quantum effects, such as zero-point energy, nuclear delocalization, and tunneling. Herein, we introduce methods within the nuclear–electronic orbital (NEO) framework, where specified nuclei are treated quantum mechanically on the same level as the electrons, for the simulation of proton transfer dynamics. In particular, NEO density functional theory (NEO-DFT) is used to treat the transferring protons quantum mechanically, and the other nuclei are propagated classically on the adiabatic vibronic ground-state surface. We formulate a NEO extended Lagrangian molecular dynamics (NEO-ELMD) approach to incorporate the motion of the nuclear basis function centers during such simulations. Density matrix extrapolation and purification are introduced as a means to accelerate the NEO self-consistent field procedure at each time step by reducing the number of iterations required for convergence. We demonstrate the fidelity and efficiency of NEO-ELMD through comparisons with related dynamical methods for intramolecular proton transfer in malonaldehyde. We also use these accelerated techniques to simulate the nonequilibrium single and double proton transfer dynamics of proton-coupled electron transfer in much larger benzimidazole–phenol systems. This work provides a foundation for future methodologies to efficiently simulate proton transfer dynamics within the NEO-DFT framework while incorporating nonadiabatic effects between adiabatic vibronic states.
Inverse design and discovery of high entropy alloy catalysts for efficient oxygen evolution reaction
High-entropy alloys (HEAs) consisting of earth-abundant elements can serve as replacement for expensive, industrial grade catalysts, such as iridium dioxide IrO2, for oxygen evolution reactions (OERs). However, navigating the exponential configuration space of possible HEAs and unknown inverse structure–property relationship has hindered the development of HEAs for efficient electrocatalytic applications. In this paper, using OH adsorption energy as a descriptor of optimal catalyst property, machine-learning-based frameworks are utilized for discovering HEA catalysts. Each designed HEA is composed of 5 elements chosen from Mn, Fe, Co, Ni, Cu, Zn, and Mo specific to OER. Calculated theoretical overpotential for one HEA catalyst composed of MnCoNiCuZn is found to be ηtheor = 0.67 V. However, deviations from scaling results can be as high as 0.99 V when compared to explicit calculations. After screening more than 163 × 109 HEA configurations using a regression model, MnCoNiCuZn with a stoichiometric ratio of 2, 2, 8, 12, and 12 displayed the highest likelihood of positive OH binding energy/active sites. To investigate the intrinsic catalytic activity of the MnCoNiCuZn HEA in an operational OER environment, a computational hydrogen electrode model was constructed to represent the oxyhydroxide layer of OER catalysts, with the MnCoNiCuZn placed at the surface. Analysis indicates that upon consistent comparison, the most stable rutile IrO2 (η = 0.33 V) exhibits superior performance relative to the proposed MnCoNiCuZn catalyst (η = 0.57 V). However, the present methodology, which resulted in statistically favorable adsorption sites, could be successfully used to discover highly active sites within a compositional space.