Machine-learning potentials (MLPs) extend the time and length scales of atomistic simulations, enabling the study of complex systems, such as electrolyte solutions. Yet most models face a tradeoff between accuracy, computational cost, and the ability to capture long-range interactions. Large foundation models promise generality but often come with substantial overhead and energy demands. In contrast, compact, system-specific models may offer a more sustainable path for large-scale simulations. Here, we benchmark the MACE architecture on aqueous sodium chloride (NaCl) solutions, systematically varying model size and the level of equivariance to assess their effect on accuracy, stability, and efficiency. We find that predictive accuracy of the investigated MLPs has little influence on key physical observables considered here but is crucial for stability, highlighting the potential of minimal, dedicated models for efficient simulations of electrolyte solutions.

Semi-empirical quantum-chemical methods such as extended tight-binding (xTB) models are widely used for large-scale simulations. Despite their popularity, their accuracy for transition-metal containing systems is lower than, for example, closed-shell organic molecules. In this work, we extend the Q-Chem-xTB framework with a geometric direct minimization (GDM) scheme for robust self-consistent convergence and Hubbard correction (+ U $$ U $$ ) to improve the description of local interactions and reduce self-interaction errors similar to those characteristic of density-functional theory calculations for transition-metal complexes. The Hubbard correction term is integrated self-consistently within the xTB Hamiltonian, allowing shell-specific U $$ U $$ values for each atom. The performance of Q-Chem-xTB+ U $$ U $$ is assessed for four benchmark sets of iron complexes, focusing on their spin-state energetics. Sensitivity and optimization analyses of the spin parameters show that parameter tuning alone cannot systematically reduce the error or consistently recover correct spin ground-state predictions across different datasets. In contrast, introducing the + U $$ U $$ correction yields significant error reduction and improved electronic linearity with respect to fractional occupation, demonstrating that the correction fulfills its intended role of reducing self-interaction error. However, the optimized U $$ U $$ values remain system-dependent, and the resulting improvements are only partially transferable. As a side effect, the + U $$ U $$ correction stabilizes the self-consistent field optimization by widening the HOMO-LUMO gap, thereby overcoming convergence instabilities of the conventional direct inversion of the iterative subspace (DIIS) scheme at low electronic temperatures.

We develop a reweighting framework to quantify the free energy difference between two equilibrium states of a strongly coupled open system at fixed temperature. For an open system described by the Hamiltonian of mean force (HMF), we show that the equilibrium free energy difference between two canonical endpoints can be written as exponential averages of the HMF shift, divided by an explicit factor built from the chi-squared divergence between the initial and final system marginals. These relations hold at the endpoint level and, under an explicit asymptotic-equilibration postulate, admit trajectory representations for protocols whose evolved system marginal reaches the prescribed final canonical endpoint. In this trajectory representation, the dynamics provide a route for generating samples from the final canonical endpoint. In the frozen-driving regime with a noninteracting reference, the equalities reduce to FEP-like expressions involving an environment functional and an explicit overlap diagnostic, with the Zwanzig formula recovered as a limiting case. We validate the approach on an open system coupled to an environment and evolved under overdamped Langevin dynamics, where conventional Zwanzig FEP suffers from poor phase-space overlap and slow numerical convergence. The finite-sampling tests show that the overlap factor can be reconstructed from the same samples entering the estimator, making the overlap burden directly observable. A multistage coupling ladder then decomposes this burden into local factors and provides direct comparison with recursive FEP, BAR, and MBAR.

We introduce a unified statistical framework for quantifying system-environment coupling by treating the interaction energy VSE as a stochastic variable. Using our proposed reference-particle decomposition, we derive exact, closed-form expressions for the mean and variance of VSE in terms of the single-particle density and correlation functions up to fourth order. These expressions are valid throughout all coupling regimes, from strongly coupled finite systems to the weak-coupling thermodynamic limit. They connect interaction-energy statistics directly to equilibrium structural information and provide a systematic route for evaluating coupling across open system-environment boundaries. We further show how the moment framework enters free energy constructions, including the Hamiltonian of mean force and the quasichemical-theory outer-shell contribution. When the relevant interaction-energy distribution is approximately Gaussian, the first two moments determine the corresponding second-cumulant free energy estimate. To validate our framework, we performed explicit Monte Carlo simulations of a Lennard-Jones system across a range of system sizes, generating reference distributions of the system-environment interaction energy VSE. We also performed independent empty-cavity Monte Carlo calculations to validate the quasichemical outer-shell specialization. We then applied our derived analytical formulas to predict these distributions and found excellent agreement in both the weak- and strong-coupling regimes. The results demonstrate that interaction-energy distributions and the associated thermodynamic contributions can be reconstructed from microscopic structural correlations.

Correction for 'Benchmarking DFT-based excited-state methods for intermolecular charge-transfer excitations' by Nicola Bogo et al., Phys. Chem. Chem. Phys., 2024, 26, 21575-21588, https://doi.org/10.1039/D4CP01866D.

Machine learning interatomic potentials (MLIPs) have revolutionized molecular simulations, but as they evolve, so does the demand for advanced computing architectures, particularly graphics processing units (GPUs). However, the high cost of GPUs limits accessibility, making it crucial to compare GPU and central processing unit (CPU) based MLIPs under practical conditions. This study examines two popular MLIPs: the GPU-accelerated multi-atomic cluster expansion model and the CPU-based Gaussian approximation potentials model, applied to a battery electrolyte system known for its complex properties. By focusing on these models, our study evaluates differences in computational performance, resource efficiency, and accuracy in reproducing experimental properties. This rigorous benchmark provides insights into the trade-offs between GPU and CPU-based approaches in molecular simulations.

We report an implementation of projection-based quantum embedding that combines periodic density functional theory in the CP2K code with correlated wavefunction calculations in the Q-Chem program. Using this interface, correlated wavefunction methods can be applied to a subset of the molecular orbitals, selected in an automated manner based on a user-defined list of nuclei, wth an embedding potential that provides electronic coupling to the remaining orbitals that comprise the environment. Our implementation uses exact projection, without the need for any level-shift operator, and is “pseudoperiodic” in the sense that periodic boundary effects are implicit in the orbitals used in the (non-periodic) wavefunction calculation. Convergence tests demonstrate that computed properties are faithful to the corresponding periodic quantities, provided that the high-level subsystem is spatially localized and small, relative to the periodic simulation cell. Spectroscopic examples for aqueous chromophores demonstrate converged results using a very limited subset of the water molecules in the simulation cell, decoupling the choice of excited-state method and basis set from the functional that is used to propagate ground-state ab initio molecular dynamics. Solvatochromic shifts for aqueous uracil are converged using equation-of-motion coupled-cluster theory, without the need for solvent molecules in the wavefunction calculation, and the embedded calculation captures solvent effects that are absent in gas-phase “microhydration” studies.

We present a self-consistent field framework for finite embedded quantum-chemical clusters with constant potential boundary conditions. The coupling is realized through an energy-independent self-energy commonly employed in quantum-transport calculations within the wide-band approximation. Starting from the corresponding non-equilibrium Green's function formalism, we derive an analytic expression for the one-particle density matrix update that can be incorporated into conventional Hartree–Fock and density functional theory. The resulting non-Hermitian self-consistent field equations are solved using adapted Pulay-type mixing schemes. Applications to a quasi-periodic hydrogen ring demonstrate that a finite fragment coupled through an optimized self-energy accurately reproduces the polarization response of the extended system, while calculations on a lithium cluster capture metallic charge transfer and fractional occupations under open-boundary conditions. The proposed framework establishes practical grand-canonical boundary conditions for finite quantum-chemical clusters and lays the methodological foundation for quantum embedding methods for electrochemical systems.

The excitation energy of intermolecular charge-transfer (ICT) states depends asymptotically on the distance between the donor and acceptor partners, and is strongly influenced by the electrostatic environment exposed by solvent molecules. Conversely, the transition dipole moment (TDM) of ICT states increases when donor and acceptor molecules are brought close together by applying hydrostatic pressure. In this work, we explore these effects with low-scaling excited-state electronic-structure methods based on density functional theory (DFT). In the first part of the study, we benchmark time-dependent (TD-)DFT and the ALMO-SGM orbital-optimized DFT method against experimental data. Results obtained with ALMO-SGM are systematically improved by more accurately modeling the electrostatic environment, whereas the performance of TD-DFT is deteriorated. ALMO-SGM results show little system dependence, whereas TD-DFT results vary significantly across systems. In the second part of our study, we investigate the effects of donor-acceptor separation on the TDM of ICT states with low-scaling methods. ALMO-SGM reproduces systematic changes in the TDM obtained by moving the donor and acceptor molecules far apart, whereas TD-DFT failed at times. Finally, we model the effects of hydrostatic pressure on a flavin-indole system, which was previously investigated experimentally. TD-DFT results depend critically on the quality of the exchange-correlation functional (XCF), whereas ALMO-SGM results remain consistent for different XCF parametrizations. Applying higher hydrostatic pressure pushes the donor and acceptor partners closer together, leading to a redshift of the excitation energy and an increase in the TDM of the ICT state. This result is consistent for three conformations of the flavin-indole dimer, and is compatible with experimental findings.

We present the Boston Open-Shell Transition Metal Complex (BOS-TMC) dataset, a set of density functional theory (DFT) properties for 159k experimentally characterized mononuclear transition metal complexes (TMCs) in multiple spin states with a range of formal charges derived from the Cambridge Structural Database (CSD). To curate this set, we carried out an iterative procedure to confidently assign overall TMC charge. From this information, we then obtained properties in up to three spin states, i.e., low-, intermediate-, and high-spin for 3d metals and low- and intermediate-spin for 4d and 5d metals, depending on compatibility with the metal electron configuration, for a total of 343.8k TMC/spin combinations. At odds with prior sets, we preserved experimental heavy-atom coordinates in these structures during optimization. We report all properties using PBE0/def2-TZVP single-point energies on these structures. We introduce a scheme for computing metal-spin-dependent atomization energies, which we report for each TMC. Alongside electronic energies, we report up to seven additional properties including: HOMO, LUMO, HOMO-LUMO gap, atomic partial charges, dipole moments, atomization energies, and spin-splitting energies for a total of over 2.9M TMC-associated properties. For a representative subset of over 10k complexes chosen based on size, we evaluate the sensitivity of computed properties to exchange-correlation (xc) functional choice from a set of twelve xcs spanning rungs of "Jacob's ladder", highlighting hotspots of TMC space that have the greatest uncertainty. In comparison to prior transition-metal datasets, BOS-TMC is both larger and more diverse in terms of charge and spin configurations and, as a result, more diverse in its range of properties. This dataset is expected to provide a high-fidelity foundation for machine-learning model development, DFT benchmarking, and exploration.

We assess the dielectrically consistent reference interaction site model (DRISM) as an implicit electrolyte framework for modeling the electrochemical double layer, and compare it with the Poisson-Boltzmann model and explicit molecular dynamics results from the literature. We use the gold-electrolyte interface as the main test case and analyze solvent and ionic density profiles, the differential capacitance, and the solvation contribution to CO adsorption. The results show a strong sensitivity to the Lennard-Jones parametrization of metal-ion and metal-water interactions. In particular, we find that the default Lorentz-Berthelot mixing rules are inadequate and lead to excessive Na + accumulation at the interface, which results in an increase of the differential capacitance at negative electrode potentials. We demonstrate that introducing pair-specific metal-ion parameters yields more symmetric charging behavior and provides greater flexibility. Our findings suggest that using pair-specific parameters, rather than relying on Lorentz-Berthelot mixing rules, improves the accuracy of the model and opens the way for future studies with this improved yet equally performant model.

The accurate description of metal-water interfaces is essential for understanding processes in heterogeneous catalysis, electrochemistry, and surface science. Capturing the delicate balance between electrostatic and charge-transfer interactions in these systems, while efficiently sampling configurations to locate minima or approximate thermodynamic ensembles, requires electronic-structure methods that are both accurate and computationally efficient. Density functional tight-binding methods have the potential to strike the right balance, and here we demonstrate how systematic parameter optimization within the GFN1-xTB framework improves the description of water-metal interactions. Using previously published reference data for five metals (Cu, Ag, Au, Pd, Pt) and their (100) and (111) facets, we explore various adsorption sites, orientations, and distances. Sobol sensitivity analysis identifies the most influential parameters for each system, which are then optimized to minimize errors in adsorption energies. This targeted optimization yields substantial accuracy gains, reducing root-mean-square errors by approximately 20-60%. The modified method provides reliable predictions for catalytic studies where the default parameterization can fail qualitatively. However, such improvements come at the cost of reduced transferability across systems and properties, emphasizing that parameter optimization must be carefully tailored to the specific chemical context.

A mechanistic paradigm for terpene cyclization driven by photocatalytic disproportionation of eosin Y in fluorinated alcohol media was discovered. By employing a 1:1 mixture of HFIP and PFTB, the neutral form of eosin Y (EH₂) undergoes efficient intersystem crossing to its triplet state, initiating hydrogen atom transfer (HAT) with ground-state EH₂. This generates two radicals, EH• and EH₃•, with EH• identified as the key species triggering polyene cyclizations. Spectroscopic and computational analyses revealed that hydrogen bonding with fluorinated alcohols stabilizes the otherwise unfavored open carboxylic acid form of eosin Y, enabling visible-light absorption and reactivity. The study clarifies the long-debated mechanism of eosin Y-mediated cyclizations, introducing a dual-radical generation strategy from a single photocatalyst molecule. These findings introduce a new paradigm in photoredox catalysis, offering a mild, selective, and sustainable approach to complex terpene synthesis and paving the way for broader applications in synthetic organic chemistry.

One approach to calculating electronic excited states treats both ground and excited states as single determinants, either by direct optimization or with the aid of constraints. In this work, we extend the theory of occupied-virtual orbitals for chemical valence (OVOCV) to analyze the orbital character of excitations computed in this way. An intermediate frozen state that is polarization-free is introduced to cleanly separate the primary excitation from the accompanying orbital relaxation of spectator orbitals. A variety of chemical examples are reported using the OVOCV excitation analysis on orbital-optimized density functional theory (OO-DFT) calculations, including charge-transfer excitations, core excitations and singly and doubly excited valence states. Orbital relaxation effects are typically collective, and can be as large as 4-5 eV (with roughly 0.1 e- promoted) in charge transfer states, and even larger in core excited states. OVOCV analysis differs from natural transition orbital (NTO) analysis; we show that direct use of NTOs can largely obscure the role of orbital relaxation in favor of the primary excitation.

Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.

Das Screening von Katalysatoren stellt eine anspruchsvolle Aufgabe für die computergestützte Chemie dar, da die große strukturelle Vielfalt von Oberflächen unter Operando‐Bedingungen mit hohen Anforderungen an die Genauigkeit der kinetischen Vorhersagen einhergeht. Einbettungsmethoden, die es ermöglichen den rechnerischen Aufwand auf die chemisch aktiven Bereiche zu konzentrieren, sind vielversprechende Werkzeuge, um ein Gleichgewicht zwischen Genauigkeit und Effizienz herzustellen. Für metallische Oberflächenkatalysatoren gestaltet sich die notwendige Trennung des Systems in einen aktiv behandelten Bereich und ein Umgebungssystem jedoch als technisch schwierig, da die Elektronen in der leitfähigen Oberfläche delokalisiert sind. Aus diesem Grund sind Studien, die das Potenzial von Einbettungsmethoden für das Screening heterogener (elektro‐)katalytischer Systeme untersuchen, bislang selten. In dieser Arbeit zeigen wir, dass einfache Einbettungsansätze zur Untersuchung metallischer Katalysatoren durchaus realisierbar sind, wenn i) der aktive Orbitalraum entlang der Reaktionskoordinaten konstant gehalten wird und ii) das zur Berechnung des Einbettungspotenzials verwendete nicht‐additive Austausch‐Korrelationsfunktional einen Anteil exakter Austauschwechselwirkung enthält, um Delokalisierungsfehler zu minimieren. Wir verifizieren diesen Ansatz anhand einer Auswahl offenschaliger und geschlossenschaliger Zwischenprodukte der CO 2 ‐Reduktionsreaktion, welche an verschiedenen Adsorptionsplätzen einer Cu(111)‐Oberfläche adsorbiert sind. Die Oberflächen sind durch Clustermodelle repräsentiert und zeigen, dass das Screening von Katalysatoren mithilfe von Einbettungsmethoden möglich ist.

We introduce a unified statistical framework for quantifying system-environment coupling by treating the interaction energy V_𝒮ℰ as a stochastic variable. Using a reference-particle decomposition, we derive exact, closed-form expressions for the mean and variance of V_𝒮ℰ in terms of the single-particle density and up to four-body correlation functions. When V_𝒮ℰ is approximately Gaussian, these two moments suffice to compute the free energy shift of the strongly coupled system. To validate our framework, we ran explicit Monte Carlo simulations of the full system-environment configurations across a range of system sizes, generating reference distributions of the interaction energy V_𝒮ℰ. We then applied our derived analytical formulas to predict these distributions and found excellent agreement in both the weak- and strong-coupling regimes.

We derive exact identities for open systems connecting two equilibrium endpoints without imposing microscopic reversibility, detailed balance (DB), fluctuation-dissipation structure, or local detailed balance (LDB) on the driven dynamics. The identities express the Hamiltonian of mean force (HMF) free energy differences through exponential moments and an explicit chi-squared overlap between the endpoint marginals. In the frozen-coupling regime, the HMF shift reduces to a bare-system increment and admits a trajectory-level heat-work-reference decomposition. The exact relations then reduce the problem to a scalar-action law. A maximum-entropy construction gives a Bessel-form scalar-action law, independent of the microscopic system, environment, and number of degrees of freedom at the level of the variational reconstruction. This law provides three outputs from the same sampled configurations: the HMF free energy difference, the endpoint-overlap burden, and a Hessian uncertainty estimate. Since many systems in biology, chemistry, physics and engineering violate the underlying assumptions of the standard Jarzynski identity, we validate the framework on a reduced-dimensional model with a non-Liouvillian, phase-space-compressing ramp followed by underdamped Langevin relaxation. The standard Jarzynski work estimator fails for this ramp because phase-space preservation is broken and no compensating Jacobian correction is included, whereas the present endpoint identities recover the exact HMF free energy difference, and the variational construction reproduces it within its local uncertainty.

Although organometallic complexes of the late 3d elements are known to undergo both one‐ and two‐electron reactions, their relative propensities to do so remain poorly understood. To gain direct insight into the competition between these different pathways, we have analyzed the unimolecular gas‐phase reactivity of a series of well‐defined model complexes [(Me3SiCH2)nM]− (M = Fe, Co, Ni, Cu; n = 2 – 4). Applying a combination of tandem‐mass spectrometry, quantum‐chemical computations, and statistical rate theory calculations, we find several different fragmentation reactions, among which the homolytic cleavage of metal‐carbon bonds and radical dissociations are particularly prominent. In all cases, these one‐electron reactions are entropically favored. For the ferrate and cobaltate complexes, they are also energetically preferred, which explains their predominance in the corresponding fragmentation experiments. For [(Me3SiCH2)4Ni]− and, even more so, for [(Me3SiCH2)4Cu]−, a concerted reductive elimination as a prototypical two‐electron reaction is energetically more favorable and gains in importance. [(Me3SiCH2)3Ni]− is special in that it has two nearly degenerate spin states, both of which react in different ways. A simple thermochemical analysis shows that the relative order of the first and second bond‐dissociation energies is of key importance in controlling the competition between radical dissociations and concerted reductive eliminations.

Obwohl metallorganische Komplexe der späten 3d‐Elemente dafür bekannt sind, sowohl Ein‐ als auch Zwei‐Elektron‐Reaktionen einzugehen, bleiben die relativen Neigungen dazu noch unzureichend verstanden. Um direkte Einblicke in die Konkurrenz zwischen den unterschiedlichen Reaktionspfaden zu gewinnen, haben wir die unimolekulare Gasphasenreaktivität einer Reihe wohldefinierter Modellkomplexe [(Me3SiCH2)nM]− (M = Fe, Co, Ni, Cu; n = 2 – 4) untersucht. Durch eine Kombination aus Tandem‐Massenspektrometrie, quantenchemischen Rechnungen und Simulationen auf Grundlage der statistischen Ratentheorie identifizieren wir verschiedene Fragmentierungsreaktionen, bei denen insbesondere die homolytische Spaltung von Metall‐Kohlenstoff‐Bindungen und die Freisetzung von Radikalen eine zentrale Rolle spielt. Diese Ein‐Elektron‐Reaktionen sind in allen Fällen entropisch begünstigt. Für die Ferrat‐ und Cobaltat‐Komplexe sind sie zudem energetisch bevorzugt, was ihr dominantes Auftreten in den entsprechenden Fragmentierungsexperimenten erklärt. Für [(Me3SiCH2)4Ni]− und insbesondere für [(Me3SiCH2)4Cu]− ist die konzertierte reduktive Eliminierung als prototypische Zwei‐Elektron‐Reaktion energetisch günstiger und gewinnt an Bedeutung. [(Me3SiCH2)3Ni]− weist als Besonderheit zwei nahezu entartete Spinzustände auf, die unterschiedlich reagieren. Eine einfache thermochemische Analyse zeigt, dass das Verhältnis der ersten und zweiten Bindungsdissoziationsenergie entscheidend für die Konkurrenz zwischen Radikalverlusten und konzertierten reduktiven Eliminierungen ist.