Constant-potential molecular dynamics is essential for realistic simulations of electrochemical interfaces under Operando conditions. Although various constant-potential frameworks exist, most are tightly coupled to specific electronic-structure codes or numerical architectures, limiting portability and extensibility─especially for codes constrained to integer electron numbers. Here, we present a flexible constant-potential framework implemented in the i-PI driver, interfacing with multiple density functional theory (DFT) engines and, in principle, extensible to constant-potential machine-learning potentials. The method regulates and samples the electronic chemical potential by introducing an explicit electronic degree of freedom and a dedicated potentiostat module in i-PI. To bypass the integer-electron constraint without modifying the underlying DFT code, we employ a mixed-Hamiltonian interpolation scheme: two adjacent integer-charge clients are run in parallel, and their energies, forces, and electronic chemical potentials (Fermi level/work function) are linearly interpolated to obtain an effective fractional-charge description. We validate the method on a one-dimensional asymmetric double-well model and an Al(111) surface, demonstrating stable potential control and well-behaved charge fluctuations. Finally, we couple constant-potential ab initio molecular dynamics (AIMD) with enhanced sampling to study CO2 reduction on NiN4-doped graphene, enabling efficient characterization of potential-dependent reactivity and free-energy landscapes. Overall, this framework provides a portable and scalable platform for conducting rigorous constant-potential simulations across diverse electronic-structure clients and, in principle, machine-learning potentials.

We present an implementation for the calculation of K-edge resonant inelastic X-ray scattering spectra based on time-dependent density functional theory in the CP2K package. The method evaluates the Kramers-Heisenberg cross section from transition dipole moments connecting the ground state, core-excited intermediate states, and valence-excited final states. The present implementation combines the existing linear response time-dependent density functional theory modules (XAS-TDP and TDDFT) within a unified framework. The resulting approach is computationally efficient and well suited for condensed-phase applications in combination with ab initio molecular dynamics. The implementation is validated against experiment and established reference calculations for gas-phase water and methanol at the oxygen K-edge. Its applicability to realistic condensed-phase systems is then demonstrated for crystalline kaolinite at the oxygen K-edge, and for aqueous ammonia at the nitrogen K-edge, where representative configurations are sampled from ab initio molecular dynamics trajectories.

Ultrafast charge transfer (CT) lies at the heart of molecular and electronic functionality. We develop a Fano-based core-hole clock (FCHC) method that captures coherent coupling between localized excitons and the directly populated delocalized CT continua in resonant Auger scattering. Applied to sulfur KLL Auger spectra of a conductive organic polymer, FCHC reveals clear Fano interference and a CT time of 27±1.8  fs, demonstrating that the conventional core-hole clock model underestimates the CT dynamics timescale. We establish FCHC as a robust method for probing ultrafast CT in complex molecular systems.

In this work, density functional theory simulations are combined with X-ray photoelectron spectroscopy (XPS) to systematically investigate the chemical structures of carbon- and oxygen-containing surface species relevant to ethylene epoxidation on silver catalysts. Core-level binding energies are calculated within a density functional theory framework using the transition-potential method to predict C 1s and O 1s shifts for adsorbed species, including hydrocarbons, carbon oxygenates, and key reaction intermediates. By rigorously validating the computational protocol against experimentally measured binding energies, we achieve reliable spectral assignments and establish quantitative relationships between local O and C chemical environments and their XPS signatures. The resulting structure-reactivity correlations provide new mechanistic insight into the evolution of oxygen and carbon species under reaction conditions and their role in controlling epoxidation selectivity. Beyond elucidating key surface reaction pathways for ethylene epoxidation, this integrated experimental-theoretical framework offers transferable guidelines for the quantitative XPS analysis of surface chemistry in heterogeneous catalysis.

Facilitating the kinetically demanding oxygen evolution reaction (OER) is essential for the sustainable conversion of renewable energy into chemical fuels. However, precisely unraveling the dynamics of active species and sites during the OER remains a significant challenge. Herein, we constructed a series of Co-substituted Ni coordination polymers (Ni-CPs) for the OER. Complementary surface-/bulk-sensitive operando time-resolved spectroscopic monitoring enables detailed mechanistic insight into the critical role of partial Co incorporation in modulating the local coordination geometry of Ni centers and thereby promoting the intrinsic OER kinetics. Our results reveal that controlled Co substitution in Ni-CPs facilitates the generation of a substantial fraction of (Ni, Co)(IV) species, which activate O-O bond formation atop the catalytically active NiIV-O-CoIV moieties. These key findings are further supported by kinetic isotopic effect studies and density functional theory calculations, in which the OER in Ni3Co1-CPs proceeds via an oxo-radical coupling mechanism, with deprotonation preferentially occurring at the Ni sites. Consequently, the engineered Ni3Co1-CPs exhibit enhanced OER activity compared to their oxide counterparts, along with durable electrochemical stability for over 4000 h. This study not only offers detailed mechanistic insights into the dynamics of active species and sites but also highlights their critical role in optimizing the OER kinetics.

The Soret band splitting of meso-meso-linked porphyrin dimers provides a quantitative optical signature of heterometallic two-qubit architecture. Time-dependent density functional theory calculations on [VO(TrPP)]2 and [Cu(TrPP)]2 (TrPP = 5,10,15-triphenylporphyrinate) show that the homodimer splitting vanishes at the orthogonal geometry, where the frontier a2-derived HOMOs are degenerate, producing a symmetry-protected node in excitonic coupling. In contrast, the heterodimer [VO(TrPP)-Cu(TrPP)] retains a two-peak Soret structure in orthogonal geometry because of the intrinsic reduction of the symmetry that cannot be removed by rotation. A two-chromophore exciton model reproduces this splitting quantitatively. Broken-symmetry DFT yields a superexchange magnetic coupling, |J| ≈ 10-2 cm-1, 5 orders of magnitude below the Soret splitting, confirming that optical and magnetic interactions are decoupled. The Soret profile and J together provide independent, complementary observables to characterize porphyrin-based two-qubit architectures.

In this study, we expand upon and benchmark the Kim-Gordon method (KG), a subsystem density functional theory (DFT) approach appended with a machine-learned correction to compensate for errors in the kinetic energy term and thereby match Kohn-Sham (KS) DFT accuracy. This correction is obtained through 'delta- learning' based on KS-DFT data. The method promises sampling of configurations for condensed molecular systems at the Kohn-Sham DFT level of accuracy at a fraction of the computational cost. Despite encouraging results for liquid water, it was not obvious whether the scheme had more general appeal. In this work, we show that the approach allows for a broad range of applications. In particular, we successfully apply it to complex molecular liquids, such as bulk ammonia and methanol. As a bonus, the correction trained on the bulk KS data is applicable to clusters, illustrating its transferability. By focusing on 'delta-learning'-predicting small corrections rather than full Kohn-Sham (KS) energies and forces-we significantly reduce the required training data. This approach, especially when combined with linear-scaling self-consistent field (LS-SCF) techniques, establishes the method as a highly efficient computational tool for molecular dynamics.

One of the distinguishing aspects of CP2K is its seamless integration of diverse structural and transition-state optimization techniques with advanced sampling approaches including Monte Carlo, molecular dynamics, and metadynamics, enabling the efficient exploration of complex potential- and free-energy landscapes, including rare events. These capabilities are combined with a broad hierarchy of energy and force evaluation methods, ranging from classical and machine-learned interaction potentials and mixed quantum-classical multiscale and semiempirical schemes, to highly accurate quantum-mechanical electronic-structure approaches. At the heart of the latter lies the Gaussian and plane-wave framework, along with its augmented all-electron generalization, which have been described in detail in our previous code review [T. D. Kühne et al., J. Chem. Phys. 152, 194103 (2020)]. Building on this foundation, the present work revisits the methods within CP2K that turn electronic structure into dynamics, transport, and spectroscopic response. Particular emphasis is placed on the coupling between static response calculations and nuclear motion: spectra may be evaluated at optimized structures, averaged over thermally sampled configurations, obtained from time-correlation functions along ab-initio or path integral molecular trajectories, or followed in real time together with electronic and nuclear dynamics. The same modular structure also enables equilibrium and biased transport simulations, from Kubo-type linear response to open-boundary approaches under external potentials, highlighting CP2K's unique capability to unify quantum chemistry with quantum and statistical mechanics within a versatile, holistic simulation environment.

Higher alcohol synthesis from syngas (CO/H2) has attracted large research efforts in the past decades. However, the analogous reaction using CO2 as a feedstock remains relatively underexplored. Due to the net reduction in anthropogenic CO2 emissions that can be achieved by this approach (provided green H2 is used), ethanol synthesis from CO2 has become a highly desirable reaction. Nevertheless, highly active and selective catalysts for this reaction have remained elusive and poorly understood, and their development presents a formidable task. By leveraging the synthesis of a well-defined, silica-supported Rh-Li based catalyst, we have improved our understanding of the role of lithium in the formation of ethanol from CO2. Using state-of-the-art spectroscopy, such as X-ray absorption spectroscopy, probe molecule infrared spectroscopy, and in-situ diffuse reflectance infrared spectroscopy, we were able to evidence the presence of an activated CO species at the interface of metallic Rh and Li+ which readily allows the insertion of -CHx species in the RhLi@SiO2 system. Complementary computational studies indicate that the insertion of CHx into CO is drastically facilitated and that the presence of Li+ protects -CHx species from overhydrogenation.

Identification of the true catalytically active species/sites holds the key to new catalyst design. In this study, combination of complementary operando surface/bulk sensitive spectroscopic techniques and density functional theory (DFT) calculations establish a clear picture of the structure-activity relations in marcasite- and pyrite-type CoSe2 for overall water splitting. Our results reveal that under acidic conditions marcasite CoSe2 undergoes slight surface corrosion, producing disordered [CoSe6] motifs with the active Se sites for catalyzing the hydrogen evolution reaction (HER). In contrast, during the alkaline HER, the marcasite CoSe2 initially interacts with the electrolyte to reconstruct an O-rich covered surface, which subsequently undergoes potential-driven restructuring to generate the metallic cobalt species as the true active species. Such dynamic changes of the active species/sites along with variations in pH values were not observed in pyrite CoSe2, either with or without heteroatom substitution, highlighting the significant importance of phase engineering in managing the HER kinetics. Further operando spectroelectrochemical monitoring demonstrates that the in situ generation of highly disordered Co4+ species is a common denominator of CoSe2 catalysts for the oxygen evolution reaction (OER). This study directly evidences the dynamic influence of local coordination geometries of the catalytic active centers on the underlying catalytic reaction kinetics.

The complexity of the intrinsic oxygen evolution reaction (OER) mechanism, particularly the precise relationships between the local coordination geometry of active metal centers and the resulting OER kinetics, remains to be fully understood. Herein, we construct a series of 3 d transition metal-incorporated cobalt hydroxide-based nanobox architectures for the OER which contain tetrahedrally coordinated Co(II) centers. Combination of bulk- and surface-sensitive operando spectroelectrochemical approaches reveals that tetrahedral Co(II) centers undergo a dynamic transformation into highly active Co(IV) intermediates acting as the true OER active species which activate lattice oxygen during the OER. Such a dynamic change in the local coordination geometry of Co centers can be further facilitated by partial Fe incorporation. In comparison, the formation of such active Co(IV) species is found to be hindered in CoOOH and Co-FeOOH, which are predominantly containing [CoIIIO6] and [CoII/FeIIIO6] octahedra, respectively, but no mono-μ-oxo-bridged [CoIIO4] moieties. This study offers a comprehensive view of the dynamic role of local coordination geometry of active metal centers in the OER kinetics. The oxygen evolution reaction and its relationship with metal center coordination remain unclear. Here, the authors report that optimization of the local coordination geometry of Co centers plays a crucial role in facilitating the O-O bond formation atop high-valent Co (IV) sites.

Identification of the true catalytically active species/sites is crucial for designing new catalysts. Herein, we combine complementary operando surface/bulk sensitive spectroscopic techniques and density functional theory (DFT) calculations to establish clear structure-activity relations for marcasite- and pyrite-type CoSe2 toward overall water splitting. Our results reveal that under acidic conditions marcasite CoSe2 undergoes slight surface corrosion, producing disordered [CoSe6] motifs with the active Se sites for catalyzing the hydrogen evolution reaction (HER). In contrast, during the alkaline HER, marcasite CoSe2 undergoes potential-driven restructuring from the initial reconstructed O-rich covered surface into the generation of metallic cobalt species as the true active species. Such dynamic changes of the active species/sites along with variations in pH values are not observed for either pristine or heteroatom-substituted pyrite CoSe2, highlighting the central importance of phase engineering in managing the HER kinetics. Further operando spectroelectrochemical monitoring demonstrates that the in situ formation of highly disordered Co(IV) species is a common denominator of chalcogenide catalysts for the oxygen evolution reaction (OER). This study illustrates the dynamic influence of local coordination geometries of the catalytically active centers on the underlying catalytic reaction kinetics.

We report the static and dynamical properties of liquid water at second-order Møller-Plesset perturbation theory level (MP2) with classical and quantum dynamics simulations using a neural network potential. We examined the temperature-dependent radial distribution function, diffusion and vibrational dynamics. MP2 theory predicts an over-structured liquid water at ambient conditions, which may be attributed to the incomplete basis set. The excellent agreement with experimental structural properties as well as the diffusion constant is observed at an elevated temperature of 340K.

We perform extensive ab initio molecular dynamics simulations to compute transport properties of a KCl solution at high concentration using Green-Kubo relations based on Onsager's system of linear equations. Our results show an increase in the electrical conductivity under confinement, with a further enhancement in the case of a positive charge on graphene. The presence of surface charges also determines the direction of electro-osmotic flow and of the diffusio-osmotic electrical current in the nanofluidic systems. Structural analysis reveals that in the case of positively charged graphene sheets, chloride ions accumulate at the surface. This promotes a spatial separation of anions and cations, thereby reducing their correlations and leading to an increased electrical conductivity in this system. We show how accounting for electronic structure by means of ab initio molecular dynamics is essential in the calculation of the transport properties. While quantitative results can be obtained for the diagonal terms of the Onsager transport matrix, only a qualitative impact can be gauged for the off-diagonal terms due to limitations in sampling. Nevertheless, our results reveal that surface charges significantly alter ionic conductivity and determine the direction of the electro-osmotic flow and of the diffusio-osmotic current, thereby advancing the understanding of transport at the nanoscale.

We present fully ab initio simulations of Fe L-edge X-ray absorption spectroscopy (XAS) for archetype single-molecule magnet tetrairon Fe4 using a linear-response time-dependent density functional theory with a spin-orbit coupling scheme. In particular, electronic and structural modifications in the Fe4 core, as induced by Li doping and by the change of R (-H and -C5S·), were studied by systematically benchmarking hybrid functionals and basis sets. A parameter-free computational protocol is, therefore, established, which reproduces experimental spectra with excellent agreement. The simulations capture key spectroscopic signatures, including L3-L2 splitting, redox-induced shifts upon Li doping, and the robustness of spectral shapes against magnetic coupling schemes and structural distortions. This study establishes a practical and accurate framework for simulating 2p XAS in complex magnetic molecules, providing valuable insight into their electronic behavior and enabling a rigorous connection between experiment and theory.

Ethylene oxide (EO) is a crucial building block in the chemical industry, and its production via ethylene epoxidation (EPO) is a pivotal process. Silver-based catalysts are known for their high selectivity and are currently largely used in the industrial process. Extensive research over the past 20 years has assumed the oxametallacycle (OMC) as a reaction intermediate, implying that ethylene reacts with adsorbed oxygen on the surface of silver. The OMC is suggested to be the common intermediate for both EO and acetaldehyde, with the latter rapidly converting into carbon dioxide. However, the detection of such intermediate is challenging. In this study, in situ X-ray photoelectron spectroscopy combined with density functional theory calculations is employed to investigate reaction intermediates formed during EPO on silver. The findings reveal that adsorbed EO is detected as a direct product of ethylene oxidation. Adsorbed ethylene is easily dehydrogenated to form C(2)Hx (x = 1-3) species. C(2)Hx, carbon monoxide, and carbonate are identified as precursors to carbon dioxide. A new methodical interpretation of complex spectral features is provided, which clarifies previous assignments. Notably, the OMC is detected neither under EPO nor under EO decomposition conditions, thus challenging the role of OMC in the reaction mechanism.

The oxygen evolution reaction (OER) is a vital bottleneck for the conversion of water and clean energy into chemical fuels through electrocatalysis. In-depth insights into the surface structural evolution of real active species on catalysts during the OER process are of great significance for knowledge-driven catalyst design. Herein, we developed iron-doped cobalt carbodiimide (CoxFe1-xNCN) nanoparticles as efficient OER precatalysts with stable overpotential for at least 290 h. Advanced structural characterizations disclosed the presence of abundant structural defects in low-crystalline (LC) CoxFe1-xNCN. Operando X-ray absorption spectroscopy and X-ray diffraction studies revealed that these intrinsic structural defects could accelerate the irreversible surface reconstruction in LC-CoxFe1-xNCN. This promoted the generation of high-valent metal oxyhydroxides as the real active OER phases, resulting in a lower overpotential compared to high-crystalline CoxFe1-xNCN. The present study highlights the introduction of structural defects as an effective approach for the rational design of efficient OER electrocatalysts.

Immobilization of molecular catalysts onto electrode surfaces using host-guest (HG) interactions enables the facile regeneration of electrodes following catalyst degradation. Beyond this practical aspect, the architecture also offers a unique way to study the electronic coupling of molecules to the electrode through a nominally insulating linker. Here, we employ surface-enhanced infrared absorption spectroscopy (SEIRAS) to characterize the binding and electronic coupling of Au-bound HG complexes. Distinct spectral features and binding kinetics differentiate host-bound species from physisorbed analogues, confirming well-defined HG assemblies on the surface. Analysis of the wavenumber shifts of the guest as a function of applied potential suggests that while the coupling of physisorbed guests with the surface is not strong, the host-bound guests show a substantial electronic coupling considering their distance from the surface of ∼1.3 nm. Density functional theory calculations reveal the key role of the host in mediating this long-range coupling between the Au surface and the guest.

Identification of the true catalytically active species/sites is crucial for catalyst design. Herein, we combine complementary operando surface/bulk sensitive spectroscopic techniques and density functional theory calculations to establish clear structure-activity relations for marcasite- and pyrite-type CoSe2 toward overall water splitting. Our results reveal that under acidic conditions marcasite CoSe2 undergoes slight surface corrosion, producing disordered Se-Co-Se moieties for catalyzing the hydrogen evolution reaction (HER). In contrast, during the alkaline HER, marcasite CoSe2 undergoes potential-driven restructuring from the initial reconstructed O-rich covered surface into the generation of metallic Se-Co-Co-Se moieties as the true active species. Such dynamic changes of the active species/sites along with variations in pH values are not observed for either pristine or heteroatom-substituted pyrite CoSe2. Further operando spectroelectrochemical monitoring demonstrates that the in situ formation of highly disordered Co(IV) species is a common denominator of chalcogenide catalysts for the oxygen evolution reaction. This study illustrates the dynamic influence of local coordination geometries of the catalytically active centers on the underlying catalytic reaction kinetics.

Despite the widespread use of scanning tunneling microscopy (STM) in atomic-scale investigations, the influence of the tip's atomic structure remains insufficiently characterized. This study addresses the issue by analyzing the electronic and magnetic properties of transition-metal-functionalized STM tips using both multireference wavefunction methods and density functional theory. The results demonstrate that strong electron correlations in transition-metal-based tips must be accounted for to accurately describe the structural and magnetic parameters involved-an essential requirement for the correct setup of inelastic and scanning tunneling spectroscopy experiments. By considering both minimal tip models and larger, more realistic pyramid structures, the approach balances computational efficiency with experimental relevance. The mechanism of spin-state reduction in NiCp2-functionalized tips is clarified, revealing the central roles of charge transfer, molecular distortion, and metal-substrate hybridization. Furthermore, selective substitution of the Cu apex atom in Cu(111)-based tips with 3d transition metals allows controlled modulation of the NiCp2 spin state. This provides a practical strategy for designing STM tips with tailored magnetic properties. Overall, the findings establish a robust theoretical framework for interpreting complex molecule-substrate interactions in spintronic systems and support the development of next-generation spin-polarized STM tips and molecular spintronic devices.