The total energy is a fundamental characteristic of solids, molecules, and nanostructures. In most first-principles calculations of the total energy, the nuclear kinetic operator is decoupled from the many-body electronic Hamiltonian and nuclear potential, and the dynamics of the nuclei is reintroduced afterward. This two-step procedure introduced by Born and Oppenheimer (BO) is approximate. Energies beyond the electronic and vibrational (or phononic) main contributions might be relevant when small energy differences are important, such as when predicting stable polymorphs or describing the magnetic energy landscape. We clarify the different flavors of BO decoupling and give an exact formulation for the total energy in the basis of BO electronic wave functions. Then, we list contributions beyond the main ones that appear in a perturbative expansion in powers of $M_0^{-1/4}$, where $M_0$ is a typical nuclear mass, up to sixth order. Some of these might be grouped and denoted as the electron-phonon contribution to total energy, $E^{\mathrm{elph}}$, which first appears at fourth order. The electronic inertial mass contributes at sixth order. We clarify that the sum of the Allen-Heine-Cardona zero-point renormalization of eigenvalues over occupied states is not the electron-phonon contribution to the total energy but rather part of the phononic contribution. The computation of the lowest-order $E^{\mathrm{elph}}$ is implemented and shown to be small but non-negligible in the case of diamond (3.8 meV per atom) and GaN (9.7 meV per atom). We also estimate the electronic inertial mass contribution and the quasiharmonic one for diamond. We confirm the size consistency of all computed terms.

Lithium-ion dynamics of garnet-type ${\text{Li}}_{6.5}{\text{La}}_3{\text{Zr}}_{1.5}{\text{Ta}}_{0.5}{\mathrm{O}}_{12}$ single crystals were investigated using pulsed field gradient (PFG) NMR and impedance spectroscopy over a wide temperature range up to 700 K. The diffusion coefficient measured by PFG-NMR exhibits non-Arrhenius behavior at elevated temperatures ($>400\mathrm{K}$). The conductivity diffusion coefficient is consistently higher than the PFG-NMR diffusion coefficient across the entire temperature range, with a Haven ratio of 0.3–0.4, indicating that the motion of mobile ${\text{Li}}^{+}$ ions is correlated. Remarkably, the Haven ratio exhibits little temperature dependence despite the non-Arrhenius behavior, representing the first experimental observation in garnet-type electrolytes and consistent with the molecular dynamics simulations. This indicates that ion-ion correlations remain essentially unchanged over a wide temperature range. Combined with the local ${\text{Li}}^{+}$ ion dynamics obtained from spin-lattice relaxation analysis, these results suggest that long-range diffusion is suppressed at low temperatures due to short-range ordering of ${\text{Li}}^{+}$ ions.

Catalytic decomposition of methane is a more sustainable alternative for hydrogen production compared to established technologies like steam methane reforming and coal gasification. This study reports iron-based catalysts supported on ${\mathrm{MAl}}_2{\mathrm{O}}_4$ $(\mathit{M}=\mathrm{Ca},\mathrm{Mg},\mathrm{Sr},\mathrm{Ba})$ prepared via a ball-milling or one-pot modified Pechini (sol-gel) method. The synthesized catalysts were evaluated for their CDM performance in the range of 750–800 °C. In general, we show that ball-mill synthesis leads to higher CDM activities than sol-gel synthesized samples, which undergo quick deactivation. Raman spectroscopy and ${\mathrm{H}}_2$-TPR indicate that synthesizing the $\mathrm{Fe}\text{−}{\mathrm{MAl}}_2{\mathrm{O}}_4$ catalysts via the sol-gel method results in iron coordination with cations (i.e., M) and with alumina to decrease iron’s reducibility and its overall catalytic activity. For the ball-mill synthesized samples, we find that a 30 wt% $\mathrm{Fe}\text{−}{\mathrm{CaAl}}_2{\mathrm{O}}_4$ catalyst tested at optimized reaction conditions of ${\mathit{T}}_{\mathit{red}}=700°\mathrm{C}$, ${\mathit{T}}_{\mathit{rxn}}=750°\mathrm{C}$, $y_{\mathrm{CH}4}=0.9$, and $\mathit{GHSV}=1.25\mathrm{L}·{\mathrm{g}}^{-1}·{\mathrm{h}}^{-1}$ obtained a competitive carbon yield of $17.86{\mathrm{g}}_{\mathrm{C}}/{\mathrm{g}}_{\mathrm{Fe}}(5.06{\mathrm{g}}_{\mathrm{C}}/{\mathrm{g}}_{\mathrm{Cat}})$. TEM and SEM of the spent product indicate that the carbon product forms primarily via a tip-growth mechanism, with both filamentous and nano-onion-type carbon being generated. Raman spectroscopy of the spent product determined most of the carbon formed on the ball-milled $\mathrm{Fe}\text{−}{\mathrm{MAl}}_2{\mathrm{O}}_4$ catalysts was graphitic in nature with ${\mathrm{I}}_{\mathrm{D}}/{\mathrm{I}}_{\mathrm{G}}$ ratios ranging between 0.400 and 0.500. Overall, ball-milling appears to be a simple yet effective strategy to prepare dispersed iron catalysts for CDM.

Machine learning interatomic potentials (MLIPs) can now reproduce the energy, forces, and stresses of bulk materials with high accuracy compared to first-principles calculations. The description of imperfections, where coordination environments and electron counts deviate from those found in pristine reference structures, remains a challenge. We find that the current generation of foundation MLIPs does not describe the defect physics of the photovoltaic absorber ${\text{Sb}}_2{\text{Se}}_3$. We introduce global defect charge embeddings that distinguish the bonding characteristics of different charge states. We further employ a multifidelity approach that combines low-cost (semilocal exchange-correlation functional) reference data with high-quality (nonlocal hybrid functional) energies and forces that describe well the subtleties of the defect energy landscape. The resulting defect-capable force fields can find stable structural configurations and predict defect thermodynamics in quantitative agreement with direct quantum mechanical calculations, at a fraction of the computational cost.

The fast cycling capability of Li-ion batteries is a key performance indicator for a range of applications including electric vehicles (EVs), in which systems must deliver/accept high currents while avoiding excessive degradation. We evaluate four leading EV battery chemistries in this context, encompassing cathodes focused on design-to-performance, ${\text{LiNi}}_{0.8}{\text{Mn}}_{0.1}{\text{Co}}_{0.1}{\mathrm{O}}_2$ (NMC811), and design-to-cost, ${\text{LiMn}}_{0.6}{\text{Fe}}_{0.4}{\text{PO}}_4$ (LMFP), alongside current state-of-the-art (graphite and $\text{graphite}@{\text{SiO}}_{\mathrm{x}}$ composite) and next-generation (high ${\text{SiO}}_{\mathrm{x}}$) anodes. These chemistries are adopted as model systems to examine three common test protocols for evaluating fast cycling, specifically tuned to fast charge, fast discharge, or both. The capacity, degradation induced, and operational state-of-charge range were highly dependent on selected testing protocols. Significant loss of lithium inventory (LLI) was observed under fast-charging conditions, associated with lithium plating, observed via monitoring of anode potential in three-electrode cells, differential voltage analysis, and visual inspection of electrodes postmortem. LMFP cells induced a greater level of Li plating than NMC, reaching negative anode potentials in the early stages of fast charging. While the ${\text{SiO}}_{\mathrm{x}}$ anode performed relatively well at high rates, it suffered a greater degree of degradation, including both LLI and impedance increase associated with excess SEI growth. This study provides a basis for battery material design and charging protocols tuned for fast cycling.

Osmotic energy systems employ charged nanoporous membranes and nanochannels to convert salinity gradients into electrical power, offering a promising route to harvest one of Earth’s most abundant yet underexploited renewable resources—the oceans—and providing reliable, carbon-free electricity. However, to date, no known self-consistent theoretical model can accurately predict the electrical response of realistic charge-selective systems. Thus, empirical and phenomenological models are used to increase the performance while attributing the increase to various mechanisms, which are mostly incorrect and incomplete. This leads to a costly empirical trial-and-error optimization process, which typically yields only incremental improvements. Here, we provide a self-consistent theoretical model for the current-voltage ($I-V$) response, verified by nonapproximated numerical simulations, that establishes a detailed framework for osmotic energy conversion in realistic systems comprising a charge-selective membrane and the often-neglected larger bulk reservoirs. Our model delineates the effects of the surface charges, the bulk concentration ratio, and the often-neglected effects of the bulk reservoirs. The model provides analytical expressions for all the major transport characteristics at zero current ($I=0$), including the Ohmic resistance, $R_{\text{Ohmic}}$, the voltage at zero current, $V_{I=0}$, and the transport number, $\tau$, which is a metric for the selectivity of the system. The $I=0$ insights are carried over to the results at the energy harvesting limit of zero voltage ($V=0$), allowing a straightforward analysis. Two of our key results are unexpected. First, the concentration at which the harvestable electrical power is maximal is not the concentration at which the harvestable electrical current is maximal. Second, overlooking the effects of the bulk reservoirs leads to overestimations of the harvestable power by several orders of magnitude. Our proposed framework lays the theoretical foundation for a new generation of sustainable nanofluidic energy systems relevant to addressing global energy and water challenges.

Quantifying the energetic cost of implementing quantum operations is essential for assessing the efficiency and scalability of quantum sensing and information-processing technologies. Here, we introduce a framework for analyzing the interplay between complexity and energy cost of quantum processes. In particular, we apply our framework to a sequential quantum phase estimation protocol, where a phase of physical significance is encoded in a quantum channel. The channel is applied to a probe state repeatedly until the probe is measured and the outcome leads to an estimate on the phase. We establish a trade-off relation between the total energy cost of the protocol and the number of times the channel is applied (complexity), while reaching a desired estimation precision. A sweet spot is located where the two quantities are co-optimized. The principles of our analysis can be adapted to benchmark the energetic requirements in other quantum protocols and devices.

Layered perovskite lithium yttrium titanate (${\text{LiYTiO}}_4$) has recently emerged as a promising low-potential, ultrahigh-rate anode material for lithium-ion batteries. However, its lattice dynamics and thermal transport behavior remain largely unexplored, limiting a complete assessment of its practical applicability. Here, we combine experimental thermal conductivity measurements with a systematic theoretical study based on a machine-learning neural evolution potential (NEP). Our computational framework integrates the temperature-dependent effective potential method with the Wigner thermal transport (WTT) formalism, explicitly accounting for both diagonal and off-diagonal components of the heat-flux operator. Phonon calculations at 0 K reveal dynamical instabilities arising from rotations of the ${\mathrm{TiO}}_6$ octahedra, which are stabilized at finite temperatures through anharmonic phonon renormalization. By incorporating particlelike phonon propagation and wavelike phonon tunneling within the WTT framework, we predict an orientation-averaged room-temperature lattice thermal conductivity (${\kappa }_{\mathrm{L}}$) of $3.6{\text{Wm}}^{-1}{\mathrm{K}}^{-1}$, which is qualitatively consistent with the experimentally measured value of $3.2\pm 0.08{\text{Wm}}^{-1}{\mathrm{K}}^{-1}$ for polycrystalline samples. To further elucidate the role of ionic motion at elevated temperatures, we compute ${\kappa }_{\mathrm{L}}$ using the Green-Kubo approach within equilibrium molecular dynamics simulations based on the trained NEP, yielding improved agreement with experiment relative to the WTT prediction. Our results identify intrinsically low thermal conductivity as a key limitation for the practical application of ${\text{LiYTiO}}_4$ and provide broader insight into anharmonic lattice dynamics and thermal transport in complex battery materials.

Recent simulations and observations suggest that clouds interact with offshore wind farms, yet the physical mechanisms governing this interaction remain unclear. Here, we investigate these processes using large-eddy simulations of stratocumulus-topped boundary layers, systematically removing key forcings to isolate their physical effects. We consider three progressively simplified scenarios: (i) a fully developed marine stratocumulus boundary layer, (ii) a case without radiative forcing, which weakens both cloud-top longwave cooling and entrainment, and (iii) a clear-sky case in which both radiative forcing and liquid water are removed. The presence of cloud-top radiative cooling increases entrainment, leading to a less stable and deeper boundary layer that promotes vertical transport of momentum and energy toward the turbines. This leads to a faster wake recovery, with direct implications for the performance of neighboring wind farms. Overall, our results demonstrate that radiatively driven cloud-top entrainment is a key mechanism linking cloud dynamics to the performance of large wind farms and underscore the need for wind-energy models that explicitly represent interactions among wind farms, the atmosphere, and cloud processes.

Nonlinear thermoelectric effects offer the potential to enable new energy technologies, such as voltage-controlled thermal switching and thermoelectric rectification. In this work, we examine how the quantum geometry of the electron bands gives rise to nonlinear thermoelectric responses in materials with suitable symmetries. We derive a series of nonlinear thermoelectric effects governed by the Berry curvature dipole and the quantum metric dipole, respectively. Among them, we identify a particularly interesting quantized thermoelectric response that directly measures the total chirality of Weyl points below the Fermi level. For general nonlinear responses, we derive the nonlinear analogs of the Wiedemann-Franz law and Mott’s formula. These provide a means to estimate the magnitude of nonlinear thermoelectric responses based on existing nonlinear Hall measurements. Our estimates suggest that these effects should be observable in several candidate materials, with In-doped ${\text{Pb}}_{1-x}{\text{Sn}}_x\text{Te}$ standing out as the most promising. Our work offers new insights into the experimental study of quantum geometry through nonlinear thermoelectric measurements.

A minimal model of ionic aggregation in concentrated ${\text{ZnCl}}_2$ is developed, guided by molecular dynamics simulations with a machine-learned potential. It explicitly incorporates solvent-site depletion, correlated chloride binding, and allows for loops within Zn–Cl clusters. Dehydration drives two coordination-controlled structural changes: a crossover at $Z=2$ from predominantly isolated Zn-containing species to Cl-bridged clusters and the onset of gelation near $Z\approx 3$. The model reproduces the concentration-dependent trends observed in the molecular dynamics simulations with two fitted parameters, while the cluster-size distribution at the highest concentration is consistent with three-dimensional percolation scaling over the accessible range of cluster sizes.

The introduction of Se in CdTe solar-cell absorbers has led to multiple beneficial effects in the devices, including an increased short-circuit current and an extended charge-carrier lifetime. A critical manufacturing step of ${\mathrm{CdSe}}_x{\mathrm{Te}}_{1-x}$ solar cells is ${\mathrm{CdCl}}_2$ annealing at high temperatures, during which Se diffuses through the absorber layer. Understanding the local Se distribution in the absorber and its impact on optical properties of the material is key for the further development of this thin-film solar cell technology. In a multimodal x-ray scanning microscopy approach, we investigated the impact of the annealing temperature of ${\mathrm{CdSe}}_x{\mathrm{Te}}_{1-x}$ solar cells on the Se distribution and on optical characteristics of the material. For this purpose, we exploited an upgraded x-ray excited optical luminescence (XEOL) detection unit that enables simultaneous spectrally and temporally resolved XEOL mapping at synchrotron facilities that are ideal for studying thin-film solar-cell materials with hard x-rays featuring high penetration depth and lateral resolution.

Electrode morphology critically determines the stability and efficiency of lithium metal anodes, yet no predictive framework has explained how measurable parameters control deposition. Here we introduce the first theoretical model of electrochemical Ostwald ripening, capturing the competition between electroplating and surface-energy-driven redistribution and identifying it as the governing process behind morphology evolution in the nondendritic regime. The framework explicitly incorporates solid electrolyte interphase (SEI) resistance, electrolyte conductivity, electrode wettability, and current density, revealing the transition from a 2D SEI-limited to a 3D electrolyte-limited growth. The model yields analytical expressions for nucleus size, density, and distribution that quantitatively reproduce independent experimental results and establishes a direct link between plating conditions, morphology, and Coulombic efficiency. By providing experimentally accessible relationships between key parameters and deposition outcomes, the framework enables a predictive understanding of lithium plating and provides a broadly applicable basis for controlling electrodeposition morphology across diverse electrochemical systems.

Understanding electrochemical phenomena at complex liquid-solid interfaces requires linking real-time structural dynamics with atomic-scale interfacial chemistry. Here, we integrate in-situ synchrotron X-ray fluorescence and diffraction with high-resolution cryogenic electron and ion multimodal microscopy to provide a mechanistic understanding of Pt-based alloying anodes across length scales. We directly observe the initial lithiation-driven formation of ${\mathrm{Li}}_2\mathrm{Pt}$ and its evolution to a stable LiPt intermetallic phase during extended cycling via a solid-solution type reaction mechanism. Simultaneously, the solid-electrolyte interphase transitions from an unstable carbonate-rich to a stable LiF-dominated composition, confirmed by cryogenic scanning transmission electron microscopy-electron energy loss spectroscopy. Crucially, cryogenic atom probe tomography reveals spatially distinct compositional regimes within the alloy anode: a lithium-flux-limited, heterogeneous interfacial zone and a diffusion-controlled, homogeneous LiPt alloy bulk. This nanoscale compositional gradient rationalizes the emergent solid-solution reaction mechanism and highlights how kinetic limitations and interface dynamics govern alloy formation and electrochemical stability. Our findings establish a correlative experimental framework that directly links in-situ structural dynamics with preserved near-atomic resolution interfacial chemistry, advancing the rational design of durable alloy electrodes for next-generation energy storage.

Alkaline water electrolyzers (AWEs) offer a carbon dioxide-emission-free route to convert renewable electricity into hydrogen. Improving their efficiency requires a deep understanding of transport and kinetics within an electrolytic cell. By combining molecular simulations of ion diffusivities with detailed multiphysics simulations, we report here a surprising finding that neglecting the temperature dependence of ion transport in an AWE could lead to erroneous predictions of current density reducing with increasing temperature. This is because ion mobilities reduce with temperature, leading to severe transport limitations if diffusivities are considered to be independent of temperature. We model ion diffusion, migration, and convection via the Nernst-Planck formulation, fluid dynamics via the continuum Euler-Euler approach, along with electrode kinetics at the Butler-Volmer level of theory. We carry out molecular dynamics simulations to determine the temperature dependence of ${\text{OH}}^{-}$ and ${\mathrm{K}}^{+}$ diffusivities and show that considering temperature-dependent diffusivities leads to the current density increasing with temperature. We also demonstrate that gas bubble formation and ${\text{OH}}^{-}$ concentration gradients lead to reduced electrolyte conductivity near the electrodes. The higher levels of cathodic gas production, as compared to those at the anode, lead to asymmetries in the concentration profiles. We provide physical understanding regarding these observations, including that at high cell potentials, transport limitations play a crucial role in modulating AWE performance. Overall, our findings provide critical insights into the interplay between ion transport, temperature, and electrochemical performance, which are crucial for accurate multiscale simulations and modeling-based optimization of such devices.

We estimate the run-time and energy consumption of simulating nonequilibrium dynamics on neutral-atom quantum computers in analog mode, directly comparing their performance to classical methods, namely matrix product states and neural quantum states. By collecting both experimental data from a quantum processing unit (QPU) in analog mode and numerical benchmarks, we enable accurate predictions of run-time and energy consumption for large-scale simulations on both QPUs and classical systems through fitting of theoretical scaling laws. Our analysis shows that neutral-atom devices are already operating in a competitive regime, achieving comparable or superior performance to classical approaches while consuming significantly less energy. These results demonstrate the potential of analog neutral-atom quantum computing for energy-efficient simulation and highlight a viable path toward sustainable computational strategies.

Photovoltaics play a key role in the renewable energy transition, where perovskite solar cells stand out as one of the most promising with high-power conversion efficiencies, desirable characteristics, and great versatility. The efficiency of these cells is mainly limited by nonradiative recombination, whether at one of the interfaces between the perovskite layer and transport layers or within the bulk of the perovskite itself. However, it is difficult to probe which of these dominates the losses during operation, which complicates further improvements. Here we introduce and demonstrate a simple, inexpensive, and easy-to-integrate method for identification of the limiting aspect of perovskite solar cells under operating conditions in terms of recombination losses. We illuminate a device with red, blue, or white light, each absorbed differently depending on the position in the device. We show that, in perovskite solar cells, the diffusion length in the bulk is of secondary importance and rather the interfaces between layers dominate the charge carrier distributions, and thus light of different wavelengths will result in changing performance. Using the fill factor from the device characteristics for each case, we are able to identify whether the front or back interface of the cell limits the performance with nearly 97% accuracy. Finally, we apply this principle experimentally using a co-evaporated perovskite solar cell, where we show a decrease of nearly 5% in fill factor depending on the wavelength of light used.

We report on a rapid, nondestructive scanning laser curvature method for directly characterizing an important and unacknowledged factor that can contribute to the stability of encapsulated single-junction and tandem perovskite solar modules, i.e., the curvature from lamination. The ability to directly identify mechanical stresses and their evolution in fully packaged modules provides critical information regarding possible risks for accelerated degradation and failure. We define a metric for the curvature relating the magnitude and variance in front-glass $z$-displacement to the “flatness” of the module. We also study the effects of package design and lamination parameters—specifically, encapsulant volume, module layout, front- and back-glass thickness, and ribbon placement with the goal of reducing the curvature and the resulting mechanical stress imposed after lamination. Critically, we show that flatter modules show significantly enhanced durability when compared to curved modules, increasing ${\mathrm{T}}_{80}$ by about a factor of 2 from $\sim 900$ to 1800 h under ISOS-L2 conditions at $65°\mathrm{C}$. A direct link between mechanical stress imparted from lamination and chemical degradation mechanisms in modules provides an important design guideline to the community toward robust and reliable perovskite module manufacturing.

Bismuth vanadate is a promising photoanode material for photoelectrocatalytic water splitting. Localized charges play a crucial role in the water-splitting mechanism by introducing charge-transition levels within the band gap and thereby modifying the band alignment. Additionally, the introduction of oxygen vacancies, which can interact with electron polarons, has been reported to improve the photoelectrocatalytic efficiency. However, charge-transition levels are typically evaluated at 0 K, whereas operating conditions involve finite temperatures and, in thin films, epitaxial strain. Capturing these effects requires free energies and extensive sampling that are generally prohibitive for ab initio methods. In this work, we train a machine-learned interatomic potential for ${\text{BiVO}}_4$, including electron polarons and oxygen vacancies in various charge states, to resolve how free energies, transition levels, and charge trapping evolve under operando temperature and strain conditions. For oxygen vacancies, the use of a machine-learned potential enables efficient sampling of charge-localization sites in the vicinity of the vacancy, revealing favored configurations. The energies of the localized polaron and oxygen-vacancy states remain essentially unchanged with temperature, while their transition levels relative to the band edges vary due to temperature-dependent band-edge shifts. In contrast, strain more strongly modifies both the localized states and the band edges. These results provide new insights into the stability of localized charges and their role in photoelectrocatalytic water splitting at finite temperature.

Understanding the origin and mechanisms of defect-induced voltage losses and recombination in metal-halide perovskites aids in the development of new strategies to achieve higher solar cell efficiencies. Photoluminescence (PL) spectroscopy provides insight into charge recombination at defects in the perovskite and at interfaces with passivation and electron transport layers. Measuring the time-resolved PL as a function of temperature for a triple-cation mixed-halide perovskite (CsFAMA) reveals that the PL decay is dominated by shallow defects and that lowering the temperature changes the trap-energy landscape, making the shallow defects shallower until they vanish into the conduction or valence bands at 90 K. Depositing fullerene $({\mathrm{C}}_{60})$ on top of the CsFAMA perovskite induces significant nonradiative recombination losses at room temperature, which can largely be reduced by applying interfacial passivation. Interestingly, cooling to 90 K makes the charge-recombination dynamics almost identical for CsFAMA and $\text{CsFAMA}/{\mathrm{C}}_{60}$ films, irrespective of interfacial passivation treatments. At such low temperatures, nonradiative recombination losses become less dominant because interfacial recombination velocities are reduced. The results provide new insight into shallow defects and recombination losses in CsFAMA perovskites and help to better understand the effect of surface treatments on shallow-defect properties.