High-Quality Data Enabling Universality of Band Gap Descriptor and Discovery of Photovoltaic Perovskites.

Extensive machine-learning-assisted research has been dedicated to predicting band gaps for perovskites, driven by their immense potential in photovoltaics. Yet, the effectiveness is often hampered by the lack of high-quality band gap data sets, particularly for perovskites involving d orbitals. In this work, we consistently calculate a large data set of band gaps with a high level of accuracy, which is rigorously validated by experimental and state-of-the-art GW band gaps. Leveraging this achievement, our machine-learning-derived descriptor exhibits exceptional universality and robustness, proving effectiveness not only for single and double, halide and oxide perovskites regardless of the underlying atomic structures but also for hybrid organic-inorganic perovskites. With this approach, we comprehensively explore up to 15,659 materials, unveiling 14 unreported lead-free perovskites with suitable band gaps for photovoltaics. Notably, MASnBr3, FA2SnGeBr6, MA2AuAuBr6, FA2AuAuBr6, FA2InBiCl6, FA2InBiBr6, and Ba2InBiO6 stand out with direct band gaps, small effective masses, low exciton binding energies, and high stabilities.

Absolute energy levels of liquid water from many-body perturbation theory with effective vertex corrections.

We demonstrate the importance of addressing the Γ vertex and thus going beyond the GW approximation for achieving the energy levels of liquid water in many-body perturbation theory. In particular, we consider an effective vertex function in both the polarizability and the self-energy, which does not produce any computational overhead compared with the GW approximation. We yield the band gap, the ionization potential, and the electron affinity in good agreement with experiment and with a hybrid functional description. The achieved electronic structure and dielectric screening further lead to a good description of the optical absorption spectrum, as obtained through the solution of the Bethe-Salpeter equation. In particular, the experimental peak position of the exciton is accurately reproduced.

Dynamics of the charge transfer to solvent process in aqueous iodide.

Charge-transfer-to-solvent states in aqueous halides are ideal systems for studying the electron-transfer dynamics to the solvent involving a complex interplay between electronic excitation and solvent polarization. Despite extensive experimental investigations, a full picture of the charge-transfer-to-solvent dynamics has remained elusive. Here, we visualise the intricate interplay between the dynamics of the electron and the solvent polarization occurring in this process. Through the combined use of ab initio molecular dynamics and machine learning methods, we investigate the structure, dynamics and free energy as the excited electron evolves through the charge-transfer-to-solvent process, which we characterize as a sequence of states denoted charge-transfer-to-solvent, contact-pair, solvent-separated, and hydrated electron states, depending on the distance between the iodine and the excited electron. Our assignment of the charge-transfer-to-solvent states is supported by the good agreement between calculated and measured vertical binding energies. Our results reveal the charge transfer process in terms of the underlying atomic processes and mechanisms.

Many-body screening effects in liquid water.

The screening arising from many-body excitations is a crucial quantity for describing absorption and inelastic X-ray scattering (IXS) of materials. Similarly, the electron screening plays a critical role in state-of-the-art approaches for determining the fundamental band gap. However, ab initio studies of the screening in liquid water have remained limited. Here, we use a combined analysis based on the Bethe-Salpeter equation and time-dependent density functional theory. We first show that absorption spectra at near-edge energies are insufficient to assess the accuracy by which the screening is described. Next, when the energy range under scrutiny is extended, we instead find that the IXS spectra are highly sensitive and allow for the selection of the optimal theoretical scheme. This leads to good agreement with experiment over a large range of transferred energies and momenta, and enables establishing the elusive fundamental band gap of liquid water at 9.3 eV.

Many-Body Self-Interaction and Polarons.

We address the many-body self-interaction in relation to polarons in density functional theory. Our study provides (i) a unified theoretical framework encompassing many-body and one-body forms of self-interaction and (ii) an efficient semilocal scheme for charge localization. Our theoretical formulation establishes a quantitative connection between the many-body and one-body forms of self-interaction in terms of electron screening, thereby conferring superiority to the concept of many-body self-interaction. Our semilocal methodology involves the use of a weak localized potential and applies equally to electron and hole polarons. We find that polarons free from many-body self-interaction have formation energies that are robust with respect to the functional adopted.

Temperature Dependent Properties of the Aqueous Electron.

The temperature-dependent properties of the aqueous electron have been extensively studied using mixed quantum-classical simulations in a wide range of thermodynamic conditions based on one-electron pseudopotentials. While the cavity model appears to explain most of the physical properties of the aqueous electron, only a non-cavity model has so far been successful in accounting for the temperature dependence of the absorption spectrum. Here, we present an accurate and efficient description of the aqueous electron under various thermodynamic conditions by combining hybrid functional-based molecular dynamics, machine learning techniques, and multiple time-step methods. Our advanced simulations accurately describe the temperature dependence of the absorption maximum in the presence of cavity formation. Specifically, our work reveals that the red shift of the absorption maximum results from an increasing gyration radius with temperature, rather than from global density variations as previously suggested.

Atomic-Level Description of Thermal Fluctuations in Inorganic Lead Halide Perovskites.

A comprehensive microscopic description of thermally induced distortions in lead halide perovskites is crucial for their realistic applications, yet still unclear. Here, we quantify the effects of thermal activation in CsPbBr3 nanocrystals across length scales with atomic-level precision, and we provide a framework for the description of phase transitions therein, beyond the simplistic picture of unit-cell symmetry increase upon heating. The temperature increase significantly enhances the short-range structural distortions of the lead halide framework as a consequence of the phonon anharmonicity, which causes the excess free energy surface to change as a function of temperature. As a result, phase transitions can be rationalized via the soft-mode model, which also describes displacive thermal phase transitions in oxide perovskites. Our findings allow to reconcile temperature-dependent modifications of physical properties, such as changes in the optical band gap, that are incompatible with the perovskite time- and space-average structures.

One-Shot Approach for Enforcing Piecewise Linearity on Hybrid Functionals: Application to Band Gap Predictions.

We present an efficient procedure for constructing nonempirical hybrid functionals to accurately predict band gaps of extended systems. We determine mixing parameters by enforcing the generalized Koopmans' condition on localized electron states, which are achieved by inserting an optimized potential probe. Application of this scheme to a large set of materials yields band gaps with a mean error of 0.30 eV with respect to experiment. Next, we consider a perturbative one-shot approach in which the single-particle eigenvalues are calculated with the wave functions obtained at the semilocal level. In this way, the computational cost is reduced by ∼85% without loss of accuracy. The scheme is found to be robust upon consideration of different defect species and functional forms.

Electronic Structure of Water from Koopmans-Compliant Functionals.

Obtaining a precise theoretical description of the spectral properties of liquid water poses challenges for both molecular dynamics (MD) and electronic structure methods. The lower computational cost of the Koopmans-compliant functionals with respect to Green's function methods allows the simulations of many MD trajectories, with a description close to the state-of-art quasi-particle self-consistent GW plus vertex corrections method (QSGW + fxc). Thus, we explore water spectral properties when different MD approaches are used, ranging from classical MD to first-principles MD, and including nuclear quantum effects. We have observed that different MD approaches lead to up to 1 eV change in the average band gap; thus, we focused on the band gap dependence with the geometrical properties of a system to explain such spread. We have evaluated the changes in the band gap due to variations in the intramolecular O-H bond distance and HOH angle, as well as the intermolecular hydrogen bond O···O distance and the OHO angles. We have observed that the dominant contribution comes from the O-H bond length; the O···O distance plays a secondary role, and the other geometrical properties do not significantly influence the gap. Furthermore, we analyze the electronic density of states (DOS), where the KIPZ functional shows good agreement with the DOS obtained with state-of-art approaches employing quasi-particle self-consistent GW plus vertex corrections. The O-H bond length also significantly influences the DOS. When nuclear quantum effects are considered, broadening of the peaks driven by the broader distribution of the O-H bond lengths is observed, leading to a closer agreement with the experimental photoemission spectra.

High-performance NiOOH/FeOOH electrode for OER catalysis.

The outstanding performance of NiOOH/FeOOH-based oxygen evolution reaction (OER) catalysts is rationalized in terms of a bifunctional mechanism involving two distinct active sites. In this mechanism, the OOHads reaction intermediate, which unfavorably affects the overall OER activity due to the linear scaling relationship, is replaced by O2 adsorbed at the active site on FeOOH and Hads adsorbed at the NiOOH substrate. Here, we use the computational hydrogen electrode method to assess promising models of both the FeOOH catalyst and the NiOOH hydrogen acceptor. These two materials are interfaced in various ways to evaluate their performance as bifunctional OER catalysts. In some cases, overpotentials as low as 0.16 V are found, supporting the bifunctional mechanism as a means to overcome the limitations imposed by linear scaling relationships.

Low-Frequency Dielectric Response of Tetragonal Perovskite CH3NH3PbI3.

The dielectric properties of tetragonal hybrid perovskite CH3NH3PbI3 are studied through molecular dynamics at a temperature of 300 K in the presence of a finite electric field. The high-frequency dielectric constant ε∞ is found to be 4.5 along the a axis and 4.7 along the c axis. The values of the respective static dielectric constants ε0 are 43 ± 1 and 53 ± 3, much larger than the value of ∼25 pertaining to the orthorhombic phase, in which the organic cations cannot rotate. At frequencies below 3 cm-1, we observe a significant increase in ε0 by ∼23 (a axis) and ∼30 (c axis) compared to a vibrational approach, which does not account for the reorientation of the molecular units. The decomposition shows that the reorientation of the organic cations accounts for an increase of only ∼10. An increase of similar size results from the displacement of the cations within the cages of the lattice. The dominant contribution is found to arise from lattice vibrations coupled to the motion of the organic cations.

Hydrogen Bonding of Ammonia with (H,OH)-Si(001) Revealed by Experimental and Ab Initio Photoelectron Spectroscopy.

Combining experimental and ab initio core-level photoelectron spectroscopy (periodic DFT and quantum chemistry calculations), we elucidated how ammonia molecules bond to the hydroxyls of the (H,OH)-Si(001) model surface at a temperature of 130 K. Indeed, theory evaluated the magnitude and direction of the N 1s (and O 1s) chemical shifts according to the nature (acceptor or donor) of the hydrogen bond and, when confronted to experiment, showed unambiguously that the probe molecule makes one acceptor and one donor bond with a pair of hydroxyls. The consistency of our approach was proved by the fact that the identified adsorption geometries are precisely those that have the largest binding strength to the surface, as calculated by periodic DFT. Real-time core-level photoemission enabled measurement of the adsorption kinetics of H-bonded ammonia and its maximum coverage (0.37 ML) under 1.5 × 10-9 mbar. Experimental desorption free energies were compared to the magnitude of the adsorption energies provided by periodic DFT calculations. Minority species were also detected on the surface. As in the case of H-bonded ammonia, DFT core-level calculations were instrumental to attribute these minority species to datively bonded ammonia molecules, associated with isolated dangling bonds remaining on the surface, and to dissociated ammonia molecules, resulting largely from beam damage.

Oxygen evolution reaction: Bifunctional mechanism breaking the linear scaling relationship.

The bifunctional mechanism for the oxygen evolution reaction (OER) involving two distinct reaction sites is studied through the computational hydrogen electrode method for a set of catalyst materials including rutile TiO2(110), anatase TiO2(101), SnO2(110), RuO2(110), IrO2(110), Ni2P(0001), and BiVO4(001). The calculations are performed both at the semilocal level and at the hybrid functional level. Moreover, anodic conditions are modeled and their effect on the OER free energy steps is evaluated. The free energies of the reaction steps indicate that for specific combinations of catalysts, the limitations due to the linear scaling relationship can be overcome, leading to smaller overpotentials for the overall OER. At the same time, a detailed analysis of the results reveals a strong dependence on the adopted functional. For both functionals, it is shown that the energy level of the highest occupied electronic state can serve as a descriptor to guide the search for the optimal catalyst acting as a hydrogen acceptor. These results support the bifunctional mechanism as a means to break the linear scaling relationship and to further reduce the overpotential of the OER.

Electron and Hole Polarons at the BiVO4-Water Interface.

We determine the transition levels of electron and hole polarons at the BiVO4-water interface through thermodynamic integration within a hybrid functional scheme, thereby accounting for the liquid nature of the water component. The electron polaron is found to be less stable at the interface than in the bulk by 0.18 eV, while for the hole polaron the binding energy increases by 0.20 eV when the charge localizes in the surface layer of BiVO4. These results indicate that interfacial effects on the polaron binding energy and charge distribution are sizeable and cannot trivially be inferred from bulk calculations.

Picture of the wet electron: a localized transient state in liquid water.

A transient state of the excess electron in liquid water preceding the development of the solvation shell, the so-called wet electron, has been invoked to explain spectroscopic observations, but its binding energy and atomic structure have remained highly elusive. Here, we carry out hybrid functional molecular dynamics to unveil the ultrafast solvation mechanism leading to the hydrated electron. In the pre-hydrated regime, the electron is found to repeatedly switch between a quasi-free electron state in the conduction band and a localized state with a binding energy of 0.26 eV, which we assign to the wet electron. This transient state self-traps in a region of the liquid which extends up to ∼4.5 Šand involves a severe disruption of the hydrogen-bond network. Our picture provides an unprecedented view on the nature of the wet electron, which is instrumental to understanding the properties of this fundamental species in liquid water.

Oxide versus Nonoxide Cathode Materials for Aqueous Zn Batteries: An Insight into the Charge Storage Mechanism and Consequences Thereof.

Aqueous Zn-ion batteries, which are being proposed as large-scale energy storage solutions because of their unparalleled safety and cost advantage, are composed of a positive host (cathode) material, a metallic zinc anode, and a mildly acidic aqueous electrolyte (pH ≈ 3-7). Typically, the charge storage mechanism is believed to be reversible Zn2+ (de)intercalation in the cathode host, with the exception of α-MnO2, for which multiple vastly different and contradicting mechanisms have been proposed. However, our present study, combining electrochemical, operando X-ray diffraction, electron microscopy in conjunction with energy-dispersive X-ray spectroscopy, and in situ pH evolution analyses on two oxide hosts-tunneled α-MnO2 and layered V3O7·H2O vis-à-vis two nonoxide hosts-layered VS2 and tunneled Zn3[Fe(CN)6]2, suggests that oxides and nonoxides follow two dissimilar charge storage mechanisms. While the oxides behave as dominant proton intercalation materials, the nonoxides undergo exclusive zinc intercalation. Stabilization of H+ on the hydroxyl-terminated oxide surface is revealed to facilitate the proton intercalation by a preliminary molecular dynamics simulation study. Proton intercalation for both oxides leads to the precipitation of layered double hydroxide (LDH)-Zn4SO4(OH)6·5H2O with a ZnSO4/H2O electrolyte and a triflate anion (CF3SO3-)-based LDH with a Zn(SO3CF3)2/H2O electrolyte-on the electrode surface. The LDH precipitation buffers the pH of the electrolytes to a mildly acidic value, sustaining the proton intercalation to deliver large specific capacities for the oxides. Moreover, we also show that the stability of the LDH precipitate is crucial for the rechargeability of the oxide cathodes, revealing a critical link between the charge storage mechanism and the performance of the oxide hosts in aqueous zinc batteries.

Reactivity and energy level of a localized hole in liquid water.

We study the reactivity and the energy level associated with the reduction of the H2O˙+ radical cation in liquid water by combining ab initio molecular dynamics simulations at the hybrid functional level, a grand-canonical formulation of solutes in aqueous solution, and nudge-elastic-band calculations. We demonstrate that this extremely oxidative solute promptly dissociates and calculate an energy barrier for the reaction of 0.06 eV, consistent with the short measured lifetimes. We calculate the energy level related to the H2O˙+/H2O redox couple with respect to the vacuum level and to the computational standard hydrogen electrode (SHE), using the thermodynamic integration method. This energy level is found to lie at 3.8 ± 0.1 eV above the SHE level, in remarkable agreement with a previous estimate based on thermodynamical data. The implications of the present results for the mechanism of water splitting at the heterogenous semiconductor-water interface are discussed.

Sizable Excitonic Effects Undermining the Photocatalytic Efficiency of ß-Cu2V2O7.

Copper vanadates have been proposed as promising photoanodes for water-splitting photoelectrochemical cells, but their performance has recently been shown to be severely limited. To understand this behavior, we study the electronic structure and the optical properties of ß-Cu2V2O7 both experimentally and computationally. The measured absorption spectrum shows an absorption peak at 1.5 eV followed by the onset of an apparent continuum at 2.26 eV, as generally found for this class of materials. We perform calculations within the framework of the QS GW̃ method and the Bethe-Salpeter equation while including effects of magnetic ordering, nuclear quantum motion, and thermal vibrations. We demonstrate the occurrence of two kinds of excitons with high binding energies upon optical excitation in ß-Cu2V2O7, which account for the first absorption peak and the lower edge of the apparent continuum. The results are confirmed by photoluminescence measurements, where sub-band-gap emissions are found for both excitons. These results provide an explanation for the low photocatalytic efficiencies of copper vanadates, despite the favorable size of their optical band gaps.

Absolute Energy Levels of Liquid Water.

We determine the ionization potential (IP) and the electron affinity (EA) of liquid water together with the absolute redox level of the standard hydrogen electrode (SHE) by combining advanced electronic-structure calculations, ab initio molecular dynamics simulations, thermodynamic integration, and potential alignment at the water-vacuum interface. The calculated SHE level lies at 4.56 eV below the vacuum level, close to the experimental reference of 4.44 eV inferred by Trasatti. The band edges are determined through a hybrid functional designed to reproduce the band gap achieved with highly accurate GW calculations. Our analysis yields IP = 9.7 eV and EA = 0.8 eV, consistent with both photoemission spectra of liquid water and thermodynamical data for the hydrated electron.

pH-Dependent Surface Chemistry from First Principles: Application to the BiVO4(010)-Water Interface.

We present a theoretical formulation for studying the pH-dependent interfacial coverage of semiconductor-water interfaces through ab initio electronic structure calculations, molecular dynamics simulations, and the thermodynamic integration method. This general methodology allows one to calculate the acidity of the individual adsorption sites on the surface and consequently the pH at the point of zero charge, pHPZC, and the preferential adsorption mode of water molecules, either molecular or dissociative, at the semiconductor-water interface. The proposed method is applied to study the BiVO4(010)-water interface, yields a pHPZC in excellent agreement with the experimental characterization. Furthermore, from the calculated p Ka values of the individual adsorption sites, we construct an ab initio concentration diagram of all adsorbed species at the interface as a function of the pH of the aqueous solution. The diagram clearly illustrates the pH-dependent coverage of the surface and indicates that protons are found to be significantly adsorbed (∼1% of available sites) only in highly acidic conditions. The surface is found to be mostly covered by molecularly adsorbed water molecules in a wide interval of pH values ranging from 2 to 8. Hydroxyl ions are identified as the dominant adsorbed species at pH larger than 8.2.