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.

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.

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.

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.

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.

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.

Note: Assessment of the SCAN+rVV10 functional for the structure of liquid water.

The performance of the SCAN+rVV10 functional in modeling the structural properties of liquid water is studied through constant-volume ab initio molecular dynamics simulations with both classical and quantum nuclei. The radial distribution functions are found to be slightly overstructured with respect to experiment, but overall similar to those achieved with the bare SCAN and the rVV10 functionals. From the pressures calculated during the dynamics, it is inferred that the SCAN+rVV10 functional leads to a noticeable overestimation of the density of liquid water.

Ab initio Electronic Structure of Liquid Water.

Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through ab initio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7 eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9 eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at -9.4 and -0.5 eV with respect to the vacuum level, respectively.

Redox levels in aqueous solution: Effect of van der Waals interactions and hybrid functionals.

We investigate redox levels in aqueous solution using a combination of ab initio molecular dynamics (MD) simulations and thermodynamic integration methods. The molecular dynamics are performed with both the semilocal Perdew-Burke-Ernzerhof functional and a nonlocal functional (rVV10) accounting for van der Waals (vdW) interactions. The band edges are determined through three different schemes, namely, from the energy of the highest occupied and of the lowest unoccupied Kohn-Sham states, from total-energy differences, and from a linear extrapolation of the density of states. It is shown that the latter does not depend on the system size while the former two are subject to significant finite-size effects. For the redox levels, we provide a formulation in analogy to the definition of charge transition levels for defects in crystalline materials. We consider the H(+)/H2 level defining the standard hydrogen electrode, the OH(-)/OH(∗) level corresponding to the oxidation of the hydroxyl ion, and the H2O/OH(∗) level for the dehydrogenation of water. In spite of the large structural modifications induced in liquid water, vdW interactions do not lead to any significant structural effect on the calculated band gap and band edges. The effect on the redox levels is also small since the solvation properties of ionic species are little affected by vdW interactions. Since the electronic properties are not significantly affected by the underlying structural properties, it is justified to perform hybrid functional calculations on the configurations of our MD simulations. The redox levels calculated as a function of the fraction α of Fock exchange are found to remain constant, reproducing a general behavior previously observed for charge transition levels of defects. Comparison with experimental values shows very good agreement. At variance, the band edges and the band gap evolve linearly with α. For α ≃ 0.40, we achieve a band gap, band-edge positions, and redox levels in overall good agreement with experiment.

Isobaric first-principles molecular dynamics of liquid water with nonlocal van der Waals interactions.

We investigate the structural properties of liquid water at near ambient conditions using first-principles molecular dynamics simulations based on a semilocal density functional augmented with nonlocal van der Waals interactions. The adopted scheme offers the advantage of simulating liquid water at essentially the same computational cost of standard semilocal functionals. Applied to the water dimer and to ice Ih, we find that the hydrogen-bond energy is only slightly enhanced compared to a standard semilocal functional. We simulate liquid water through molecular dynamics in the NpH statistical ensemble allowing for fluctuations of the system density. The structure of the liquid departs from that found with a semilocal functional leading to more compact structural arrangements. This indicates that the directionality of the hydrogen-bond interaction has a diminished role as compared to the overall attractions, as expected when dispersion interactions are accounted for. This is substantiated through a detailed analysis comprising the study of the partial radial distribution functions, various local order indices, the hydrogen-bond network, and the selfdiffusion coefficient. The explicit treatment of the van der Waals interactions leads to an overall improved description of liquid water.

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.

Finite-size supercell correction for charged defects at surfaces and interfaces.

A finite-size supercell correction scheme is introduced for the formation energy of charged defects at surfaces and interfaces. The scheme combines classical electrostatics with the dielectric profile and the electrostatic potential extracted from the electronic-structure calculation. Spurious electrostatic interactions are removed while retaining the dielectric and quantum-mechanical features of the system of interest, which may have no interface (bulk), a single interface or surface, or two interfaces. A pertinent extrapolation scheme validates the proposed corrections. Applications to the charged Cl vacancy at the surface of NaCl and to the dangling bond at the Si(100) surface show that the corrected formation energies are largely independent of the supercell dimensions and of the size of the vacuum region.

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.

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.

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.

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.

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.