Density functional theory (DFT) calculations of charged molecules and surfaces are critical to applications in electro-catalysis, energy materials and related fields of materials science. DFT implementations such as the Vienna ab-initio Simulation Package (VASP) compute the electrostatic potential under 3D periodic boundary conditions, necessitating charge neutrality. In this work, we implement 0D and 2D periodic boundary conditions to facilitate DFT calculations of charged molecules and surfaces respectively. We implement these boundary conditions using the Coulomb kernel truncation method. Our implementation computes the potential under 0D and 2D boundary conditions by selectively subtracting unwanted long-range interactions in the potential computed under 3D boundary conditions. By combining the Coulomb kernel truncation method with a computationally efficient padding approach, we remove nonphysical potentials from vacuum in 0D and 2D systems. To illustrate the computational efficiency of our method, we perform large supercell calculations of the formation energy of a charged chlorine defect on a sodium chloride (001) surface and perform long time-scale molecular dynamics simulations on a stepped gold (211) | water electrode-electrolyte interface.

We present a constrained Random Phase Approximation (cRPA) method, termed spectral cRPA (s-cRPA), and compare it to established cRPA approaches for Scandium and Copper by varying the 3d shell filling. The s-cRPA method generally produces larger Hubbard U interaction values compared to conventional approaches. When applied to the realistic system CaFeO$_3$ , s-cRPA yields interaction parameters that align more closely with those required within DFT+U to reproduce the experimentally observed insulating state, addressing the metallic behaviour predicted by standard density functionals. We examine the issue of negative interaction values encountered in the projector cRPA method for filled d-shells. We show that s-cRPA provides improved numerical stability by preserving electron number conservation, a constraint that is violated in the projector cRPA method. The s-cRPA approach addresses some limitations of standard cRPA methods, particularly the tendency to underestimate U values, suggesting its potential utility for the community. Additionally, we have enhanced our implementation to include computation of multi-centre interactions for analysing spatial decay and developed an efficient low-scaling variant employing a compressed Matsubara grid to obtain full frequency-dependent interactions.

The atomic structure of the most stable reconstructed surface of cuprous oxide (Cu$_{2}$O)(111) surface has been a longstanding topic of debate. In this study, we develop on-the-fly machine-learned force fields (MLFFs) to systematically investigate the various reconstructions of the Cu$_{2}$O(111) surface under stoichiometric as well as O- and Cu-deficient or rich conditions, focusing on both ($\sqrt{3}$$\times$$\sqrt{3}$)R30° and (2$\times$2) supercells. By utilizing parallel tempering simulations supported by MLFFs, we confirm that the previously described nanopyramidal and Cu-deficient (1$\times$1) structures are the lowest energy structures from moderately to strong oxidizing conditions. In addition, we identify two promising nanopyramidal reconstructions at highly reducing conditions, a stoichiometric and a Cu-rich one. Surface energy calculations performed using spin-polarized PBE, PBE+U, r$^{2}$SCAN, and HSE06 functionals show that the previously known Cu-deficient configuration and nanopyramidal configurations are at the convex hull (and, thus, equilibrium structures) for all functionals, whereas the stability of the other structures depends on the functional and is therefore uncertain. Our findings demonstrate that on-the-fly trained MLFFs provide a simple, efficient, and rapid approach to explore the complex surface reconstructions commonly encountered in experimental studies, and also enhance our understanding of the stability of Cu$_{2}$O(111) surfaces.

Monolayers of transition-metal dichalcogenides (TMDs) hold great promise as future nanoelectronic and optoelectronic devices. An essential feature for achieving high device performance is the use of suitable supporting substrates, which can affect the electronic and optical properties of these two-dimensional (2D) materials. Here, we perform many-body GW calculations using the SternheimerGW method to investigate the quasiparticle band structure of monolayer MoS2 subject to an effective dielectric screening model, which is meant to approximately describe substrate polarization in real device applications. We show that, within this model, the dielectric screening has a sizable effect on the quasiparticle band gap; for example, the gap renormalization is as large as 250 meV for MoS2 with model screening corresponding to SiO2. Within the G0W0 approximation, we also find that the inclusion of the effective screening induces a direct band gap, in contrast to the unscreened monolayer. We also find that the dielectric screening induces an enhancement of the carrier effective masses by as much as 27% for holes, shifts plasmon satellites, and redistributes quasiparticle weight. Our results highlight the importance of the dielectric environment in the design of 2D TMD-based devices.

We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $\Delta$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.

This study presents a long-range descriptor for machine learning force fields (MLFFs) that maintains translational and rotational symmetry, similar to short-range descriptors while being able to incorporate long-range electrostatic interactions. The proposed descriptor is based on an atomic density representation and is structurally similar to classical short-range atom-centered descriptors, making it straightforward to integrate into machine learning schemes. The effectiveness of our model is demonstrated through comparative analysis with the long-distance equivariant (LODE) descriptor. In a toy model with purely electrostatic interactions, our model achieves errors below 0.1%, worse than LODE but still very good. For real materials, we perform tests for liquid NaCl, rock salt NaCl, and solid zirconia. For NaCl, the present descriptors improve on short-range density descriptors, reducing errors by a factor of two to three and coming close to message-passing networks. However, for solid zirconia, no improvements are observed with the present approach, while message-passing networks reduce the error by almost a factor of two to three. Possible shortcomings of the present model are briefly discussed.

We evaluate the zero-point renormalization (ZPR) due to electron-phonon interactions of 28 solids using the projector-augmented-wave (PAW) method. The calculations cover diamond, many zincblende semiconductors, rock-salt and wurtzite oxides, as well as silicate and titania. Particular care is taken to include long-range electrostatic interactions via a generalized Fr\"ohlich model, as discussed in Phys. Rev. Lett. 115, 176401 (2015) and Phys. Rev. B 92, 054307 (2015). The data are compared to recent calculations, npj Computational Materials 6, 167 (2020), and generally very good agreement is found. We discuss in detail the evaluation of the electron-phonon matrix elements within the PAW method. We show that two distinct versions can be obtained depending on when the atomic derivatives are taken. If the PAW transformation is applied before taking derivatives with respect to the ionic positions, equations similar to the ones conventionally used in pseudopotential codes are obtained. If the PAW transformation is used after taking the derivatives, the full-potential spirit is largely maintained. We show that both variants yield very similar ZPRs for selected materials when the rigid-ion approximation is employed. In practice, we find however that the pseudo version converges more rapidly with respect to the number of included unoccupied states.

Realistic finite temperature simulations of matter are a formidable challenge for first principles methods. Long simulation times and large length scales are required, demanding years of compute time. Here we present an on-the-fly machine learning scheme that generates force fields automatically during molecular dynamics simulations. This opens up the required time and length scales, while retaining the distinctive chemical precision of first principles methods and minimizing the need for human intervention. The method is widely applicable to multi-element complex systems. We demonstrate its predictive power on the entropy driven phase transitions of hybrid perovskites, which have never been accurately described in simulations. Using machine learned potentials, isothermal-isobaric simulations give direct insight into the underlying microscopic mechanisms. Finally, we relate the phase transition temperatures of different perovskites to the radii of the involved species, and we determine the order of the transitions in Landau theory.

Redox potentials of electron transfer reactions are of fundamental importance for the performance and description of electrochemical devices. Despite decades of research, accurate computational predictions for the redox potential of even simple metals remain very challenging. Here we use a combination of first principles calculations and machine learning to predict the redox potentials of three redox couples, $\mathrm{Fe}^{2+}$/$\mathrm{Fe}^{3+}$, $\mathrm{Cu}^{+}$/$\mathrm{Cu}^{2+}$ and $\mathrm{Ag}^{+}$/$\mathrm{Ag}^{2+}$. Using a hybrid functional with a fraction of 25\% exact exchange (PBE0) the predicted values are 0.92, 0.26 and 1.99 V in good agreement with the best experimental estimates (0.77, 0.15, 1.98 V). We explain in detail, how we combine machine learning, thermodynamic integration from machine learning to semi-local functionals, as well as a combination of thermodynamic perturbation theory and $\Delta$-machine learning to determine the redox potentials for computationally expensive hybrid functionals. The combination of these approaches allows one to obtain statistically accurate results.

We introduce SurfFlow, an open-source high-throughput workflow package designed for automated first-principles calculations of surface energies in arbitrary crystals. Our package offers a comprehensive solution capable of handling multi-element crystals, nonstoichiometric compositions, and asymmetric slabs, for all potential terminations. To streamline the computational process, SurfFlow employs an efficient pre-screening method that discards surfaces with suspected high surface energy before conducting resource-intensive density functional theory computations. The results generated are seamlessly compiled into an optimade-compliant database, ensuring easy access and compatibility. Additionally, a user-friendly web interface facilitates workflow submission and management, provides result visualization, and enables the examination of Wulff shapes. SurfFlow represents a valuable tool for researchers looking to explore surface energies and their implications in a diverse range of systems.

The GW approximation represents the state-of-the-art ab-initio method for computing excited-state properties. Its execution requires control over a larger number of (often interdependent) parameters, and therefore its application in high-throughput studies is hindered by the intricate and time-consuming convergence process across a multi-dimensional parameter space. To address these challenges, here we develop a fully-automated open-source workflow for G$_0$W$_0$ calculations within the AiiDA-VASP plugin architecture. The workflow is based on an efficient estimation of the errors on the quasi-particle (QP) energies due to basis-set truncation and the pseudo-potential norm violation, which allows a reduction of the dimensionality of the parameter space and avoids the need for multi-dimensional convergence searches. Protocol validation is conducted through a systematic comparison against established experimental and state-of-the-art GW data. To demonstrate the effectiveness of the approach, we construct a database of QP energies for a diverse dataset of over 320 bulk structures. The openly accessible workflow and resulting dataset can serve as a valuable resource and reference for conducting accurate data-driven research.

In the past decades many density-functional theory methods and codes adopting periodic boundary conditions have been developed and are now extensively used in condensed matter physics and materials science research. Only in 2016, however, their precision (i.e., to which extent properties computed with different codes agree among each other) was systematically assessed on elemental crystals: a first crucial step to evaluate the reliability of such computations. We discuss here general recommendations for verification studies aiming at further testing precision and transferability of density-functional-theory computational approaches and codes. We illustrate such recommendations using a greatly expanded protocol covering the whole periodic table from Z=1 to 96 and characterizing 10 prototypical cubic compounds for each element: 4 unaries and 6 oxides, spanning a wide range of coordination numbers and oxidation states. The primary outcome is a reference dataset of 960 equations of state cross-checked between two all-electron codes, then used to verify and improve nine pseudopotential-based approaches. Such effort is facilitated by deploying AiiDA common workflows that perform automatic input parameter selection, provide identical input/output interfaces across codes, and ensure full reproducibility. Finally, we discuss the extent to which the current results for total energies can be reused for different goals (e.g., obtaining formation energies).

In this study, we present a systematic comparison of various approaches within the constrained random-phase approximation (cRPA) for calculating the Coulomb interaction parameter $U$. While defining the correlated space is straightforward for disentangled bands, the situation is more complex for entangled bands, where different projection schemes from hybridized bands to the target space can yield varying sizes of interaction parameters. We systematically evaluated different methods for calculating the polarizability functions within the correlated space. Furthermore, we analyze how different definitions of the correlated space, often constructed through Wannierization from Kohn-Sham orbitals, defines the orbital localization and play a crucial role in determining the interaction parameter. To illustrate these effects, we consider two sets of representative correlated d-orbital oxides: LiMO$_{2}$ (M = V-Ni) as examples of isolated d-electron systems and SrMO$_{3}$ (M = Mn, Fe, and Co) as cases of entangled d-electron systems. Through this systematic comparison, we provide a detailed analysis of different cRPA methodologies for computing the Hubbard parameters.

Intriguing analogies between the nickelates and the cuprates provide a promising avenue for unraveling the microscopic mechanisms underlying high-$T_c$ superconductivity. While electron correlation effects in the nickelates have been extensively studied, the role of electron-phonon coupling (EPC) remains highly controversial. Here, by taking pristine LaNiO$_2$ as an exemplar nickelate, we present an in-depth study of EPC for both the non-magnetic (NM) and the $C$-type antiferromagnetic ($C$-AFM) phase using advanced density functional theory methods without invoking $U$ or other free parameters. The weak EPC strength $\lambda$ in the NM phase is found to be greatly enhanced ($\sim$4$\times$) due to the presence of magnetism in the $C$-AFM phase. This enhancement arises from strong interactions between the flat bands associated with the Ni-3$d_{z^2}$ orbitals and the low-frequency phonon modes driven by the vibrations of Ni and La atoms. The resulting phonon softening is shown to yield a distinctive kink in the electronic structure around 15 meV, which would provide an experimentally testable signature of our predictions. Our study highlights the critical role of local magnetic moments and interply EPC in the nickelate.

We present an implementation of spin-orbit coupling (SOC) for the computation of nuclear magnetic resonance (NMR) chemical shielding tensors within linear response theory. Our implementation in the Vienna {\it Ab initio} Simulation Package (VASP) is tailored to solid-state systems by employing periodic boundary conditions and the gauge-including projector augmented waves (GIPAW) approach. Relativistic effects are included on the level of the zeroth-order regular approximation (ZORA). We discuss the challenges posed by the PAW partial wave basis in describing SOC regarding chemical shielding tensors. Our method is in good agreement with existing local-basis ZORA implementations for a series of Sn, Hg, and Pb molecules and cluster approximations for crystalline systems.

Polarons are widespread in functional materials and are key to device performance in several technological applications. However, their effective impact on material behavior remains elusive, as condensed matter studies struggle to capture their intricate interplay with atomic defects in the crystal. In this work, we present an automated workflow for modeling polarons within density functional theory (DFT). Our approach enables a fully automatic identification of the most favorable polaronic configurations in the system. Machine learning techniques accelerate predictions, allowing for an efficient exploration of the defect-polaron configuration space. We apply this methodology to Nb-doped TiO$_2$(110) surfaces, providing new insights into the role of defects in surface reactivity. Using CO adsorbates as a probe, we find that Nb doping has minimal impact on reactivity, whereas oxygen vacancies contribute significantly depending on their local arrangement via the stabilization of polarons on the surface atomic layer. Our package streamlines the modeling of charge trapping and polaron localization with high efficiency, enabling systematic, large-scale investigations of polaronic effects across complex material systems.

We implement the phaseless auxiliary field quantum Monte Carlo method using the plane-wave based projector augmented wave method and explore the accuracy and the feasibility of applying our implementation to solids. We use a singular value decomposition to compress the two-body Hamiltonian and thus reduce the computational cost. Consistent correlation energies from the primitive-cell sampling and the corresponding supercell calculations numerically verify our implementation. We calculate the equation of state for diamond and the correlation energies for a range of prototypical solid materials. A down-sampling technique along with natural orbitals accelerates the convergence with respect to the number of orbitals and crystal momentum points. We illustrate the competitiveness of our implementation in accuracy and computational cost for dense crystal momentum point meshes comparing to a well-established quantum-chemistry approach, the coupled-cluster ansatz including singles, doubles and perturbative triple particle-hole excitation operators.

Modern computing facilities grant access to first-principles density-functional theory study of complex physical and chemical phenomena in materials, that require large supercell to properly model the system. However, supercells are associated to small Brillouin zones in the reciprocal space, leading to folded electronic eigenstates that make the analysis and interpretation extremely challenging. Various techniques have been proposed and developed in order to reconstruct the electronic band structures of super cells, unfolded into the reciprocal space of an ideal primitive cell. Here, we propose an efficient unfolding scheme embedded directly in the Vienna Ab-initio Simulation Package (VASP), that requires modest computational resources and allows for an automatized mapping from the reciprocal space of the supercell to primitive cell Brillouin zone. This algorithm can computes band structures, Fermi surfaces and spectral functions, by using an integrated post-processing tool (bands4vasp). The method is here applied to a selected variety of complex physical situations: the effect of doping on the band dispersion in the BaFe$_{\rm 2(1-x)}$Ru$_{\rm 2x}$As$_2$ superconductor, the interaction between adsorbates and polaronic states on the TiO$_2$(110) surface, and the band splitting induced by non-collinear spin fluctuations in EuCd$_2$As$_2$.

Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zirconia, an important transition metal oxide. This machine-learned potential accurately captures the temperature-induced phase transitions below the melting point. We further showcase the predictive power of the potential by calculating the heat transport on the basis of Green-Kubo theory, which allows to account for anharmonic effects to all orders. This study indicates that machine-learned potentials trained on the fly offer a routine solution for accurate and efficient simulations of the thermodynamic properties of a vast class of anharmonic materials.

Adsorption of carbon monoxide (CO) on transition-metal surfaces is a prototypical process in surface sciences and catalysis. Despite its simplicity, it has posed great challenges to theoretical modeling. Pretty much all existing density functionals fail to accurately describe surface energies, CO adsorption site preference, as well as adsorption energies simultaneously. Although the random phase approximation (RPA) cures these density functional theory failures, its large computational cost makes it prohibitive to study the CO adsorption for any but the simplest ordered cases. Here, we address these challenges by developing a machine-learned force field (MLFF) with near RPA accuracy for the prediction of coverage-dependent adsorption of CO on the Rh(111) surface through an efficient on-the-fly active learning procedure and a $\Delta$-machine learning approach. We show that the RPA-derived MLFF is capable to accurately predict the Rh(111) surface energy, CO adsorption site preference as well as adsorption energies at different coverages that are all in good agreement with experiments. Moreover, the coverage-dependent ground-state adsorption patterns and adsorption saturation coverage are identified.