Many interesting systems, such as interfaces, surfaces, grain boundaries, and nanoparticles, cont... more Many interesting systems, such as interfaces, surfaces, grain boundaries, and nanoparticles, contain so many atoms that quantum-mechanical atomistic simulations become inconvenient or outright impossible. It is therefore desirable to develop accurate and flexible general-purpose interatomic potentials to make it possible to explore the potential energy surface of such structures. In this work we generate a neural-network potential through charge equilibration technique (CENT) for Ti x Zr 1−x O 2 with 0 x 1. Optimized symmetry functions for multicomponent systems make it possible to train the potential on less than 10 000 diverse structures containing different cation ratios x, from pure TiO 2 to ZrO 2 , in free and periodic boundary conditions in the framework of density functional theory. The combination of the CENT potential with the symmetry functions generates a flexible and reliable method to reproduce the complexity of the energy landscape of these mixed materials with different boundary conditions at zero pressure. The reliability and transferability of the potential are verified by calculating some properties of bulk and slab configurations. Moreover, in order to investigate the performance of potential for different crystal phases and cluster configurations which are not included in our training data set, we performed a crystal structure search by minima hopping method. Beside reproducing known results in agreement with DFT calculations, we discovered novel crystal structures for bulk TiZr 3 O 8 and TiZrO 4 , as well as for small clusters and ZrO 2 nanoparticles.
Hematite is a promising material for photoelectrochemical water splitting applications and unders... more Hematite is a promising material for photoelectrochemical water splitting applications and understanding the complete mechanism of water oxidation reaction close to its surfaces is of great importance. Herein, we present a theoretical investigation of the electronic states of nonstoichiometric hematite(0001) films in the presence of absorbed H on the surfaces, as well as Ti doping. The calculations, performed at the DFT + U level, indicate that iron can appear in different oxidation states, from Fe 2+ to Fe 4+ and Fe 5+ in the vicinity of impurities or surfaces. The electron and hole distributions in hematite slabs could control the bending and local state of valence and conduction bands. The projected density of states in different atomic positions shows an upward band bending close to the surfaces, which varies with the number of absorbed H or with Ti doping. In the dark, the width of the depletion layer is computed as less than 12 Å for neutral slabs, while adding excess electrons expands it to involve more atomic layers, depending on the number of absorbed H on the surface. In the neutral slabs in the presence of H, we obtain an upward band bending of 0.18, 0.42, and 0.24 eV by increasing the number of H from one to three on each side, respectively. The evolution of bands in neutral slabs, with/without Ti doping, occurs in a few layers in nearby the surface and also Fe with an oxidation state rather than Fe 3+. According to our results, doping Ti creates a polaron and locally affects the band structure. In the charged surface with excess electrons, a metallic behavior is observed on the surface and a large band bending in the middle layers. This work shows that a substantial upward bending of the bands in hematite can exist even at neutral surfaces in contact with a vacuum.
Measuring similarities/dissimilarities between atomic structures is important for the exploration... more Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.
We report on an extensive study of ZnO materials with cage-like motives in clusters and bulk phas... more We report on an extensive study of ZnO materials with cage-like motives in clusters and bulk phases through structural searches using the minima hopping method. A novel putative ground state was discovered for the (ZnO)32 cluster with a tube-like structure, closely related to the previously reported (ZnO)24 ground state cage geometry. Furthermore, the effect of ionization on the geometries and energetic ordering of (ZnO)n clusters with n = 3 − 10, 12 was studied by directly sampling the energy landscape of the ionized system. Our results indicate that the transition from ring and planar structures to 3D cages occurs at larger cluster sizes than in the neutral system. Inspired by the bottom-up design philosophy and the predominance of cage-like structures in medium-sized clusters, a search for crystalline ZnO was conducted aimed specifically at low density polymorphs, resulting in the discovery of 57 novel metastable phases. The voids in these low-density materials closely resemble the hollow cage structures of small (ZnO)n/(ZnO) + n clusters with n < 16. In analogy to clathrate materials, these voids could serve to accommodate guest atoms to tailor the materials properties for various applications.
We investigate the accuracy and transferability of a recently developed high-dimensional neural n... more We investigate the accuracy and transferability of a recently developed high-dimensional neural network (NN) method for calcium fluoride, fitted to a database of ab initio density functional theory (DFT) calculations based on the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional. We call the method charge equilibration via neural network technique (CENT). Although the fitting database contains only clusters (i.e., nonperiodic structures), the NN scheme accurately describes a variety of bulk properties. In contrast to other available empirical methods the CENT potential has a much simpler functional form, nevertheless it correctly reproduces the PBE energetics of various crystalline phases both at ambient and high pressure. Surface energies and structures as well as dynamical properties derived from phonon calculations are also in good agreement with PBE results. Overall, the difference between the values obtained by the CENT potential and the PBE reference values is less than or equal to the difference between the values of local density approximation (LDA) and Born-Mayer-Huggins (BMH) with those calculated by the PBE exchange correlation functional.
We present an accurate and efficient algorithm to calculate the electrostatic interaction of char... more We present an accurate and efficient algorithm to calculate the electrostatic interaction of charged point particles with partially periodic boundary conditions that are confined along the nonperiodic direction by two metallic parallel plates. The method preserves the original boundary conditions and hence, it does not introduce any kind of artifacts. In addition, it enjoys the quasilinear complexity of O(N ln(N)), where N being the number of particles in the simulation box. In fact, based on the superposition principle in electrostatics, the problem is split into two electrostatic problems where each one can be calculated by the appropriate Poisson solver. In this paper we apply the method to sodium chloride ultrathin films and investigate its dielectric response with respect to external bias voltage. We show how accurately in this method one can obtain the total charge induced on metallic boundaries to an arbitrary precision.
Many interesting systems, such as interfaces, surfaces, grain boundaries, and nanoparticles, cont... more Many interesting systems, such as interfaces, surfaces, grain boundaries, and nanoparticles, contain so many atoms that quantum-mechanical atomistic simulations become inconvenient or outright impossible. It is therefore desirable to develop accurate and flexible general-purpose interatomic potentials to make it possible to explore the potential energy surface of such structures. In this work we generate a neural-network potential through charge equilibration technique (CENT) for Ti x Zr 1−x O 2 with 0 x 1. Optimized symmetry functions for multicomponent systems make it possible to train the potential on less than 10 000 diverse structures containing different cation ratios x, from pure TiO 2 to ZrO 2 , in free and periodic boundary conditions in the framework of density functional theory. The combination of the CENT potential with the symmetry functions generates a flexible and reliable method to reproduce the complexity of the energy landscape of these mixed materials with different boundary conditions at zero pressure. The reliability and transferability of the potential are verified by calculating some properties of bulk and slab configurations. Moreover, in order to investigate the performance of potential for different crystal phases and cluster configurations which are not included in our training data set, we performed a crystal structure search by minima hopping method. Beside reproducing known results in agreement with DFT calculations, we discovered novel crystal structures for bulk TiZr 3 O 8 and TiZrO 4 , as well as for small clusters and ZrO 2 nanoparticles.
Hematite is a promising material for photoelectrochemical water splitting applications and unders... more Hematite is a promising material for photoelectrochemical water splitting applications and understanding the complete mechanism of water oxidation reaction close to its surfaces is of great importance. Herein, we present a theoretical investigation of the electronic states of nonstoichiometric hematite(0001) films in the presence of absorbed H on the surfaces, as well as Ti doping. The calculations, performed at the DFT + U level, indicate that iron can appear in different oxidation states, from Fe 2+ to Fe 4+ and Fe 5+ in the vicinity of impurities or surfaces. The electron and hole distributions in hematite slabs could control the bending and local state of valence and conduction bands. The projected density of states in different atomic positions shows an upward band bending close to the surfaces, which varies with the number of absorbed H or with Ti doping. In the dark, the width of the depletion layer is computed as less than 12 Å for neutral slabs, while adding excess electrons expands it to involve more atomic layers, depending on the number of absorbed H on the surface. In the neutral slabs in the presence of H, we obtain an upward band bending of 0.18, 0.42, and 0.24 eV by increasing the number of H from one to three on each side, respectively. The evolution of bands in neutral slabs, with/without Ti doping, occurs in a few layers in nearby the surface and also Fe with an oxidation state rather than Fe 3+. According to our results, doping Ti creates a polaron and locally affects the band structure. In the charged surface with excess electrons, a metallic behavior is observed on the surface and a large band bending in the middle layers. This work shows that a substantial upward bending of the bands in hematite can exist even at neutral surfaces in contact with a vacuum.
Measuring similarities/dissimilarities between atomic structures is important for the exploration... more Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.
We report on an extensive study of ZnO materials with cage-like motives in clusters and bulk phas... more We report on an extensive study of ZnO materials with cage-like motives in clusters and bulk phases through structural searches using the minima hopping method. A novel putative ground state was discovered for the (ZnO)32 cluster with a tube-like structure, closely related to the previously reported (ZnO)24 ground state cage geometry. Furthermore, the effect of ionization on the geometries and energetic ordering of (ZnO)n clusters with n = 3 − 10, 12 was studied by directly sampling the energy landscape of the ionized system. Our results indicate that the transition from ring and planar structures to 3D cages occurs at larger cluster sizes than in the neutral system. Inspired by the bottom-up design philosophy and the predominance of cage-like structures in medium-sized clusters, a search for crystalline ZnO was conducted aimed specifically at low density polymorphs, resulting in the discovery of 57 novel metastable phases. The voids in these low-density materials closely resemble the hollow cage structures of small (ZnO)n/(ZnO) + n clusters with n < 16. In analogy to clathrate materials, these voids could serve to accommodate guest atoms to tailor the materials properties for various applications.
We investigate the accuracy and transferability of a recently developed high-dimensional neural n... more We investigate the accuracy and transferability of a recently developed high-dimensional neural network (NN) method for calcium fluoride, fitted to a database of ab initio density functional theory (DFT) calculations based on the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional. We call the method charge equilibration via neural network technique (CENT). Although the fitting database contains only clusters (i.e., nonperiodic structures), the NN scheme accurately describes a variety of bulk properties. In contrast to other available empirical methods the CENT potential has a much simpler functional form, nevertheless it correctly reproduces the PBE energetics of various crystalline phases both at ambient and high pressure. Surface energies and structures as well as dynamical properties derived from phonon calculations are also in good agreement with PBE results. Overall, the difference between the values obtained by the CENT potential and the PBE reference values is less than or equal to the difference between the values of local density approximation (LDA) and Born-Mayer-Huggins (BMH) with those calculated by the PBE exchange correlation functional.
We present an accurate and efficient algorithm to calculate the electrostatic interaction of char... more We present an accurate and efficient algorithm to calculate the electrostatic interaction of charged point particles with partially periodic boundary conditions that are confined along the nonperiodic direction by two metallic parallel plates. The method preserves the original boundary conditions and hence, it does not introduce any kind of artifacts. In addition, it enjoys the quasilinear complexity of O(N ln(N)), where N being the number of particles in the simulation box. In fact, based on the superposition principle in electrostatics, the problem is split into two electrostatic problems where each one can be calculated by the appropriate Poisson solver. In this paper we apply the method to sodium chloride ultrathin films and investigate its dielectric response with respect to external bias voltage. We show how accurately in this method one can obtain the total charge induced on metallic boundaries to an arbitrary precision.
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