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When determining machine-learning models for inter-atomic potentials, the potential energy surface is often described as a non-linear function of descriptors representing two- and three-body atomic distribution functions. It is not obvious how the choice of the descriptors affects the efficiency of the training and the accuracy of the final machine-learned model. In this work, we formulate an efficient method to calculate descriptors that can separately represent two- and three-body atomic distribution functions, and we examine the effects of including only two- or three-body descriptors, as well as including both, in the regression model. Our study indicates that non-linear mixing of two- and three-body descriptors is essential for an efficient training and a high accuracy of the final machine-learned model. The efficiency can be further improved by weighting the two-body descriptors more strongly. We furthermore examine a sparsification of the three-body descriptors. The three-body descriptors usually provide redundant representations of the atomistic structure, and the number of descriptors can be significantly reduced without loss of accuracy by applying an automatic sparsification using a principal component analysis. Visualization of the reduced descriptors using three-body distribution functions in real-space indicates that the sparsification automatically removes the components that are less significant for describing the distribution function.

No abstract is provided for this article.

The (110) surface of many transition metals undergoes reconstructions either on the clean substrate or induced by adsorbates. The reconstructions can be induced by a variety of strongly bound adsorbates, e.g., H, O, S, and alkali-metal atoms. In this work, H/Pd(110) is chosen as a prototype of such reconstructions. The pairing-row and missing-row reconstructions are studied in a wide range of coverages, $\ensuremath{\theta}=0.5--1.5\mathrm{ML},$ by using density-functional theory with the local-density approximation and the generalized gradient approximation. The driving force for the reconstructions is also analyzed in detail. The pairing-row reconstruction is driven essentially by the repulsion between the hydrogen atoms adsorbed in the same trough while the driving force for the missing-row reconstruction is the better adsorbate-substrate interaction on the reconstructed surface.

The hydration free energy of atoms and molecules adsorbed at liquid–solid interfaces strongly influences the stability and reactivity of solid surfaces. However, its evaluation is challenging in both experiments and theories. In this work, a machine learning aided molecular dynamics method is proposed and applied to oxygen atoms and hydroxyl groups adsorbed on Pt(111) and Pt(100) surfaces in water. The proposed method adopts thermodynamic integration with respect to a coupling parameter specifying a path from well-defined non-interacting species to the fully interacting ones. The atomistic interactions are described by a machine-learned inter-atomic potential trained on first-principles data. The free energy calculated by the machine-learned potential is further corrected by using thermodynamic perturbation theory to provide the first-principles free energy. The calculated hydration free energies indicate that only the hydroxyl group adsorbed on the Pt(111) surface attains a hydration stabilization. The observed trend is attributed to differences in the adsorption site and surface morphology.

The reduction of vanadium oxide monolayer structures on Rh(111) has been investigated by variable-temperature scanning tunneling microscopy, low energy electron diffraction, photoelectron spectroscopy of the core levels, and the valence band, and by probing the phonon spectra of the oxide structures in high-resolution electron energy loss spectroscopy. A sequence of oxide phases has been observed following the reduction from the highly oxidized $(\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7})\mathrm{R}19.1\ifmmode^\circ\else\textdegree\fi{}$ V-oxide monolayer: $(5\ifmmode\times\else\texttimes\fi{}5)$, $(5\ifmmode\times\else\texttimes\fi{}3\sqrt{3})\mathrm{rect}$, $(9\ifmmode\times\else\texttimes\fi{}9)$, and ``wagon-wheel'' oxide structures are formed with decreasing chemical potential of oxygen ${\ensuremath{\mu}}_{\mathrm{O}}$. The structures have been simulated by ab initio density functional theory, and structure models are presented. The various V-oxide structures are interrelated by common $\mathrm{V}\mathrm{O}$ coordination units, and the reduction progresses mainly via the removal of $\mathrm{V}\mathrm{O}$ vanadyl groups. All oxide structures are stable at the appropriate ${\ensuremath{\mu}}_{\mathrm{O}}$ only in the two-dimensional V-oxide/Rh(111) phase diagram and are thus stabilized by the metal-oxide interface. The results demonstrate that oxides in ultrathin layer form display modified physical and chemical properties as compared to the bulk oxides.

The athermal equilibrium structure, the equation of state, the elastic constants, and O atom charges were calculated for Mg2SiO4 wadsleyite over a range of pressures using a plane-wave pseudopotential method. The zero-pressure volume is 2% lower and the bulk modulus is 4.5% higher than experimentally observed. After correcting for zero point motion and the 300 K temperature difference between theory and experiment, using a Debye model, the calculated zero pressure volume is within 1% of experiment and the bulk modulus agrees within experimental error. The structure compresses anisotropically with linear moduli for the a, b, and c axes of 610 GPa, 599 GPa, and 454 GPa, respectively. The compression is largely taken up by the Mg octahedra M1, M2, and M3 which are much softer than the Si tetrahedra, with polyhedral bulk moduli of 161 GPa, 159 GPa, 157 GPa, and 331 GPa, respectively. The M1 and M3 octahedra were found to compress anisotropically which explains the greater compressibility of the c axis. The geometry of the Si2O7 group is characterized by a small Si-O-Si angle of 121.2°; compression of this group is largely accommodated by shortening of the Si-O bonds, while the inter-tetrahedral angle is almost pressure independent. We find that our results at ambient pressure are consistent with previously established systematics relating bulk modulus to volume, and Si-O-Si angle to Si-O bond length. However the variation of these quantities upon the application of pressure leads to trends that are distinct from the systematics. The calculated zero pressure elastic constants agree to within 10% with available Brillouin scattering data, with the exception of C12 which is 15% higher than experimentally observed. The calculated isotropically averaged bulk and shear modulus and their pressure derivatives are K0 = 182 GPa, K0' = 4.23, and G0 = 116 GPa, G0' = 1.10, respectively. The aggregate velocities and their pressure derivatives are VP = 9.75 km/s, VP' = 0.056 km/s/GPa, and VS = 5.72 km/s, VS = 0.012 km/s/GPa. We find that the elastic anisotropy of wadsleyite is intermediate between the two other Mg2SiO4 polymorphs, forsterite, and ringwoodite. The anisotropy is only weakly pressure dependent and decreases with increasing pressure. The azimuthal and polarization anisotropy for S waves 14.5% and 12.8% respectively, is almost pressure independent, while the azimuthal anisotropy for P waves decreases from 12.5% at ambient pressure to 10.5% in the upper part of the transition zone (14-17 GPa). Our calculated O atom charges suggest that Ol is the most likely hydroxyl site and remains so throughout the stability field of wadsleyite.

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.

This Special Topic section on Advanced Electronic Structure Methods for Solids and Surfaces contains a collection of research papers that showcase recent advances in the high accuracy prediction of materials and surface properties. It provides a timely snapshot of a growing field that is of broad importance to chemistry, physics, and materials science.

We have studied the submonolayer growth of vanadium on the Pd(111) surface at different substrate temperatures. By means of low-energy ion spectroscopy (LEIS), Auger electron spectroscopy (AES) scanning tunnelling microscopy (STM), X-ray photoelectron diffraction (XPD) and ab initio local density functional calculation we find that, at room temperature, deposited vanadium atoms substitute surface palladium atoms. In addition, islands are formed on the surface that consist mostly of the substituted palladium atoms. At higher temperatures vanadium diffuses into subsurface layers and, at a temperature of 300°C, only a small amount of vanadium is observed in the topmost layer. STM revealed the formation of a ( 3 × 3 )R30° superstructure and XPD measurements demonstrated that this structure is due to vanadium atoms incorporated in the second layer. This finding is confirmed by ab initio calculations. A model for the ( 3 × 3 )R30° structure based on the experiments and the ab initio calculations is given.