Publications

Surface oxides on Pd(111): STM and density functional calculations

The formation of one-layer surface oxides on Pd(111) has been studied by scanning tunneling microscopy (STM) and density functional theory (DFT). Besides the ${\mathrm{Pd}}_{5}{\mathrm{O}}_{4}$ structure determined previously, structural details of six different surface oxides on Pd(111) will be presented. These oxides are observed for preparation in oxygen-rich conditions, approaching the thermodynamic stability limit of the PdO bulk oxide at an oxygen chemical potential of $\ensuremath{-}0.95\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}\ensuremath{-}1.02\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ ($570--605\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, $5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{mbar}$ ${\mathrm{O}}_{2}$). Sorted by increasing oxygen fraction in the primitive unit cell, the stoichiometry of the surface oxides is ${\mathrm{Pd}}_{5}{\mathrm{O}}_{4}$, ${\mathrm{Pd}}_{9}{\mathrm{O}}_{8}$, ${\mathrm{Pd}}_{20}{\mathrm{O}}_{18}$, ${\mathrm{Pd}}_{23}{\mathrm{O}}_{21}$, ${\mathrm{Pd}}_{19}{\mathrm{O}}_{18}$, ${\mathrm{Pd}}_{8}{\mathrm{O}}_{8}$, and ${\mathrm{Pd}}_{32}{\mathrm{O}}_{32}$. All structures are one-layer oxides, in which oxygen atoms form a rectangular lattice, and all structures follow the same rules of favorable alignment of the oxide layer on the Pd(111) substrate. DFT calculations were used to simulate STM images as well as to determine the stability of the surface oxide structures. Simulated and measured STM images are in excellent agreement, indicating that the structural models are correct. Since the newly found surface oxides are clearly less stable than ${\mathrm{Pd}}_{5}{\mathrm{O}}_{4}$, we conclude that ${\mathrm{Pd}}_{5}{\mathrm{O}}_{4}$ is the only thermodynamically stable phase, whereas all newly found structures are only kinetically stabilized. We also discuss possible mechanisms for the formation of these oxide structures.

Density-Based Long-Range Electrostatic Descriptors for Machine Learning Force Fields

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%. The application of our descriptors, in combination with local descriptors representing the atomic density, to materials where monopole-monopole interactions are important such as sodium chloride successfully captures long-range interactions, improving predictive accuracy. The study highlights the limitations of the combined LODE method in materials where intermediate-range effects play a significant role. Our work presents a promising approach to addressing the challenge of incorporating long-range interactions into MLFFs, which enhances predictive accuracy for charged materials to the level of state-of-the-art Message Passing Neural Networks.

Hybrid functional and selfconsistent GW$\Gamma$ calculations for solids

Effective on-site interaction for dynamical mean-field theory

A scheme to incorporate nonlocal polarizations into the dynamical mean-field theory (DMFT) and a tailor-made way to determine the effective interaction for DMFT are systematically investigated. Applying it to the two-dimensional Hubbard model, we find that nonlocal polarizations induce a nontrivial filling-dependent antiscreening effect for the effective interaction. The present scheme combined with density functional theory offers an ab initio way to derive effective on-site interactions for the impurity problem in DMFT. We apply it to SrVO${}_{3}$ and find that the antiscreening competes with the screening caused by the off-site interaction.

Growth and structure of ultrathin vanadium oxide layers on Pd(111)

The growth of thin vanadium oxide films on Pd(111) prepared by reactive evaporation of vanadium in an oxygen atmosphere has been studied by scanning tunneling microscopy (STM), low-energy electron diffraction (LEED), and ab initio density-functional-theory (DFT) calculations. Two-dimensional (2D) oxide growth is observed at coverages below one-half of a monolayer (ML), displaying both random island and step-flow growth modes. Above the critical coverage of 0.5 ML, three-dimensional oxide island growth is initiated. The morphology of the low-coverage 2D oxide phase depends strongly on the oxide preparation conditions, as a result of the varying balance of the mobilities of adspecies on the substrate terraces and at the edges of the growing oxide islands. Under typical V oxide evaporation conditions of $p({\mathrm{O}}_{2})=2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\mathrm{mbar},$ $T(\mathrm{substrate})=523\mathrm{K},$ the 2D oxide film exhibits a porous fractal-type network structure with atomic-scale ordered branches, showing a $p(2\ifmmode\times\else\texttimes\fi{}2)$ honeycomb structure. Ab initio DFT total-energy calculations reveal that a surface oxide model with a formal ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ stoichiometry is energetically the most stable configuration. The simulated STM images show a $(2\ifmmode\times\else\texttimes\fi{}2)$ honeycomb structure in agreement with experimental observation. This ${\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}\ensuremath{-}\mathrm{V}}_{2}{\mathrm{O}}_{3}$ layer is very different from bulk ${\mathrm{V}}_{2}{\mathrm{O}}_{3}$ and represents an interface stabilized oxide structure. The V oxide layers decompose on annealing above 673 K and 2D island structures of V/Pd surface alloy and metallic V are then formed on the Pd(111) surface.

Role of silicon vacancies in yttrium-disilicide compounds from ab initio calculations

The structural properties of the compound ${\mathrm{YSi}}_{2}$ are investigated by means of ab initio simulations based on density-functional theory. More particularly we emphasize the role played by Si vacancies, show that the ${\mathrm{Th}}_{3}$${\mathrm{Pd}}_{5}$ structure can be deduced from the ${\mathrm{AlB}}_{2}$ structure by a relaxation process around the Si vacancies within the (0001) plane. A specific ordered arrangement of the Si vacancies along the [0001] direction is found to be energetically the most favorable. Geometries obtained from our theoretical calculations are in good agreement with experimental results.

Electron-phonon interactions using the projector augmented-wave method and Wannier functions

We present an ab-initio density-functional-theory approach for calculating electron-phonon interactions within the projector augmented-wave method. The required electron-phonon matrix elements are defined as the second derivative of the one-electron energies in the PAW method. As the PAW method leads to a generalized eigenvalue problem, the resulting electron-phonon matrix elements lack some symmetries that are usually present for simple eigenvalue problems and all-electron formulations. We discuss the relation between our definition of the electron-phonon matrix element and other formulations. To allow for efficient evaluation of physical properties, we introduce a Wannier-interpolation scheme, again adapted to generalized eigenvalue problems. To explore the method's numerical characteristics, the temperature-dependent band-gap renormalization of diamond is calculated and compared with previous publications. Furthermore, we apply the method to selected binary compounds and show that the obtained zero-point renormalizations agree well with other values found in literature and experiments.

X-ray absorption using the projector augmented-wave method and the Bethe-Salpeter equation

We present an implementation of the Bethe-Salpeter equation (BSE) for core-conduction band pairs within the framework of the projector augmented-wave method. For validation, the method is applied to the $K$ edges of diamond, graphite and hexagonal boron-nitride, as well as four lithium-halides (LiF, LiCl, LiI, LiBr). We compare our results with experiment, previous theoretical BSE results, and the density functional theory-based supercell core-hole method. In all considered cases, the agreement with experiment is excellent, in particular, for the relative position of the peaks as well as the fine structure. Comparing BSE to supercell core-hole spectra, we find that the latter often qualitatively reproduces the experimental spectrum, however, it sometimes lacks important details. This is shown for the $K$ edges of diamond and nitrogen in hexagonal boron nitride, where we can resolve within the BSE experimental features that are lacking in the supercell core-hole method. Additionally, we show that in certain systems the supercell core-hole method performs better if the excited electron is added to the background charge rather than to the lowest conduction band. We attribute this improved performance to a reduced self-interaction.

Ab Initio Study of the H2–H2S/MoS2 Gas–Solid Interface: The Nature of the Catalytically Active Sites

Despite the intense research efforts directed toward understanding the microscopic mechanism of hydrodesulfurization reactions on transition-metal–sulfide catalysts, the nature of active sites remains an open question. Industrial catalysts are mostly based on supported highly dispersed MoS2. There is a general agreement that the active centers are coordinatively unsaturated sites at the edge surfaces oriented parallel to the hexagonal axis of this layered sulfide, but the precise local structure is still unknown. In the present ab initio study, we show that the nature and the concentration of the active sites as well as the shape of the MoS2 crystallite can vary with the chemical potentials in the reactive atmosphere above the surface. We also report a precise investigation of the surface structure, chemical composition, and electronic properties of the MoS2 edge surface under working conditions.

Stabilization Principles for Polar Surfaces of ZnO

ZnO is a wide band gap metal oxide with a very interesting combination of semiconducting, transparent optical and catalytic properties. Recently, an amplified interest in ZnO has appeared due to the impressive progress made in nanofabrication of tailored ZnO nanostructures and functional surfaces. However, the fundamental principles governing the structure of even the clean low-index ZnO surfaces have not been adequately explained. From an interplay of high-resolution scanning probe microscopy (SPM), X-ray photoelectron spectroscopy (XPS), near edge X-ray absorption fine structure (NEXAFS) spectroscopy experiments, and density functional theory (DFT) calculations, we identify here a group of hitherto unresolved surface structures which stabilize the clean polar O-terminated ZnO(0001) surface. The found honeycomb structures are truly remarkable since their existence deviates from expectations using a conventional electrostatic model which applies to the opposite Zn-terminated (0001) surface. As a common principle, the differences for the clean polar ZnO surfaces are explained by a higher bonding flexibility of the exposed 3-fold coordinated surface Zn atoms as compared to O atoms.

Self-consistent<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math>calculations for semiconductors and insulators

We present $GW$ calculations for small and large gap systems comprising typical semiconductors (Si, SiC, GaAs, GaN, ZnO, ZnS, CdS, and AlP), small gap semiconductors (PbS, PbSe, and PbTe), insulators (C, BN, MgO, and LiF), and noble gas solids (Ar and Ne). It is shown that the ${G}_{0}{W}_{0}$ approximation always yields too small band gaps. To improve agreement with experiment, the eigenvalues in the Green's function $G$ $(G{W}_{0})$ and in the Green's function and the dielectric matrix $(GW)$ are updated until self-consistency is reached. The first approximation leads to excellent agreement with experiment, whereas an update of the eigenvalues in $G$ and $W$ gives too large band gaps for virtually all materials. From a pragmatic point of view, the $G{W}_{0}$ approximation thus seems to be an accurate and still reasonably fast method for predicting quasiparticle energies in simple $sp$-bonded systems. We furthermore observe that the band gaps in materials with shallow $d$ states (GaAs, GaN, and ZnO) are systematically underestimated. We propose that an inaccurate description of the static dielectric properties of these materials is responsible for the underestimation of the band gaps in $G{W}_{0}$, which is itself a result of the incomplete cancellation of the Hartree self-energy within the $d$ shell by local or gradient corrected density functionals.

Absolute standard hydrogen electrode potential and redox potentials of atoms and molecules: machine learning aided first principles calculations

Constructing a self-consistent first-principles framework that accurately predicts the properties of electron transfer reactions through finite-temperature molecular dynamics simulations is a dream of theoretical electrochemists and physical chemists. Yet, predicting even the absolute standard hydrogen electrode potential, the most fundamental reference for electrode potentials, proves to be extremely challenging. Here, we show that a hybrid functional incorporating 25 % exact exchange enables quantitative predictions when statistically accurate phase-space sampling is achieved via thermodynamic integrations and thermodynamic perturbation theory calculations, utilizing machine-learned force fields and $\Delta$-machine learning models. The application to seven redox couples, including molecules and transition metal ions, demonstrates that the hybrid functional can predict redox potentials across a wide range of potentials with an average error of 80 mV.

First principles molecular dynamics simulations for amorphous HfO2 and Hf1-xSixO2 systems

Amorphous phases of HfO2 and Hf1–xSixO2 were obtained using the Projector Augmented Plane Wave method through the melt and quench technique. For the pure HfO2 system, several pore channels appear in the structures. Changes to x in the Hf1–xSixO2 were also studied. As the concentration of Si increases, the size of the pore channels increases, much space appears and two-fold oxygen atoms increase. By calculating the heat of formation energy, it was found that phase separation between amorphous HfO2 and SiO2 occurs at x>0.1.

Chemisorption of H on Pd(111): An<i>ab</i><i>initio</i>approach with ultrasoft pseudopotentials

An ab initio study based on local-density-functional (LDF) theory is presented for the chemisorption of hydrogen on the Pd(111) surface. Our calculation uses the Vienna ab initio molecular-dynamics program (VAMP) based on (i) finite-temperature LDF, (ii) exact calculation of the electronic ground state and Hellmann-Feynman forces after each ionic move, and (iii) ultrasoft pseudopotentials for the electron-ion interaction. Complete geometry optimization for different adsorption sites are carried out. The energetic stability of the adsorption site correlates with the coordination number of the site. The larger the coordination number, the more stable the site. Both geometries and the electronic structure obtained from our theoretical calculations are in good agreement with experimental results. \textcopyright{} 1996 The American Physical Society.

Surface core level shift observed on NiAl(1 1 0)

Using high resolution core level spectroscopy, a surface core level shift towards lower binding energy of −0.13 eV is determined for the 2p level of the outwardly relaxed Al surface atoms on NiAl(110). Density functional theory based calculations with inclusion of final state effects yield a value of −0.14 eV for this shift in excellent agreement with experiment. We show that the initial state approximation yields a value of +0.09 eV, i.e. the inclusion of final state relaxation effects is vital not only to obtain the correct value but even the correct sign for this shift.

Structural stability of LaCu₂and YCu₂studied by high-pressure x-ray diffraction and<i>ab initio</i>total energy calculations

LaCu2is the only compound among the RCu2series (R from La to Lu, and Y) which crystallizes in the hexagonal AlB2 -type structure, whereas the other compounds show the orthorhombic CeCu2 -type structure. In agreement with ab initiocalculations our high-pressure x-ray diffraction experiments show that LaCu2transforms at relatively low pressures to the CeCu2 -type structure, which can be regarded as a low-symmetry variant of the AlB2 -type structure.

Why clathrates are good thermoelectrics: A theoretical study of Sr8Ga16Ge30

Recent measurements have shown that the inorganic clathrate Sr8Ga16Ge30 has good thermoelectric properties. This discovery has caused intense experimental activity to synthesize and test other compounds in this class. It has been conjectured that clathrates may be good thermoelectrics if they satisfy several conditions. The Sr atoms, trapped inside the clathrate cages, scatter phonons efficiently, leading to low thermal conductivity. Electric conductivity takes place mostly through the clathrate frame and the conduction electrons are not scattered by Sr vibrations. The compounds, being made of atoms that are semiconductors in the solid state, may have a high Seebeck coefficient. There has been no direct evidence, experimental or theoretical, for this scenario. By performing density functional calculations we show that these ideas are correct. The Sr atoms are weakly bound to the cage and do undergo large-amplitude motion. An analysis of conductivity shows that the largest contribution comes from a band in which the electrons are located on the clathrate frame. Bands originating from the Sr atoms contribute little to conductivity. There is very little charge transfer between the Sr atoms and the frame, and as a result, Sr vibrations are weakly coupled to the conduction electrons. The calculated Seebeck coefficient is in reasonable agreement with the measured one. We find that it is strongly affected by the positions of the Ga atoms in the frame and by doping.

Screened hybrid density functionals applied to solids

Hybrid Fock exchange/density functional theory functionals have shown to be very successful in describing a wide range of molecular properties. For periodic systems, however, the long-range nature of the Fock exchange interaction and the resultant large computational requirements present a major drawback. This is especially true for metallic systems, which require a dense Brillouin zone sampling. Recently, a new hybrid functional [HSE03, J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003)] that addresses this problem within the context of methods that evaluate the Fock exchange in real space was introduced. We discuss the advantages the HSE03 functional brings to methods that rely on a reciprocal space description of the Fock exchange interaction, e.g., all methods that use plane wave basis sets. Furthermore, we present a detailed comparison of the performance of the HSE03 and PBE0 functionals for a set of archetypical solid state systems by calculating lattice parameters, bulk moduli, heats of formation, and band gaps. The results indicate that the hybrid functionals indeed often improve the description of these properties, but in several cases the results are not yet on par with standard gradient corrected functionals. This concerns in particular metallic systems for which the bandwidth and exchange splitting are seriously overestimated.