Publications

The structure of the oxygen-induced c(6×2) reconstruction of V(110)

The adsorption of 2.4 Langmuir oxygen on V(110) induces a c(6×2) reconstruction with an oxygen coverage of 0.5 ML. Its structure was determined using STM, quantitative LEED and ab initio density functional calculations in combination with molecular dynamics. Driven by the strong vanadium–oxygen bonding, the vanadium atoms at the surface are significantly rearranged compared to their bulk positions. The reconstructed geometry offers threefold and fourfold coordinated hollow sites, which are partially occupied by oxygen. The large set of structural data derived from LEED I–V analysis (R Pe=0.11) and ab initio calculations, as well as the experimental and simulated STM images agree well. Additionally the structure of clean V(110) was determined.

Phase transitions of zirconia: Machine-learned force fields beyond density functional theory

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.

Second-order Møller–Plesset perturbation theory applied to extended systems. I. Within the projector-augmented-wave formalism using a plane wave basis set

We present an implementation of the canonical formulation of second-order Møller-Plesset (MP2) perturbation theory within the projector-augmented-wave method under periodic boundary conditions using a plane wave basis set. To demonstrate the accuracy of our approach we show that our result for the atomization energy of a LiH molecule at the Hartree-Fock+MP2 level is in excellent agreement with well converged Gaussian-type-orbital calculations. To establish the feasibility of employing MP2 perturbation theory in its canonical form to systems that are periodic in three dimensions we calculated the cohesive energy of bulk LiH.

Correlation energy for the homogeneous electron gas: Exact Bethe-Salpeter solution and an approximate evaluation

The correlation energy of the homogeneous electron gas is evaluated by solving the Bethe-Salpeter equation (BSE) beyond the Tamm-Dancoff approximation for the electronic polarisation propagator. The BSE is expected to improve upon the random phase approximation, owing to the inclusion of exchange diagrams. For instance, since the BSE reduces in second order to M{\o}ller-Plesset perturbation theory, it is self-interaction free in second order. Results for the correlatione energy are compared with Quantum Monte Carlo benchmarks and excellent agreement is observed. For low densities, however, we find imaginary eigenmodes in the polarisation propagator. To avoid the occurence of imaginary eigenmodes, an approximation to the BSE kernel is proposed, which allows to completely remove this issue in the low electron density region. We refer to this approximation as the random phase approximation with screened exchange (RPAsX). We show that this approximation even slightly improves upon the standard BSE kernel.

Computing Gibbs free energy differences by interface pinning

We propose an approach for computing the Gibbs free energy difference between phases of a material. The method is based on the determination of the average force acting on interfaces that separate the two phases of interest. This force, which depends on the Gibbs free energy difference between the phases, is computed by applying an external harmonic field that couples to a parameter which specifies the two phases. Validated first for the Lennard-Jones model, we demonstrate the flexibility, efficiency, and practical applicability of this approach by computing the melting temperatures of sodium, magnesium, aluminum, and silicon at ambient pressure using density functional theory. Excellent agreement with experiment is found for all four elements, except for silicon, for which the melting temperature is, in agreement with previous simulations, seriously underestimated.

Nonrad: Computing nonradiative capture coefficients from first principles

Point defects in semiconductor crystals provide a means for carriers to recombine nonradiatively. This recombination process impacts the performance of devices. We present the Nonrad code that implements the first-principles approach of Alkauskas et al. (2014) [8] for the evaluation of nonradiative capture coefficients based on a quantum-mechanical description of the capture process. An approach for evaluating electron-phonon coupling within the projector augmented wave formalism is presented. We also show that the common procedure of replacing Dirac delta functions with Gaussians can introduce errors into the resulting capture rate, and implement an alternative scheme to properly account for vibrational broadening. Lastly, we assess the accuracy of using an analytic approximation to the Sommerfeld parameter by comparing with direct numerical evaluation. Program summary Program Title: Nonrad CPC Library link to program files: https://doi.org/10.17632/xmfj4zxmn3.1 Developer's repository link: https://doi.org/10.5281/zenodo.4274317 Code Ocean capsule: https://codeocean.com/capsule/5582062 Licensing provisions: MIT License Programming language: Python 3 Nature of problem: Nonradiative carrier capture at point defects in semiconductors and insulators significantly impacts the performance of devices. A first-principles approach to calculating nonradiative capture rates is necessary to guide materials design and provide atomistic insight into the nonradiative capture process. Solution method: Our code, written in the Python language, implements the first-principles methodology developed by Alkauskas et al. (2014) [8]. Nonradiative capture rates are calculated using a one-dimensional approach, which maps the prohibitively large phonon problem onto a single, effective phonon mode. Harmonic phonon matrix elements may then be computed using an analytic technique or by direct numerical integration of the harmonic oscillator wavefunctions. The electron-phonon coupling is evaluated using the VASP code [Kresse and Furthmüller (1996) [27]] to linear order for the effective mode.

Thermodynamically Controlled Self‐Assembly of Two‐Dimensional Oxide Nanostructures

Seeing stars: surface-supported nanoscale oxide materials are prepared by a chemical driven self-assembly process involving a novel star-shaped [V6O12] cluster molecules (see STM image). The [V6O12] clusters are not stable units in the gas phase but form spontaneously on a metal surface. On the surface the oxide building blocks can be organized into different 2D oxide structures by adjustment of the oxygen chemical potential.

Molecular adsorption on the surface of strongly correlated transition-metal oxides: A case study for CO/NiO(100)

It is well known that the physical properties of some transition-metal compounds (mostly oxides) are strongly affected by intra-atomic correlations. Very recently, investigations of the adsorption of small molecules such as CO on the surfaces of transition-metal oxides have led to rather surprising results: the weak adsorbate-substrate bonding and the asymmetric (tilted) adsorption geometries contrast sharply the strong bonding and symmetric geometries characteristic for metallic surfaces. Calculations based on either Hartree-Fock or density-functional methods have failed to explain these observations. For bulk transition-metal oxides it has been demonstrated that the addition of a Hubbard-type on-site Coulomb repulsion U to the local-density Hamiltonian leads to an improved description of the electronic structure of these materials, but a consistent description of all physical properties proved to be elusive. In the present work, we present a comprehensive investigation of bulk NiO and of clean and CO-covered NiO(100) surfaces. We demonstrate that adding the on-site Coulomb repulsion to the spin-polarized gradient-corrected density-functional Hamiltonian leads to a consistently improved description of a wide range of cohesive, electronic, and magnetic properties of NiO (bulk and surface) and a very accurate description of the adsorption properties of CO. The effects of the strong electronic correlations in the substrate on the adsorbate-substrate bonding are discussed in detail.

Structure and catalytic reactivity of Rh oxides

Using a combination of experimental and theoretical techniques, we show that a thin RhO2 surface oxide film forms prior to the bulk Rh2O3 corundum oxide on all close-packed single crystal Rh surfaces. Based on previous reports, we argue that the RhO2 surface oxide also forms on vicinal Rh surfaces as well as on Rh nanoparticles. The detailed structure of this film was previously determined using UHV based techniques and density functional theory. In the present paper, we also examine the structure of the bulk Rh2O3 corundum oxide using surface X-ray diffraction. Being armed with this structural information, we have explored the CO oxidation reaction over Rh(111), Rh(100) and Pt25Rh75(100) at realistic pressures using in situ surface X-ray diffraction and online mass spectrometry. In all three cases we find that an increase of the CO2 production coincides with the formation of the thin RhO2 surface oxide film. In the case of Pt25Rh75(100), our measurements demonstrate that the formation of bulk Rh2O3 corundum oxide poisons the reaction, and argue that this is also valid for all other Rh surfaces. Our study implies that the CO oxidation reaction over Rh surfaces at realistic conditions is insensitive to the exact Rh substrate orientation, but is rather governed by the formation of a specific surface oxide phase.

Prediction of new thermodynamically stable aluminum oxides

Recently, it has been shown that under pressure, unexpected and counterintuitive chemical compounds become stable. Laser shock experiments (A. Rode, unpublished) on alumina (Al 2 O 3 ) have shown non-equilibrium decomposition of alumina with the formation of free Al and a mysterious transparent phase. Inspired by these observations, we have explored the possibility of the formation of new chemical compounds in the system Al-O. Using the variable-composition structure prediction algorithm USPEX, in addition to the well-known Al 2 O 3 , we have found two extraordinary compounds Al 4 O 7 and AlO 2 to be thermodynamically stable in the pressure ranges 330-443 GPa and above 332 GPa, respectively. Both of these compounds at the same time contain oxide O 2− and peroxide O 2 2− ions and both are insulating. Peroxo-groups are responsible for gap states, which significantly reduce the electronic band gap of both Al 4 O 7 and AlO 2 .

A systematic study of the surface energetics and structure of TiO2(110) by first-principles calculations

First-principles calculations based on density functional theory and the pseudopotential method have been used to study the surface energetics and structure of the TiO2(110) surface. Periodically repeating slab geometry is used, and we have investigated the effect of variable vacuum width and slab thickness on the predicted surface energy and surface atomic displacements. We find that vacuum widths of only 4 Å are sufficient to converge the surface energy to within 0.01 J m−2. Slab thicknesses of at least 6 layers are necessary to achieve similar convergence of the surface energy. Predicted surface atomic displacements are found to differ significantly for slab thicknesses of four layers or less. The displacements are in semi-quantitative agreement with those from other calculations and a recent experimental study. However, in common with all other calculations, the displacement of the bridging oxygen is significantly underestimated when compared to the experimental value.

Accurate surface and adsorption energies from many-body perturbation theory

No abstract is provided for this article.

Natural Orbitals for Wave Function Based Correlated Calculations Using a Plane Wave Basis Set

We demonstrate that natural orbitals allow for reducing the computational cost of wave function based correlated calculations, especially for atoms and molecules in a large box, when a plane wave basis set under periodic boundary conditions is used. The employed natural orbitals are evaluated on the level of second-order Møller–Plesset perturbation theory (MP2), which requires a computational effort that scales as O(N5), where N is a measure of the system size. Moreover, we find that a simple approximation reducing the scaling to O(N4) yields orbitals that allow for a similar reduction of the number of virtual orbitals. The MP2 natural orbitals are applied to coupled-cluster singles and doubles (CCSD) as well as full configuration interaction Quantum Monte Carlo calculations of the H2 molecule to test our implementation. Finally, the atomization energies of the LiH molecule and solid are calculated on the level of MP2 and CCSD.

Stabilization mechanism for the polar ZnO(000<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mover accent="true"><mml:mn>1</mml:mn><mml:mo>¯</mml:mo></mml:mover></mml:math>)-O surface

When wurtzite ZnO is sliced perpendicular to the (0001) axis, two different polar surfaces, the (0001)-Zn and (000$\overline{1}$)-O terminated surfaces, are formed. In a simple ionic picture, both surfaces are electrostatically unstable due to a diverging electrostatic energy. Although the ionic picture is an oversimplification, the surfaces adopt a modified surface structure to compensate for the polarity. In close collaboration with experiment, a hexagonal honeycomblike reconstruction has been suggested [J. V. Lauritsen et al., ACS Nano 5, 5987 (2011)]. The remarkable observation is that the (000$\overline{1}$)-O surface behaves very differently than the (0001)-Zn surface. Here, we present a detailed density functional theory investigation of the (000$\overline{1}$)-O surface, including a systematic investigation of H and Zn coverage as well as an investigation of various surface reconstructions. The difference between the two polar surfaces is explained by the different bonding preferences of Zn and O atoms: as a $d$ element, Zn atoms are more flexible in their bond formation than O atoms.

Self-Consistent $GW$ calculations for semiconductors and insulators

We present quasiparticle (QP) energies from fully self-consistent $GW$ (sc$GW$) calculations for a set of prototypical semiconductors and insulators within the framework of the projector-augmented wave methodology. To obtain converged results, both finite basis-set corrections and $k$-point corrections are included, and a simple procedure is suggested to deal with the singularity of the Coulomb kernel in the long-wavelength limit, the so called head correction. It is shown that the inclusion of the head corrections in the sc$GW$ calculations is critical to obtain accurate QP energies with a reasonable $k$-point set. We first validate our implementation by presenting detailed results for the selected case of diamond, and then we discuss the converged QP energies, in particular the band gaps, for the entire set of gapped compounds and compare them to single-shot $G_0W_0$, QP self-consistent $GW$, and previously available sc$GW$ results as well as experimental results.

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

Correction for ‘Absolute standard hydrogen electrode potential and redox potentials of atoms and molecules: machine learning aided first principles calculations’ by Ryosuke Jinnouchi et al. , Chem. Sci. , 2025, 16 , 2335–2343, https://doi.org/10.1039/D4SC03378G.

Analytic Interatomic Forces in the Random Phase Approximation

Cubic scaling<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math>: Towards fast quasiparticle calculations

The $G\phantom{\rule{0}{0ex}}W$ method is the standard method for predicting quasiparticle energies as measured in experimental photoemission spectroscopy. Until recently, routine $G\phantom{\rule{0}{0ex}}W$ calculations have been restricted to fairly small systems and few $k$ points for sampling the Brillouin zone, since the computational demand usually scales quartic with the number of atoms and quadratic with the number of $k$ points. The original work of Lars Hedin suggests that one can do better by calculating the self-energy as $\mathrm{\ensuremath{\Sigma}}$(1,2)=$i\phantom{\rule{0}{0ex}}G$(1,2)$W$(1,2) -- the equation that coined the phrase ''$G\phantom{\rule{0}{0ex}}W$''. Here, $G$ is the one-particle Green's function and $W$ the screened interaction between the electrons. Using this relation directly in computations brings the scaling down to linear in the number of $k$ points and cubic in the number of atoms. Although this approach has been used in the past by others, in this work its full potential is unveiled by implementing it in a massively parallel code and adopting it to the projector augmented wave method. This makes $G\phantom{\rule{0}{0ex}}W$ calculations as convenient as calculations based on local density functionals and allows for calculations for hundred atoms in few hours.