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We demonstrate an approach for calculating temperature-dependent quantum and anharmonic effects with beyond density-functional theory accuracy. By combining machine-learned potentials and the stochastic self-consistent harmonic approximation, we investigate the cubic to tetragonal transition in strontium titanate and show that the paraelectric phase is stabilized by anharmonic quantum fluctuations. We find that a quantitative understanding of the quantum paraelectric behavior requires a higher-level treatment of electronic correlation effects via the random phase approximation. This approach enables detailed studies of emergent properties in strongly anharmonic materials beyond density-functional theory.

The adsorption energy of benzene on various metal substrates is predicted using the random phase approximation (RPA) for the correlation energy. Agreement with available experimental data is systematically better than 10% for both coinage and reactive metals. The results are also compared with more approximate methods, including van der Waals density functional theory (DFT), as well as dispersion-corrected DFT functionals. Although dispersion-corrected DFT can yield accurate results, for instance, on coinage metals, the adsorption energies are clearly overestimated on more reactive transition metals. Furthermore, coverage dependent adsorption energies are well described by the RPA. This shows that for the description of aromatic molecules on metal surfaces further improvements in density functionals are necessary, or more involved many-body methods such as the RPA are required.

Growth and decomposition of the Pd5O4 surface oxide on Pd(111) were studied at sample temperatures between 573 and 683K and O2 gas pressures between 10−7 and 6×10−5 mbar, by means of an effusive O2 beam from a capillary array doser, scanning tunnelling microscopy (STM) and thermal desorption spectrometry (TDS). Exposures beyond the p(2×2)O adlayer (saturation coverage 0.25) at 683K (near thermodynamic equilibrium with respect to Pd5O4 surface oxide formation) lead to incorporation of additional oxygen into the surface. To initiate the incorporation, a critical pressure beyond the thermodynamic stability limit of the surface oxide is required. This thermodynamic stability limit is near 8.9×10−6 mbar at 683K, in good agreement with calculations by density functional theory. A controlled kinetic study was feasible by generating nuclei by only a short O2 pressure pulse and then following further growth kinetics in the lower (10−6 mbar) pressure range. Growth of the surface oxide layer at a lower temperature (573K) studied by STM is characterized by a high degree of heterogeneity. Among various metastable local structures, a seam of disordered oxide formed at the step edges is a common structural feature characteristic of initial oxide growth. Further oxide nucleation appears to be favoured along the interface between the p(2×2)O structure and these disordered seams. Among the intermediate phases one specifically stable phase was detected both during growth and decomposition of the Pd5O4 layer. It is hexagonal with a distance of about 0.62nm between the protrusions. Its well-ordered form is a ( 67 × 67 ) R 12.2 ° superstructure. Isothermal decay of the Pd5O4 oxide layer at 693K involves at first a rearrangement into the ( 67 × 67 ) R 12.2 ° structure, indicating its high-temperature stability. This structure can break up into small clusters of uniform size and leaves a free metal surface area covered by a p(2×2)O adlayer. The rate of desorption increases autocatalytically with increasing phase boundary metal-oxide. We propose that at close-to-equilibrium conditions (693K) surface oxide growth and decay occur via this intermediate structure.

Present local and semilocal functionals show significant errors, for instance, in the energetics of small molecules and in the description of band gaps. One possible solution to these problems is the introduction of exact exchange and hybrid functionals. A plane-wave-based algorithm was implemented in VASP (Vienna ab-initio simulation package) to allow for the calculation of the exact exchange. To systematically assess the precision of the present implementation, calculations for the 55 molecules of the G2-1 quantum chemical test set were performed applying the PBE and PBE0 functionals. Excellent agreement for both atomization energies and geometries compared with the results obtained by GAUSSIAN 03 calculations using large basis sets (augmented correlation consistent polarized valence quadruple zeta for the geometry optimization and augmented correlation-consistent polarized valence quintuple zeta for the energy calculations) was found. The mean absolute error for atomization energies between VASP and the experiment is 8.6 and 3.7kcal∕mol, as calculated with the PBE and PBE0 functionals, respectively. The mean deviations between VASP and GAUSSIAN are 0.46 and 0.49kcal∕mol for the PBE and PBE0 functionals, respectively.

The oxidation of the Rh(111) surface at oxygen pressures from ${10}^{\ensuremath{-}10}\text{ }\mathrm{mbar}$ to 0.5 bar and temperatures between 300 and 900 K has been studied on the atomic scale using a multimethod approach of experimental and theoretical techniques. Oxidation starts at the steps, resulting in a trilayer O-Rh-O surface oxide which, although not thermodynamically stable, prevents further oxidation at intermediate pressures. A thick corundum like ${\mathrm{Rh}}_{2}{\mathrm{O}}_{3}$ bulk oxide is formed only at significantly higher pressures and temperatures.

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we construct a DFT substitute functional for the RPA using supervised and unsupervised machine learning (ML) techniques. Our ML-RPA model can be interpreted as a non-local extension to the standard gradient approximation. We train an ML-RPA functional for diamond surfaces and liquid water and show that ML-RPA can outperform the standard gradient functionals in terms of accuracy. Our work demonstrates how ML-RPA can extend the applicability of the RPA to larger system sizes, time scales and chemical spaces.

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.