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The electronic structures of the stable face-centered-icosahedral alloy ${\mathrm{Al}}_{70}$${\mathrm{Pd}}_{20}$${\mathrm{Mn}}_{10}$ and of a hierarchy of rational approximants to the icosahedral phase have been calculated using ab initio pseudopotential, linear-muffin-tin-orbital (LMTO), and tight-binding (TB)-LMTO techniques. The description of the aotmic structure is based on a projection from six-dimensional space, with acceptance volumes chosen such as to reproduce the observed diffraction data. For the lowest-order approximants (1/1 and 2/1 with 128 and 544 atoms in the periodically repeated cell), the electronic eigenvalues and eigenfunctions have been calculated self-consistently using LMTO and ab initio pseudopotential techniques. For the 1/1 approximant, we have also performed a relaxation of the idealized structure using the Hellmann-Feynman forces. For the higher-order approximants (we go up to the 8/5 approximants with 41 068 atoms), the electronic densities of states and the spectral functions have been calculated from the TB-LMTO Hamiltonian via a real-space recursion technique. The electronic density of states (DOS) of the higher-order approximants is characterized by a structure-induced minimum at the Fermi level, indicating the possibility of a Hume-Rothery-type electronic mechanism for the stabilization of the icosahedral phase. However, in the lowest-order approximants the DOS minimum is either flattened or shifted away from the Fermi energy. This is in contrast to the simple icosahedral alloys such as Al-Cu-Li, where the DOS minimum exists in the quasiperiodic phase and in the crystalline approximants. Hence it appears that for the face-centered icosahedral alloys, the structure-induced DOS minimum may be not only a generic, but also a specific property of the quasicrystalline phase. In addition to the spectral properties, we have also studied the character of the electronic states via a calculation of the participation ratio. We find that the states in the vicinity of the Fermi level tend to be more localized than in the rest of the valence band and that the localization is related to certain aspects of the quasicrystalline structure. This is important for understanding the anomalous transport properties of these alloys.

We investigate the density isobar of water and the melting temperature of ice using six different density functionals. Machine-learning potentials are employed to ensure computational affordability. Our findings reveal significant discrepancies between various base functionals. Notably, even the choice of damping can result in substantial differences. Overall, the outcomes obtained through density functional theory are not entirely satisfactory across most utilized functionals. All functionals exhibit significant deviations either in the melting temperature or equilibrium volume, with most of them even predicting an incorrect volume difference between ice and water. Our heuristic analysis indicates that a hybrid functional with 25% exact exchange and van der Waals damping averaged between zero and Becke–Johnson dampings yields the closest agreement with experimental data. This study underscores the necessity for further enhancements in the treatment of van der Waals interactions and, more broadly, density functional theory to enable accurate quantitative predictions for molecular liquids.

The cohesive energy of bulk copernicium is accurately determined using the incremental method within a relativistic coupled-cluster approach. For the lowest energy structure of hexagonal close-packed (hcp) symmetry, we obtain a cohesive energy of -36.3 kJ mol-1 (inclusion of uncertainties leads to a lower bound of -39.6 kJ mol-1), in excellent agreement with the experimentally estimated sublimation enthalpy of -38 kJ mol-1 [R. Eichler et al., Angew. Chem. Int. Ed., 2008, 47, 3262]. At the coupled-cluster singles, doubles and perturbative triples level of theory, we find that the hcp structure is energetically quasi-degenerate with both face-centred and body-centred cubic structures. These results provide a basis for testing various density-functionals, of which the PBEsol functional yields a cohesive energy of -34.1 kJ mol-1 in good agreement with our coupled-cluster value.

Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zirconia, an important transition metal oxide. This machine-learned potential accurately captures the temperature-induced phase transitions below the melting point. We further showcase the predictive power of the potential by calculating the heat transport on the basis of Green-Kubo theory, which allows to account for anharmonic effects to all orders. This study indicates that machine-learned potentials trained on the fly offer a routine solution for accurate and efficient simulations of the thermodynamic properties of a vast class of anharmonic materials.

Machine-learned interatomic potentials enable realistic finite temperature calculations of complex materials properties with first-principles accuracy. It is not yet clear, however, how accurately they describe anharmonic properties, which are crucial for predicting the lattice thermal conductivity and phase transitions in solids and, thus, shape their technological applications. Here we employ a recently developed on-the-fly learning technique based on molecular dynamics and Bayesian inference in order to generate an interatomic potential capable to describe the thermodynamic properties of zirconia, an important transition metal oxide. This machine-learned potential accurately captures the temperature-induced phase transitions below the melting point. We further showcase the predictive power of the potential by calculating the heat transport on the basis of Green-Kubo theory, which allows to account for anharmonic effects to all orders. This study indicates that machine-learned potentials trained on the fly offer a routine solution for accurate and efficient simulations of the thermodynamic properties of a vast class of anharmonic materials.

We report periodic density functional theory (DFT) calculations for ${\mathrm{CeO}}_{2}$ and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ using the Perdew-Burke-Ernzerhof (PBE0) and Heyd-Scuseria-Ernzerhof (HSE) hybrid functionals that include nonlocal Fock exchange. We study structural, electronic, and magnetic ground state properties. Hybrid functionals correctly predict ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ to be an insulator as opposed to the ferromagnetic metal predicted by the local spin density (LDA) and generalized gradient (GGA) approximations. The equilibrium volumes of both structures are in very good agreement with experiments, improving upon the description of the LDA and GGA. The calculated ${\mathrm{CeO}}_{2}$ (O $2p$--Ce $5d$) and ${\mathrm{Ce}}_{2}{\mathrm{O}}_{3}$ $(\mathrm{Ce}\phantom{\rule{0.3em}{0ex}}4f\text{\ensuremath{-}}5d4f)$ band gaps are larger by up to 45% (PBE0) and 15% (HSE) than found in experiments. Furthermore, we calculate atomization energies, heats of formation, and the reduction energy of $2{\mathrm{CeO}}_{2}\ensuremath{\rightarrow}{\mathrm{Ce}}_{2}{\mathrm{O}}_{3}+(1∕2){\mathrm{O}}_{2}$. The latter is underestimated by $\ensuremath{\sim}0.4--0.9\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ with respect to available experimental data at room temperature. We compare our results with the more traditional DFT+$U$ (LDA$+U$ and PBE$+U$) approach and discuss the role played by the Hubbard $U$ parameter.

Two finite-field implementations for the calculation of chemical shieldings of molecular systems using a plane-wave basis set and the Gauge-Including Projector-Augmented-Wave method are presented. The direct approach mimics the nuclear magnetic resonance experiment in that it puts the molecule in a uniform magnetic field and obtains shieldings from the current response. The other is based on the recently introduced "converse method" [T. Thonhauser, D. Ceresoli, A. A. Mostofi et al., J. Chem. Phys. 131, 101101 (2009)]. In both methods two-center contributions to the shieldings can be included via a numerically simple augmentation construction. Results obtained with both methods are discussed as well as (dis)similarities in their behaviors.

We present an embedding approach for semiconductors and insulators based on or- bital rotations in the space of occupied Kohn-Sham orbitals. We have implemented our approach in the popular VASP software package. We demonstrate its power for defect structures in silicon and polaron formation in titania, two challenging cases for conventional Kohn-Sham density functional theory.