We present investigations of the structural and electronic properties of the low-index surfaces of rhodium based on selfconsistent ab initio local-density-functional calculations. Our technique is based on ultra-soft pseudopotentials, a preconditioned conjugate-gradient technique for the calculation of the electronic ground-state and of the Hellmann-Feynman forces, and a conjugate-gradient approach for the optimization of the atomic structure. For the (111), (100), and (110) surfaces inward relaxations of the top layer by − 1.7 ± 0.2, − 3.8 ± 0.2, and − 9.8 ± 0.6%, and an oscillatory decreasing relaxation of the deeper layers are predicted. A detailed analysis of electronic surface states is presented.
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.
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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.
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.
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.
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.
For optimal accuracy, auxiliary-field quantum Monte Carlo (AFQMC) requires trial states consisting of multiple Slater determinants. We develop an efficient algorithm to select the determinants from an AFQMC random walk eliminating the need for other methods. When determinants contribute significantly to the nonorthogonal configuration interaction energy, we include them in the trial state. These refined trial wave functions significantly reduce the phaseless bias and sampling variance of the local energy estimator. With 100 to 200 determinants, we lower the error of AFQMC by up to a factor of 10 for second-row elements that are not accurately described with a Hartree–Fock trial wave function. For the HEAT set, we improve the average error to within chemical accuracy. For benzene, the largest studied system, we reduce AFQMC error by 80% with 214 Slater determinants and find a 10-fold increase of the time to solution. We show that phaseless errors prevail in systems with static correlation or strong spin contamination. For such systems, improved trial states enable stable free-projection AFQMC calculations, achieving chemical accuracy even in the strongly correlated regime.
We present detailed density functional calculations for CO on Rh(111). At low coverage, the applied semilocal functionals clearly favor CO adsorption in the hollow site. This is in disagreement with experimental studies which all point towards atop adsorption at low coverage. The experimental assignment is confirmed by theoretical calculations of the vibrational frequencies and core level shifts at various coverages, ranging from $1∕9\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}3∕4$ $[(2\ifmmode\times\else\texttimes\fi{}2)\text{\ensuremath{-}}3\mathrm{C}\mathrm{O}]$ monolayer CO. For atop adsorption the calculated vibrational frequencies and the Rh surface core level shifts are indeed found to agree very well with experiment. To understand these controversial results, a molecular $\mathrm{GGA}+\mathrm{U}$ method is applied, which allows one to shift the CO $2\ensuremath{\pi}*$ orbital towards the vacuum level. This reduces the binding energy in the hollow site and brings the theoretical site preference in agreement with experiment. It is investigated how this molecular $\mathrm{GGA}+\mathrm{U}$ method influences the vibrational properties and the surface core level shifts. Furthermore, details on the molecular $\mathrm{GGA}+\mathrm{U}$ method are presented.
Using the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) metageneralized gradient approximation, a computationally efficient semilocal functional, we studied the desorption energies of the molecule CO on the (111) surfaces of transition metals as well as the surface energies and lattice constants of the underlying transition metals. Due to its ability to distinguish single-orbital regions from regions of high orbital overlap, revTPSS improves all three properties over the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation. No generalized gradient approximation matches this performance, which has been regarded as unreachable by semilocal approximations.
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.