Atomistic Thermodynamics Research Articles

Efficient ab initio schemes for finding thermodynamically stable and metastable atomic structures: benchmark of cascade genetic algorithms

A first principles-based methodology for efficiently and accurately finding thermodynamically stable and metastable atomic structures is introduced and benchmarked. The approach is demonstrated for gas-phase metal-oxide clusters in thermodynamic equilibrium with a reactive (oxygen) atmosphere at finite pressure and temperature. It consists of two steps. First, the potential-energy surface is scanned by means of a global-optimization technique, i.e., a massive-parallel first-principles cascade genetic algorithm for which the choice of all parameters is validated against higher-level methods. In particular, we validate (a) the criteria for selection and combination of structures used for the assemblage of new candidate structures, and (b) the choice of the exchange-correlation functional. The selection criteria are validated against a fully unbiased method: replica-exchange molecular dynamics. Our choice of exchange-correlation functional, the van der Waals-corrected PBE0 hybrid functional, is justified by comparisons up to the highest level currently achievable within density-functional theory, i.e., the renormalized second-order perturbation theory. In the second step, the low-energy structures are analyzed by means of ab initio atomistic thermodynamics in order to determine compositions and structures that minimize the Gibbs free energy at given temperature and pressure of the reactive atmosphere.

Ab initio prediction of the equilibrium shape of supported Ag nanoparticles on α-Al2O3(0 0 0 1)

We combine first-principles atomistic thermodynamics with a Wulff–Kaichew construction to determine the equilibrium shape of Ag particles supported on α-Al2O3(0001) under gas-phase conditions representative for ethylene epoxidation. The formation of three-dimensional truncated octahedra is predicted for both the Al-terminated (AlO3Al-R) and the fully hydroxylated O-terminated (H3O3Al-R) alumina surface, albeit with largely different contact angles. Overall, this is fully consistent with the common description of hemispherical Ag microcrystals on this support, but at variance with the cubic Ag nanoparticles reported recently by Christopher and Linic (2008). This result suggests the latter particles to be stabilized kinetically. We establish a framework from which strategies to thermodynamically stabilize cubic particles can be explored. The Wulff–Kaichew construction is proposed to provide a straightforward criterion that may be used as a suitable descriptor in the computational screening of surface additives that would stabilize the arguably highly selective Ag(100) facets.

Re-visiting the O/Cu(111) system--when metastable surface oxides could become an issue!

Surface oxidation processes are crucial for the functionality of Cu-based catalytic systems used for methanol synthesis, partial oxidation of methanol or the water-gas shift reaction. We assess the stability and population of the "8"-structure, a [formula, see text:] oxide phase, on the Cu(111) surface. This structure has been observed in X-ray photoelectron spectroscopy and low-energy electron diffraction experiments as a Cu(111) surface reconstruction that can be induced by a hyperthermal oxygen molecular beam. Using density-functional theory calculations in combination with ab initio atomistic thermodynamics and Boltzmann statistical mechanics, we find that the proposed oxide superstructure is indeed metastable and that the population of the "8"-structure is competitive with the known "29" and "44" oxide film structures on Cu(111). We show that the configuration of O and Cu atoms in the first and second layers of the "8"-structure closely resembles the arrangement of atoms in the first two layers of Cu2O(110), where the atoms in the "8"-structure are more constricted. Cu2O(110) has been suggested in the literature as the most active low index facet for reactions such as water splitting under light illumination. If the "8"-structure were to form during a catalytic process, it is therefore likely to be one of the reactive phases.

Structural, electronic and magnetic properties of the (001), (110) and (111) surfaces of rocksalt sodium sulfide: A first-principles study

First principles study of the structural, electronic and magnetic properties of the (111), (110) and (001) surfaces of rocksalt sodium sulfide (rs-NaS) are reported. The results show that the bulk half-metallicity of this compound is well preserved on the surfaces considered here except for Na-terminated (111) surface. The spin-flip gap at the S-terminated (111), (001) and (110) surfaces are close to the bulk value. Using ab-initio atomistic thermodynamics, we calculate the surface energies as a function of chemical potential to find the most stable surface. We find that the Na-terminated (111) surface is the most stable one over the whole allowed range of chemical potential, while the surface energies of the (001) and (110) surfaces approach the most stable surface energy at the sulfur rich environment. We have also calculated the interlayer exchange interaction in bulk and Na-terminated (111) surface by classical Heisenberg model and we found that the surface effects do not change these kinds of interactions significantly.

Ab-initio study of hydrogen doping and oxygen vacancy at anatase TiO2 surface

Density functional–pseudopotential calculations were performed to study the effects of hydrogen doping and oxygen vacancy, both individually and together, on the electronic structure and stability of (001) surface of TiO2 in the anatase phase. Based on our calculations, O/Ti termination is the most stable one, and it appears that p-states of deep and surface O atoms and d-orbitals of surface Ti atoms have roles in the valence band and, the conduction band comes from the d-orbitals of deep Ti atoms. Although, no considerable change was seen during H doping, a mid-gap state appeared below the conduction band in the O vacancy configuration. In the framework of ab-initio atomistic thermodynamics, we argue that the anatase TiO2 prefers a defected O layer termination in the [001] direction. The obtained electronic structures indicate that H doping in the bulk creates the empty mid-gap state below the conduction band and hence decreases the band gap of the system. This phenomenon may explain the enhanced photocatalytic activity of the anatase TiO2 (001) surface after hydrogenation.

Nitrogen-induced reconstruction and faceting of Re($11\bar 21$112¯1)

The surface morphology of Re(11̄21), tailored on the nanometer scale by kinetic control of nitrogen, has been investigated using low energy electron diffraction, scanning tunneling microscopy, Auger electron spectroscopy, and density functional theory (DFT) in combination with the ab initio atomistic thermodynamics approach. Experiments show that when exposing to NH3 (>0.5 L) at 300 K followed by annealing in ultra-high vacuum at 700 K or 900 K, the initially planar Re(11̄21) surface becomes (2 × 1) reconstructed or partially faceted, respectively. Upon annealing in 100 L NH3 at 900 K, Re(11̄21) becomes fully faceted and covered by N. The fully faceted surface consists of two-sided ridges formed by (13̄42) and (31̄42) facets. The (2 × 1) reconstruction may serve as a precursor state for faceting of Re(11̄21). The DFT calculations provide an atomistic understanding of facet formation in terms of binding sites and energies of N on Re surfaces of the substrate and facets as well as the corresponding surface phase diagram. The N-covered faceted Re(11̄21) surfaces are promising nanoscale model catalysts and nanotemplates. Our findings should be of importance for the design and development of Re-based heterogeneous catalysts operating under nitrogen-rich conditions.

Tuning the crystal shape of materials by chemical potential: a combined theoretical and experimental study for NiSe2

Understanding and controlling the shape of materials has attracted considerable attention over the past few decades. Taking a typical transition metal chalcogenide NiSe2 as an example, we have figured out the role of chemical potential in the equilibrium shape of materials by a combined theoretical and experimental study. The theoretical equilibrium shape evolution of NiSe2 with chemical potential has been investigated using ab initio atomistic thermodynamics and Wulff construction. Moreover, in order to confirm our theoretical results, a series of NiSe2 crystals with different morphologies were also synthesized via a solvothermal route in mixed solvents of hydrazine hydrate, ethylenediamine and reactant. X-ray powder diffraction (XRD) and field emission scanning electron microscopy (FESEM) were used to analyze the products. Our results indicated that the theoretical equilibrium shapes of NiSe2 change from pyritohedron enclosed by (210) facet, truncated octahedron to perfect octahedron occupied by (111) facet, which agrees with the experimental shapes of NiSe2 synthesized with different volume ratios of mixed solvents. The present theory and experimental work indicates that controlling the chemical potential is a general and efficient way to tailor the shape of materials.

Adsorption and oxidation of sulfur dioxide on the yttria-stabilized zirconia surface: ab initio atomistic thermodynamics study

The interaction of SO2 with the yttria-stabilized zirconia (YSZ) (111) and oxygen-enriched YSZ (111) (YSZ+O) surface is investigated using the first-principles method based density functional theory (DFT). It is found that SO2 is adsorbed either as a molecule or forms SO2−3 species with new SO bonds to a surface oxygen on the YSZ (111) surface. In addition, there exist other species, e.g., SO3 and SO2−4 on the very active YSZ+O (111) surface. Using the ab initio atomistic thermodynamics method, we present a detailed analysis on the stability of the SO2YSZ/YSZ+O system as a function of the ambient conditions.

An ab initio thermodynamics study of cobalt surface phases under ethanol steam reforming conditions

A combination of DFT and ab initio atomistic thermodynamics study illustrated the surface structure evolution of Co0/Co2+ catalysts under ethanol steam reforming conditions.

Reduction mechanisms of the CuO(111) surface through surface oxygen vacancy formation and hydrogen adsorption

We studied the reduction of CuO(111) surface using density functional theory (DFT) with the generalized gradient approximation corrected for on-site Coulomb interactions (GGA + U) and screened hybrid DFT (HSE06 functional). The surface reduction process by oxygen vacancy formation and H2 adsorption on the CuO(111) surface is investigated as two different reduction mechanisms. It is found that both GGA + U and HSE06 predict the same trend in the relative stability of oxygen vacancies. We found that loss of the subsurface oxygen is initially thermodynamically favourable. As the oxygen vacancy concentration increases, mixture of subsurface and surface vacancies is energetically preferred over full reduction of the surface or subsurface monolayer. The reduction of Cu(2+) to Cu(+) is found to be more favourable than that of Cu(+) to Cu(0) in the most stable vacancy structures at all concentrations. Consistent with the oxygen vacancy calculations, H2 adsorption occurs initially on under-coordinated surface oxygen. Water molecules are formed upon the adsorption of H2 and this gives a mechanism for H2 reduction of CuO to Cu. Ab initio atomistic thermodynamics shows that reducing CuO to metallic Cu at the surface is more energetically difficult than in the bulk so that the surface oxide protects the bulk from reduction. Using H2 as the reducing agent, it is found that the CuO surface is reduced to Cu2O at approximately 360 K and that complete reduction from Cu2O to metallic Cu occurs at 780 K.

Ab initio atomistic thermodynamics study on the sulfur tolerance mechanism of the oxygen-enriched yttria-stabilized zirconia surface

The first-principles method based on density functional theory (DFT) is used to investigate the reaction mechanism for the adsorption of H2S on the oxygen-enriched yttria-stabilized zirconia (YSZ+O) (111) surface. It is found that the H2S dissociation processes have low energy barriers (<0.5eV) and high exothermicities (2.5eV), and the dissociative S atoms may result in the poisoning of the YSZ+O surface by forming the SO and the hyposulfite (SO22−) species with very strong bonds to the surface. In addition, using the ab initio atomistic thermodynamics method, the surface regeneration or de-sulfurization process of a sulfur-poisoned (i.e. sulfur-covered) YSZ+O(111) surface is studied. According to the phase diagram, the adsorbed atomic sulfur can be oxidized to SO2 and removed from the YSZ+O surface by introducing oxidizing reagents, e.g. O2 and H2O.

Oxidation of step edges on vicinal 4H-SiC(0001) surfaces

The oxidation processes of stepped SiC(0001) surfaces are studied within the ab initio atomistic thermodynamics approach. Our calculations show that a one-dimensional -Si-O- chain structure as a precursor for oxide growth on stepped SiC surfaces is formed along the step edge, promoting further oxidation of the step edges. Following the modified Deal-Grove oxidation model, we also find that the oxidation rate at steps is higher than that at terraces by three orders of magnitude. These findings give a reasonable explanation for the oxide thickness fluctuation between the step and the terrace observed in the previous experiments.

Tuning patterning conditions by co-adsorption of gases: Br2 and H2 on Si(001)

We have studied the co-adsorption of Br2 and H2 on Si(001), and obtained co-adsorption energies and the surface phase diagram as a function of the chemical potential and pressure of the two gases. To do this, we have used density functional theory calculations in combination with ab initio atomistic thermodynamics. Over large ranges of bromine and hydrogen chemical potentials, the favored configuration is found to be either one with only Br atoms adsorbed on the surface, at full coverage, in a (3 × 2) pattern, or a fully H-covered surface in a (2 × 1) structure. However, we also find regions of the phase diagram where there are configurations with either only Br atoms, or Br and H atoms, arranged in a two-atom-wide checkerboard pattern with a (4 × 2) surface unit cell. Most interestingly, we find that by co-adsorbing with H2, we bring this pattern into a region of the phase diagram corresponding to pressures that are significantly higher than those where it is observed with Br2 alone. We also find small regions of the phase diagram with several other interesting patterns.

First-Principles Predictions of the Structure, Stability, and Photocatalytic Potential of Cu2O Surfaces

For a photocatalytic reaction to be thermodynamically allowed, a semiconductor's band edges need to be placed appropriately relative to the reaction redox potentials. We apply a recently developed scheme for calculating band edges with density functional theory (DFT)-based methods to Cu2O, evaluating its available thermodynamic overpotential for redox reactions such as water splitting and conversion of CO2 to methanol. Because these calculations are surface dependent, we first study the low-index surfaces of Cu2O using periodic DFT+U theory to characterize and identify the most stable surface, which will be the most catalytically relevant. We employ various techniques to calculate the surface energy, including the method of "ab initio atomistic thermodynamics". The Cu2O(111) surface with (1 × 1) periodicity and surface copper vacancies is identified as the most stable at all oxygen partial pressures, although the ideal stoichiometric Cu2O(111) surface is relatively close in energy under oxygen-poor conditions. These surfaces are then used to calculate the band edges. Comparison of the band edges to redox potentials reveals that Cu2O is thermodynamically capable of photocatalytic reduction of CO2 to methanol and the reduction and oxidation of water.

Stability and Metastability of Clusters in a Reactive Atmosphere: Theoretical Evidence for Unexpected Stoichiometries ofMgMOx

By applying a genetic algorithm and ab initio atomistic thermodynamics, we identify the stable and metastable compositions and structures of MgMOx clusters at realistic temperatures and oxygen pressures. We find that small clusters (M≲5) are in thermodynamic equilibrium when x>M. The nonstoichiometric clusters exhibit peculiar magnetic behavior, suggesting the possibility of tuning magnetic properties by changing environmental pressure and temperature conditions. Furthermore, we show that density-functional theory with a hybrid exchange-correlation functional is needed for predicting accurate phase diagrams of metal-oxide clusters. Neither a (sophisticated) force field nor density-functional theory with (semi)local exchange-correlation functionals is sufficient for even a qualitative prediction.

The Development of the Solar System — Relations to Physics and Cosmology

The Kantian cosmology “based on Newtonian principles” is founded on celestial mechanics, statistical mechanics and atomistic thermodynamics. However, these fundamental physical laws are working in the given cosmos.

Origin of the unique activity of Pt/TiO2 catalysts for the water–gas shift reaction

Periodic density functional theory calculations and microkinetic modeling are used to illustrate the specific role of the three-phase boundary (TPB) in determining the activity and selectivity of TiO2-supported Pt catalysts for the water–gas shift (WGS) reaction. The Pt8/TiO2(110) catalyst model identified from a systematic ab initio atomistic thermodynamics study is used to investigate the redox mechanism and associative pathway with redox regeneration of the WGS reaction. Analysis of a microkinetic model determined exclusively from first principles suggests that a CO-promoted redox pathway dominates in the low-temperature range of 473–623K and the classical redox pathway becomes dominant at temperatures above 673K. The improved activity of the TPB compared to the Pt(111) surface can be explained by a reduced CO adsorption strength on Pt sites at the TPB, an increased number of oxygen vacancy at the TPB, and a significantly facilitated water activation and dissociation.

Reaction cycles and poisoning in catalysis by gold clusters: A thermodynamics approach

In heterogeneous catalysis, a catalytic process takes place at finite temperature and at finite pressure of the atmosphere of the reactant gases. By applying ab initio atomistic thermodynamics to the model case of free Au2 and clusters in an atmosphere of O2 and CO, we derive all the thermodynamically possible reaction paths for the oxidation of CO to CO2. This analysis lets us explain how gold clusters enable oxidation reactions without breaking the spin-conservation rule. Furthermore, we identify special cluster + ligands compositions such as reaction intermediates and poisoned species. In particular, a thermodynamically driven poisoning is identified for the catalytic system containing free Au2, and the experimental (p, T) conditions that avoid its formation are suggested. This implies that for some systems a catalytic cycle can be established, on thermodynamics grounds, only in a defined range of temperatures and pressures. In addition, our predictions for provide the so far most complete interpretation of the available experimental data (Socaciu et al, J. Am. Chem. Soc. 2003). © 2013 Wiley Periodicals, Inc.

An atomistic thermodynamics study of the structural evolution of the Pt3Ni(111) surface in an oxygen environment

The structural evolution of the Pt 3 Ni(111) surface under oxidizing conditions was studied by ab initio atomistic thermodynamics. The thermodynamic phase diagram from Ni-rich to Pt-rich conditions with oxygen coverages up to one monolayer was constructed from their 560 possible surface structures. With an increase in the oxygen chemical potential, there were only two types of thermodynamically stable structures, which were a clean Pt-skin surface and a Ni-skin surface with chemisorbed oxygen, regardless of the underlying Pt-rich or Ni-rich conditions. Bimetallic surfaces with chemisorbed oxygen were only metastable. The detail analysis revealed that the structural evolution is determined by the factors of segregation cost, difference between oxygen-metal (Pt and Ni) bonding strength, and oxygen chemical potential. With a gradual increase of oxygen chemical potential, the clean Pt-skin surfaces of Pt 3 Ni(111) transit to the oxygen-chemisorbed Ni-skin surfaces without stable oxygen-chemisorbed PtNi surface alloys formed.

First-principles prediction of half-metallicity at the low index surfaces of rocksalt KS

The structural, electronic and magnetic properties of the low index (111), (110) and (001) surfaces of the rocksalt Potassium Sulfide (rs-KS) are investigated by using pseudo-potential calculations in the framework of spin density functional theory. The results show that the bulk half-metallicity of this compound is well preserved on its low index surfaces. The spin flip gap at the studied surfaces is close to the bulk value except for the potassium terminated (111) surface which exhibits about half of the bulk spin flip gap. The calculated surface energies in the framework of ab-initio atomistic thermodynamics indicate that the potassium terminated (111) surface of KS has the lowest energy over entire allowed range of the chemical potentials, while the surface energy of the (001) and (110) surfaces approaches the surface energy of the stable surface at the sulfur rich environment. In the framework of the Heisenberg model, it is argued that the surface effects have small effects on the interlayer exchange interaction in the stable K-terminated (111) surface, compared with the bulk KS.