RPBE Functionals Research Articles

Electronic structure transition of cubic CsSnCl3 under pressure: effect of rPBE and PBEsol functionals and GW method

The antiperovskites based on metal halides have emerged as potential materials for advanced photovoltaic and electronic device applications. But the wide bandgap of non-toxic CsSnCl3 reduces its photovoltaic efficiency. Here, we report the change of electronic structure of CsSnCl3 at different pressure by using GGA-rPBE and GGA-PBEsol functionals and the GW method. We have shown that the prediction of electronic structure transition (semiconducting to metallic state) strongly depends on the exchange-correlation and the GW method gives the most reasonable values of the bandgap under pressure. The pressure increases the electronic density of states close to the Fermi level by pushing the valence electrons upward and thus, reduces the bandgap linearly. Afterward, we have also investigated the influence of pressure on absorption coefficient, and mechanical properties meticulously. Although the pressure shifts the absorption peak to lower photon energies, the absorption coefficient is slightly improved.

Critical Role of Thermal Fluctuations for CO Binding on Electrocatalytic Metal Surfaces.

This work considers the evaluation of density functional theory (DFT) when comparing against experimental observations of CO binding trends on the strong binding Pt(111) and intermediate binding Cu(111) and for weak binding Ag(111) and Au(111) surfaces important in electrocatalysis. By introducing thermal fluctuations using appropriate statistical mechanical NVT and NPT ensembles, we find that the RPBE and B97M-rV DFT functionals yield qualitatively better metal surface strain trends and CO enthalpies of binding for Cu(111) and Pt(111) than found at 0 K, thereby correcting the overbinding by 0.2 to 0.3 eV to yield better agreement with the enthalpies determined from experiment. The importance of dispersion effects are manifest for the weak CO binding Ag(111) and Au(111) surfaces at finite temperatures in which the RPBE functional does not bind CO at all, while the B97M-rV functional shows that the CO–metal interactions are a mixture of chemisorbed and physisorbed species with binding enthalpies that are within ∼0.05 eV of experiment. Across all M(111) surfaces, we show that the B97M-rV functional consistently predicts the correct atop site preference for all metals due to thermally induced surface distortions that preferentially favor the undercoordinated site. This study demonstrates the need to fully account for finite temperature fluctuations to make contact with the binding enthalpies from surface science experiments and electrocatalysis applications.

Investigation of Structural, Electronic and Optical Properties of Na2InAgCl6, K2InAgCl6, and Rb2InAgCl6 Lead-Free Halide Double Perovskites Regarding with Cs2InAgCl6 Perovskites Cell and a Comparative Study by DFT Functionals

Electronics band structures, the total density of state, the partial density of state and optical properties were investigated by DFT method for A2InAgCl6 (A= Cs, Na, K, and Rb). Moreover, the band gap of Na2InAgCl6, K2InAgCl6, Rb2InAgCl6 and Cs2InAgCl6 were calculated at 1.039 eV, 1.041 eV, 1.039 eV and 1.089 eV by GGA with PBE, 0.784 eV, 0.769 eV, 0.775 eV and 0.770 eV by LDA with CA-PZ and 1.310 eV, 1.152 eV, 1.180 eV and 1.169 eV by GGA with RPBE functionals. The density of states (DOS) and partial density of states (PDOS) were evaluated. Among of used functionals, GGA with RPBE functional has considered the appropriate and acceptable method for calculation of band gap where the 1.310 eV of band gap was reported for Cs2InAgCl6, which is close to experimental value at 1.370 eV. The crystal, Na2InAgCl6, has considered as the best perovskites cell among other four due to low band gap, and the main cause is revealed that it has attached the lightest Na atom to convey the low band gap as lower surface or atomic size atom.

A Semiempirical Method to Detect and Correct DFT-Based Gas-Phase Errors and Its Application in Electrocatalysis

Computational models of adsorption at metal surfaces are often based on DFT and make use of the generalized gradient approximation. This likely implies the presence of sizable errors in the gas-phase energetics. Here, we take a step closer toward chemical accuracy with a semiempirical method to correct the gas-phase energetics of PBE, PW91, RPBE, and BEEF-vdW exchange-correlation functionals. The proposed two-step method is tested on a data set of 27 gas-phase molecules belonging to the carbon cycle: first, the errors are pinpointed based on formation energies, and second, the respective corrections are sequentially applied to ensure the progressive lowering of the data set's mean and maximum errors. We illustrate the benefits of the method in electrocatalysis by a substantial improvement of the calculated equilibrium and onset potentials for CO2 reduction to CO on Au, Ag, and Cu electrodes. This suggests that fast and systematic gas-phase corrections can be devised to augment the predictive power of computational catalysis models.

Specific Reaction Parameter Density Functional Based on the Meta-Generalized Gradient Approximation: Application to H2 + Cu(111) and H2 + Ag(111).

Specific reaction parameter density functionals (SRP-DFs), which can describe dissociative chemisorption reactions on metals to within chemical accuracy, have so far been based on exchange functionals within the generalized gradient approximation (GGA) and on GGA correlation functionals or van der Waals correlation functionals. These functionals are capable of describing the molecule–metal surface interaction accurately, but they suffer from the general GGA problem that this can be done only at the cost of a rather poor description of the metal. Here, we show that it is possible also to construct SRP-DFs for H2 dissociation on Cu(111) based on meta-GGA functionals, introducing three new functionals based on the “made-simple” (MS) concept. The exchange parts of the three functionals (MS-PBEl, MS-B86bl, and MS-RPBEl) are based on the expressions for the PBE, B86b, and RPBE exchange functionals. Quasi-classical trajectory (QCT) calculations performed with potential energy surfaces (PESs) obtained with the three MS functionals reproduce molecular beam experiments on H2, D2 + Cu(111) with chemical accuracy. Therefore, these three non-empirical functionals themselves are also capable of describing H2 dissociation on Cu(111) with chemical accuracy. Similarly, QCT calculations performed on the MS-PBEl and MS-B86bl PESs reproduced molecular beam and associative desorption experiments on D2, H2 + Ag(111) more accurately than was possible with the SRP48 density functional for H2 + Cu(111). Also, the three new MS functionals describe the Cu, Ag, Au, and Pt metals more accurately than the all-purpose Perdew–Burke–Ernzerhof (PBE) functional. The only disadvantage we noted of the new MS functionals is that, as found for the example of H2 + Cu(111), the reaction barrier height obtained by taking weighted averages of the MS-PBEl and MS-RPBEl functionals is tunable over a smaller range (9 kJ/mol) than possible with the standard GGA PBE and RPBE functionals (33 kJ/mol). As a result of this restricted tunability, it is not possible to construct an SRP-DF for H2 + Ag(111) on the basis of the three examined MS meta-GGA functionals.

Effect of Functional and Electron Correlation on the Structure and Spectroscopy of the Al2O3(001)-H2O Interface.

Oxide-water interfaces are ubiquitous, with many applications in industry and the environment, yet there is a great deal of controversy over their properties and microscopic structure. This controversy stems, in part, from the unique H-bond networks formed at different surface terminations and mineral compositions. Density functional theory simulations of these interfaces require an accurate description of both the oxide mineral and water in diverse H-bond environments. Thus, herein we simulate the Al2O3(001)-H2O interface using the PBE, PBE-TS, RPBE, SCAN, and HSE06-TS functionals to determine how calculated interfacial properties depend on the choice of functional. We find that the structure of the first few layers of water at the surface is determined by electron correlation in a way that cannot be approximated using semiemipirical van der Waals corrections. Of the functionals investigated, we find that SCAN yields the most accurate interfacial structure, dynamics, and sum frequency generation spectrum. Furthermore, SCAN leads to a reduction in the order of the 2D H-bond network of water at the alumina surface predicted by GGA functionals, leading to a significant decrease in the anisotropy of the diffusion coefficient at the surface. We emphasize the importance of using a functional which accurately describes electron correlation for more complex oxides, such as transition-metal oxides, where electron correlation may play an even greater role in determining the structure and dynamics of the oxide-water interface.

Density anomaly of water at negative pressures from first principles

Using molecular dynamics simulations based on ab initio trained high-dimensional neural network potentials, we study the equation of state of liquid water at negative pressures. From density isobars computed for various pressures down to p = −230 MPa we determine the line of density maxima for two potentials based on the BLYP and the RPBE functionals, respectively. In both cases, dispersion corrections are included to account for non-local long-range correlations that give rise to van der Waals forces. We have followed the density maximum down to negative pressures close to the spinodal instability. For both functionals, the temperature of maximum density increases with decreasing pressure under moderate stretching, but changes slope at MPa and MPa for BLYP and RPBE, respectively. Our calculations confirm qualitatively the retracing shape of the line of density maxima found for empirical water models, indicating that the spinodal line maintains a positive slope even at strongly negative pressures.

DFT-Based Method for More Accurate Adsorption Energies: An Adaptive Sum of Energies from RPBE and vdW Density Functionals

In recent years, the popularity of density functional theory with periodic boundary conditions (DFT) has surged for the design and optimization of functional materials. However, no single DFT exchange–correlation functional currently available gives accurate adsorption energies on transition metals both when bonding to the surface is dominated by strong covalent or ionic bonding and when it has strong contributions from van der Waals interactions (i.e., dispersion forces). Here we present a new, simple method for accurately predicting adsorption energies on transition-metal surfaces based on DFT calculations, using an adaptively weighted sum of energies from RPBE and optB86b-vdW (or optB88-vdW) density functionals. This method has been benchmarked against a set of 39 reliable experimental energies for adsorption reactions. Our results show that this method has a mean absolute error and root mean squared error relative to experiments of 13.4 and 19.3 kJ/mol, respectively, compared to 20.4 and 26.4 kJ/mol f...

Enigmatic HCl + Au(111) Reaction: A Puzzle for Theory and Experiment

The reactive scattering of HCl on Au(111) is currently one of the most peculiar reactions in the field of surface chemistry, as it so far eludes an accurate theoretical description. Possible reasons for the observed mismatch between theory and experiment that were not yet all considered in the computations are (i) dissipative effects due to the creation of electron hole pairs and excitations of surface atom motion that might inhibit reaction and (ii) use of an inappropriate density functional theory method or even its failure due to the occurrence of a charge transfer at the transition state. In this work, we address all of these possibilities and perform quasiclassical molecular dynamics simulations employing different methodologies. We use ab initio molecular dynamics simulations to account for surface atom motion and surface temperature effects, employing the PBE and the RPBE functionals. We also construct an accurate potential energy surface incorporating the six adsorbate degrees of freedom of HCl on...

The plane-wave DFT investigations into the structure and the 11B solid-state NMR parameters of lithium fluorooxoborates

The strategy for an application of the first-principles calculations on crystalline systems to predict the 11B solid-state NMR powder-patterns is described, and its efficacy is demonstrated for two novel lithium-containing fluorooxborates, Li2B3O4F3 and Li2B6O9F2. This strategy involves the plane-wave DFT computations of the NMR parameters, whose values are then scaled and used in the spectral simulations, and are supposed to be directly applicable in the NMR crystallography studies of boron-containing systems. In particular, the GIPAW method and the PBE, PW91, and RPBE functionals are applied. Issues specific to the signal-assignment of the two compounds are also discussed.

Dispersion corrected RPBE studies of liquid water.

The structure of liquid water has been addressed by ab initio molecular dynamics simulations based on density functional theory. Exchange-correlation effects have been described by the popular PBE and RPBE functionals within the generalized gradient approximation as these functionals also yield satisfactory results for metals which is important to model electrochemical interfaces from first principles. In addition, dispersive interactions are included by using dispersion-corrected schemes. It turns out that the dispersion-corrected RPBE functional reproduces liquid water properties quite well in contrast to the PBE functional. This is caused by the replacement of the over-estimated directional hydrogen-bonding in the PBE functional by non-directional dispersive interactions.

Thermochemistry and micro-kinetic analysis of methanol synthesis on ZnO (0 0 0 1)

In this work, we examine the thermochemistry of methanol synthesis intermediates using density functional theory (DFT) and analyze the methanol synthesis reaction network using a steady-state micro-kinetic model. The energetics for methanol synthesis over Zn-terminated ZnO (0001) are obtained from DFT calculations using the RPBE and BEEF-vdW functionals. The energies obtained from the two functionals are compared and it is determined that the BEEF-vdW functional is more appropriate for the reaction. The BEEF-vdW energetics are used to construct surface phase diagrams as a function of CO, H2O, and H2 chemical potentials. The computed binding energies along with activation barriers from literature are used as inputs for a mean-field micro-kinetic model for methanol synthesis including the CO and CO2 hydrogenation routes and the water–gas shift reaction. The kinetic model is used to investigate the methanol synthesis rate as a function of temperature and pressure. The results show qualitative agreement with experiment and yield information on the optimal working conditions of ZnO catalysts.

Dispersive interactions in water bilayers at metallic surfaces: A comparison of the PBE and RPBE functional including semiempirical dispersion corrections

The accuracy and reliability of the density functional theory (DFT)-D approach to account for dispersion effects in first-principles studies of water-metal interfaces has been addressed by studying several water-metal systems. In addition to performing periodic DFT calculations for semi-infinite substrates using the popular PBE and RPBE functionals, the water dimer and water-metal atom systems have also been treated by coupled-cluster calculations. We show that indeed semiempirical dispersion correction schemes can be used to yield thermodynamically stable water bilayers at surfaces. However, the actual density functional needs to be chosen carefully. Whereas the dispersion-corrected RPBE functional yields a good description of both the water-water and the water-metal interaction, the dispersion-corrected PBE functional overestimates the energies of both systems. In contrast thereto, the adsorption distances predicted by the PBE functional is hardly changed due to the additional dispersion interaction, explaining the good performance of previous DFT-PBE studies of water-metal systems.

Diffractive and reactive scattering of H2 from Ru(0001): experimental and theoretical study

We present a combined experimental and theoretical study of the diffraction of H(2) from Ru(0001) in the incident energy range 78-150 meV, and a theoretical study of dissociative chemisorption of H(2) in the same system. Pronounced out-of-plane diffraction was observed in the whole energy range studied. The energy dependence of the elastic diffraction intensities was measured along the two main symmetry directions for a fixed parallel translational energy. The data were compared with quantum dynamics calculations performed by using DFT-based, six-dimensional potential energy surfaces calculated with both the PW91 and RPBE functionals, as well as with a functional obtained from a weighted average of both (the MIX functional, which was earlier shown to perform quite well for H(2) + Cu(111)). Our results show that the PW91 functional describes the H(2) diffraction intensities more accurately than the RPBE and the MIX functionals, although the absolute values of these intensities are overestimated in the calculations. For the reaction probabilities a preference for one or the other functional cannot be given over the entire energy range probed by the sticking experiments. The PW91 functional yields too high reaction probabilities over the entire investigated energy range, but is better than RPBE at low collision energies (<0.1 eV). The RPBE functional gives too low reaction probabilities at low energy and somewhat too high reaction probabilities at high energy, but agrees better with experiment than PW91 for energies >0.1 eV. The results suggest that, in order to get a better description of both H(2) diffraction and dissociative chemisorption for this system, a specific reaction parameter functional for H(2) + Ru(0001) is needed that is a weighted average of functionals other than PW91 and RPBE. We speculate that differences between the H(2) + Ru(0001) system (early and low reaction barrier) and H(2) + Cu(111) (late and high reaction barrier) may well lead to fundamentally different specific reaction parameter functionals, and that including a reasonable accurate description of the van der Waals interaction might be important for H(2) + Ru(0001) which has barriers localised far away from the surface. Based on our results we advocate new, systematic combined theoretical and experimental studies of H(2) interacting with transition metals in early and late barrier systems, with the aim of determining whether specific reaction parameter functionals for these systems might differ in a systematic way.

Dynamics on Six-Dimensional Potential Energy Surfaces for H2/Cu(111): Corrugation Reducing Procedure versus Modified Shepard Interpolation Method and PW91 versus RPBE

We have constructed first principle based six-dimensional (6D) potential energy surfaces (PESs) describing the interaction of H2 with Cu(111) obtained by interpolation of a set of density functional theory (DFT) total energy data. The DFT calculations have been performed within the generalized gradient approximation (GGA) framework. In applying the GGA we have tested the two exchange−correlation (XC) functionals most popular in surface science, i.e., the PW91 and RPBE functionals. The interpolation of the PW91 PES has been performed using two different methods, the corrugation reducing procedure (CRP), which has been proven to be one of the most successful interpolation methods to build 6D PESs, and the modified Shepard (MS) interpolation method, a very promising method to build high dimensional (nD) PESs, which is computationally cheaper than the CRP. We show that, in spite of the difference between the CRP-PES and the MS-PES and the inaccuracies found in the latter, quantum and classical reaction and scattering probabilities obtained for both PESs are very similar. We also show that PW91 predicts higher reactivity than RPBE, due to the presence of lower energy dissociation barriers in the PW91-PES. The differences between the PW91-PES and the RPBE-PES are also reflected in the vibrational excitation and rotational excitation probabilities, and the diffraction patterns.

Tests of the RPBE, revPBE, τ-HCTHhyb, ωB97X-D, and MOHLYP density functional approximations and 29 others against representative databases for diverse bond energies and barrier heights in catalysis

Thirty four density functional approximations are tested against two diverse databases, one with 18 bond energies and one with 24 barriers. These two databases are chosen to include bond energies and barrier heights which are relevant to catalysis, and in particular the bond energy database includes metal-metal bonds, metal-ligand bonds, alkyl bond dissociation energies, and atomization energies of small main group molecules. Two revised versions of the Perdew-Burke-Ernzerhof (PBE) functional, namely the RPBE and revPBE functionals, widely used for catalysis, do improve the performance of PBE against the two diverse databases, but give worse results than B3LYP (which denotes the combination of Becke's 3-parameter hybrid treatment with Lee-Yang-Parr correlation functional). Our results show that the Minnesota functionals, M05, M06, and M06-L give the best performance for the two diverse databases, which suggests that they deserve more attention for applications to catalysis. We also obtain notably good performance with the tau-HCTHhyb, omegaB97X-D, and MOHLYP functional (where MOHLYP denotes the combination of the OptX exchange functional as modified by Schultz, Zhao, and Truhlar with half of the LYP correlation functional).

Effect of Sn on the Reactivity of Cu Surfaces

Periodic, density functional theory (DFT-GGA) calculations, using PW91 (self-consistently) and RPBE functionals, have been employed to determine preferred binding sites, adsorbate structures, and binding energies for the adsorption of atomic (H, N, O, S, and C), molecular (NO and CO), and radical (OH) species on Cu(111) and CuSn(0001) alloy surfaces. Our results indicate the following order in the binding energies from the least to the most strongly bound: NO < CO < H < OH < N < O < S < C for Cu-terminated CuSn(0001). On Cu(111), the corresponding relative order of adsorbates from the least strongly bound to the most strongly bound is CO < NO < H < OH < N < O < S < C. On the Sn-terminated CuSn(0001) surface, CO does not adsorb and the relative order of adsorbates from the least strongly bound to the most strongly bound is NO < H < OH < N < S < O < C. For all adsorbates, the binding on Cu-terminated CuSn(0001) is stronger than on Cu(111), resulting from a combination of electronic and strain effects cause...

Atomic and Molecular Adsorption on Ir(111)

The chemisorption of atomic (H, O, N, S, C), molecular (N2, CO, NO, NH3), and radical (CH3, OH, NOH) species on Ir(111) has been systematically studied. Self-consistent, periodic, density functional theory (DFT-GGA) calculations, using PW91 and RPBE functionals, have been used to determine preferred binding sites, chemisorbed structures, binding energies, vibrational frequencies, and the effect of surface relaxation for the above species at 0.25 ML surface coverage. The following order in binding energies from least to most strongly bound was determined: N2 < NH3 < NO < CH3 < CO < OH < H < NOH < O < N < S < C. A preference for 3-fold sites for the atomic adsorbates was observed, with the exception of atomic H, which prefers top sites. Molecular species showed a preference for top sites with the exception of NOH; this species preferred fcc sites. Surface relaxation had only a small effect on energetics in most cases. Calculated vibrational frequencies, in general, were in good agreement with experimental frequencies and support experimentally proposed site preferences for all adsorbates where data are available. Finally, the thermochemistry of CO, NO, NOH, N2, NH3, and CH3 decomposition on Ir(111) was examined, leading to predictions for each species of the preference for either desorption or decomposition.

Atomic and molecular adsorption on Rh(111)

A systematic study of the chemisorption of both atomic (H, O, N, S, C), molecular (N2, CO, NO), and radical (CH3, OH) species on Rh(111) has been performed. Self-consistent, periodic, density functional theory (DFT-GGA) calculations, using both PW91 and RPBE functionals, have been employed to determine preferred binding sites, detailed chemisorption structures, binding energies, and the effects of surface relaxation for each one of the considered species at a surface coverage of 0.25 ML. The thermochemical results indicate the following order in the binding energies from the least to the most strongly bound: N2&amp;lt;CH3&amp;lt;CO&amp;lt;NO&amp;lt;H&amp;lt;OH&amp;lt;O&amp;lt;N&amp;lt;S&amp;lt;C. A preference for threefold sites for the atomic adsorbates is observed. Molecular adsorbates, in contrast, favor top sites with the exceptions of NO (hcp) and OH (fcc or bridge tilted). Surface relaxation leads to insignificant changes in binding energies but to considerable changes in the spacing between surface rhodium atoms, particularly for on-top adsorption where the rhodium atom directly below the adsorbate is lifted above the plane of the surface. RPBE binding energies are found to be in remarkable agreement with the available experimental values. All atomic adsorbates, except for H, have a significant diffusion barrier [between 0.4 and 0.6 eV (RPBE)] on Rh(111). Atomic H and molecular/radical adsorbates appear to be much more mobile on Rh(111), with an estimated diffusion barrier between 0.1 and 0.2 eV (RPBE). Finally, the thermochemistry for dissociation of CO, NO, and N2 on Rh(111) has been examined. In all three cases, decomposition is found to be thermodynamically preferable to desorption.