Generalized Gradient Approximation Level Research Articles

Understanding the Source of Error in First-Principles-Based Micro-Kinetic Modeling: Density Functional Theory Calculations Versus the Mean-Field Approximation

First-principles-based micro-kinetic modeling has become an essential tool in the rational design of heterogeneous catalysts. Currently, most theoretical understandings and predictions are provided by this model, which combines results from density functional theory (DFT) calculations at the generalized gradient approximation level with the simulations using the mean-field micro-kinetic modeling (MF-MKM). In spite of its popularity and success in the catalyst design and screening, sometimes this combination yields undesired predictions that significantly deviate from experimental observations. It is, therefore, important to understand its success and failure and to locate the bottleneck of applying/improving the conventional MF-MKM. To this end, we have compared the errors that come from different DFT functionals with those introduced by the MF approximations against the kinetic Monte Carlo (KMC) results for the Pt-catalyzed water gas shift reaction system. It was found that the shape of the volcano map is less sensitive to the differences in the DFT functionals, even though their predictions of the key energetic parameters are distinctly different. On the other hand, the top of the volcano map, the detailed mechanism, as well as some key kinetic properties are markedly affected by the change of the energetic data. In comparison, the traditional MF-MKM that neglects the adsorbate–adsorbate interactions totally fails to describe the reaction kinetics. The inclusion of the adsorbate–adsorbate interaction effect can significantly improve the performance of the MF-MKM, which results in largely similar predictions to the reference data provided by KMC simulations. Nevertheless, the missing spatial correlation in the MF treatment can lead to an improper description in the high coverage region. Our analyses demonstrate that the accuracy of the MKM might not always be improved by only modifying the DFT-calculated energetic parameters, and close attention should be paid to the kinetic simulation method employed, particularly when quantitative kinetic properties are to be expected.

Hardness of molecules and bandgap of solids from a generalized gradient approximation exchange energy functional.

The deviations from linearity of the energy as a function of the number of electrons that arise with current approximations to the exchange-correlation (XC) energy functional have important consequences for the frontier eigenvalues of molecules and the corresponding valence-band maxima for solids. In this work, we present an analysis of the exact theory that allows one to infer the effects of such approximations on the highest occupied and lowest unoccupied molecular orbital eigenvalues. Then, we show the importance of the asymptotic behavior of the XC potential in the generalized gradient approximation (GGA) in the case of the NCAPR functional (nearly correct asymptotic potential revised) for determining the shift of the frontier orbital eigenvalues toward the exact values. Thereby we establish a procedure at the GGA level of refinement that allows one to make a single calculation to determine the ionization potential, the electron affinity, and the hardness of molecules (and its solid counterpart, the bandgap) with an accuracy equivalent to that obtained for those properties through energy differences, a procedure that requires three calculations. For solids, the accuracy achieved for the bandgap lies rather close to that which is obtained through hybrid XC energy functionals, but those also demand much greater computational effort than what is required with the simple NCAPR GGA calculation.

Modeling Electrochemical Processes with Grand Canonical Treatment of Many-Body Perturbation Theory.

Electrocatalysis plays a key role in sustainable energy conversion and storage. It is critical to model the grand canonical treatment of electrons, which accounts for the electrochemical potential explicitly, at the atomic scale and understand these reactions at electrified interfaces. However, such a grand canonical treatment for electrocatalytic modeling is in practice restricted to a treatment of electronic structure with density functional theory, and more accurate methods are in many cases desirable. Here, we develop an original workflow combining the grand canonical treatment of electrons with many-body perturbation theory in its random phase approximation (RPA). Using the potential dependent adsorption of carbon monoxide on the copper (100) facet, we show that the grand canonical RPA energetics provide the correct on-top Cu geometry for CO at reducing potential. The match with experimental results is significantly improved compared to the functionals at the generalized gradient approximation level, which is the most commonly used approximation for electrochemical applications. We expect this development to pave the way to further electrochemical applications using RPA.

Spin-valley-coupled quantum spin Hall insulator with topological Rashba-splitting edge states in Janus monolayer CSb1.5Bi1.5

Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer CSb1.5Bi1.5 with dynamic, mechanical and thermal stabilities. Calculated results show that the CSb1.5Bi1.5 is a direct band gap semiconductor with and without spin–orbit coupling, and the conduction-band minimum and valence-band maximum are at valley point. The inequivalent valleys have opposite Berry curvature and spin moment, which can produce a spin-valley Hall effect. In the center of Brillouin zone, a Rashba-type spin splitting can be observed due to missing horizontal mirror symmetry. The topological characteristic of CSb1.5Bi1.5 is confirmed by the Z 2 invariant and topological protected conducting helical edge states. Moreover, the CSb1.5Bi1.5 shows unique Rashba-splitting edge states. Both energy band gap and spin-splitting at the valley point are larger than the thermal energy of room temperature (25 meV) with generalized gradient approximation level, which is very important at room temperature for device applications. It is proved that the spin-valley-coupling and nontrivial quantum spin Hall state are robust again biaxial strain. Our work may provide a new platform to achieve integration of topological physics, spintronics and valleytronics.

Reinvestigating oxygen adsorption on Ag(111) by using strongly constrained and appropriately normed semi-local density functional with the revised Vydrov van Voorhis van der Waals force correction.

While density functional theory (DFT) at the generalized gradient approximation (GGA) level has made great success in catalysis, it fails in some important systems such as the adsorption of the oxygen molecule on the Ag(111) surface. Previous DFT studies at the GGA level revealed theoretical inconsistencies on the adsorption energies and dissociation barriers of O2 on Ag(111) in comparison with the experimental conclusion. In this study, the strongly constrained and appropriately normed-revised Vydrov van Voorhis van der Waals correction functional (SCAN-rVV10) method at the meta-GGA level with the nonlocal van der Waals (vdW) force correction was used to reinvestigate the adsorption properties of O2 on the Ag(111) surface. The SCAN-rVV10 results successfully confirm the experimental observation that both molecular and dissociative adsorptions can exist for oxygen on Ag(111). The calculated adsorption energy for the physisorption state and the relevant dissociation energy barrier are close to the experimental data. It demonstrates that SCAN-rVV10 can outperform functionals at the GGA level for O2/Ag(111). Therefore, our findings suggest that SCAN-rVV10 can be the desired method for systems where the correct description of intermediate-ranged vdW forces is essential, such as the physisorption of small molecules on the solid surface.

A DFT Investigation on Structural and Electronic Properties of Pure and Sr-Doped Wurtzite ZnO

The aim of this study was to investigate structural and electronic properties of pure and Strontium-doped wurtzite ZnO using first principles density functional calculations (DFT). The first principle calculation is a computational method to study the electronic structure of materials. The self-consistent calculation was done using Generalized Gradient Approximation (GGA) with BLYP functional implemented on Quantum ESPRESSO package to generate the band structure and density of states of the materials taken under consideration. The Strontium doping caused the increase in lattice volume and slight distortions at the unit cell parameters in a wurtzite structure. This doping process increased the band-gap energy (E g ) at low percentage 25% (E g = 1.55eV) and 50% (E g = 2.33eV) with indirect band-gap and direct band gap at high percentages 75% (E g = 2.38eV) and 100% (E g = 3.368eV), which we call it wide direct band gap. The lattice parameters obtained at the level of GGA–BLYP approach was found to be (a = b = 3.412A o , and c = 5.205A o ) in good agreement with either previously reported theoretical or experimental work. The calculated band-gap of the pure wurtzite ZnO is found to be 0.935eV. This is a new result because in our knowledge nobody has been work in wurtzite ZnO used the exchange correlation BLYP functional based on DFT. Compared with experimental value (3.37eV), the calculated band-gap was much smaller because of the well-known conduction band, but the result did not affect the accuracy of the comparison of the related properties of the crystals. The results obtained can be used as a basis for more in depth calculations, which may include calculating the optical properties with additional dopant that can be used on optical and photo-catalytic applications.

Fully numerical calculations on atoms with fractional occupations and range-separated exchange functionals

A recently developed finite element approach for fully numerical atomic structure calculations [S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019)] is extended to the description of atoms with spherically symmetric densities via fractionally occupied orbitals. Specialized versions of Hartree-Fock as well as local density and generalized gradient approximation density functionals are developed, allowing extremely rapid calculations at the basis set limit on the ground and low-lying excited states even for heavy atoms. The implementation of range-separation based on the Yukawa or complementary error function (erfc) kernels is also described, allowing complete basis set benchmarks of modern range-separated hybrid functionals with either integer or fractional occupation numbers. Finally, computation of atomic effective potentials at the local density or generalized gradient approximation levels for the superposition of atomic potentials (SAP) approach [S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019)] that has been shown to be a simple and efficient way to initialize electronic structure calculations is described. The present numerical approach is shown to afford beyond microhartree accuracy with a small number of numerical basis functions, and to reproduce literature results for the ground states of atoms and their cations for $1 \leq Z \leq 86 $. Our results indicate that the literature values deviate by up to 10 {\mu}Eh from the complete basis set limit. The numerical scheme for the erfc kernel is shown to work by comparison to results from large Gaussian basis set calculations from the literature. Spin-restricted ground states are reported for Hartree-Fock and Hartree-Fock-Slater calculations with fractional occupations for $1 \leq Z \leq 118$.

Phase diagram of uranium fromab initiocalculations and machine learning

Experimental studies of materials at extreme conditions are challenging, and as a consequence, P-T phase diagrams are still unknown for many elements and materials. In this work, we present the P-T phase diagram of uranium calculated up to extreme conditions. First, we searched for possible crystal structures using the evolutionary algorithm USPEX. Their free energies were then calculated using thermodynamic integration (TI) and temperature-dependent effective potential techniques. TI was performed using molecular dynamics, employing a machine learning (ML) force field trained on energies and forces from density-functional calculations at the generalized gradient approximation level. The prediction error of the ML force field for the energy was less than 10 meV/atom. Using thermodynamic perturbation theory (including first and second order corrections), from the free energies of the ML force field, we obtained free energies and phase diagram at the level of quality of the underlying density-functional calculations at pressures up to 800 GPa and temperatures up to 16 000 K.

Assessing exchange-correlation functional performance in the chalcogenide lacunar spinels GaM4Q8 (M=Mo, V, Nb, Ta; Q=S,Se)

We perform systematic density functional theory (DFT) calculations to assess the performance of various exchange-correlation potentials $V_{xc}$ in describing the chalcogenide GaM$_4$Q$_8$ lacunar spinels (M=Mo, V, Nb, Ta; Q=S, Se). We examine the dependency of crystal structure (in cubic and rhombohedral symmetries), electronic structure, magnetism, optical conductivity, and lattice dynamics in lacunar spinels at four different levels of $V_{xc}$: the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, and hybrid with fractional Fock exchange. We find that LDA significantly underperforms GGA and higher level functionals in predicting lattice constants. LDA also fails to properly describe the magnetism in the family, and for some compositions it does not find the ground state distorted crystal structure. The Perdew-Burke-Ernzerhof (PBE) and PBE revised for solids (PBEsol) GGA functionals perform reasonably well in predicting lattice constants as well as the electronic structures. We find that the GGA with an on-site Coulomb interaction (GGA$+U$) is unnecessary to produce a semiconducting state in the distorted polar $R3m$ phase. Plus Hubbard $U$ values ranging from 1$\sim$2 eV, however, improve the quantitative performance of the GGA functionals. The meta-GGA functional SCAN predicts reasonable lattice constants and electronic structures; it exhibits behavior similar to the GGA$+U$ functionals for small $U$ values. The hybrid functional HSE06 is accurate in predicting the lattice constants, but leads to a band gap of $\approx$1 eV in the rhombohedral phase, which is higher than the experimental estimation of 0.2 eV. Our findings suggest that accurate qualitative and quantitative simulations of the lacunar spinel family with DFT requires careful attention to the nuances of the exchange-correlation functional and considered spin structures.

First-principles study of the infrared spectrum in liquid water from a systematically improved description of H-bond network

An accurate ab initio theory of the H-bond structure of liquid water requires a high-level exchange correlation approximation from density functional theory. Based on the liquid structures modeled by ab initio molecular dynamics by using maximally localized Wannier functions as a basis, we study the infrared spectrum of water within the canonical ensemble. In particular, we employ both the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) and the state-of-the-art meta-GGA level approximation provided by the strongly constrained and appropriately normed (SCAN) functional. We demonstrate that the SCAN functional improves not only the water structure but also the theoretical infrared spectrum of water. Our analyses show that the improvement in the stretching and bending bands can be mainly attributed to better descriptions of directional H bonding and the covalency at the inter- and intramolecular levels, respectively. On the other hand, better agreements in libration and hindered translation bands are due to the improved dynamics of the H-bond network enabled by a less structured liquid in the experimental direction. The spectrum predicted by SCAN shows much better agreement with experimental data than the conventionally widely adopted PBE functional at the GGA level.

A Study of the electronic structure of CdS Nanocrystals using density functional theory

Density Functional Theory at the generalized-gradient approximation level coupled with large unit cell method is used to simulate the electronic structure of (II-VI) zinc-blende cadmium sulfide nanocrystals that have dimensions 2-2.5 nm. The calculated properties include lattice constant, conduction and valence bands width, energy of the highest occupied orbital, energy of the lowest unoccupied orbital, energy gap, density of states etc. Results show that lattice constant and energy gap converge to definite values. However, highest occupied orbital, lowest unoccupied orbital fluctuates indefinitely depending on the shape of the nanocrystal.

Space partitioning of exchange-correlation functionals with the projector augmented-wave method.

We implement a Becke fuzzy cells type space partitioning scheme for the purposes of exchange-correlation within the GPAW projector augmented-wave method based density functional theory code. Space partitioning is needed in the situation where one needs to treat different parts of a combined system with different exchange-correlation functionals. For example, bulk and surface regions of a system could be treated with functionals that are specifically designed to capture the distinct physics of those regions. Here, we use the space partitioning scheme to implement the quasi-nonuniform exchange-correlation scheme, which is a useful practical approach for calculating metallic alloys on the generalized gradient approximation level. We also confirm the correctness of our implementation with a set of test calculations.

Reactive and Nonreactive Scattering of HCl from Au(111): An Ab Initio Molecular Dynamics Study.

The HCl + Au(111) system has recently become a benchmark for highly activated dissociative chemisorption, which presumably is strongly affected by electron–hole pair excitation. Previous dynamics calculations, which were based on density functional theory at the generalized gradient approximation level (GGA-DFT) for the molecule–surface interaction, have all overestimated measured reaction probabilities by at least an order of magnitude. Here, we perform ab initio molecular dynamics (AIMD) and AIMD with electronic friction (AIMDEF) calculations employing a density functional that includes the attractive van der Waals interaction. Our calculations model the simultaneous and possibly synergistic effects of surface temperature, surface atom motion, electron–hole pair excitation, the molecular beam conditions of the experiments, and the van der Waals interaction on the reactivity. We find that reaction probabilities computed with AIMDEF and the SRP32-vdW functional still overestimate the measured reaction probabilities, by a factor 18 for the highest incidence energy at which measurements were performed (≈2.5 eV). Even granting that the experiment could have underestimated the sticking probability by about a factor three, this still translates into a considerable overestimation of the reactivity by the current theory. Likewise, scaled transition probabilities for vibrational excitation from ν = 1, j = 1 to ν = 2 are overestimated by the AIMDEF theory, by factors 3–8 depending on the initial conditions modeled. Energy losses to the surface and translational energy losses are, however, in good agreement with experimental values.

A local environment descriptor for machine-learned density functional theory at the generalized gradient approximation level.

We propose a grid-based local representation of electronic quantities that can be used in machine learning applications for molecules, which is compact, fixed in size, and able to distinguish different chemical environments. We apply the proposed approach to represent the external potential in density functional theory with modified pseudopotentials and demonstrate its proof of concept by predicting the Perdew-Burke-Ernzerhof and local density approximation electronic density and exchange-correlation potentials by kernel ridge regression. For 16 small molecules consisting of C, H, N, and O, the mean absolute error of exchange-correlation energy was 0.78 kcal/mol when trained for individual molecules. Furthermore, the model is shown to predict the exchange-correlation energy with an accuracy of 3.68 kcal/mol when the model is trained with a small fraction (4%) of all 16 molecules of the present dataset, suggesting a promising possibility that the current machine-learned model may predict the exchange-correlation energies of an arbitrary molecule with reasonable accuracy when trained with a sufficient amount of data covering an extensive variety of chemical environments.

Structures and electronic properties of $$\hbox {W}_{m}\hbox {Cu}_{n}\,(n + m \le 7)$$ W m Cu n ( n + m ≤ 7 ) clusters

Geometric and electronic structures of \(\hbox {W}_{m}\hbox {Cu}_{n}\, (m + n \le 7)\) cluster have been systematically calculated by density functional theory at the generalized gradient approximation level for ground-state structures. \(\hbox {W}_{m}\hbox {Cu}_{n}\) clusters with \(n = 1, 3, 5\) tend to form bipyramid structures, whereas \(\hbox {WCu}_{n}\) favour planar shapes except for \(\hbox {WCu}_{5}\). The configurations of \(\hbox {W}_{m}\hbox {Cu}_{n}\) clusters are more sensitive to the Cu atoms than the W atoms, while the average atomic binding energies and the total magnetic moments are determined by W atoms. The calculated second-order differences in energies and HOMO–LOMO energy gaps show pronounced odd–even oscillating behaviours. From the Mulliken electron population analysis, we found that Cu 4p and W 6p orbitals exhibit electronic charges and both Cu 4s and W 6s orbitals transfer electronic charges to the W 5d orbital, which lead to the extension of W–Cu bond lengths.

Ultra-small Ag clusters in zeolite A4: Antibacterial and thermochromic applications

The physical and chemical properties of metal clusters depend on their atomic structure, therefore, it is important to determine the lowest-energy structures of the clusters in order to understand and utilize their properties. In this work, we use the Density Functional Theory (DFT) at the generalized gradient approximation level Becke's three-parameter and the gradient corrected functional of Lee, Yang and Puar (B3LYP) in combination with the basis set LANL2DZ (the effective core potentials and associated double-zeta valence) to determine some of the structural, electronic and vibrational properties of the planar silver clusters (Agn clusters n = 2–24). Additionally, the study reports the experimental synthesis of small silver clusters in synthetic zeolite A4. The synthesis was possible using the ion exchange method with some precursors like silver nitrate (AgNO3) and synthetic zeolite A4. The silver clusters in zeolite powder underwent thermal treatment at 450 °C to release the remaining water or humidity on it. The morphology of the particles was determined by Transmission Electron microscopy. The nanomaterials obtained show thermochromic properties. The structural parameters were correlated theoretically and experimentally.

Half-Metallicity in Co-Doped WSe2 Nanoribbons.

The recent development of two-dimensional transition-metal dichalcogenides in electronics and optoelelectronics has triggered the exploration in spintronics, with high demand in search for half-metallicity in these systems. Here, through density functional theory (DFT) calculations, we predict robust half-metallic behaviors in Co-edge-doped WSe2 nanoribbons (NRs). With electrons partially occupying the antibonding state consisting of Co 3dyz and Se 4pz orbitals, the system becomes spin-polarized due to the defect-state-induced Stoner effect and the strong exchange splitting eventually gives rise to the half-metallicity. The half-metal gap reaches 0.15 eV on the DFT generalized gradient approximation level and increases significantly to 0.67 eV using hybrid functional. Furthermore, we find that the half-metallicity sustains even under large external strain and relatively low edge doping concentration, which promises the potential of such Co-edge-doped WSe2 NRs in spintronics applications.

Study of the structural and electronic properties of FeO at the LDA and GGA level

Due to its strongly correlated insulating nature, FeO is used in various catalytic applications. Structural and electronic properties of FeO are investigated by using density functional theory (DFT) with the BAND code in Amsterdam Density Functional (ADF) software at ambient conditions. The generalized gradient approximation (GGA) and local density approximation (LDA) without and with the Hubbard potential (U eV) are used to investigate the structural and electronic properties of FeO. Geometric optimization of FeO is carried out by using the LDA and GGA method. CAPZ (Ceperley–Alder–Perdew–Zunger) and PBE (Perdew–Burke–Ernzerhof) are used as exchange correlation potentials for the LDA and GGA, respectively. The Hubbard potential is optimized and U= 0.6eV is used to overcome the under-estimation of the band gap of FeO in both approximations. The band structure shows the metallic nature of FeO with the GGA and LDA while band gap of 2.34 and 2.08eV is observed by using GGA+U and LDA+U, respectively. Our calculated band gap value with the GGA+U is in good agreement with the reported experimental value, i.e. 2.4eV. The total and partial density of states are also plotted to show the band structure. To the best of our knowledge, no study has been reported yet at the U= 0.6eV value of the Hubbard potential.

A power series revisit of the PBE exchange density-functional approximation: The PBEpow model.

PBEpow is a power series extension of the Perdew-Burke-Ernzerhof (PBE) exchange generalized gradient approximation. This novel variant is constructed by an inductive determination of the power series coefficients to fulfill physical fundamental constants in the slowly and rapidly varying density limits. When combined with the PBE correlation, PBEpow significantly improves the estimation of molecular covalent interactions such as energies of atomization reactions and keeps the line of performance of PBE for noncovalent interactions. More generally this work provides new insights about how to improve the modeling of short- and long-range interactions at the generalized gradient approximation level without the help of any kind of empirical parameterization.

Assessing the Accuracy of Across-the-Scale Methods for Predicting Carbohydrate Conformational Energies for the Examples of Glucose and α-Maltose.

A big hurdle when entering the field of carbohydrate research stems from the complications in the analytical and computational treatment. In effect, this extremely important class of biomolecules remains underinvestigated when compared, for example, with the maturity of genomics and proteomics research. On the theory side, the commonly used empirical methods suffer from an insufficient amount of high-quality experimental data against which they can be thoroughly validated. In order to provide a pivotal point for an ascent of accurate carbohydrate simulations, we present here a structure/energy benchmark set of diverse glucose (in three isomeric forms) and α-maltose conformations at the coupled-cluster level as well as an assessment of commonly used energy functions. We observe that empirical force fields and semiempirical approaches, on average, do not reproduce accurately the reference energy hierarchies. While the force fields maintain accuracy for the low-energy structures, the semiempirical methods perform unsatisfactory for the entire range. On the contrary, density-functional approximations reproduce the reference energy hierarchies with better than chemical accuracy already at the generalized gradient approximation level (GGA). Particularly, the novel meta-GGA functional SCAN provides the accuracy of more expensive hybrid functionals at fraction of their computational cost. In conclusion, we advocate for electronic-structure theory methods to become the routine tool for simulations of carbohydrates.