meta-GGA Functionals Research Articles

Structural and energetic properties of cluster models of anatase-supported single late transition metal atoms: a density functional theory benchmark study.

Single-atom catalytic systems constitute an intriguing research topic due to their inherently different chemical behavior as compared to classic heterogeneous catalysts. In this study, cluster systems representing single late transition metal atoms adsorbed on anatase were constructed starting from previously generated periodic models and subjected to a density functional theory (DFT) benchmark study. The ability of different density functional approximations representing all rungs of the Jacob's Ladder classification to accurately describe bond lengths and adsorption energies was assessed for these clusters with the aim of revealing the functional that allows to retain the structural characteristics of the initial periodic system, while also delivering reliable energetics. In this regard, our results indicate that optimisation of the clusters with the meta-GGA functionals TPSS or RevTPSS provides the lowest mean unsigned error and root-mean-square deviations with respect to the periodic models. Moreover, these functionals and, to a slightly lesser degree, PW91 were also found to provide adsorption energies that are statistically the least deviating from the CCSD(T) reference data. More complex hybrid functionals appear to be performing less well. Cluster geometries were determined at the Kohn-Sham DFT level using the LANL2DZ basis set for the transition metals and the Pople 6-31G(d) basis set for O and H. The density functional approximations considered were SVWN, PBE, BP86, BLYP, PW91, TPSS, RevTPSS, M06L, M11L, B3LYP, PBE0, M06, M06-2X, MN15, ωB97X-D, CAM-B3LYP, M11, and MN12-SX. Reference adsorption energies of the metals on the support cluster were obtained at the CCSD(T)/LANL2TZ (transition metals)/6-311 + + G(d,p)//RevTPSS/LANLD2DZ (transition metals)/6-31G*. Besides the above-mentioned functionals, energy calculations using the double-hybrid functionals, DSDPBEP86, PBE0-DH, and B2PLYP, were also performed. All adsorption energy calculations were carried out on the RevTPSS geometries.

Evaluating the Chemical Reactivity of DFT-Simulated Liquid Water with Hydrated Electrons via the Dual Descriptor.

Modeling the various properties of liquid water, particularly its reactivity, has been a longstanding challenge for simulation methods. Recently, ab initio simulations based on density functional theory (DFT) have come to the fore as tenable methods for calculating the properties and reactivity of water, with varying degrees of success for different exchange-correlation functionals. In particular, hybrid-GGA and meta-GGA functionals have been shown to reproduce many of the structural, dynamical, and energetic properties of water to a high degree of accuracy relative to their computational cost. Here, we show that the dual descriptor (DD) measure of nucleophilicity and electrophilicity, which is sometimes used to elucidate organic chemistry reaction mechanisms, can also be used to characterize the reactivity of DFT-simulated liquid water. The DD is especially apt for understanding the reactivity of excess electrons with water as its calculation explicitly involves adding and removing an excess electron from a reference system. We use the DD to explore the reactivity of water simulated using three different DFT functionals: the LDA functional (LDA), a hybrid-GGA functional (PBE0), and a hybrid meta-GGA functional (SCAN0). Using the DD, we show that the SCAN0 functional with the standard 25% Hartree-Fock exchange produces simulated liquid water with many regions that are far more reactive than either PBE0 or LDA. To understand the implications of these highly reactive regions, we then add a strong nucleophile in the form of an excess electron and find that although PBE0 and LDA predict stable hydrated electrons, the excess electron reacts nearly instantaneously with SCAN0 water via proton abstraction to form a hydrogen atom and hydroxide ion. We show that the DD provides the ability to not only predict whether or not liquid water will react with a hydrated electron but also which particular waters will be involved solely from analyzing pure water configurations generated with each functional. We rationalize this result in terms of the known trap-seeking behavior of injected hydrated electrons, which are able to find the most electronegative region in bulk water. These results highlight the utility of the dual descriptor as a fast and interpretable method for investigating condensed-phase reactivity with excess electrons.

Insulating behaviour in room temperature rhombohedral LiNiO2 cathodes is driven by dynamic correlation

Abstract Inspired by the experimental finding of a paramagnetic insulating state in rhombohedral LiNiO2, a lithium-ion battery cathode of great interest, we calculate the electronic, magnetic, and optical properties of LiNiO2 employing a range of single-particle and many-body methods. Within density-functional theory (DFT) using the generalized-gradient approximation (GGA), meta-GGA, and hybrid functionals, we obtain a ferromagnetic half-metallic ground state for rhombohedral LiNiO2, as has been seen previously. Self-consistent GW calculations including self-interaction corrections beyond DFT for various flavours show an electronic band gap albeit with a small quasiparticle peak at the Fermi energy. Moving beyond this, room temperature state-of-the-art dynamical mean-field theory (DMFT) calculations on rhombohedral LiNiO2 show for the first time a gap of combined Mott and charge-transfer character. The paramagnetic insulating state has a band gap of ~0.6 eV, in excellent agreement with experiments and is in sharp contrast to DFT calculations that require the presence of an extra structural symmetry breaking in the form of Jahn–Teller distortions to open a gap. We observe Ni to be in a +2 state in a d 8L configuration, with a charge-transfer ligand hole in O p, and identify the ligand hole state from the DMFT DOS. We further show that whereas DFT shows the presence of an unphysical metallic Drude peak in the optical absorption spectra, DMFT calculations capture the correct form of the optical absorption spectra, and have an excellent match with the calculated band gap as well. Our results clarify that at room temperature, it is the charge transfer gap with a Mott character that causes rhombohedral LiNiO2’s insulating nature; a structural distortion is not required.

Accuracy of metaGGA functionals in describing transition metal fluorides

Accuracy of metaGGA functionals in describing transition metal fluorides

Polarized Raman, infrared and dielectric spectra of lead-free K0.5Na0.5NbO3 piezoelectric system: insights from ab-initio theoretical and experimental studies

The K0.5Na0.5NbO3 (KNN) system has emerged as one of the most promising lead-free piezoelectric over the years. In this work, we perform a comprehensive investigation of electronic structure, lattice dynamics and dielectric properties of room temperature phase of KNN by combining ab-initio DFT based theoretical analysis and experimental characterization. We assign the symmetry labels to KNN vibrational modes and obtain ab-initio polarized Raman spectra, Infrared reflectivity, Born-effective charge tensors, oscillator strengths etc. The KNN ceramic samples are prepared using conventional solid-state method and Raman and UV–Vis diffuse reflectance spectra are obtained. The computed Raman spectrum is found to agree well with the experimental spectrum. In particular, the results suggest that the mode in range ∼840–870 cm−1 reported in the experimental studies is longitudinal optical with A1 symmetry. The Raman mode intensities are calculated for different light polarization set-ups that suggests the observation of different symmetry modes in different polarization set-ups. The electronic structure of KNN is investigated and optical absorption spectrum is obtained. Further, the performances of DFT semi-local, meta-GGA and hybrid exchange-correlations functionals, in the estimation of KNN band gaps are investigated. The KNN bandgap computed using GGA-1/2 and HSE06 hybrid functional schemes are found to be in excellent agreement with the experimental value. The COHP, electron localization function and Bader charge analysis is also performed to deduce the nature of chemical bonding in the KNN. Overall, our study provides several bench-mark important results on KNN that have not been reported so far.

Benchmarking Periodic Density Functional Theory Calculations for Spin-State Energies in Spin-Crossover Systems.

Spin energetics is one of the biggest challenges associated with energy calculations for electronic structure methods. The energy differences of the spin states in spin-crossover compounds are very small, making them one of the most difficult systems to calculate. Few methods provide accurate results for calculating these energy differences. In addition, studies have usually focused on calculating energetics of single molecules, while spin-crossover properties are usually experimentally studied in the solid phase. In this paper, we have used periodic boundary conditions employing methods based on density functional theory to calculate the high- and low-spin energy differences for a test case of 20 extended systems. Compounds with different metals and ligands have been selected, and the results indicate that a semiquantitative description of the energy differences can be obtained with the combination of geometry optimization using the PBE functional including many-body dispersion approach and the use of meta-GGA functionals, such as r2SCAN but especially KTBM24, for the energy calculation. Other hybrid functionals, such as TPSSh, give generally good results, but the calculation of the exact exchange with periodic boundary conditions involves a huge increase in computer time and computational resources. It makes the proposed nonhybrid functional approach (KTBM24//PBE+MB) a great advantage for the study of periodic systems.

The comparative study of structural, optoelectronic and thermoelectric properties of Li-based half-Heusler alloys via GGA and meta-GGA functionals

The present work aims to investigate the effects of meta-GGA functionals on the structural, optoelectronic and thermoelectric properties of LiXY(X=Be, Mg, Zn, Cd and Y=N, P, As, Sb, Bi) half-Heusler alloys using density functional theory (DFT) and classical Boltzmann transport theory. The obtained lattice constants of these alloys are in good agreement with the experimental values, exhibiting a slight decrease slightly with meta-GGA functionals compared with GGA-PBE. Band structure calculations demonstrate that the materials exhibit semiconductor character and provide validation for the use of meta-GGA functionals, particularly the r2SCAN and rSCAN, to predict the band gap values of LiXY more accurately. Optical and thermoelectric properties are calculated and discussed in detail. The results reveal that the meta-GGA functionals predict a significant change compared with GGA-PBE in the low energy and temperature region, while in the high energy and temperature regions, all four functionals present almost the same change trends.

Analysis of Na2CuP ternary semiconductor compound for optoelectronic application by first-principles methods using GGA and mGGA functionals

An ab initio study of Zintl Na2CuP ternary semiconductor compounds was carried out by applying first-principles methods to calculate the structural, electronic, elastic, mechanical, and optical properties using generalised gradient approximation (GGA) and metaGGA exchange-correlation functionals. The bandgap was determined to be 0.7523 eV and 0.7848 eV using GGA with Wu-Cohen and Perdew-Burke-Ernzerhof (PBE) functionals, respectively. The bandgap was re-approximated using the more accurate metaGGA functionals as 1.078 eV and 1.084 eV using the Tran-Blaha modified Becke Johnson exchange and correlation functional (TB-mBJ) and the strongly constrained and appropriately normed (SCAN) functional, respectively. The projected density of states using the GGA revealed that the conduction band formation was mainly by Cu 2p, P 2p, and Na 2s orbitals with the rest of the orbitals making a minor contribution. In contrast, the valence band formation was mainly formed by Cu 3d and P 2p, with the rest of the orbital playing a minor role in the formation. The material was found to be mechanically brittle with a covalent bond, which is a characteristic of Zintl-phased materials. The Na2CuP material was also observed to have a strong absorption coefficient between 1.15 eV and 15 eV, a characteristic suitable for photovoltaic applications.

Thermodynamics of the gas-phase dimerization of formic acid: Fully anharmonic finite temperature calculations at the CCSD(T) and many DFT levels.

A proof-of-concept study is undertaken to demonstrate the utility of the machine learning combined with the thermodynamic perturbation theory (MLPT) to test the accuracy of electronic structure methods in finite-temperature thermodynamic calculations. As a test example, formic acid dimer is chosen, which is one of the systems included in the popular benchmark set S22 [Jurečka et al., Phys. Chem. Chem. Phys. 8, 1985-1993 (2006)]. Starting from the explicit molecular dynamics and thermodynamic integration performed at the PBE + D2 level, the MLPT is used to obtain fully anharmonic dimerization free and internal energies at the reference quality CCSD(T) level and 19 different density functional approximations, including GGA, meta-GGA, non-local, and hybrid functionals with and without dispersion corrections. Our finite-temperature results are shown to be both qualitatively and quantitatively different from those obtained using the conventional benchmarking strategy based on fixed structures. The hybrid functional HSE06 is identified as the best performing approximate method tested, with the errors in free and internal energies of dimerization being 36 and 41meV, respectively.

Partially deorbitalized meta-GGA

Mejia-Rodriguez and Trickey recently proposed a procedure for removing the explicit dependence of meta-GGA exchange-correlation energy functionals Exc on the kinetic energy density τ. We present a simple modification to this approach in which the exact Kohn-Sham τ is used as input for Exc but the functional derivative of τ with respect to the density ρ, required to calculate the potential term ∫d3r′δExc∕δτ(r′)∣ρ⋅δτ(r′)∕δρ(r), is evaluated using an approximate kinetic energy density functional. This ‘half-way’ strategy ensures that the Kohn-Sham potential is a local multiplicative function (as opposed to the non-local potential of a generalized Kohn-Sham approach) while preserving the inherent non-locality of the functional itself. Electronic structure codes can be easily modified to use the new method. We validate it by quantifying the accuracy of the predicted lattice parameters, bulk moduli, magnetic moments and cohesive energies of a large set of periodic solids. An unanticipated benefit of this method is to gauge the quality of approximate kinetic energy functionals by checking if the self-consistent solution is indeed at the variational minimum.

Performance of Density Functionals for Excited-State Properties of Isolated Chromophores and Exciplexes: Emission Spectra, Solvatochromic Shifts, and Charge-Transfer Character.

This study assesses the performance of various meta-generalized gradient approximation (meta-GGA), global hybrid, and range-separated hybrid (RSH) density functionals in capturing the excited-state properties of organic chromophores and their excited-state complexes (exciplexes). Motivated by their uses in solar energy harvesting and photoredox CO2 reduction, we use oligo-(p-phenylenes) and their excited-state complexes with triethylamine as model systems. We focus on the fluorescence properties of these systems, specifically emission energies. We also consider solvatochromic shifts and wave function characteristics. The latter is described by using reduced quantities such as natural transition orbitals (NTOs) and exciton descriptors. The functionals are benchmarked against the experimental fluorescence spectra and the equation-of-motion coupled-cluster method with single and double excitations. Both in isolated chromophores and in exciplexes, meta-GGA functionals drastically underestimate the emission energies and exhibit significant exciton delocalization and anticorrelation between electron and hole motion. The performance of global hybrid functionals is strongly dependent on the percentage of exact exchange. Our study identifies RSH GGAs as the best-performing functionals, with ωPBE demonstrating the best agreement with experimental results. RSH meta-GGAs often overestimate emission energies in exciplexes and yield larger hole NTOs. Their performance can be improved by optimally tuning the range-separation parameter.

Photoredox matching of earth-abundant photosensitizers with hydrogen evolving catalysts by first-principles predictions.

Photoredox properties of several earth-abundant light-harvesting transition metal complexes in combination with cobalt-based proton reduction catalysts have been investigated computationally to assess the fundamental viability of different photocatalytic systems of current experimental interest. Density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations using several GGA (BP86, BLYP), hybrid-GGA (B3LYP, B3LYP*), hybrid meta-GGA (M06, TPSSh), and range-separated hybrid (ωB97X, CAM-B3LYP) functionals were used to calculate relevant ground and excited state reduction potentials for photosensitizers, catalysts, and sacrificial electron donors. Linear energy correction factors for the DFT/TD-DFT results that provide the best agreement with available experimental reference results were determined in order to provide more accurate predictions. Among the selection of functionals, the B3LYP* and TPSSh sets of correction parameters were determined to give the best redox potentials and excited states energies, ΔEexc, with errors of ∼0.2eV. Linear corrections for both reduction and oxidation processes significantly improve the predictions for all the redox pairs. In particular, for TPSSh and B3LYP*, the calculated errors decrease by more than 0.5V against experimental values for catalyst reduction potentials, photosensitizer oxidation potentials, and electron donor oxidation potentials. Energy-corrected TPSSh results were finally used to predict the energetics of complete photocatalytic cycles for the light-driven activation of selected proton reduction cobalt catalysts. These predictions demonstrate the broader usefulness of the adopted approach to systematically predict full photocycle behavior for first-row transition metal photosensitizer-catalyst combinations more broadly.

First-principle investigation of structural, electronic, and phase stabilities in chalcopyrite semiconductors: insights from Meta-GGA functionals

We undertake a comprehensive first-principles investigation into the factors influencing the optoelectronic efficiencies of P I Q III R 2VI chalcopyrite semiconductors. The structural attributes, electronic properties, and phase stabilities are explored using various meta-GGA exchange-correlation (XC) functionals within the density functional framework. In particular, we assess the relative performance of these XC functionals in obtaining estimates of various relevant parameters. The structural parameter u in chalcopyrite semiconductors is a noteworthy aspect, as it is intrinsically tied to the extent of orbital hybridization between distinct atoms and thereby strongly influences the electronic properties. In general, the application of widely used GGA-PBE XC functional to these chalcopyrites results in unreliable predictions of band gaps and ‘u’ parameter due to delocalization errors that in turn arise due to the inclusion of d and f core electrons. While hybrid functionals offer remarkable accuracy through state-of-the-art methods, their main drawback lies in their computational expense and resource demands. Our findings strongly suggest that in comparison to GGA-PBE, the meta-GGA XC functionals perform quite well and provide results that closely align with experimental values. In particular, the r 2SCAN and rMGGAC XC functionals are preferable and superior for investigating chalcopyrites and other solid-state systems. This preference is rooted in their excellent performance and substantially reduced computational costs compared to hybrid functionals.

Toward Accurate Two-Photon Absorption Spectrum Simulations: Exploring the Landscape beyond the Generalized Gradient Approximation.

In this Letter, we present a pioneering analysis of the density functional approximations (DFAs) beyond the generalized gradient approximation (GGA) for predicting two-photon absorption (2PA) strengths of a set of push-pull π-conjugated molecules. In more detail, we have employed a variety of meta-generalized gradient approximation (meta-GGA) functionals, including SCAN, MN15, and M06-2X, to assess their accuracy in describing the 2PA properties of a chosen set of 48 organic molecules. Analytic quadratic response theory is employed for these functionals, and their performance is compared against the previously studied DFAs and reference data obtained at the coupled-cluster CC2 level combined with the resolution-of-identity approximation (RI-CC2). A detailed analysis of the meta-GGA functional performance is provided, demonstrating that they improve upon their predecessors in capturing the key electronic features of the π-conjugated two-photon absorbers. In particular, the Minnesota functional MN15 shows very promising results as it delivers pleasingly accurate chemical rankings for two-photon transition strengths and excited-state dipole moments.

Accurate state energetics in spin-crossover systems using pure density functional theory.

The energy difference between different spin states of systems with transition metals is an outstanding challenge for electronic structure calculation methods. The small energy difference between high- and low-spin states in spin-crossover systems makes most post-Hartree-Fock or density functional theory-based methods provide inaccurate values. A test case of twenty systems showing spin transitions has been used to evaluate the accuracy of a new family of training meta-GGA (Generalized Gradient Approximation) functionals. One of the functionals of this new family provides comparable or even better values than the best functional reported so far for this type of system, the TPSSh hybrid meta-GGA functional, but without having to use the exact exchange term. It also improves the results obtained with the r2SCAN meta-GGA functional, which was the best alternative to the TPSSh hybrid functional. This makes it possible to calculate the spin energetics of any kind of compound, especially large systems or periodic structures where the exact exchange requires large computational resources.

Orbital-optimized density functional calculations of molecular Rydberg excited states with real space grid representation and self-interaction correction.

Density functional calculations of Rydberg excited states up to high energy are carried out for several molecules using an approach where the orbitals are variationally optimized by converging on saddle points on the electronic energy surface within a real space grid representation. Remarkably good agreement with experimental estimates of the excitation energy is obtained using the generalized gradient approximation (GGA) functional of Perdew, Burke, and Ernzerhof (PBE) when Perdew-Zunger self-interaction correction is applied in combination with complex-valued orbitals. Even without the correction, the PBE functional gives quite good results despite the fact that corresponding Rydberg virtual orbitals have positive energy in the ground state calculation. Results obtained using the Tao, Perdew, Staroverov, and Scuseria (TPSS) and r2SCAN meta-GGA functionals are also presented, but they do not provide a systematic improvement over the results from the uncorrected PBE functional. The grid representation combined with the projector augmented-wave approach gives a simpler and better representation of diffuse Rydberg orbitals than a linear combination of atomic orbitals with commonly used basis sets, the latter leading to an overestimation of the excitation energy due to confinement of the excited states.

First-principles prediction of energy bandgaps in 18-valence electron semiconducting half-Heusler compounds: Exploring the role of exchange and correlation

The choice of exchange functional is a critical factor in determining the energy bandgap of semiconductors. Ab initio calculations using different exchange functionals, including the conventional generalized-gradient approximation (GGA) functionals, meta-GGA functionals, and hybrid functionals, show significant differences in the calculated energy bandgap for semiconducting half-Heusler compounds. These compounds, which have 18 valence electrons per unit cell, are of great interest due to their thermoelectric properties, making them suitable for energy conversion applications. In addition, accounting for electronic correlations using the GW method also affects the calculated energy bandgaps compared to standard GGA calculations. The variations in calculated energy bandgaps are specific to each material when using different functionals. Hence, a detailed investigation of the electronic properties of each compound is necessary to determine the most appropriate functional for an accurate description of the electronic properties. Our results indicate that no general rules can be established and a comparison with experimental results is required to determine the most appropriate functional.

Comparative first-principles structural and vibrational properties of rutile and anatase TiO2

The structural and vibrational properties of two polymorphs of TiO2, rutile and anatase, have been investigated by first-principles methods at different levels of exchange-correlational (XC) energy functionals in density functional theory (DFT). Reports in the literature to date are contradictory regarding the stability of the rutile phase using DFT XC-functionals more sophisticated than simple local-density approximation. Here the PBEsol generalized gradient approximation (GGA), TPSS meta-GGA, and HSE06 hybrid functionals have been employed to demonstrate the XC-functional effects on the calculated structural, phonon and thermodynamic properties of rutile and anatase TiO2. Lattice and elastic parameters correctly calculated with these XC-functionals show good agreement with the experimental values. Calculated phonon frequencies generated stable phonon dispersion relations for both rutile and anatase TiO2 when correctly converged, in agreement with the experimental observations. The phonon frequencies along high symmetry Brillouin zone paths and their corresponding phonon density of states showed sensitivity to different levels of XC-functional employed in phonon dispersion prediction. Nevertheless, the thermodynamic properties of rutile and anatase TiO2 estimated by harmonic approximations are in excellent experimental agreement and are effectively invariant to the level of theory employed in the DFT XC-functional.

Minimum conditions for accurate modeling of urea production via co-electrolysis

Co-electrolysis of carbon oxides and nitrogen oxides promise to simultaneously help restore the balance of the C and N cycles while producing valuable chemicals such as urea. However, co-electrolysis processes are still largely inefficient and numerous knowledge voids persist. Here, we provide a solid thermodynamic basis for modelling urea production via co-electrolysis. First, we determine the energetics of aqueous urea produced under electrochemical conditions based on experimental data, which enables an accurate assessment of equilibrium potentials and overpotentials. Next, we use density functional theory (DFT) calculations to model various co-electrolysis reactions producing urea. The calculated reaction free energies deviate significantly from experimental values for well-known GGA, meta-GGA and hybrid functionals. These deviations stem from errors in the DFT-calculated energies of molecular reactants and products. In particular, the error for urea is approximately -0.25 ± 0.10 eV. Finally, we show that all these errors introduce large inconsistencies in the calculated free-energy diagrams of urea production via co-electrolysis, such that gas-phase corrections are strongly advised.

The application of the SCAN density functional to color centers in diamond.

Detailed characterization of deep-level color centers requires understanding their electronic and atomic structure, which is most commonly investigated utilizing the Kohn-Sham density functional theory. Standard semilocal functionals based on the generalized gradient approximation (GGA) are inclined toward an imprecise quantitative description of defects' electronic structure. Hybrid functionals provide an improved prediction of electronic properties, albeit at a much higher computational cost. In this work, we test the newly developed Strongly Constrained and Appropriately Normed (SCAN) family of meta-GGA density functionals for selected color centers in diamond. In particular, we study nitrogen-, silicon-, germanium-, and tin-vacancy centers that have been recently investigated for their use in quantum technological applications. We show that SCAN and its derivatives, the rSCAN and r2SCAN functionals, significantly improve the calculated energies of optical transitions within the delta-self-consistent-field approach, almost reaching the accuracy of the hybrid Heyd-Scuseria-Ernzerhof (HSE) functional. In the case of the NV- center, we also show that the SCAN family of functionals improves the description of the adiabatic potential energy surfaces compared to both GGA and hybrid functionals, improving calculated luminescence lineshapes. As a result of these findings, we recommend using the SCAN family of functionals as a promising alternative for studying color centers in solids.