meta-GGA Exchange-correlation Research Articles

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.

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.

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.

Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations.

The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high- and low-density limits of the Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.

Electronic Properties of Zn2V(1-x)NbxN3 Alloys to Model Novel Materials for Light-Emitting Diodes.

We propose the Zn2V(1-x)NbxN3 alloy as a new promising material for optoelectronic applications, in particular for light-emitting diodes (LEDs). We perform accurate electronic-structure calculations of the alloy for several concentrations x using density-functional theory with meta-GGA exchange-correlation functional TB09. The band gap is found to vary between 2.2 and 2.9 eV with varying V/Nb concentration. This range is suitable for developing bright LEDs with tunable band gap as potential replacements for the more expensive Ga(1-x)In(x)N systems. Effects of configurational disorder are taken into account by explicitly considering all possible distributions of the metal ions within the metal sublattice for the chosen supercells. We have evaluated the band gap's nonlinear behavior (bowing) with variation of V/Nb concentration for two possible scenarios: (i) only the structure with the lowest total energy is present at each concentration and (ii) the structure with minimum band gap is present at each concentration, which corresponds to experimental conditions when also metastable structures are presents. We found that the bowing is about twice larger in the latter case. However, in both cases, the bowing parameter is found to be lower than 1 eV, which is about twice smaller than that in the widely used Ga(1-x)In(x)N alloy. Furthermore, we found that both crystal volume changes due to alloying and local effects (atomic relaxation and the V-N/Nb-N bonding difference) have important contributions to the band gap bowing in Zn2V(1-x)NbxN3.

Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals.

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Periodic hybrid-DFT study on the N-doped TiO2 (001) nanotubes as solar water splitting catalysts: A comparison with the rutile and anatase bulk phases

TiO2 is a routinely used catalyst due to its photocatalytic activity. The main problem of TiO2 is its large band gap. Doping metal and non-metal atoms in TiO2 crystals reduce the band gap. In this work, first-principle calculations by the full-potential numeric atom-center orbital theory were used to investigate detailed electronic properties of N-doped one monolayer (1 ML) and two monolayers (2 ML) (4,4), (8,8) and (16,16) TiO2 (001) nanotubes. The proposed model first validated by comparing its data with the experimental available data for rutile and anatase bulk phases, and then was used to predict the electronic properties of proposed nanotubes. PBE0 hybrid method was used to align the valence and conduction bands and to predict their standard reduction potential. In addition, different routine generalized gradient approximation (GGA) and meta-GGA exchange-correlation functionals were used to show how much their errors are in predicting the band gaps of nanotubes. Hybrid data showed that a 2 ML (8,8) nanotube is a proper candidate for photocatalyst not only for its band gap but also from its formation energy point of view. Contrary to the N-doped rutile and anatase phases, there is no electron-hole recombination center for the N-doped 2 ML (8,8) TiO2 nanotube.

Strongly Correlated Electronic Properties of FeO Studied by the SCAN+U Functional

The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA exchange-correlation functional has been demonstrated to be able to give an accurate description of strongly correlated cuprates. However, it remains to be seen if SCAN calculations can predict the physics of compounds involving partially filled 3d orbitals. In this work, we present the first-principles electronic structure studies about the phase transition of FeO using the SCAN functional. Compared with the exchange-correlation functionals widely used in density functional theory, such as the local-density approximation (LDA) or the generalized gradient approximation (GGA), SCAN correctly predicts an antiferromagnetic insulating ground state. However, it still significantly underestimates the band gap for compounds involving partially filled 3d orbitals and, hence, predicts an incorrect phase transition pressure of FeO. Interestingly, the electronic structure and band gap properties of FeO from the SCAN calculations are similar to those from the GGA+U calculations with U0 = 0.7 eV. An on-site interelectronic interaction U is therefore still needed in order to correctly describe the phase transition physics of FeO for the SCAN calculations, predominantly as a simplified self-interaction-error reduction term that enhances the spatial compactness of 3d orbitals. The required value of U in SCAN+U is less than that required in GGA+U, and their difference is rightly equal to the value of U0. Most importantly, in comparison with GGA+U, the SCAN+U method no longer needs to use the prior-known knowledge to break orbital symmetry avoiding the metastability issue, benefiting from the spontaneous symmetry breaking it allows. The calculated properties of FeO from SCAN+U agree well with experiments.

Revealing the ground‐state geometry, optoelectronic, mechanical and thermodynamic behaviors, and efficiency of formamidinium mixed halide perovskites for solar cell applications

Hybrid organic-inorganic lead halide perovskites are the revolutionary materials that have brought a new era of low-cost and highly efficient solar cells. Generally, high-performing perovskite solar cells incorporate formamidinium-based lead halide perovskites. Using density functional theory, we employed generalized gradient approximation (GGA) and meta-GGA (MGGA) exchange-correlation functionals to investigate the structural, electronic, optical, mechanical, and thermodynamic properties of the perovskite series FAPbI3, FAPbBr2I, FAPbBrI2, and FAPbBr3. Both the functionals successfully determined the most stable structure for each mixed halide perovskite. Electronic properties such as band structure, the density of states, and effective masses have been calculated and discussed. Our estimated band gap values using MGGA functional are more close to the experiments than PBE. Optical properties of the perovskite series such as dielectric function, complex refractive index, absorption coefficient, and reflectivity have been explained in the light of photovoltaic applications. Moreover, we predicted the maximum absorber efficiency via the spectroscopic limited maximum efficiency method. FAPbI3 achieved the highest efficiency by virtue of its suitable band gap and maximum absorption. Mechanical properties have also been studied through elastic constants, elastic moduli, Pugh ratio, Poisson ratio, and other several properties, which reveal the declining flexibility of perovskites with bromine. Further, thermodynamic properties like heat capacity, Debye temperature, vibrational internal energy, vibrational entropy, thermal expansion, and thermal stability have been discussed and analyzed. Among all perovskites, the thermodynamic stability of FAPbBr2I is found superior due to strong Br-I bonds and the tougher attraction of the ionic system in the perovskite lattice. All the results are compared with earlier reported values and found to be in fair agreement.

TDDFT Investigation of the Raman and Resonant Raman Spectra of Fluorescent Protein Chromophore Models.

The off-resonance and resonant Raman spectra have been simulated for models of fluorescent protein chromophores, those of the green fluorescent protein (GFP, called FP1) and of DsRed (called FP2), which presents a longer π-conjugated path, with the aim of providing a systematic investigation of structural but also computational aspects. These were performed at the (time-dependent) density functional theory [(TD)DFT] level. The off-resonance intensities have been calculated from the derivatives of the frequency-dependent polarizability with respect to the normal coordinates while the resonant ones have been evaluated using Huang-Rhys factors determined from the gradients of the excitation energies with respect to the normal coordinates. When applied with the M05 meta-GGA exchange-correlation functional, this simple computational scheme can reproduce most of the experimental Raman signatures of FP1 in its protonated and deprotonated forms, the differences of vibrational signatures of the cis (Z) and trans (E) isomers, as well as their changes as a function of the excitation wavelength. On the other hand, testing the predictions made for FP2 would require new experimental work. It was also observed that simulations with methods that inadequately predict the resonant Raman spectra could nevertheless produce a UV-vis absorption spectrum that is quite similar to the one obtained with better methods, once realistic peak broadening has been applied.

Meta-GGA exchange-correlation free energy density functional to increase the accuracy of warm dense matter simulations

We discuss strategies for thermalization of the ground-state meta-generalized gradient approximation (meta-GGA) exchange-correlation (XC) functionals. A simple but accurate scheme is implemented via universal additive thermal correction to XC using a perturbativelike self-consistent approach. The additive correction with explicit temperature dependence is applied to the ground-state deorbitalized, strongly constrained, and appropriately normed (SCAN-L) meta-GGA XC leading to a thermal XC functional denoted here as T-SCAN-L. The thermal T-SCAN-L meta-GGA functional shows significant improvement in density functional theory calculation accuracy for warm dense matter by a factor of 3 to 10, achieving an accuracy of total pressure between a few tenths and $\ensuremath{\sim}1$% when compared to traditional XC functionals, as demonstrated by the comparison to path-integral Monte Carlo simulations for helium equation of state. The T-SCAN-L calculations of dc conductivity of warm dense aluminum also give better agreement with experiments over other XC functionals such as PBE and SCAN-L.

Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals.

The strongly constrained and appropriately normed (SCAN) meta-GGA exchange-correlation functional [Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single-orbital electron densities accurately and another describes slowly varying densities accurately. To conserve constraints known for the exact exchange-correlation functional, the derivatives of this interpolation vanish in the slowly varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional's efficiency. We have recently reported a modification to the SCAN meta-GGA, termed restored-regularized-SCAN (r2SCAN) [Furness et al., J. Phys. Chem. Lett. 11, 8208 (2020)], that introduces two regularizations into SCAN, which improve its numerical performance at the expense of not recovering the fourth order term of the slowly varying density gradient expansion for exchange. Here, we show the derivation of a progression of density functional approximations [regularized SCAN (rSCAN), r++SCAN, r2SCAN, and r4SCAN] with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r2SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r4SCAN does.

Pure and Hybrid SCAN, rSCAN, and r2SCAN: Which One Is Preferred in KS- and HF-DFT Calculations, and How Does D4 Dispersion Correction Affect This Ranking?

Using the large and chemically diverse GMTKN55 dataset, we have tested the performance of pure and hybrid KS-DFT and HF-DFT functionals constructed from three variants of the SCAN meta-GGA exchange-correlation functional: original SCAN, rSCAN, and r2SCAN. Without any dispersion correction involved, HF-SCANn outperforms the two other HF-DFT functionals. In contrast, among the self-consistent variants, SCANn and r2SCANn offer essentially the same performance at lower percentages of HF-exchange, while at higher percentages, SCANn marginally outperforms r2SCANn and rSCANn. However, with D4 dispersion correction included, all three HF-DFT-D4 variants perform similarly, and among the self-consistent counterparts, r2SCANn-D4 outperforms the other two variants across the board. In view of the much milder grid dependence of r2SCAN vs. SCAN, r2SCAN is to be preferred across the board, also in HF-DFT and hybrid KS-DFT contexts.

Band gap bowing and spectral width of Ga[formula omitted]In[formula omitted]N alloys for modelling light emitting diodes

Ga(1−x)InxN alloys, widely employed to produce light-emitting diodes, exhibit a bowing of the band gap as a function of concentration x, and a luminescence spectral width which differs from the expected value of 1.8 kT. Through first-principles calculations, based on many-body perturbation theory and density-functional theory with a meta-GGA exchange–correlation functional, we explore jointly these effects, in an exhaustive set of Ga(1−x)InxN supercells with 16 atoms. We disentangle the bowing due to the average volume change with the one due local atomic configuration and local relaxation. The first one account for about 40% of the bowing, despite that fact that the change of volume with respect to concentration is nearly linear (Vegard’s law). The computed bowing parameter is 1.39 eV. The experimental broadening between 3 kT and 8 kT, not examined theoretically until now, is well accounted by local atomic configuration changes and lifting of the degeneracy of the top of the valence band.

Defect levels from SCAN and MBJ meta-GGA exchange-correlation potentials

For more than a decade the HSE06 hybrid exchange-correlation functional developed by Heyd, Scuseria and Ernzerhof has provided a tool for reliable defect level calculations in density functional theory for which postprocessing tools are not necessary, in contrast to previous calculations using semilocal density functionals. One of the main reasons for its reliability is the high precision of HSE06 for band gap calculations. Recently, other functionals from the meta-generalized gradient approximation (meta-GGA) class have been used extensively to calculate the electronic properties of solids. In particular, band gaps can be accurately evaluated with the modified Becke-Johnson (MBJ) potential, and relaxed atomic structures close to experimental findings can be obtained with the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Both approaches are computationally cheaper than HSE06, and we consider here their performance for defect level calculations. We compare results for the $\ensuremath{\epsilon}(+/0)$ transition levels of seven donors and $\ensuremath{\epsilon}(0/\ensuremath{-})$ transition levels of four acceptors in group IV semiconductors. We conclude that in certain situations where HSE06 cannot be applied because of excessive computational costs, SCAN and MBJ might provide a good alternative.

What Types of Chemical Problems Benefit from Density-Corrected DFT? A Probe Using an Extensive and Chemically Diverse Test Suite.

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange–correlation (XC) functionals (PBE, BLYP, TPSS, and SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation, HF-DFT is highly beneficial, particularly at low HF exchange percentages. This is especially true for noncovalent interactions where the electrostatic component is dominant, such as hydrogen and halogen bonds: for π-stacking, HF-DFT is detrimental. For subsets with significant nondynamical correlation (i.e., where a Hartree–Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals—consistent with Grimme’s proposal of the PBE38 functional—HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4) as the use of HF orbitals greatly mitigates the error at 25% for barrier heights. Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that for HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree–Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorially optimized empirical range-separated hybrids ωB97X-V and ωB97M-V.

The DFT study on pentannulation reaction of tungsten Fischer carbene complexes

One of the most valuable reactions in organometallic chemistry is the coupling of the Fischer carbene complexes with alkynes to furnish five or six membered rings among other products. However, the mechanism of the reaction is still controversial due to its complexity. In this work, a plausible mechanistic pathway of the annulation reaction between the [(CO)5W=C(OMe)Ph] and PhC≡CPh was investigated with the meta-GGA exchange-correlation functionals TPSS-D3(BJ) and a def2-TZVP basis set to examine two possible mechanistic pathways that lead to the five and six membered aromatic rings, respectively. It was found that the minimum energy pathway leads to the cyclopentannulation product rather than a phenol in accordance with the experiment.

Spin-Crossover from a Well-Behaved, Low-Cost meta-GGA Density Functional.

The recent major modification, r2SCAN, of the SCAN (strongly constrained and appropriately normed) meta-GGA exchange-correlation functional is shown to give substantially better spin-crossover electronic energies (high spin minus low spin) on a benchmark data set than the original SCAN as well as on some Fe complexes. The deorbitalized counterpart r2SCAN-L is almost as good as SCAN and much faster in periodically bounded systems. A combination strategy for the balanced treatment of molecular and periodic spin-crossover therefore is recommended.

Meta-GGA performance in solids at almost GGA cost

A recent modification, r$^2$SCAN, of the SCAN (strongly constrained and appropriately normed) meta-GGA exchange-correlation functional mostly eliminates numerical instabilities and attendant integration grid sensitivities exhibited by SCAN. Here we show that the successful deorbitalization of SCAN to SCAN-L (SCAN with density Laplacian dependence) carries over directly to yield r$^2$SCAN-L. A major benefit is that the high iteration counts that hindered use of SCAN-L are eliminated in r$^2$SCAN-L. It therefore is a computationally much faster meta-GGA than its orbital-dependent antecedent. Validation data for molecular heats of formation, bond lengths, and vibration frequencies (G3/99X, T96-R, T82-F test sets respectively) and on lattice constants, and cohesive energies (for 55 solids) and bulk moduli (for 40 solids) are provided. In addition, we show that the over-magnetization of bcc Fe from SCAN persists in r$^2$SCAN but does not appear in r$^2$SCAN-L, just as with SCAN-L.

Fully consistent density functional theory determination of the insulator-metal transition boundary in warm dense hydrogen

Using conceptually and procedurally consistent density functional theory (DFT) calculations with an advanced meta-GGA exchange-correlation functional in ab initio molecular dynamics simulations, we determine the insulator-metal transition (IMT) of warm dense fluid hydrogen over the pressure range 50 to 300 GPa. Inclusion of nuclear quantum effects via path-integral molecular dynamics (PIMD) sharpens the metallic transition and lowers the transition temperature relative to results from Born-Oppenheimer (BO) MD. BOMD itself gives improved agreement with experimental results compared to previous DFT predictions. Examination of the ionic pair correlation function in the context of the abrupt conductivity increase at the transition confirms a metallic transition due to the dissociation of molecular hydrogen that coincides with an abrupt band gap closure. Direct comparison of the PIMD and BOMD results clearly demonstrates an isotope effect on the IMT. Distinct from stochastic simulations, these results do not depend upon any ad hoc combination of ground-state and finite-T methodologies.