meta-GGA Functionals Research Articles

How Good Is the Density-Corrected SCAN Functional for Neutral and Ionic Aqueous Systems, and What Is So Right about the Hartree-Fock Density?

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H*, covalently bound to the donor oxygen atom) from the acceptor (OA) and donor (OD) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.

Probing the Site-Specific Reactivity and Catalytic Activity of Ag n (n = 15-20) Silver Clusters.

Density functional theory calculations within the framework of generalized gradient approximation (GGA), meta-GGA, and local functionals were carried out to investigate the reactivity and catalytic activity of Agn (n = 15–20) clusters. Our results reveal that all the Agn clusters in this size range, except Ag20, adsorb O2 preferably in the bridged mode with enhanced binding energy as compared to the atop mode. The O2 binding energies range from 0.77 to 0.29 in the bridged mode and from 0.36 to 0.15 eV in the atop mode of O2 adsorption. The strong binding in the case of the bridged mode of O2 adsorption is also reflected in the increase in O–O bond distance. Natural bond orbital charge analysis and vibrational frequency calculations reveal that enhanced charge transfer occurs to the O2 molecule and there is significant red shift in the stretching frequency of O–O bond in the case of the bridged mode of O2 adsorption on the clusters, thereby confirming the above results. Moreover, the simulated CO oxidation reaction pathways show that the oxidation of the CO molecule is highly facile on Ag16 and Ag18 clusters involving small kinetic barriers and higher heats toward CO2 formation.

Assessing the Interplay between Functional-Driven and Density-Driven Errors in DFT Models of Water.

We investigate the interplay between functional-driven and density-driven errors in different density functional approximations within density functional theory (DFT) and the implications of these errors for simulations of water with DFT-based data-driven potentials. Specifically, we quantify density-driven errors in two widely used dispersion-corrected functionals derived within the generalized gradient approximation (GGA), namely BLYP-D3 and revPBE-D3, and two modern meta-GGA functionals, namely strongly constrained and appropriately normed (SCAN) and B97M-rV. The effects of functional-driven and density-driven errors on the interaction energies are first assessed for the water clusters of the BEGDB dataset. Further insights into the nature of functional-driven errors are gained from applying the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) to the interaction energies, which demonstrates that functional-driven errors are strongly correlated with the nature of the interactions. We discuss cases where density-corrected DFT (DC-DFT) models display higher accuracy than the original DFT models and cases where reducing the density-driven errors leads to larger deviations from the reference energies due to the presence of large functional-driven errors. Finally, molecular dynamics simulations are performed with data-driven many-body potentials derived from DFT and DC-DFT data to determine the effect that minimizing density-driven errors has on the description of liquid water. Besides rationalizing the performance of widely used DFT models of water, we believe that our findings unveil fundamental relations between the shortcomings of some common DFT approximations and the requirements for accurate descriptions of molecular interactions, which will aid the development of a consistent, DFT-based framework for the development of data-driven and machine-learned potentials for simulations of condensed-phase systems.

Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods.

We examine the role of self-interaction error (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular, we analyze the effect of scaling down the self-interaction correction (SIC) for three nonempirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger SIC [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048.], the orbitalwise scaled SIC method [Vydrov, O. A. et al. J. Chem. Phys. 2006, 124, 094108.], and the recent local scaling method [Zope, R. R. et al. J. Chem. Phys. 2019, 151, 214108.]. We compute the magnetic exchange coupling constants using the spin projection and nonprojection approaches for sets of molecules composed of dinuclear and polynuclear H···He models, organic radical molecules, and chlorocuprate and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single-electron regions, PZSIC performs well, but for more complex organic systems and the chlorocuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases, LSIC with kinetic energy density ratio performs better than PZSIC. Analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.

O2 on Ag(110): A puzzle for exchange-correlation functionals

Despite the great success of density functional theory in describing materials, there are still a few examples where current exchange-correlation functionals fail. We add another example to this list that drives further development of functionals. We show that the interaction of O$_2$ with Ag(110) cannot be properly described by some of the most popular GGA, meta GGA, and hybrid functionals. We identify problems and provide clues for a functional that should be able to describe this and similar systems properly.

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.

Comparative density functional studies of BiMO3 polymorphs (M = Al, Ga, In) based on LDA, GGA, and meta-GGA functionals

The meta-GGA functionals, MS2 and SCAN, are the only approximations that correctly describe the crystallographic ground-state of BiMO3 (M = Al, Ga, In).

Heat transport in liquid water from first-principles and deep neural network simulations

We compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represented by a deep neural network (DNN) trained on DFT data, whereby the PES has an explicit local decomposition and the energy flux takes a particularly simple expression. By virtue of a gauge invariance principle, established by Marcolongo, Umari, and Baroni, the two approaches should be equivalent if the PES were reproduced accurately by the DNN model. We test this hypothesis by calculating the thermal conductivity, at the GGA (PBE) level of theory, using the direct formulation and its DNN proxy, finding that both approaches yield the same conductivity, in excess of the experimental value by approximately 60%. Besides being numerically much more efficient than its direct DFT counterpart, the DNN scheme has the advantage of being easily applicable to more sophisticated DFT approximations, such as meta-GGA and hybrid functionals, for which it would be hard to derive analytically the expression of the energy flux. We find in this way, that a DNN model, trained on meta-GGA (SCAN) data, reduce the deviation from experiment of the predicted thermal conductivity by about 50%, leaving the question open as to whether the residual error is due to deficiencies of the functional, to a neglect of nuclear quantum effects in the atomic dynamics, or, likely, to a combination of the two.

Reactivity and Fe-complexation investigation by computational simulation studies on phenyltetrazole derivatives as mild steel corrosion inhibitors in aqueous acidic medium

B3LYP, B3PW91, CAM-B3LYP, HCTH, ωB97XD, and M06-2X are six hybrid correlation-exchange and meta-GGA functionals, with 6-31G(d,p) basis set for the H, C, N, O and Cl atoms and the LANL2DZ basis set for the Fe atom. Utilized to determine the most favorable to be applied with phenyltetrazole derivatives, namely: 5-phenyl-1H-tetrazole (Ph-T), 5-p-tolyl-1H-tetrazole (Me-Ph-T), 5-(4-methoxyphenyl)-1H-tetrazole (Me-O-Ph-T), 5-(4-chlorophenyl)-1H-tetrazole (Me-O-Ph-T), and 5-(4-chlorophenyl) (Cl-Ph-T). Aside from that, the quintet complexes were the most stable of the spin multiplicities studied. Furthermore, three forms of interactions between Fe and phenyltetrazole compounds are identified using Fukui functions, including Fe-Me/Me-O/Cl, Fe-ϕ, and Fe-N among eleven complexes. The meta-GGA functionals are ideally suited to predict metal–ligand interaction in the complexes investigated, which contain the transition metal iron with unsaturated valences. While the bond energies and enthalpies estimated for the two Fe- Me-O-Ph-T and Fe- Cl-Ph-T complexes are the lowest and almost identical, the two inhibitors investigated act similarly. Furthermore, chemisorption is promoted by the flatness of the Cl-Ph-T and Me-O-Ph-T inhibitors. Moreover, the adsorption energy of the Cl-Ph-T and Me-O-Ph-T inhibitors.(-185.661 and −186.005 kcal/mol, respectively), suggests that they are the most stable and strongest adsorption systems demonstrated by MDS. The discovered dynamic descriptors were in excellent accord with the quantum study's findings.

Comparative first-principles study of elastic constants of covalent and ionic materials with LDA, GGA, and meta-GGA functionals and the prediction of mechanical hardness

Comparative first-principles study of elastic constants of covalent and ionic materials with LDA, GGA, and meta-GGA functionals and the prediction of mechanical hardness

Assessment of the Accuracy of Density Functionals for Calculating Oxygen Reduction Reaction on Nitrogen-Doped Graphene.

Experimental studies of the oxygen reduction reaction (ORR) at nitrogen-doped graphene electrodes have reported a remarkably low overpotential, on the order of 0.5 V, similar to Pt-based electrodes. Theoretical calculations using density functional theory have lent support to this claim. However, other measurements have indicated that transition metal impurities are actually responsible for the ORR activity, thereby raising questions about the reliability of both the experiments and the calculations. To assess the accuracy of the theoretical calculations, various generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are employed here and calibrated against high-level wave-function-based coupled-cluster calculations (CCSD(T)) of the overpotential as well as self-interaction corrected density functional calculations and published quantum Monte Carlo calculations of O adatom binding to graphene. The PBE0 and HSE06 hybrid functionals are found to give more accurate results than the GGA and meta-GGA functionals, as would be expected, and for a low dopant concentration, 3.1%, the overpotential is calculated to be 1.0 V. The GGA and meta-GGA functionals give a lower estimate by as much as 0.4 V. When the dopant concentration is doubled, the overpotential calculated with hybrid functionals decreases, while it increases in GGA functional calculations. The opposite trends result from different potential-determining steps, the *OOH species being of central importance in the hybrid functional calculations, while the reduction of *O determines the overpotential obtained in GGA and meta-GGA calculations. The results presented here are mainly based on calculations of periodic representations of the system, but a comparison is also made with molecular flake models that are found to give erratic results due to finite size effects and geometric distortions during energy minimization. The presence of the electrolyte has not been taken into account explicitly in the calculations presented here but is estimated to be important for definitive calculations of the overpotential.

Surprisingly Good Performance of XYG3 Family Functionals Using a Scaled KS-MP3 Correlation

By adding a GLPT3 (third-order Görling-Levy perturbation theory, or KS-MP3) term E3 to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wave function ab initio approaches. Intriguingly, (a) the introduction of E3 makes an empirical dispersion correction redundant; (b) generalized gradient approximation (GGA) or meta-GGA semilocal correlation functionals offer no advantage over the local density approximation (LDA) in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a six-parameter functional with WTMAD2 = 1.42 that has no post-LDA density functional theory components and no dispersion correction in the final energy.

The Se-S Bond Formation in the Covalent Inhibition Mechanism of SARS-CoV-2 Main Protease by Ebselen-like Inhibitors: A Computational Study.

The inhibition mechanism of the main protease (Mpro) of SARS-CoV-2 by ebselen (EBS) and its analog with a hydroxyl group at position 2 of the benzisoselenazol-3(2H)-one ring (EBS-OH) was studied by using a density functional level of theory. Preliminary molecular dynamics simulations on the apo form of Mpro were performed taking into account both the hydrogen donor and acceptor natures of the Nδ and Nε of His41, a member of the catalytic dyad. The potential energy surfaces for the formation of the Se–S covalent bond mediated by EBS and EBS-OH on Mpro are discussed in detail. The EBS-OH shows a distinctive behavior with respect to EBS in the formation of the noncovalent complex. Due to the presence of canonical H-bonds and noncanonical ones involving less electronegative atoms, such as sulfur and selenium, the influence on the energy barriers and reaction energy of the Minnesota hybrid meta-GGA functionals M06, M06-2X and M08HX, and the more recent range-separated hybrid functional wB97X were also considered. The knowledge of the inhibition mechanism of Mpro by the small protease inhibitors EBS or EBS-OH can enlarge the possibilities for designing more potent and selective inhibitor-based drugs to be used in combination with other antiviral therapies.

EQE 2.0: Subsystem DFT beyond GGA functionals

By adopting a divide-and-conquer strategy, subsystem-DFT (sDFT) can dramatically reduce the computational cost of large-scale electronic structure calculations. The key ingredients of sDFT are the nonadditive kinetic energy and exchange-correlation functionals which dominate it's accuracy. Even though, available semilocal nonadditive functionals find a broad range of applications, their accuracy is somewhat limited especially for those systems where achieving balance between exchange-correlation interactions on one side and nonadditive kinetic energy on the other is crucial. In eQE 2.0, we improve dramatically the accuracy of sDFT simulations by (1) implementing nonlocal nonadditive kinetic energy functionals based on the LMGP family of functionals; (2) adapting Quantum ESPRESSO's implementation of rVV10 and vdW-DF nonlocal exchange-correlation functionals to be employed in sDFT simulations; (3) implementing “deorbitalized” meta GGA functionals (e.g., SCAN-L). We carefully assess the performance of the newly implemented tools on the S22-5 test set. eQE 2.0 delivers excellent interaction energies compared to conventional Kohn-Sham DFT and CCSD(T). The improved performance does not come at a loss of computational efficiency. We show that eQE 2.0 with nonlocal nonadditive functionals retains the same linear scaling behavior achieved previously in eQE 1.0 with semilocal nonadditive functionals. Program summaryProgram title: eQECPC Library link to program files:https://doi.org/10.17632/g55n9xmnt2.1Developer's repository link:https://gitlab.com/Pavanello/eqeLicensing provisions: GPLv2Programming language: Fortran 90External routines/libraries: BLACS, MPINature of problem: Solving the electronic structure of molecules and materials with subsystem density functional theorySolution method: This version of eQE uses subsystem Density-Functional Theory (DFT) to compute the electronic structure of molecules and materials. Subsystem DFT is a divide-and-conquer version of DFT that can be massively parallelized and is linear scaling in work and data. However, it requires the use of density functionals for kinetic and exchange-correlation energies. eQE can now employ nonlocal functionals as well as meta-GGA functionals for these energy terms.Additional comments: Url of stable release http://eqe.rutgers.edu

Excitation energies for anionic drugs predicted by PBE0, TPSS and τHCTH density functionals

Numerous benchmarking studies dealing with TD-DFT calculated excitation energies for neutral molecules are reported in the scientific literature. However, charged species, both anionic and cationic, have received much less attention from this point of view. Against this background, here we report a comparative study of calculated excitation energies corresponding to the vertical singlet-singlet electronic transitions for a set of 96 anionic compounds containing basic well-known small-sized drugs and essential medicines. The objective of the work was to check the accuracy provided by one hybrid functional (PBE0), and two meta-GGA functionals (TPSS and τHCTH) in reproducing the experimental maximum absorption wavelengths. Computed data have been compared to available experimental data found in the literature. For the selected set of anions, it is shown that the two meta-GGA functionals performs similar to PBE0, with a slight advantage of TPSS density functional, which offers better values than PBE0 for mean signed-error and mean absolute error.

Analyzing Discrepancies in Chemical-Shift Predictions of Solid Pyridinium Fumarates.

Highly accurate chemical-shift predictions in molecular solids are behind the success and rapid development of NMR crystallography. However, unusually large errors of predicted hydrogen and carbon chemical shifts are sometimes reported. An understanding of these deviations is crucial for the reliability of NMR crystallography. Here, recently reported large deviations of predicted hydrogen and carbon chemical shifts of a series of solid pyridinium fumarates are thoroughly analyzed. The influence of the geometry optimization protocol and of the computational level of NMR calculations on the accuracy of predicted chemical shifts is investigated. Periodic calculations with GGA, meta-GGA and hybrid functionals are employed. Furthermore, molecular corrections at the coupled-cluster singles-and-doubles (CCSD) level are calculated. The effect of nuclear delocalization on the structure and NMR shielding is also investigated. The geometry optimization with a computationally demanding hybrid functional leads to a substantial improvement in proton chemical-shift predictions.

Mn Dimer Can Be Described Accurately with Density Functional Calculations When Self-Interaction Correction Is Applied.

Qualitatively incorrect results are obtained for the Mn dimer in density functional theory calculations using the generalized gradient approximation (GGA), and similar results are obtained from local density and meta-GGA functionals. The coupling is predicted to be ferromagnetic rather than antiferromagnetic, and the bond between the atoms is predicted to be an order of magnitude too strong and approximately an Ångstrøm too short. Explicit, self-interaction correction (SIC) applied to a commonly used GGA energy functional, however, provides close agreement with both experimental data and high-level, multireference wave function calculations. These results show that the failure is not due to a strong correlation but rather the single electron self-interaction that is necessarily introduced in estimates of the classical Coulomb and exchange-correlation energy when only the total electron density is used as the input. The corrected functional depends explicitly on the orbital densities and can, therefore, avoid the introduction of a self-Coulomb interaction. The error arises because of an overstabilization of bonding d-states in the minority spin channel resulting from an overestimate of the d-electron self-interaction in the semilocal exchange-correlation functionals. Since the computational effort in the SIC calculations scales with the system size in the same way as for regular semilocal functional calculations, this approach provides a way to calculate properties of Mn nanoclusters as well as biomolecules and extended solids, where Mn dimers and larger cluster are present, while multireference wave function calculations can only be applied to small systems.

Performance of SCAN Meta-GGA Functionals on Nonlinear Mechanics of Graphene-Like g-SiC

Although meta-generalized-gradient approximations (meta-GGAs) are believed potentially the most accurate among the efficient first-principles calculations, the performance has not been accessed on the nonlinear mechanical properties of two-dimensional nanomaterials. Graphene, like two-dimensional silicon carbide g-SiC, has a wide direct band-gap with applications in high-power electronics and solar energy. Taken g-SiC as a paradigm, we have investigated the performance of meta-GGA functionals on the nonlinear mechanical properties under large strains, both compressive and tensile, along three deformation modes using Strongly Constrained and Appropriately Normed Semilocal Density Functional (SCAN) as an example. A close comparison suggests that the nonlinear mechanics predicted from SCAN are very similar to that of Perdew-Burke-Ernzerhof (PBE) formulated functional, a standard Density Functional Theory (DFT) functional. The improvement from SCAN calculation over PBE calculation is minor, despite the considerable increase of computing demand. This study could be helpful in selection of density functionals in simulations and modeling of mechanics of materials.

Born-Oppenheimer molecular dynamics simulations on structures of high-density and low-density water: a comparison of the SCAN meta-GGA and PBE GGA functionals.

Using Born-Oppenheimer ab initio molecular dynamics (BOAIMD) simulations, the high-density water (HDW) and low-density water (LDW) structures based on SCAN meta-GGA are compared with those based on PBE GGA. Compared with Car-Parrinello ab initio molecular dynamics (CPAIMD) simulations, BOAIMD simulations can produce more accurate results because no fictitious electron mass is introduced. At each state point, our simulations continue for 100 ps after the system reached equilibrium, which is the longest ab initio simulations of liquid water reported so far and can ensure an accurate statistical average. The influence of the size effect and nuclear quantum effect on structure is not considered in the present work, but only that of two different functionals on the structure is discussed. It is found that, in HDW, just as shown using CPAIMD simulations, the SCAN-based hydrogen-bonds (HBs) are more flexible than the PBE-based ones, which makes the structure based on SCAN obviously closer to the experimental results than that based on PBE. However, it is not the case in LDW, and the difference between the results based on these two functionals is very small.

Revisiting the structural, electronic and photocatalytic properties of Ti and Zr based perovskites with meta-GGA functionals of DFT

Combining the SCAN and mBJ-LDA meta-GGA functionals of DFT facilitates accurate and efficient computation of physical properties of photocatalysts which is either comparable or better than computationally expansive hybrid functionals or GW methods.