Efficient hybrid density functional calculations in solids: assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional

The present work introduces an efficient screening technique to take advantage of the fast spatial decay of the short range Hartree-Fock (HF) exchange used in the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional. The screened HF exchange decay properties and screening efficiency are compared with traditional hybrid functional calculations on solids. The HSE functional is then assessed using 21 metallic, semiconducting, and insulating solids. The examined properties include lattice constants, bulk moduli, and band gaps. The results obtained with HSE exhibit significantly smaller errors than pure density functional theory (DFT) calculations. For structural properties, the errors produced by HSE are up to 50% smaller than the errors of the local density approximation, PBE, and TPSS functionals used for comparison. When predicting band gaps of semiconductors, we found smaller errors with HSE, resulting in a mean absolute error of 0.2 eV (1.3 eV error for all pure DFT functionals). In addition, we present timing results which show the computational time requirements of HSE to be only a factor of 2-4 higher than pure DFT functionals. These results make HSE an attractive choice for calculations of all types of solids.     

一些密度泛函方法预测电子亲和势

选取了杂化泛函B3LYP, B3PW91, O3LYP, PBE0, 以及与之相对应的GGA泛函BLYP, BPW91, OLYP和PBE, 还选取了能更好地兼顾强相互作用和弱相互作用的X3LYP泛函和在预测NMR的化学位移有较好表现的OPBE泛函, 以及两种meta-GGA泛函VSXC和TPSS, 共12种泛函, 详细地考察了这些泛函在预测EA方面的准确性.     

Ab initio investigation of the n --> pi* transitions in thiocarbonyl dyes

The n --> pi* transitions in more than 100 thiocarbonyl dyes have been calculated with an ab initio procedure relying on the combination of time-dependent density functional theory (TD-DFT) for evaluating excited states and the polarizable continuum model (PCM) for modeling the bulk solvent effects on both the geometrical and electronic structures. Two hybrid functionals (B3LYP and PBE0) and several basis sets, some including f polarization functions, have been used. B3LYP provides the most accurate raw estimates, but once simple linear regression is performed, both functionals give similar results with a small advantage for PBE0. By use of the latter, the mean absolute deviation with respect to experiment is limited to 0.06 eV whereas less than 20% of the estimates differ from absorption data by more than 0.10 eV. To assess the validity limits of our model, compounds containing multiple C=S chromophores have also been considered.     

TD-DFT investigation of the UV spectra of pyranone derivatives

The UV absorption spectra of more than 80 substituted coumarins and chromones have been investigated with the PCM-TD-DFT theoretical scheme using three hybrid functionals (O3LYP, B3LYP, and PBE0) and taking into account methanol or ethanol solvation effects. For most of the studied derivatives, there are at least two allowed excited states presenting a strong oscillator strength in the UV region. The first allowed excitation is associated to a HOMO-LUMO transition whereas the second corresponds to a transition from the HOMO-1 to the LUMO. Both involve a charge transfer from the benzenic cycle to the pyranone moiety. Statistically treating the PBE0 results allows a prediction of the lambda(max) with small standard deviations: in methanol, 6 nm (0.07 eV) for the first excitation (lambda(max)(1)) and 5 nm (0.08 eV) for the second one (lambda(max)(2)), whereas in ethanol 6 nm (0.08 eV) for (lambda(max)(1)) and 6 nm (0.13 eV) for (lambda(max)(2)).     

Accurate prediction for electron affinities of the radicals derived from the halide benzene

The molecular structures and electron affinities of eight radicals derived from the halide benzene by removing a hydrogen atom have been determined using seven hybrid Hartree-Fock/density-functional methods. The basis set used in this work is of double-zeta plus polarization quality with additional diffuse s- and p-type functions, denoted as DZP++. These methods have been carefully calibrated [J. C. Rienstra-Kiracofe, G. S. Tschumper, H. F. Schaefer, S. Nandi, and G. B. Ellison, Chem. Rev. (Washington, D. C.) 102, 231 (2002)]. The geometries are fully optimized with each density-functional theory method and discussed, respectively. The three different types of the neutral-anion energy separations reported in this work are the adiabatic electron affinity, the vertical electron affinity, and the vertical detachment energy. The most reliable adiabatic electron affinities (with zero-point vibrational energy correction), obtained at the DZP++ B3LYP level of theory, are 1.74 eV (o-C6H4F), 1.39 eV (m-C6H4F), 1.34 eV (p-C6H4F), 1.78 eV (o-C6H4Cl), 1.53 eV (m-C6H4Cl), 1.45 eV (p-C6H4Cl), 2.06 eV (o-C6H3F2), and 2.04 eV (p-C6H3F2), respectively. Compared with the experimental values, the average absolute error of the B3LYP method is 0.03 eV. The BLYP, BP86, and BPW91 functionals also gave excellent predictions, with average absolute errors of 0.05, 0.08, and 0.08 eV, respectively.     

Structures, electron affinities, and harmonic vibrational frequencies of C6H5X/C6H5X- (X = N, S, NH, PH, CH2, and SiH2)

The molecular structures and electron affinities of the C6H5X/C6H5X- (X = N, S, NH, PH, CH2, and SiH2) species have been determined using seven different density functional or hybrid Hartree-Fock density functional methods. The basis set used in this work is of double-zeta plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. These methods have been carefully calibrated (Chem. Rev. 2002, 102, 231). The geometries are fully optimized with each density functional theory (DFT) method, and discussed. Harmonic vibrational frequencies were found to be within 3.2% of available experimental values for most functionals. Three different types of the neutral-anion energy separations reported in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). The most reliable adiabatic electron affinities, obtained at the DZP++ BPW91 level of theory, are 1.45 (C6H5N), 2.29 (C6H5S), 1.57 (C6H5NH), 1.51 (C6H5PH), 0.91 (C6H5CH2), and 1.48 eV (C6H5SiH2), respectively. Compared with the experimental values, the average absolute error of the BPW91 method is 0.04 eV. The B3LYP and B3PW91 functionals also gave excellent predictions, with average absolute errors of 0.06 and 0.07 eV, respectively.     

Predicting core level binding energies shifts: Suitability of the projector augmented wave approach as implemented in VASP

Here, we assess the accuracy of various approaches implemented in Vienna ab initio simulation package code to estimate core‐level binding energy shifts (ΔBEs) using a projector augmented wave method to treat core electrons. The performance of the Perdew–Burke–Ernzerhof (PBE) and the Tao–Perdew–Staroverov–Scuseria (TPSS) exchange‐correlation density functionals is examined on a dataset of 68 molecules containing B→F atoms in diverse chemical environments, accounting for 185 different 1s core level binding energy shifts, for which both experimental gas‐phase X‐ray photoemission (XPS) data and accurate all electron ΔBEs are available. Four procedures to calculate core‐level shifts are investigated. Janak–Slater transition state approach yields mean absolute errors of 0.37 (0.21) eV at PBE (TPSS) level, similar to highly accurate all electron ΔSCF approaches using same functionals, and close to XPS experimental accuracy of 0.1 eV. The study supports the use of these procedures to assign ΔBEs of molecular moieties on material surfaces of interest in surface science, nanotechnology, and heterogeneous catalysis. © 2017 Wiley Periodicals, Inc.     

An ab initio study of the absorption spectra of indirubin, isoindigo, and related derivatives

The UV/visible spectra of a series of indirubin, isoindigo, and other indigo/thioindigo related dyes have been evaluated in various solvent environments by using the time-dependent density functional theory in conjunction with the polarizable continuum model. Even for molecules of the same family, significant differences in the excitation processes have been noted. Two hybrid functionals have been selected: B3LYP and PBE0. For a set of the 50 selected molecular cases, both functionals provide accurate lambda(max), with mean absolute deviations limited to 0.1 eV. Actually, isoindigo is the main challenging series, with systematically underestimated excitation energies, due to the different nature of the excitation process. In most cases, we found that PBE0 is more efficient in reproducing the experimental values than B3LYP for sulfur-containing dyes not featuring internal hydrogen bonds, the reverse assertion being also true. In addition, the spectra of a series of unknown dyes have been predicted.     

Assessing alkyl-, silyl-, and halo-substituent effects on the electron affinities of silyl radicals

Neutral anion energy differences for a large class of alpha-substituted silyl radicals have been computed to determine the effect of alkyl, silyl, and halo substituents on their electron affinities. In particular, we report theoretical predictions of the adiabatic electron affinities (AEAs), vertical electron affinities (VEAs), and vertical detachment energies (VDEs) for a series of methyl-, silyl-, and halo-substituted silyl radical compounds. This work utilizes the carefully calibrated DZP++ basis set, in conjunction with the pure BLYP and OLYP functionals, as well as with the hybrid B3LYP, BHLYP, PBE1PBE, MPW1K, and O3LYP functionals. Bromine has the largest effect in stabilizing the anions, and the BLYP/DZP++ AEA for SiBr(3) is 3.29 eV. The other predicted electron affinities are for SiH(3) (1.37 eV), SiH(2)CH(3) (1.09 eV), SiH(2)F (1.54 eV), SiH(2)Cl (1.94 eV), SiH(2)Br (2.05 eV), SiH(2)(SiH(3)) (1.77 eV), SiH(CH(3))(2) (0.92 eV), SiHF(2) (1.86 eV), SiHCl(2) (2.53 eV), SiHBr(2) (2.67 eV), Si(CH(3))(3) (0.86 eV), SiF(3) (2.66 eV), SiCl(3) (3.21 eV), Si(SiH(3))(3) (2.25 eV), and SiFClBr (3.13 eV). For the five silyl radicals where experimental data are available, the BLYP functional gives the most accurate determination of AEAs; the average absolute error is 0.04(1) eV, whereas the corresponding errors for the O3LYP, MPW1K, PBE1PBE, B3LYP, OLYP, and BHLYP functionals are 0.05(8), 0.06(0), 0.06(3), 0.08(5), 0.11(5), and 0.15(3) eV, respectively.     

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional

This work assesses the Heyd-Scuseria-Ernzerhof (HSE) screened Coulomb hybrid density functional for the prediction of lattice constants and band gaps using a set of 40 simple and binary semiconductors. An extensive analysis of both basis set and relativistic effects is given. Results are compared with established pure density functionals. For lattice constants, HSE outperforms local spin-density approximation (LSDA) with a mean absolute error (MAE) of 0.037 A for HSE vs 0.047 A for LSDA. For this specific test set, all pure functionals tested produce MAEs for band gaps of 1.0-1.3 eV, consistent with the very well-known fact that pure functionals severely underestimate this property. On the other hand, HSE yields a MAE smaller than 0.3 eV. Importantly, HSE correctly predicts semiconducting behavior in systems where pure functionals erroneously predict a metal, such as, for instance, Ge. The short-range nature of the exchange integrals involved in HSE calculations makes their computation notably faster than regular hybrid functionals. The current results, paired with earlier work, suggest that HSE is a fast and accurate alternative to established density functionals, especially for solid state calculations.     

Reaction energy benchmarks of hydrocarbon combustion by Gaussian basis and plane wave basis approaches

The reaction energies of 275 elementary reactions from the hydrocarbon combustion model GRI-Mech 3.0 were evaluated by electronic structure calculations using both localized Gaussian basis and plane wave basis sets. In the Gaussian basis calculations, the d-polarization function on C, N, and O elements reduces the mean absolute deviation (MAD) from the experimental value by 53%, a significant improvement in computational accuracy. In the plane wave basis calculation using different exchange-correlation (XC) functionals, the MAD values were 0.316–0.426 eV when non-hybrid type XC functionals such as RPBE, PBE, PW91, revPBE, and PBEsol were used. On the other hand, hybrid functionals like B3LYP and HSE06 reduced the MAD values significantly down to 0.182 and 0.233 eV, respectively. The B3LYP results have 49% less MAD compared to the PBE results. These demonstrated the strong advantage of the hybrid functional for calculating gas-phase reaction energies. The present comprehensive benchmarks will be crucial for future microkinetics as well as machine learning studies on the catalytic reactions. © 2019 Wiley Periodicals, Inc.     

Polyfunctional methodology for improved DFT thermochemical predictions

Statistical error distributions for enthalpies of formation as predicted by 18 different density functionals have been analyzed using a test set of 675 molecules. Systematic errors, dependent on the number of valence electrons, have been identified for some functionals. A simple empirical correction makes a significant improvement in the prediction error for these single functionals. Linear combinations of enthalpy estimates from different density functionals are identified that exploit the error correlations among the functionals and allow for further improvements in the accuracy of thermodynamic predictions. A good compromise between accuracy and computational efforts is achieved by the BLUE (best linear unbiased estimator) combination of three functionals, B3LYP, BLYP, and VSXC (polyfunctional 3 or PF3). The PF3 method has a mean absolute deviation (MAD) from experiment of 2.4 kcal/mol on the G3 set of 271 molecules. This can be compared to the MAD of 4.9 kcal/mol for B3LYP and 1.2 kcal/mol for the more costly G3 method. On the larger set of 675 molecules, the MAD for PF3 is 3.0 kcal/mol. Opportunities for further improvements in the accuracy of this method are discussed.     

Size resolved infrared spectroscopy of Na(CH3OH)n (n = 4-7) clusters in the OH stretching region: unravelling the interaction of methanol clusters with a sodium atom and the emergence of the solvated electron

Size resolved IR action spectra of neutral sodium doped methanol clusters have been measured using IR excitation modulated photoionisation mass spectroscopy. The Na(CH(3)OH)(n) clusters were generated in a supersonic He seeded expansion of methanol by subsequent Na doping in a pick-up cell. A combined analysis of IR action spectra, IP evolutions and harmonic predictions of IR spectra (using density functional theory) of the most stable structures revealed that for n = 4, 5 structures with an exterior Na atom showing high ionisation potentials (IPs) of ~4 eV dominate, while for n = 6, 7 clusters with lower IPs (~3.2 eV) featuring fully solvated Na atoms and solvated electrons emerge and dominate the IR action spectra. For n = 4 simulations of photoionisation spectra using an ab initio MD approach confirm the dominance of exterior structures and explain the previously reported appearance IP of 3.48 eV by small fractions of clusters with partly solvated Na atoms. Only for this cluster size a shift in the isomer composition with cluster temperature has been observed, which may be related to kinetic stabilisation of less Na solvated clusters at low temperatures. Features of slow fragmentation dynamics of cationic Na(+)(CH(3)OH)(6) clusters have been observed for the photoionisation near the adiabatic limit. This finding points to the relevance of previously proposed non-vertical photoionisation dynamics of this system.     

Comparison of DFT methods for molecular orbital eigenvalue calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.     

Benchmarking the performance of time-dependent density functional methods

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.     

Local hybrid functionals: an assessment for thermochemical kinetics

Local hybrid functionals with position-dependent exact-exchange admixture are a new class of exchange-correlation functionals in density functional theory that promise to advance the available accuracy in many areas of application. Local hybrids with different local mixing functions (LMFs) governing the position dependence are validated for the heats of formation of the extended G3/99 set, and for two sets of barriers of hydrogen-transfer and heavy-atom transfer reactions (HTBH38 and NHTBH38 databases). A simple local hybrid Lh-SVWN with only Slater and exact exchange plus local correlation and a one-parameter LMF, g(r)=b(tau(W)(r)tau(r)), performs best and provides overall mean absolute errors for thermochemistry and kinetics that are a significant improvement over standard state-of-the-art global hybrid functionals. In particular, this local hybrid functional does not suffer from the systematic deterioration that standard functionals exhibit for larger molecules. In contrast, local hybrids based on generalized gradient approximation exchange tend to give rise to nonintuitive LMFs, and no improved functionals have been obtained along this route. The LMF is a real-space function and thus can be analyzed in detail. We use, in particular, graphical analyses to rationalize the performance of different local hybrids for thermochemistry and reaction barriers.     

Oxidative addition of the fluoromethane C-F bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for two reaction pathways (oxidative insertion, OxIn, and S(N)2) for oxidative addition of the fluoromethane C-F bond to the palladium atom and have used this to evaluate the performance of 26 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing these reactions. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods (HF, MP2, CCSD, CCSD(T)) in combination with a hierarchical series of seven Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -5.3 (-6.1) kcal/mol for the formation of the reactant complex, 27.8 (25.4) kcal/mol for the activation energy for oxidative insertion (OxIn) relative to the separate reactants, 37.5 (31.8) kcal/mol for the activation energy for the alternative S(N)2 pathway, and -6.4 (-7.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.4-2.7 kcal/mol and errors in activation energies ranging from 0.3 to 2.8 kcal/mol. The B3LYP functional compares very well with a slight underestimation of the overall barrier for OxIn by -0.9 kcal/mol. For comparison, the well-known BLYP functional underestimates the overall barrier by -10.1 kcal/mol. The relative performance of these two functionals is inverted with respect to previous findings for the insertion of Pd into the C-H and C-C bonds. However, all major functionals yield correct trends and qualitative features of the PES, in particular, a clear preference for the OxIn over the alternative S(N)2 pathway.     

A TDDFT study of the low-lying excitation energies of polycyclic cinnolines and their carbocyclic analogues

The low-lying excited states of 21 compounds of polycyclic cinnoline, monoaza-hydrocarbon and their corresponding polycyclic aromatic hydrocarbon (PAH) analogues have been investigated in the framework of time-dependent density functional theory (TDDFT). The gradient corrected BLYP, hybrid B3LYP and B3P86 functionals together with 6-31G (d) basis set have been used. The hybrid-type B3LYP and B3P86 systematically overestimate the excitation energies for states with dominating ionic character (corresponding to group III band), with a mean absolute deviation (MAD) of 0.33 eV (B3LYP) and 0.34 eV (B3P86), respectively. However, they can accurately predict the excitation energies for states with covalent character (corresponding to group II and I bands). The MAD for group II (B3LYP: 0.05 eV; B3P86: 0.05 eV) and I bands (B3LYP: 0.12 eV; B3P86: 0.12 eV) are significantly smaller. The BLYP outperforms B3LYP and B3P86 for group III band (MAD: 0.09 eV), but has a worse performance for group II (MAD: 0.15 eV) and I (MAD: 0.13 eV) bands. Comparison of the lowest-lying excited states for polycyclic cinnolines with those of the corresponding PAH analogues, the first excited states of polycyclic cinnolines mainly result from n→π₀* transitions. Therefore, in non-polar solvents, the spectra of some polycyclic cinnolines exhibit an additional absorption band at longer wavelengths.     

Assessment of Gaussian-3 and density-functional theories on the G3/05 test set of experimental energies

The G3/99 test set [L. A. Curtiss, K. Raghavachari, P. C. Redfern, and J. A. Pople, J. Chem. Phys. 112, 7374 (2000)] of thermochemical data for validation of quantum chemical methods is expanded to include 78 additional energies including 14 enthalpies of formation of the first- and second-row nonhydrogen molecules, 58 energies of molecules containing the third-row elements K, Ca, and Ga-Kr, and 6 hydrogen-bonded complexes. The criterion used for selecting the additional systems is the same as before, i.e., experimental uncertainties less than +/- 1 kcal/mol. This new set, referred to as the G3/05 test set, has a total of 454 energies. The G3 and G3X theories are found to have mean absolute deviations of 1.13 and 1.01 kcal/mol, respectively, when applied to the G3/05 test set. Both methods have larger errors for the nonhydrogen subset of 79 species for which they have mean absolute deviations of 2.10 and 1.64 kcal/mol, respectively. On all of the other types of energies the G3 and G3X methods are very reliable. The G3/05 test set is also used to assess density-functional methods including a series of new functionals. The most accurate functional for the G3/05 test set is B98 with a mean absolute deviation of 3.33 kcal/mol, compared to 4.14 kcal/mol for B3LYP. The latter functional has especially large errors for larger molecules with a mean absolute deviation of 9 kcal/mol for molecules having 28 or more valence electrons. For smaller molecules B3LYP does as well or better than B98 and the other functionals. It is found that many of the density-functional methods have significant errors for the larger molecules in the test set.