Comparison of one‐parameter and linearly scaled one‐parameter double‐hybrid density functionals for noncovalent interactions

We have compared the performances of the one‐parameter and linearly scaled one‐parameter double‐hybrid density functionals (1DH‐DFs and LS1DH‐DFs) for noncovalent interactions. The only one parameter related to the Hartree–Fock (HF) exchange for each of the tested 1DH‐DFs and LS1DH‐DFs has been fitted with the well‐designed S66 database. The obtained DHDFs are dubbed as 1DH‐PBE‐NC, LS1DH‐PBE‐NC, 1DH‐TPSS‐NC, LS1DH‐TPSS‐NC, 1DH‐PWB95‐NC, and LS1DH‐PWB95‐NC, where “NC” denotes noncovalent interactions. With a specific combination of exchange and correlation functionals, the dependent parameters related to the nonlocal second‐order perturbative energies are nearly identical for the 1DH and LS1DH models. According to our benchmark computations against the S66, S22B, NCCE31, ADIM6, and L7 databases, we suggest that the 1DH‐PWB95‐NC and LS1DH‐PWB95‐NC functionals are much more suitable for evaluating noncovalent interaction energies. Unlike the versatile DHDFs with dispersion corrections for general purpose, our optimized 1DH‐DFs and LS1DH‐DFs only aim at noncovalent interactions. © 2016 Wiley Periodicals, Inc.     

First‐principles calculations on the four phases of BaTiO3

The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO₃ crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange‐correlation density functional theory (DFT) functionals for four stable phases of BaTiO₃. A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO₃. The comparative phonon symmetry analysis in BaTiO₃ four phases has been made basing on the site symmetry and irreducible representation indexes for the first time. © 2012 Wiley Periodicals, Inc.     

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.     

Electronic structure and spectroscopic properties of 6‐aminophenanthridine and its derivatives: Insights from density functional theory

6‐Aminophenanthridine (6AP) and its derivatives show important biological activities as antiprion compounds and inhibitors of the protein folding activity of the ribosome. Both of these activities depend on the RNA binding property of these compounds, which has been recently characterized by fluorescence spectroscopy. Hence, fundamental insights into the photophysical properties of 6AP compounds are highly important to understand their biological activities. In this work, we have calculated electronic structures and optical properties of 6AP and its three derivatives 6AP8CF₃, 6AP8Cl, and 6APi by density functional theory (DFT) and time‐dependent density functional theory (TDDFT). Our calculated spectra show a good agreement with the experimental absorption and fluorescence spectra, and thus, provide deep insights into the optical properties of the compounds. Furthermore, comparing the results obtained with four different hybrid functionals, we demonstrate that the accuracy of the functionals varies in the order B3LYP > PBE0 > M062X > M06HF. © 2015 Wiley Periodicals, Inc.     

Static and Frequency‐Dependent Dipole–Dipole Polarizabilities of All Closed‐Shell Atoms up to Radium: A Four‐Component Relativistic DFT Study

We test the performance of four‐component relativistic density functional theory by calculating the static and frequency‐dependent electric dipole–dipole polarizabilities of all (ground‐state) closed‐shell atoms up to Ra. We consider 12 nonrelativistic functionals, including three asymptotically shape‐corrected functionals, by using two smooth interpolation schemes introduced by the Baerends group: the gradient‐regulated asymptotic connection (GRAC) procedure and the statistical averaging of (model) orbital potentials (SAOP). Basis sets of doubly augmented triple‐zeta quality are used. The results are compared to experimental data or to accurate ab initio results. The reference static electric dipole polarizability of palladium has been obtained by finite‐field calculations using the coupled‐cluster singles, doubles, and perturbative triples method within this work. The best overall performance is obtained using hybrid functionals and their GRAC shape‐corrected versions. The performance of SAOP is among the best for nonhybrid functionals for Group 18 atoms but its precision degrades when considering the full set of atoms. In general, we find that conclusions based on results obtained for the rare‐gas atoms are not necessarily representative of the complete set of atoms. GRAC cannot be used with effective core potentials since the asymptotic correction is switched on in the core region.     

Scrutinizing “Invisible” astatine: A challenge for modern density functionals

The main‐group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two‐component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta‐generalized gradient approximation (meta‐GGA) PW6B95 functional is overall the best choice. It is worth noting that the range‐separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid‐GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc.     

Parallel implementation of γ‐point pseudopotential plane‐wave DFT with exact exchange

Semi‐local functionals commonly used in density functional theory (DFT) studies of solids usually fail to reproduce localized states such as trapped holes, polarons, excitons, and solitons. This failure is ascribed to self‐interaction which creates a Coulomb barrier to localization. Pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange (hybrid‐DFT, e.g., B3LYP and PBE0) have shown to promise in rectifying this type of failure, as well as producing more accurate band gaps and reaction barriers. The evaluation of exact exchange is challenging for large, solid state systems with periodic boundary conditions, especially when plane‐wave basis sets are used. We have developed parallel algorithms for implementing exact exchange into pseudopotential plane‐wave DFT program and we have implemented them in the NWChem program package. The technique developed can readily be employed in Γ‐point plane‐wave DFT programs. Furthermore, atomic forces and stresses are straightforward to implement, making it applicable to both confined and extended systems, as well as to Car‐Parrinello ab initio molecular dynamic simulations. This method has been applied to several systems for which conventional DFT methods do not work well, including calculations for band gaps in oxides and the electronic structure of a charge trapped state in the Fe(II) containing mica, annite. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

The confirmation of accurate combination of functional and basis set for transition‐metal dimers: Fe2, Co2, Ni2, Ru2, Rh2, Pd2, Os2, Ir2, and Pt2

Eight kinds of density functionals named B3LYP, PBE1PBE, B1B95, BLYP, BP86, G96PW91, mPWPW91, and SVWN along with two different valence basis sets (LANL2DZ and CEP‐121g) are employed to study the transition‐metal dimers for the elements of group VIII. By comparing the equilibrium bond distances, vibrational frequencies, and dissociation energies of the ground state of these dimers with the available experimental values and theoretical data, we show that the “pure” DFT methods (G96PW91, BLYP, and BP86) with great‐gradient approximation always give better results relative to the hybrid HF/DFT schemes (B3LYP, PBE1PBE, and B1B95). The striking case found by us is that the G96PW91 functional, which is not tested in previous systemic studies, always predicts the dissociation energy to be well. The Ru₂ and Os₂ dimers are sensitive to not only the functionals employed but also the valence basis sets adopted. The natural bond orbital population is analyzed, and the molecular orbitals of the unpaired electrons are determined. Furthermore, our results indicate that the s and d orbitals of these dimers always hybridize with each other except for Rh₂ and Pt₂ molecules. And by analyzing the electron configuration of the bonding atom, the dissociation limit of the ground state is obtained. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Standard grids for high‐precision integration of modern density functionals: SG‐2 and SG‐3

Density‐functional approximations developed in the past decade necessitate the use of quadrature grids that are far more dense than those required to integrate older generations of functionals. This category of difficult‐to‐integrate functionals includes meta‐generalized gradient approximations, which depend on orbital gradients and/or the Laplacian of the density, as well as functionals based on B97 and the popular “Minnesota” class of functionals, each of which contain complicated and/or oscillatory expressions for the exchange inhomogeneity factor. Following a strategy introduced previously by Gill and co‐workers to develop the relatively sparse “SG‐0” and “SG‐1” standard quadrature grids, we introduce two higher‐quality grids that we designate SG‐2 and SG‐3, obtained by systematically “pruning” medium‐ and high‐quality atom‐centered grids. The pruning procedure affords computational speedups approaching a factor of two for hybrid functionals applied to systems of atoms, without significant loss of accuracy. The grid dependence of several popular density functionals is characterized for various properties. © 2017 Wiley Periodicals, Inc.     

On the applicability of density functional theory to manganese‐based complexes with catalytic activity toward water oxidation

The present contribution assesses the performance of several popular and accurate density functionals, namely B3LYP, BP86, M06, MN12L, mPWPW91, PBE0, and TPSSh toward manganese‐based coordination complexes. These compounds show promising properties toward application to catalytic water oxidation. Although manganese with N‐ and O‐biding ligands tends to give rise to high spin complexes, the results show that BP86, mPWPW91, and specially MN12L, tend to yield low‐spin complexes. The usage of these functionals for such compounds is, thus, discouraged. All the functionals considered deliver accurate geometries. The present results show, however, that B3LYP delivers geometries deviating from experimental values when compared to the other functionals of the set. M06, PBE0, and TPSSh deliver geometries of similar accuracy, PBE0 outstanding slightly with respect to the other two. © 2017 Wiley Periodicals, Inc.     

Nonempirical (double-hybrid) density functionals applied to atomic excitation energies: A systematic basis set investigation

We investigate here the lowest-energy (spin-conserving) excitation energies for the set of He-Ne atoms, with the family of nonempirical PBE, PBE0, PBE0-1/3, PBE0-DH, PBE-CIDH, PBE-QIDH, and PBE0-2 functionals, after employing a wide variety of basis sets systematically approaching the basis set limit: def2-nVP(D), cc-pVnZ, aug-cc-pVnZ, and d-aug-cc-pVnZ. We find that an accuracy (ie, mean unsigned error) of 0.3 to 0.4 eV for time-dependent density functional theory (DFT) atomic excitation energies can be robustly achieved with modern double-hybrid methods, which are also stable with respect to the addition of a double set of diffuse functions, contrarily to hybrid versions, in agreement with recent findings employing sophisticated multiconfigurational DFT methods.     

Single wall carbon nanotubes density of states: comparison of experiment and theory

We study the electronic structure of a variety of single wall carbon nanotubes and report density of states obtained with the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation and hybrid PBE0 approximation of density functional theory using Gaussian orbitals and periodic boundary conditions. PBE gives very good results for metallic tubes but the addition of a portion of exact exchange in the hybrid PBE0 functional worsens the agreement between experiment and theory. On the other hand, the PBE0 hybrid significantly improves the theoretical predictions (compared to PBE) for semiconducting tubes.     

Accurate prediction of vertical electronic transitions of Ni(II) coordination compounds via time dependent density functional theory

Time dependent density functional theory calculations are completed for five Ni(II) complexes formed by polydentate peptides to predict the electronic absorption spectrum. The ligands examined were glycyl‐glycyl‐glycine (GGG), glycyl‐glycyl‐glycyl‐glycine (GGGG), glycyl‐glycyl‐histidine (GGH), glycyl‐glycyl‐cysteine (GGC), and triethylenetetramine (trien). Fifteen functionals and two basis sets were tested. On the basis of the mean absolute percent deviation (MAPD), the ranking among the functionals is: HSE06 ∼ MPW1PW91 ∼ PBE0 > ω‐B97x‐D ∼ B3P86 ∼ B3LYP ∼ CAM‐B3LYP > PBE ∼ BLYP ∼ BP86 > TPSS > TPSSh > BHandHLYP > M06 ≫ M06‐2X. Concerning the basis sets, the triple‐ζ def2‐TZVP performs better than the double‐ζ LANL2DZ. With the functional HSE06 and basis set def2‐TZVP the MAPD with respect to the experimental λ_max is 1.65% with a standard deviation of 1.26%. The absorption electronic spectra were interpreted in terms of vertical excitations between occupied and virtual MOs based on Ni‐d atomic orbitals. The electronic structure of the Ni(II) species is also discussed.     

XYG3型双杂化密度泛函方法新进展：从能量到能量的解析梯度

本文回顾了现代密度泛函理论的基础,着重评述了XYG3型双杂化（XYG3typeofdoublyhybrid,xDH）泛函的最新进展,解析能量梯度的实现．XYG3是首个依照绝热途径理论建立的双杂化泛函,在具体实现上具有独特的构架．该类型泛函利用常用泛函（如B3LYP或PBE0等）作母泛函来进行自洽计算,以期获得更好的密度和轨道,然后将所得到的轨道和密度信息带入到xDH泛函中以得到最终能量．由于自洽泛函和最终能量泛函不同,因而在计算解析能量梯度时需要求解耦合微扰Kohn—Sham方程．在此基础上,还评述了xDH泛函在能量,尤其是构型优化方面的具体表现．测试的构型集包括以共价键键合的分子和非键相互作用体系的平衡结构,以及反应过渡态结构．结果表明,xDH双杂化泛函总体上给出了比母泛函更好的能量和几何构型．     

Assessment of density functional methods for reaction energetics: Iridium‐catalyzed water oxidation as case study

We investigate basis set convergence for a series of density functional theory (DFT) functionals (both hybrid and nonhybrid) and compare to coupled‐cluster with single and double excitations and perturbative triples [CCSD(T)] benchmark calculations. The case studied is the energetics of the water oxidation reaction by an iridium‐oxo complex. Complexation energies for the reactants and products complexes as well as the transition state (TS) energy are considered. Contrary to the expectation of relatively weak basis set dependence for DFT, the basis set effects are large, for example, more than 10 kcal mol^?1 difference from converged basis for the activation energy with “small” basis sets (DZ/6‐31G** for Ir/other atoms, or SVP) and still more than 6 kcal mol^?1 for def2‐TZVPP/6‐31G**. Inclusion of the dispersion correction in DFT‐D3 schemes affects the energies of reactant complex (RC), TS, and product complex (PC) by almost the same amount; it significantly improves the complexation energy (the formation of RC), but has little effect on the activation energy with respect to RC. With converged basis, some pure GGAs (PBE‐D3, BP86‐D3) as well as the hybrid functional B3LYP‐D3 are very accurate compared to benchmark CCSD(T) calculations. © 2012 Wiley Periodicals, Inc.     

The role of range-separated Hartree-Fock exchange in the calculation of magnetic exchange couplings in transition metal complexes

We assess the dependence of magnetic exchange couplings on the variation of Hartree-Fock exchange (HFX) admixture in global hybrid functionals and the range-separation parameter ω in range-separated hybrid functionals in a set of 12 spin-1/2 binuclear transition metal complexes. The global hybrid PBEh (hybrid Perdew-Burke-Ernzerhof) and range-separated hybrids HSE (Heyd-Scuseria-Ernzerhof) and LC-ωPBE (long-range corrected hybrid PBE) are employed for this assessment, and exchange couplings are calculated from energy differences within the framework of the spin-projected approach. It is found that these functionals perform optimally for magnetic exchange couplings with 35% HFX admixture for PBEh, ω = 0.50 a.u.(-1) for LC-ωPBE, and ω at or near 0.0 a.u.(-1) for HSE (which corresponds to PBEh). We find that in their standard respective forms, LC-ωPBE slightly outperforms PBEh, while PBEh with 35% HFX yields exchange couplings closer to experiment than those of LC-ωPBE with ω = 0.50 a.u.(-1). Additionally, we show that the profile of exchange couplings with respect to ω in HSE is appreciably flat from 0 to 0.2 a.u.(-1). This combined with the fact that HSE is computationally more tractable than global hybrids makes HSE an attractive alternative for the evaluation of exchange couplings in extended systems. These results are rationalized with respect to how varying the parameters within these functionals affects the delocalization of the magnetic orbitals, and conclusions are made regarding the relative importance of range separation versus global mixing of HFX for the calculation of exchange couplings.