DFT Exchange-correlation Functionals Research Articles

Dependence of tetragonal barium titanate spontaneous polarization and refractive indices on DFT exchange-correlation functionals

The present work aims to use the Quantum Espresso software to theoretically investigate the spontaneous polarization and refractive indices of barium titanate (BaTiO3) in its tetragonal phase, and their dependence on the considered DFT exchange-correlation functionals. Among the functionals implemented in Quantum Espresso, twenty-four functionals were considered. The calculations, in which pseudopotentials of type ultrasoft were used, show that the values of all studied magnitudes depend on the used exchange-correlation functional. According to the obtained results, for the considered functionals, it appears that there is a linearity between the spontaneous polarization and the ionic shift difference Δz(Ti)-Δz(Oz); this linearity can be explained by the fact that the dipolar interaction Ti-Oz is the main contributor to the spontaneous polarization, being seen that: (i) the spontaneous polarization is a consequence of the coupling between the displacements of the constituent ions and their effective charges, (ii) the ionic shifts lead to a decrease in the Ti-Oz distance and an increase in the Ti-Ox and Ti-Oy distances, and then an increase in the Ti-Oz dipolar interaction compared to the Ti-Ox and Ti-Oy dipolar interactions, and (iii) the Ti and Oz ions possess the highest Born effective charges (in absolute values), in the polar direction, compared to the other ions, as reported in the literature. However, the closest values of the spontaneous polarization to the experimental data were obtained for the exchange-correlation functionals VDW-DF-C09, PZ, VDW-DF-CX, VDW-DF3-OPT1, VDW-DF2-C09, WC, and PBESOL. For these functionals, the refractive indices of ordinary and extraordinary polarizations were studied as a function of the light wavelength, in the range 160–940 nm. The obtained results show that the behavior of both refractive indices with respect to the wavelength, for visible light, is quit similar to that of Sellmeier equation with good agreement with the experimental data, particularly for the van der Waals functionals VDW-DF3-OPT1, VDW-DF-CX, VDW-DF2-C09, and VDW-DF-C09.

Adsorption of atomic and molecular monolayers on Pt-supported graphene

Adsorption energies of monolayers of noble gases (Ar, Kr, Xe) and small molecules (N2, O2, CO, CH4, C2H6, and C3H8) on graphene supported by Pt(111) surface were computed by DFT, corrected for temperature and zero-point effects, and, compared to the recent temperature-programmed desorption experiments (Smith et al., 2016). The results indicate that some of the considered DFT exchange–correlation functionals reasonably well describe molecule–graphene/Pt(111) noncovalent interactions. For selected models, fixed-node diffusion Monte Carlo computations were used for ultimate cross-validation of interaction energies between the molecule and free-standing graphene.

Can Density Functional Theory Predict Mössbauer Spectra in Pyrolyzed Fe-N-C Catalysts?

57Fe Mössbauer spectroscopy, based on the recoil-free emission and resonant absorption of γ-rays, allows an easier separation of the signals arising from the different Fe environments. This is in the basis of the growing interest of using 57Mössbauer spectroscopy for identification of Fe-based species present in pyrolyzed Fe-N-C catalysts. Because of their high temperature synthesis, these catalysts often comprise different coordinations of atomically-dispersed Fe ions covalently bound to the nitrogen-doped carbon matrix (FeNxCy moieties), but also metallic iron and iron carbides with long-range order.1-3 In the 57Fe Mössbauer spectra (recorded in the absence of a strong external magnetic field) metallic iron and iron carbides result in sextets (except for the paramagnetic γ-Fe structure, leading to singlet spectral component) while the fingerprint of FeNxCy moieties is a doublet spectral component. Precise interpretation of the doublets (often labeled as D1 and D2) allowing to distinguish between iron coordination geometries, spin- and oxidation state remains however challenging and has so far lacked strong theoretical or experimental reference basis for their unambiguous assignments. D1 doublet has an isomer value ranging from 0.33 to 0.4 mm/s and quadrupole splitting (QS) ranging from 0.7 to 1.2 mm/s, which is usually attributed to Fe-N4 defects with Fe2+ in its low spin state. The assignment of the D2 doublet with isomer shifts ranging from 0.36 to 0.52 mm/s and with quadrupole splitting ranging from 2.4 to 2.7 mm/s is more ambiguous. It is attributed to Fe-N4 defects similar to iron phthalocyanine with Fe2+ in its intermediate spin state or to a Fe-N2+2 defect in which Fe binds to four pyridinic nitrogen atoms from two adjacent nitrogen-doped graphene layers. However, these assignments have been based on experimental records of carbon-supported FeN4 macrocycles, which differ greatly from the case in which the Fe-Nx moieties are integrated into the graphene matrix. It appears, therefore, obvious that theoretical Mössbauer spectra should be highly beneficial to rationally assign the D1 and D2 spectra of Fe-N-C materials. Theoretical studies (mostly obtained with density-functional-theory, DFT, based approaches) of 57Fe Mössbauer spectra, have evidenced that the choice of the exchange-correlation functional and atomic basis sets has a strong impact on the accuracy of QS values, in particular for intermediate and high spin iron complexes. It is therefore necessary to examine for every new class of Fe-containing compounds the variation of QS with the DFT functional and other computational details. Theoretical 57Fe Mössbauer spectra in pyrolyzed Fe-N-C catalysts have not yet been made available, which prompted us toward the present DFT study of the quadrupole splitting energies in Fe-N4 defects that are identified as the active sites in the pyrolyzed Fe-N-C materials. Extensive computations of QS in Fe-N4 models with Fe in various coordinations and with different oxidation/spin states have been carried out. The use of several DFT exchange-correlation functionals and basis sets in cluster and periodic approaches are compared and will be reported. The analysis of the DFT calculated values in comparison with experimental data are used to interpret quadrupole doublets ubiquitous in the Mössbauer spectra of pyrolyzed Fe-N-C catalysts. Acknowledgement: This work is supported by the LabEx CheMISyst ANR-10-LABX-05-01.

Accuracy of TD-DFT Geometries: A Fresh Look.

We benchmark a panel of 48 DFT exchange-correlation functionals in the framework of TD-DFT optimizations of the geometry of valence singlet excited states. To this end, we use a set of 41 small- and medium-sized organic molecules for which reference geometries were obtained at high level of theory, typically, CC3 or CCSDR(3), with the aug-cc-pVTZ atomic basis set. For the ground-state parameters, the tested functionals provide average deviations that are small (0.010 Å and 0.5° for bond lengths and valence angles) and not very sensitive to the selected (hybrid) functional, but the errors are larger for the most polarized bonds (CO, CN, and so on). Nevertheless, DFT has a tendency to provide too compact distances, a trend slightly enhanced for functionals including a large amount of exact exchange. The average errors largely increase when going to the excited-state for most bond types, that is, TD-DFT delivers less accurate excited-state distances than DFT for ground state. In particular TD-DFT combined with hybrid functionals provides significantly too short CO and CS/CSe bonds with respective average errors in the -0.026/-0.052 Å and -0.015/-0.082 Å ranges, depending on the selected hybrid functional. For the carbonyl bonds, the sizes of the TD-DFT deviations obtained when selecting standard hybrid functionals are of the same order of magnitude as the EOM-CCSD ones.

Optical Gaps in Pristine and Heavily Doped Silicon Nanocrystals: DFT versus Quantum Monte Carlo Benchmarks.

We present a time-dependent density functional theory (TDDFT) study of the optical gaps of light-emitting nanomaterials, namely, pristine and heavily B- and P-codoped silicon crystalline nanoparticles. Twenty DFT exchange-correlation functionals sampled from the best currently available inventory such as hybrids and range-separated hybrids are benchmarked against ultra-accurate quantum Monte Carlo results on small model Si nanocrystals. Overall, the range-separated hybrids are found to perform best. The quality of the DFT gaps is correlated with the deviation from Koopmans' theorem as a possible quality guide. In addition to providing a generic test of the ability of TDDFT to describe optical properties of silicon crystalline nanoparticles, the results also open up a route to benchmark-quality DFT studies of nanoparticle sizes approaching those studied experimentally.

Kinetics and Thermodynamics of the Reaction between the (•)OH Radical and Adenine: A Theoretical Investigation.

The accessibility of all possible reaction paths for the reaction between the nucleobase adenine and the (•)OH radical is investigated through quantum chemical calculations of barrier heights and rate constants at the ωB97X-D/6-311++G(2df,2pd) level with Eckart tunneling corrections. First the computational method is validated by considering the hydrogen abstraction from the heterocyclic N9 nitrogen in adenine as a test system. Geometries for all molecules in the reaction are optimized with four different DFT exchange-correlation functionals (B3LYP, BHandHLYP, M06-2X, and ωB97X-D), in combination with Pople and Dunning basis sets, all of which have been employed in similar investigations in the literature. Improved energies are obtained through single point calculations with CCSD(T) and the same basis sets, and reaction rate constants are calculated for all methods both without tunneling corrections and with the Wigner, Bell, and Eckart corrections. In comparison to CCSD(T)//BHandHLYP/aug-cc-pVTZ reference results, the ωB97X-D/6-311++G(2df,2pd) method combined with Eckart tunneling corrections provides a sensible compromise between accuracy and time. Using this method, all subreactions of the reaction between adenine and the (•)OH radical are investigated. The total rate constants for hydrogen abstraction and addition for adenine are predicted with this method to be 1.06 × 10(-12) and 1.10 × 10(-12) cm(3) molecules(-1) s(-1), respectively. Abstractions of H61 and H62 contribute the most, while only addition to the C8 carbon is found to be of any significance, in contrast to previous claims that addition is the dominant reaction pathway. The overall rate constant for the complete reaction is found to be 2.17 × 10(-12) cm(3) molecules(-1) s(-1), which agrees exceptionally well with experimental results.

Electronic circular dichroism of chiral alkenes: B3LYP and CAM-B3LYP calculations.

Time-dependent density functional theory (TDDFT) calculations of electronic circular dichroism (ECD) are widely used to determine absolute configurations (ACs) of chiral molecules. Two very popular DFT exchange-correlation functionals, one hybrid (B3LYP) and one long-range corrected (CAM-B3LYP), along with a hierarchical sequence of basis sets were investigated, and the ECD spectra predicted for eight alkenes and compared to gas-phase experimental spectra. Little variation in predicted ECD spectra was found with the basis set size enlargement, but the sensitivity to the functional is greater. Good agreement was obtained only with the CAM-B3LYP functional, leading to the conclusion that TDDFT calculations of ECD spectra can routinely provide reliable ACs if and only if an appropriate functional is used. For camphene, twistene, syn-(E)-bisfenchylidene, and phyllocladene, solvent effects were estimated.

Benchmarking DFT and TD-DFT Functionals for the Ground and Excited States of Hydrogen-Rich Peptide Radicals.

We assess the pros and cons of a large panel of DFT exchange-correlation functionals for the prediction of the electronic structure of hydrogen-rich peptide radicals formed after electron attachment on a protonated peptide. Indeed, despite its importance in the understanding of the chemical changes associated with the reduction step, the question of the attachment site of an electron and, more generally, of the reduced species formed in the gas phase through electron-induced dissociation (ExD) processes in mass spectrometry is still a matter of debate. For hydrogen-rich peptide radicals in which several positive groups and low-lying π* orbitals can capture the incoming electron in ExD, inclusion of full Hartree-Fock exchange at long-range interelectronic distance is a prerequisite for an accurate description of the electronic states, thereby excluding several popular exchange-correlation functionals, e.g., B3LYP, M06-2X, or CAM-B3LYP. However, we show that this condition is not sufficient by comparing the results obtained with asymptotically correct range-separated hybrids (M11, LC-BLYP, LC-BPW91, ωB97, ωB97X, and ωB97X-D) and with reference CASSCF-MRCI and EOM-CCSD calculations. The attenuation parameter ω significantly tunes the spin density distribution and the excited states vertical energies. The investigated model structures, ranging from methylammonium to hexapeptide, allow us to obtain a description of the nature and energy of the electronic states, depending on (i) the presence of hydrogen bond(s) around the cationic site(s), (ii) the presence of π* molecular orbitals (MOs), and (iii) the selected DFT approach. It turns out that, in the present framework, LC-BLYP and ωB97 yields the most accurate results.

Modeling the adsorption of short alkanes in the zeolite SSZ-13 using “van der Waals” DFT exchange correlation functionals: Understanding the advantages and limitations of such functionals

The inclusion of non-local interactions is one of the large challenges in density functional theory. Very promising methods are the vdW-DF2 and BEEF-vdW functionals, which combine a semi-local approximation for exchange interactions and a non-local correlation expression. In this work we apply those functionals to model the adsorption of short alkanes in the zeolite SSZ-13. Even though results for energetics are improved with respect to other vdW-DF based methods, we still find a comparatively large error compared to high-level calculations. These errors result from approximations in the determination of the dielectric function and of the van der Waals kernel. The insights presented in this work will help to understand the performance not only of vdW-DF2 and BEEF-vdW, but all vdW-DF based functionals in various chemically or physically important systems.

Benchmarking Time-Dependent Density Functional Theory for Excited State Geometries of Organic Molecules in Gas-Phase and in Solution.

We analyze potentials and limits of the Time-Dependent Density Functional Theory (TD-DFT) approach for the determination of excited-state geometries of organic molecules in gas-phase and in solution. Three very popular DFT exchange-correlation functionals, two hybrids (B3LYP and PBE0) and one long-range corrected (CAM-B3LYP), are here investigated, and the results are compared to the correlated RI-CC2 wave function approach. Solvent effects are further analyzed by means of a polarizable continuum model. A total of 15 organic chromophores (including both small molecules and larger push-pull systems) are considered as prototypes of n → π* and π → π* singlet excitations. Our analysis allows to point out specific correlations between the accuracy of the various functionals and the type of excitation and/or the type of chemical bonds involved. We find that while the best ground-state geometries are obtained with PBE0 and B3LYP, CAM-B3LYP yields the most accurate description of electronic and geometrical characteristics of excited states, both in gas-phase and in solution.

Assessment of DFT Exchange-Correlation Functionals for Evaluating the Multipolar Contributions to the Quadratic Nonlinear Optical Responses of Small Reference Molecules.

The hyper-Rayleigh scattering responses as well as the multipolar contributions to the first hyperpolarizabilities are calculated by means of density functional theory for a series of reference molecules (acetonitrile, dichloromethane, trichloroacetonitrile, chloroform, carbon tetrachloride), covering the whole range of dipolar/octupolar character. The performance of various exchange-correlation functionals is addressed by comparison to CCSD(T) calculations. The best functionals turn out to be LC-BLYP, M05-2X, and M06-2X.

Correlations between Computation and Experimental Thermodynamics of Halogen Bonding

Correlations between experimental, solution-phase thermodynamic data and calculated gas-phase energies of interaction are investigated for noncovalent halogen bonding interactions between electron-deficient iodo compounds and Lewis bases. The experimental data consist of free energies of interaction spanning roughly 7 kcal/mol; they encompass halogen bonds involving both organic (iodoperfluoroarene or iodoperfluoroalkane) and inorganic (I(2), IBr, ICN) donors with nitrogen- and oxygen-based acceptors and are divided into two sets according to the identity of the solvent in which they were determined (alkanes or CCl(4)). Adiabatic energies of halogen bonding were calculated using a variety of methods, including 22 DFT exchange-correlation functionals, using geometries optimized at the MP2/6-31+G(d,p) level of theory. Certain DFT functionals, particularly the B97-1, B97-2, and B98 family, provide outstanding linear correlations with the experimental thermodynamic data, as assessed by a variety of statistical methods.

Evaluating London Dispersion Interactions in DFT: A Nonlocal Anisotropic Buckingham-Hirshfeld Model.

In this work, we present a novel model, referred to as BH-DFT-D, for the evaluation of London dispersion, with the purpose to correct the performance of local DFT exchange-correlation functionals for the description of van der Waals interactions. The new BH-DFT-D model combines the equations originally derived by Buckingham [Buckingham, A. D. Adv. Chem. Phys1967, 12, 107] with the definition of distributed multipole polarizability tensors within the Hirshfeld method [Hirshfeld, F.L. Theor. Chim. Acta1977, 44, 129], resulting in nonlocal, fully anisotropic expressions. Since no damping function has been introduced yet into the model, it is suitable in its present form for the evaluation of dispersion interactions in van der Waals dimers with no or negligible overlap. The new method is tested for an extended collection of van der Waals dimers against high-level data, where it is found to reproduce interaction energies at the BH-B3LYP-D/aug-cc-pVTZ level with a mean average error (MAE) of 0.20 kcal/mol. Next, development steps of the model will consist of adding a damping function, analytical gradients, and generalization to a supramolecular system.

A Comparative Hybrid DFT Study of Phonons in Several SrTiO3 Phases

Three SrTiO3 phases (cubic, tetragonal antiferrodistortive and tetragonal ferroelectric) are studied at the ab initio level. Lattice dynamics was calculated via the PBE0 and B3PW hybrid DFT exchange-correlation functionals within the LCAO formalism using the direct frozen-phonon method. The soft-mode-induced phase transitions and thermodynamics (heat capacity and Helmholtz free energy) are discussed. The results obtained are in good agreement with experiments, except for reproduction of the phase transition temperature. The study represents an important first step in considering defective and more complicated perovskite systems.

On the TD-DFT Accuracy in Determining Single and Double Bonds in Excited-State Structures of Organic Molecules

We present an analysis on the behavior of the TD-DFT approach in the determination of excited-state structures with particular attention to single and double bonds. The analysis is based on a direct comparison with the highly correlated CASPT2 ab initio approach. Six DFT exchange-correlation functionals differing in the Hartree-Fock exchange percentage and the type of correlation functional are considered and applied to the study of seven prototype organic molecules characterized by two families of excitations (acrolein, acetone, diazomethane, and propanoic acid anion for n-π* and cis-1,3-butadiene, trans-1,3-butadiene, and pyrrole for π-π*), and three protonated Schiff bases, used as model chromophores for 11-cis retinal. Our analysis allows pinpointing specific correlations between accuracy of the various functionals and category of excitation and/or type of chemical bond involved in the corresponding geometry relaxation. We confirm the role of the long-range correction of the potential to obtain a balanced description of excitation energies and excited-state structures, but we also point out that, for a small system, B3LYP and PBE0 also give results close to CASPT2.

Triplet Excitation Energy Transfer with Constrained Density Functional Theory

We study the electronic coupling matrix element for triplet excitation energy-transfer processes with a number of different computational methods. For the first time, constrained density functional theory (CDFT) is applied to the problem of energy transfer, and results are compared with direct coupling calculations of broken symmetry and fragment densities, as well as the splitting method. A naive calculation of the electronic coupling using diabatic and adiabatic energy differences is shown to yield erroneous results due to the fractional spin error present in both Hartree-Fock and commonly used DFT exchange-correlation functionals. Some potential issues concerning the splitting method with triplet references within Hartree-Fock and DFT are discussed. We find that only methods that compute the matrix element directly (either from CDFT, broken symmetry, or fragment states) appear to be robust. Several illustrative examples are presented.

Electron Affinities, Fluoride Affinities, and Heats of Formation of the Second Row Transition Metal Hexafluorides: MF6(M = Mo, Tc, Ru, Rh, Pd, Ag)

High-level electronic structure calculations were used to evaluate reliable, self-consistent thermochemical data sets for the second row transition metal hexafluorides. The electron affinities, heats of formation, first (MF(6) --> MF(5) + F) and average M-F bond dissociation energies, and fluoride affinities of MF(6) (MF(6) + F(-) --> MF(7)(-)) and MF(5) (MF(5) + F(-) --> MF(6)(-)) were calculated. The electron affinities are higher than those of the corresponding third row hexafluorides, making them stronger one-electron oxidizers. The calculated electron affinities, in good agreement with the available experimental values, are 4.23 eV for MoF(6), 5.89 eV for TcF(6), 7.01 eV for RuF(6), 6.80 eV for RhF(6), 7.95 eV for PdF(6), and 8.89 eV for AgF(6). The corresponding pentafluorides are also very strong Lewis acids, although their acidities on the pF(-) scale are about one unit lower than those of the third row pentafluorides. The performance of a wide range of DFT exchange-correlation functionals was benchmarked by comparing them to our more accurate CCSD(T) results.

Post-CCSD(T) ab Initio Thermochemistry of Halogen Oxides and Related Hydrides XOX, XOOX, HOX, XOn, and HXOn (X = F, Cl), and Evaluation of DFT Methods for These Systems

Benchmark-quality W4 (and related) thermochemical data were obtained for the fluorine and chlorine oxides and some related hydrides, all of which are of interest for computational modeling of atmospheric processes. Our best available estimates for total atomization energies at 0 K are the following: HO2 165.97 +/- 0.14, H2O2 252.08 +/- 0.14, HOF 149.24 +/- 0.14, FO 51.17 +/- 0.10, F2O 89.43 +/- 0.14, FO2 130.15 +/- 0.16, F2O2 146.00 +/- 0.16, ClO 63.40 +/- 0.10, HOCl 156.73 +/- 0.14, Cl2O 96.93 +/- 0.16, OClO 122.33 +/- 0.16, ClOO 121.88 +/- 0.32, Cl2O2 142.9 +/- 0.3, ClO3 159.9 +/- 0.4, HClO2 192.0 +/- 0.4, HClO3 258.1 +/- 0.3, and HClO4 313.4 +/- 1 kcal/mol. For several of these species, the total atomization energy contains unusually large components from correlation effects beyond CCSD(T). The geometry of FOOF is significantly affected by connected quadruple excitations. A large variety of DFT exchange-correlation functionals have been evaluated for these systems and observations on their performance are offered. Our best available estimates for deltaHf,0o are the following: HO2 3.65 +/- 0.14, H2O2 -30.82 +/- 0.14, HOF -20.15 +/- 0.14, FO 26.28 +/- 0.11, F2O 6.48 +/- 0.14, FO2 6.30 +/- 0.16, F2O2 8.90 +/- 0.18, ClO 24.19 +/- 0.10, HOCl -17.51 +/- 0.14, Cl2O 19.24 +/- 0.16, OClO 24.26 +/- 0.16, ClOO 24.69 +/- 0.16, Cl2O2 32.3 +/- 0.3, ClO3 45.7 +/- 0.4, HClO2 6.2 +/- 0.4, HClO3 -0.9 +/- 0.3, and HClO4 2.9 +/- 1.0 kcal/mol. (The corresponding values at 298.15 K are 2.96 +/- 0.14, -32.24 +/- 0.14, -20.84 +/- 0.14, 26.43 +/- 0.11, 5.94 +/- 0.14, 5.87 +/- 0.16, 7.84 +/- 0.18, 24.18 +/- 0.10, -18.20 +/- 0.14, 18.82 +/- 0.16, 23.67 +/- 0.16, 24.30 +/- 0.16, 31.5 +/- 0.3, 44.3 +/- 0.4, 5.0 +/- 0.4, -2.6 +/- 0.3, and -0.1 +/- 1.0 kcal/mol, respectively.)

A resonating broken symmetry configuration interaction approach for double-exchangemagnetic systems

The correct description for ion–radical systems has recently attracted much attention fromdensity functional theory (DFT) researchers. Although several hybridization schemes usingexact (Hartree–Fock) exchange and DFT exchange–correlation functionals have beenproposed, it has been reported that such treatments do not work for the description ofion–radical systems. In this study we show that combining the exact exchange term in theKohn–Sham DFT (or the Hartree–Fock equation) with the following resonatingconfiguration interaction method is effective for the description of double-exchangetype molecular magnetic interactions. The results are analyzed in relation to the‘many-electron self-interaction’ concept that was recently proposed by DFT researchers.

Density functionals for calculating NMR 1JCH coupling constants in electron-rich systems

Several DFT exchange-correlation functionals were used to calculate one-bond carbon–hydrogen spin–spin coupling constant ( 1 J CH) for halocyclohexanes and 2-substituted-tetrahydropyrans. The prediction of 1 J CH for halocyclohexanes using the B3LYP and BLYP functionals gave better results than other functionals, while the PBE functional showed to be more appropriate to predict 1 J CH for some electron-rich systems – the tetrahydropyran derivatives.