van der Waals corrected density functional calculations of the adsorption of benzene on the Cu (111) surface

We investigate the performance of several van der Waals (vdW) functionals at calculating the interactions between benzene and the copper (111) surface, using the local orbital approach in the SIESTA code. We demonstrate the importance of using surface optimized basis sets to calculate properties of pure surfaces, including surface energies and the work function. We quantify the errors created using (3 × 3) supercells to study adsorbate interactions using much larger supercells, and show non‐negligible errors in the binding energies and separation distances. We examine the eight high‐symmetry orientations of benzene on the Cu (111) surface, reporting the binding energies, separation distance, and change in work function. The optimized vdW‐DF(optB88‐vdW) functional provides superior results to the vdW‐DF(revPBE) and vdW‐DF2(rPW86) functionals, and closely matches the experimental and experimentally deduced values. This work demonstrates that local orbital methods using appropriate basis sets combined with a vdW functional can model adsorption between metal surfaces and organic molecules.     

On the van der Waals interactions and the stability of polypeptide chains in helical conformations

In this work, we aim to investigate the contribution of van der Waals (vdW) interactions to the stability of polypeptides in helical conformations studying infinitely long chains of alanine and glycine with density functional theory. To account for vdW interactions, we have used the interatomic pairwise dispersion approach proposed by Tkatchenko–Scheffler (TS), the TS approach with self‐consistent screening (SCS) that self‐consistently includes long‐range electrostatic effects (TS + SCS), the D2 and D3 methods of Grimme et al., and the Langreth–Lundqvist procedure that treats nonlocally the correlation part of the approximation to the exchange‐correlation (xc) functional (called DF). First, we have tested the performance of these strategies studying a set of representative hydrogen bonded dimers. Next, we have studied polyalanine and polyglicine in π‐helix, α‐helix, ‐helix, 2₇, and polyproline‐II conformations and in a fully extended structure. We have found that the DF methodology in combination with a modified version for the Becke approximation to the exchange (optB86b), the D2, D3, TS, and TS + SCS strategies in combination with the Perdew–Burke–Ernzerhof approximation to the xc functional, describe fairly well dimer association energies. Furthermore, the DF method and the D2, D3, TS, and TS + SCS strategies predict very similar helical stabilities even though the approximation used in DF for describing the long‐range dispersion interactions is different that the one used in D2/D3 and TS/TS + SCS. We found that the stability doubles for π and α helices if vdW interactions are taken into account. © 2015 Wiley Periodicals, Inc.     

Understanding the Effect of the Exchange-Correlation Functionals on Methane and Ethane Formation over Ruthenium Catalysts

Density functional theory (DFT) has been established as a powerful research tool for heterogeneous catalysis research in obtaining key thermodynamic and/or kinetic parameters like adsorption energies, enthalpies of reaction, activation barriers, and rate constants. Understanding of density functional exchange-correlation approximations is essential to reveal the mechanism and performance of a catalyst. In the present work, we reported the influence of six exchange-correlation density functionals, including PBE, RPBE, BEEF+vdW, optB86b+vdW, SCAN, and SCAN+rVV10, on the adsorption energies, reaction energies and activation barriers of carbon hydrogenation and carbon-carbon couplings during the formation of methane and ethane over Ru(0001) and Ru(1011) surfaces. We found the calculated reaction energies are strongly dependent on exchange-correlation density functionals due to the difference in coordination number between reactants and products on surfaces. The deviation of the calculated elementary reaction energies can be accumulated to a large value for chemical reaction involving multiple steps and vary considerably with different exchange-correlation density functionals calculations. The different exchange-correlation density functionals are found to influence considerably the selectivity of Ru(0001) surface for methane, ethylene, and ethane formation determined by the adsorption energies of intermediates involved. However, the influence on the barriers of the elementary surface reactions and the structural sensitivity of Ru(0001) and Ru(1011) are modest. Our work highlights the limitation of exchange-correlation density functionals on computational catalysis and the importance of choosing a proper exchange-correlation density functional in correctly evaluating the activity and selectivity of a catalyst.     

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.     

Computational NMR coupling constants: Shifting and scaling factors for evaluating 1JCH

Optimized shifting and/or scaling factors for calculating one‐bond carbon–hydrogen spin–spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97‐2 and M06‐L) and basis sets (TZVP, HIII‐su3, EPR‐III, aug‐cc‐pVTZ‐J, ccJ‐pVDZ, ccJ‐pVTZ, ccJ‐pVQZ, pcJ‐2 and pcJ‐3) using 68 organic molecular systems with 88 ¹J_CH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of ¹J_CH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root‐mean‐square deviations lie between 4.7 and 16.4 Hz and are reduced to 4–6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97‐2 functionals in combination with HIII‐su3, aug‐cc‐pVTZ‐J and pcJ‐2 basis sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Predicting adsorption enthalpies on silicalite and HZSM‐5: A benchmark study on DFT strategies addressing dispersion interactions

We evaluated the accuracy of periodic density functional calculations for adsorption enthalpies of water, alkanes, and alcohols in silicalite and HZSM‐5 zeolites using a gradient‐corrected density functional with empirical dispersion corrections (PBE‐D) as well as a nonlocal correlation functional (vdW‐DF2). Results of both approaches agree in acceptable fashion with experimental adsorption energies of alcohols in silicalite, but the adsorption energies for n‐alkanes in both zeolite models are overestimated, by 21?46 kJ mol^?1. For PBE‐D calculations, the adsorption of alkanes is exclusively determined by the empirical dispersion term, while the generalized gradient approximation‐DFT part is purely repulsive, preventing the molecule to come too close to the zeolite walls. The vdW‐DF2 results are comparable to those of PBE‐D calculations, but the latter values are slightly closer to the experiment in most cases. Thus, both computational approaches are unable to reproduce available experimental adsorption energies of alkanes in silicalite and HZSM‐5 zeolite with chemical accuracy. © 2014 Wiley Periodicals, Inc.     

Sensing Characteristics of a Graphene‐like Boron Carbide Monolayer towards Selected Toxic Gases

By using first‐principles calculations based on density functional theory, we study the adsorption efficiency of a BC₃ sheet for various gases, such as CO, CO₂, NO, NO₂, and NH₃. The optimal adsorption position and orientation of these gas molecules on the BC₃ surface is determined and the adsorption energies are calculated. Among the gas molecules, CO₂ is predicted to be weakly adsorbed on the graphene‐like BC₃ sheet, whereas the NH₃ gas molecule shows a strong interaction with the BC₃ sheet. The charge transfer between the molecules and the sheet is discussed in terms of Bader charge analysis and density of states. The calculated work function of BC₃ in the presence of CO, CO₂, and NO is greater than that of a bare BC₃ sheet. The decrease in the work function of BC₃ sheets in the presence of NO₂ and NH₃ further explains the affinity of the sheet towards the gas molecules. The energy gap of the BC₃ sheets is sensitive to the adsorption of the gas molecules, which implies possible future applications in gas sensors.     

Effect of the damping function in dispersion corrected density functional theory

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.     

Accurate description of van der Waals complexes by density functional theory including empirical corrections

An empirical method to account for van der Waals interactions in practical calculations with the density functional theory (termed DFT-D) is tested for a wide variety of molecular complexes. As in previous schemes, the dispersive energy is described by damped interatomic potentials of the form C6R(-6). The use of pure, gradient-corrected density functionals (BLYP and PBE), together with the resolution-of-the-identity (RI) approximation for the Coulomb operator, allows very efficient computations for large systems. Opposed to previous work, extended AO basis sets of polarized TZV or QZV quality are employed, which reduces the basis set superposition error to a negligible extend. By using a global scaling factor for the atomic C6 coefficients, the functional dependence of the results could be strongly reduced. The "double counting" of correlation effects for strongly bound complexes is found to be insignificant if steep damping functions are employed. The method is applied to a total of 29 complexes of atoms and small molecules (Ne, CH4, NH3, H2O, CH3F, N2, F2, formic acid, ethene, and ethine) with each other and with benzene, to benzene, naphthalene, pyrene, and coronene dimers, the naphthalene trimer, coronene. H2O and four H-bonded and stacked DNA base pairs (AT and GC). In almost all cases, very good agreement with reliable theoretical or experimental results for binding energies and intermolecular distances is obtained. For stacked aromatic systems and the important base pairs, the DFT-D-BLYP model seems to be even superior to standard MP2 treatments that systematically overbind. The good results obtained suggest the approach as a practical tool to describe the properties of many important van der Waals systems in chemistry. Furthermore, the DFT-D data may either be used to calibrate much simpler (e.g., force-field) potentials or the optimized structures can be used as input for more accurate ab initio calculations of the interaction energies.     

Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations

Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high-level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated-B-LYP, B3-LYP, PBE, TPSS, TPSSh, and BH-LYP-and even surpass the MP2/cc-pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, s(R), scaling globally the vdW radii. For good results, a basis set of at least triple-zeta quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen-bonded and stacked complexes considered, respectively.     

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.     

甲烷晶体的晶格能和弹性性质: 不同方法及泛函的评估

通过对甲烷晶体进行结构、晶格能和弹性特性的研究, 评估了不包含和包含色散能量修正的密度泛函理论的性能. 我们分别利用不包含色散能量修正的密度泛函理论(DFT) (包含不同的标准泛函和杂化泛函)和包含色散能量修正的密度泛函理论(DFT-D)计算了甲烷晶体特性, 并与实验作对比. 尽管DFT-D 与传统密度泛函理论及杂化密度泛函理论相比, 修正了甲烷晶体中的范德华(vdW)相互作用, 但是一些修正方案过分修正了这种相互作用. 因此, 人们在使用DFT-D方法时务必谨慎.     

Theoretical Modelling of Photoswitching of Hyperpolarisabilities in Ruthenium Complexes

Static excited‐state polarisabilities and hyperpolarisabilities of three Ru^II ammine complexes are computed at the density functional theory (DFT) and several correlated ab initio levels. Most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals B3LYP, B3P86 or M06 for the complex [Ru^II(NH₃)₅(MeQ⁺)]³⁺ (MeQ⁺=N‐methyl‐4,4′‐bipyridinium, 3 ) in acetonitrile. The match with experimental data is less good for [Ru^II(NH₃)₅L]³⁺ (L=N‐methylpyrazinium, 2 ; N‐methyl‐4‐{E,E‐4‐(4‐pyridyl)buta‐1,3‐dienyl}pyridinium, 4 ). These calculations confirm that the first dipole‐ allowed excited state (FDAES) has metal‐to‐ligand charge‐transfer (MLCT) character. Both the solution and gas‐phase results obtained for 3 by using B3LYP, B3P86 or M06 are very similar to those from restricted active‐space SCF second‐order perturbation theory (RASPT2) with a very large basis set and large active space. However, the time‐dependent DFT λ_max predictions from the long‐range corrected functionals CAM‐B3LYP, LC‐ωPBE and wB97XB and also the fully ab initio resolution of identity approximate coupled‐cluster method (gas‐phase only) are less accurate for all three complexes. The ground state (GS) two‐state approximation first hyperpolarisability β_2SA for 3 from RASPT2 is very close to that derived experimentally via hyper‐Rayleigh scattering, whereas the corresponding DFT‐based values are considerably larger. The β responses calculated by using B3LYP, B3P86 or M06 increase markedly as the π‐conjugation extends on moving along the series 2 → 4 , for both the GS and FDAES species. All three functionals predict substantial FDAES β enhancements for each complex, increasing with the π‐conjugation, up to about sevenfold for 4 . Also, the computed second hyperpolarisabilities γ generally increase in the FDAES, but the results vary between the different functionals.     

Performance of density functionals for modeling vapor liquid equilibria of CO2 and SO2

Vapor liquid equilibria (VLE) and condensed phase properties of carbon dioxide and sulfur dioxide are calculated using first principles Monte Carlo (FPMC) simulations to assess the performance of several density functionals, notably PBE‐D3, BLYP‐D3, PBE0‐D3, M062X‐D3, and rVV10. GGA functionals were used to compute complete vapor liquid coexistence curves (VLCCs) to estimate critical properties, while the hybrid and nonlocal van der Waals functionals were used only for computing density at a single state point due to the high computational cost. Our results show that the BLYP‐D3 functional performs well in predicting VLE properties for both molecules when compared with other functionals. In the liquid phase, pair correlation functions reveal that there is not a significant difference in the location of the peak for the first solvation shell while the peak heights are different for different functionals. Overall, the BLYP‐D3 functional is a good choice for modeling VLE of acidic gases with significant environmental implications such as CO₂ and SO₂. © 2017 Wiley Periodicals, Inc.     

On the accuracy of DFT methods in reproducing ligand substitution energies for transition metal complexes in solution: the role of dispersive interactions

The performance of a series of density functionals when tested on the prediction of the phosphane substitution energy of transition metal complexes is evaluated. The complexes Fe-BDA and Ru-COD (BDA=benzylideneacetone, COD=cyclooctadiene) serve as reference systems, and calculated values are compared with the experimental values in THF as obtained from calorimetry. Results clearly indicate that functionals specifically developed to include dispersion interactions usually outperform other functionals when BDA or COD substitution is considered. However, when phosphanes of different sizes are compared, functionals including dispersion interactions, at odd with experimental evidence, predict that larger phosphanes bind more strongly than smaller phosphanes, while functionals not including dispersion interaction reproduce the experimental trends with reasonable accuracy. In case of the DFT-D functionals, inclusion of a cut-off distance on the dispersive term resolves this issue, and results in a rather robust behavior whatever ligand substitution reaction is considered.     

Reparameterization of a meta-generalized gradient approximation functional by combining TPSS exchange with τ1 correlation

We present a new local meta-GGA exchange-correlation density functional by combining the TPSS meta-GGA exchange and the τ1 meta-GGA correlation functionals. The TPSS meta-GGA exchange-correlation and the τ1 meta-GGA correlation functionals have been implemented in the deMon code. The parameters in the τ1 meta-GGA correlation model are reoptimized in a synchronized way to match the original TPSS meta-GGA exchange counterpart. This reparametrized meta-GGA functional is referred to as “TPSSτ3”. The TPSSτ3 and TPSSτ1 meta-GGAs are validated using a test set that consists of covalent molecules, hydrogen-bonded complexes, and van der Waals interactions. The calculated results from TPSSτ1 and TPSSτ3 are analyzed and compared with reliable experimental data and theoretical data, as well as with those from Bmτ1 and TPSS calculations. The τ1 correlation model describes the aromatic compounds better than TPSS. TPSSτ3 yields satisfactory results for the covalent molecules, the hydrogen-bonded complexes, and the van der Waals complexes in the test set compared with TPSS, Bmτ1 and TPSSτ1. Contribution to the Serafin Fraga Memorial Issue.     

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.