Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite Mg2SiO4

The performance of six different density functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in describing the infrared spectrum of forsterite, a crystalline periodic system with orthorhombic unit cell (28 atoms in the primitive cell, Pbmn space group), is investigated by using the periodic ab initio CRYSTAL09 code and an all‐electron Gaussian‐type basis set. The transverse optical (TO) branches of the 35 IR active modes are evaluated at the equilibrium geometry together with the oscillator strengths and the high‐frequency dielectric tensor ?_∞. These quantities are essential to compute the dielectric function ?(ν), and then the reflectance spectrum R(ν), which is compared with experiment. It turns out that hybrid functionals perform better than LDA and GGA, in general; that B3LYP overperforms WC1LYP and, in turn, PBE0; that PBESOL is better than PBE; that LDA is the worst performing functional among the six under study. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

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.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

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.     

How reliable is DFT in predicting relative energies of polycyclic aromatic hydrocarbon isomers? comparison of functionals from different rungs of jacob's ladder

Density functional theory (DFT) is the only quantum‐chemical avenue for calculating thermochemical/kinetic properties of large polycyclic aromatic hydrocarbons (PAHs) such as graphene nanoflakes. Using CCSD(T)/CBS PAH isomerization energies, we find that all generalized gradient approximation (GGA) and meta GGA DFT functionals have severe difficulties in describing isomerization energies in PAHs. The poor performance of these functionals is demonstrated by the following root‐mean‐square deviations (RMSDs) obtained for a database of C₁₄H₁₀ and C₁₈H₁₂ isomerization energies. The RMSDs for the GGAs range between 6.0 (BP86‐D3) and 23.0 (SOGGA11) and for the meta GGAs they range between 3.5 (MN12‐L) and 11.9 (τ‐HCTH) kJ mol⁻¹. These functionals (including the dispersion‐corrected methods) systematically and significantly underestimate the isomerization energies. A consequence of this behavior is that they all predict that chrysene (rather than triphenylene) is the most stable C₁₈H₁₂ isomer. A general improvement in performance is observed along the rungs of Jacob's Ladder; however, only a handful of functionals from rung four give good performance for PAH isomerization energies. These include functionals with high percentages (40–50%) of exact Hartree–Fock exchange such as the hybrid GGA SOGGA11‐X (RMSD = 1.7 kJ mol⁻¹) and the hybrid‐meta GGA BMK (RMSD = 1.3 kJ mol⁻¹). Alternatively, the inclusion of lower percentages (20–30%) of exact exchange in conjunction with an empirical dispersion correction results in good performance. For example, the hybrid GGA PBE0‐D3 attains an RMSD of 1.5 kJ mol⁻¹, and the hybrid‐meta GGAs PW6B95‐D3 and B1B95‐D3 result in RMSDs below 1 kJ mol⁻¹. © 2016 Wiley Periodicals, Inc.     

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.     

Assessment of dispersion‐improved exchange‐correlation functionals for the simulation of CO2 binding by alcoholamines

In this study, 12 bound complexes were selected to construct a database for testing 15 dispersion‐improved exchange‐correlation (XC) functionals, including hybrid generalized gradient approximation (GGA), modified using the Grimme's pairwise strategy, and double hybrid XC functionals, for specifically characterizing the CO₂ binding by alcoholamines. Bound complexes were selected based on the characteristics of their hydrogen bonds, dispersion, and electrostatic (particularly between the positive charge of CO₂ and the lone pair of N of alcoholamines) interactions. The extrapolated binding energy from the aug‐cc‐pVTZ (ATZ) to aug‐cc‐pVQZ (AQZ) basis set at the CCSD(T)/CBS(MP2+DZ) level was used as the reference for the XC functional comparison. M06‐2X produced the optimal agreement if the optimized geometries at MP2/ATZ level were chosen for all the test bound complexes. However, M06‐L, ωB97X, and ωB97, and were preferred if the corresponding density functional theory (DFT) optimized geometries were adapted for the benchmark. Simple bimolecular reaction between CO₂ and monoethanolamine simulated using polarizable continuum solvation model confirmed that ωB97, ωB97X, and ωB97XD qualitatively reproduced the energetics of MP2 level. The inconsistent performance of the tested XC functionals, observed when using MP2 or DFT optimized geometries, raised concerns regarding using the single‐point ab initio correction combined with DFT optimized geometry, particularly for determining the nucleophilic attack by alcoholamines to CO₂. © 2014 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.     

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

Density functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (M_S = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being M_S = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, g_av, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about ?7 cm^?1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Assessment of density functionals for the high-spin/low-spin energy difference in the low-spin iron(II) tris(2,2'-bipyridine) complex.

In the iron(II) low-spin complex [Fe(bpy)3]2+, the zero-point energy difference between the 5T2g(t4(2g)e2g) high-spin and the 1A(1g)(t(6)2g) low-spin states, Delta(E)0HL, is estimated to lie in the range of 2500-5000 cm(-1). This estimate is based on the low-temperature dynamics of the high-spin-->low-spin relaxation following the light-induced population of the high-spin state and on the assumption that the bond-length difference between the two states Delta(r)HL is equal to the average value of approximately 0.2 A, as found experimentally for the spin-crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low-spin-state optimised geometries are found to be in very good agreement with the experimental X-ray structure of the complex and the predicted high-spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of Delta(E)0HL from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from -1000 to 12000 cm(-1), the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment.     

Density functional theory study of trans-dioxo complexes of iron, ruthenium, and osmium with saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), and detection of [Fe(qpy)(O)2]n+ (n=1, 2) by high-resolution ESI mass spectrometry

Density functional theory (DFT) calculations on trans-dioxo metal complexes containing saturated amine ligands, trans-[M(O)2(NH3)2(NMeH2)2]2+ (M=Fe, Ru, Os), were performed with different types of density functionals (DFs): 1) pure generalized gradient approximations (pure GGAs): PW91, BP86, and OLYP; 2) meta-GGAs: VSXC and HCTH407; and 3) hybrid DFs: B3LYP and PBE1PBE. With pure GGAs and meta-GGAs, a singlet d2 ground state for trans-[Fe(O)2(NH3)2(NMeH2)2]2+ was obtained, but a quintet ground state was predicted by the hybrid DFs B3LYP and PBE1PBE. The lowest transition energies in water were calculated to be at lambda approximately 509 and 515 nm in the respective ground-state geometries from PW91 and B3LYP calculations. The nature of this transition is dependent on the DFs used: a ligand-to-metal charge-transfer (LMCT) transition with PW91, but a pi(Fe-O)-->pi*(Fe-O) transition with B3LYP, in which pi and pi* are the bonding and antibonding combinations between the dpi(Fe) and ppi(O(2-)) orbitals. The FeVI/V reduction potential of trans-[Fe(O)2(NH3)2NMeH2)2]2+ was estimated to be +1.30 V versus NHE based on PW91 results. The [Fe(qpy)(O)2](n+) (qpy=2,2':6',2':6',2':6',2'-quinquepyridine; n=1 and 2) ions, tentatively assigned to dioxo iron(V) and dioxo iron(VI), respectively, were detected in the gas phase by high-resolution ESI-MS spectroscopy.     

Periodic DFT investigation on the structure and properties of TNAD crystal

Density function theory calculations were performed at the GGA/PW91, GGA/PBE, and LDA/CA‐PZ levels to study the structures and properties of the crystalline TNAD (trans‐1,4,5,8‐tetranitrotetraazadecalin). The relaxed crystal structure compares well with the experimental data. Analysis on the band structures shows that the frontier energy bands are generally quite flat, and the energy gap between the highest occupied crystal orbital and the lowest unoccupied crystal orbital is about 3.4 eV, indicating that the crystal is an electrical insulator. All the atoms of TNAD make up both the lower and the higher energy bands. The projection of density of state demonstrates that the N? NO₂ bond is the most reactive region of the material. The lattice energy is predicted to be ?155.13 kJ/mol at the LDA/CA‐PZ level, consistent with the previous studies, whereas it is underestimated by the GGA/PW91 (?70.41 kJ/mol) and GGA/PBE (?74.33 kJ/mol). The optical properties under ambient condition were investigated, including dielectric function, absorption coefficient, and reflectivity. The calculated absorption spectra show a number of absorption peaks in the fundamental absorption region, which are believed to be associated with different exciton states. And the reflectivity spectra are mainly composed of four peak structures, where the magnitude changes in the order of GGA/PBE < GGA/PW91 < LDA/CA‐PZ on the whole. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical study of the magnetic exchange coupling behavior substituting Cr(III) with Mo(III) in cyano‐bridged transition metal complexes

Molecular magnetism in a series of cyano‐bridged first and second transition metal complexes has been investigated using density functional theory (DFT) combined with the broken‐symmetry (BS) approach. Several exchange‐correlation (XC) functionals in the ADF package were used to investigate complexes I [?(Me₃tacn)₂(cyclam)NiMo₂(CN)₆]²⁺, II [?(Me₃tacn)₂(cyclam)Ni‐Cr₂(CN)₆]²⁺, III [(Me₃tacn)₆MnMo₆(CN)₁₈]²⁺, and IV [(Me₃tacn)₆MnCr₆(CN)₁₈]²⁺ (Me₃tacn = N,N′,N?‐trimethyl‐1,4,7‐triazacyclononane). For models A (the molded structure of complex I) and B (the modeled structure of complex II), all the XCs given qualitatively reasonable results and predict ferromagnetic coupling character between M (M = Mo^III for A or Cr^III for B) and Ni^II in coincidence with the experimental results (see Tables I and II ). The calculated using Operdew, OPBE, O3LYP, and B3LYP functionals and experimental J values show that substituting Cr^III with Mo^III will enhance the ferromagnetic exchange coupling interactions. But VWN, PW91, PBE, VSXC, and tau‐HCTH functionals have no way to differentiate the relative strength of the intramolecular magnetic exchange coupling interactions of A and B correctly. For models C (the modeled structure of complex III) and D (the modeled structure of complex IV), all the XCs in ADF and B3LYP in Gaussian 03 with several basis sets show that substituting Cr^III with Mo^III will enhance the antiferromagnetic exchange coupling interactions. From the above calculations, the substitution of Cr^III by Mo^III will enhance the magnetic coupling interactions, whether the magnetic coupling interactions are ferro‐ or antiferromagnetic. Moreover, Kahn's model was applied to investigate the above facts. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 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.     

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.