Stacking of Metal Chelates with Benzene: Can Dispersion‐Corrected DFT Be Used to Calculate Organic–Inorganic Stacking?

CCSD(T)/CBS energies for stacking of nickel and copper chelates are calculated and used as benchmark data for evaluating the performance of dispersion‐corrected density functionals for calculating the interaction energies. The best functionals for modeling the stacking of benzene with the nickel chelate are M06HF‐D3 with the def2‐TZVP basis set, and B3LYP‐D3 with either def2‐TZVP or aug‐cc‐pVDZ basis set, whereas for copper chelate the PBE0‐D3 with def2‐TZVP basis set yielded the best results. M06L‐D3 with aug‐cc‐pVDZ gives satisfying results for both chelates. Most of the tested dispersion‐corrected density functionals do not reproduce the benchmark data for stacking of benzene with both nickel (no unpaired electrons) and copper chelate (one unpaired electron), whereas a number of these functionals perform well for interactions of organic molecules.     

A DFT study on Cu(I) coordination in Cu‐ZSM‐5: Effects of the functional choice and tuning of the ONIOM approach

The coordination of Cu⁺ at the T1 and T7 positions of the M7 ring of Cu‐ZSM‐5, and the interaction of NO with coordinated Cu⁺ were investigated by means of DFT/ONIOM calculations. The B3LYP, BLYP, PBE1PBE, PBE, M06, and M062X functionals with the def2‐TZVP (def2‐QZVP for Cu) basis set were used in the high‐level part of ONIOM calculations, with the HF/3‐21G, B3LYP/LANL2DZ, M06/LANL2DZ, and M062X/LANL2DZ methods in the low‐level part. The ability of suitable combinations of the above methods to reproduce (i) the crystallographic structure of purely siliceous ZSM‐5, (ii) the tendency of Cu⁺ to be twofold or fourfold coordinated by framework oxygen atoms of Cu‐ZSM‐5, and (iii) the interaction energy and the N? O stretching frequency of adsorbed nitrogen oxide are discussed, showing that different results are obtained depending on the adopted computational approach. With reference to above properties, some considerations about the employment of the ONIOM approximations are also included. © 2015 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.     

Computational studies on ethylene addition to nickel bis(dithiolene)

The density functionals B3LYP, B3PW91, BMK, HSE06, LC-ωPBE, M05, M06, O3LYP, TPSS, ω-B97X, and ω-B97XD are used to optimize key transition states and intermediates for ethylene addition to Ni(edt)(2) (edt = S(2)C(2)H(2)). The efficacy of the basis sets 6-31G**, 6-31++G**, cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ is also examined. The geometric parameters optimized with different basis sets and density functionals are similar and agree well with experimental values. The ω-B97XD functional gives relative energies closest to those from CCSD, while M06 and HSE06 yield results close to those from CCSD(T). CASSCF and CASSCF-PT2 calculation results are also given. Variation of the relative energies from different density functionals appears to arise, in part, from the multireference character of this system, as confirmed by the T1 diagnostic and CASSCF calculations.     

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.     

A TDDFT investigation of bay substituted perylenediimides: Absorption and intersystem crossing

The conformational structure and electronic spectra properties of a series of bay substituted perylenediimides (PDI) derivatives have been investigated by means of density functional theory (DFT) and time‐dependent DFT. The B3LYP and PBE0 hybrid exchange‐correlation functionals were applied in conjunction with the double‐ζ quality SVP basis set. These compounds are interesting for organic materials science and as photosensitizers in cancer phototherapy (PDT), because of their intense absorption in the visible region. Results show that the substitution at the bay position of the PDI parent molecule with N‐alkyl groups shifts the absorption maxima towards the red part of the visible spectrum (around 650–700 nm) as required for the applications in PDT. The main PDT action mechanisms have been investigated by computing of electron affinities, ionization potentials, triplet energies and spin‐orbit matrix elements between singlet and triplet excited states. © 2012 Wiley Periodicals, Inc.     

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

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

Calculations of ionization energies and electron affinities for atoms and molecules: A comparative study with different methods

In the present work, we examined the performance of 36 density functionals, including the newly developed doubly hybrid density functional XYG3 (Y. Zhang, X. Xu, and W. A. Goddard III, Proc. Natl. Acad. Sci, USA, 2009, 106, 4963), to calculate ionization energies (IEs) and electron affinities (EAs). We used the well-established G2-1 set as reference, which contains 14 atoms and 24 molecules for IE, along with 7 atoms and 18 molecules for EA. XYG3 leads to mean absolute deviations (MADs) of 0.057 and 0.080 eV for IEs and EAs, respectively, using the basis set of 6-311 + G (3df,2p). In comparison with some other functionals, MADs for IEs are 0.109 (B2PLYP), 0.119 (M06-2X), 0.159 (X3LYP), 0.161 (PBE), 0.162 (B3LYP), 0.165 (PBE0), 0.173 (TPSS), 0.200 (BLYP), and 0.215 eV (LC-BLYP). MADs for EAs are 0.090 (X3LYP), 0.090 (B2PLYP), 0.102 (PBE), 0.103 (M06-2X), 0.104 (TPSS), 0.105 (BLYP), 0.106 (B3LYP), 0.126 (LC-BLYP), and 0.128 eV (PBE0).     

DFT,DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T₁ and T₂ diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.     

How computational methods and relativistic effects influence the study of chemical reactions involving Ru‐NO complexes?

Two treatments of relativistic effects, namely effective core potentials (ECP) and all‐electron scalar relativistic effects (DKH2), are used to obtain geometries and chemical reaction energies for a series of ruthenium complexes in B3LYP/def2‐TZVP calculations. Specifically, the reaction energies of reduction ( A ‐ F ), isomerization ( G‐I ), and Cl⁻ negative trans influence in relation to NH₃ ( J ‐ L ) are considered. The ECP and DKH2 approaches provided geometric parameters close to experimental data and the same ordering for energy changes of reactions A ‐ L . From geometries optimized with ECP, the electronic energies are also determined by means of the same ECP and basis set combined with the computational methods: MP2, M06, BP86, and its derivatives, so as B2PLYP, LC‐wPBE, and CCSD(T) (reference method). For reactions A ‐ I , B2PLYP provides the best agreement with CCSD(T) results. Additionally, B3LYP gave the smallest error for the energies of reactions J ‐ L . © 2017 Wiley Periodicals, Inc.     

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     

Role of nonlocal exchange in molecular crystals: The case of two proton‐ordered phases of ice

We present a periodic density functional theory investigation of twoproton‐ordered phases of ice. Their equilibrium lattice parameters,relative stabilities, formation energies, and densities of states havebeen evaluated. Nine exchange‐correlation functionals, representativeof the generalized gradient approximation (GGA), global hybrids,range‐separated hybrids, meta‐GGA, and hybrid meta‐GGA families havebeen taken into account, considering two oxygen basis sets. Althoughthe hydrogen‐bond network of ice is well reproduced at the B3LYP,M06‐L, or LC‐ wPBE levels, formation energies are only correctlyevaluated with the two former functionals. Band gaps on the other handare only quantitatively reproduced at the B3LYP level. These resultsindicate that this last functional, a de facto reference formolecular calculations, gives in average the most accurate results forthe considered ice properties. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Performance of Density Functional Theory for Transition Metal Oxygen Bonds

The accuracy of density functional theory (DFT) limits predictions in theoretical catalysis, and strong chemical bonds between transition metals and oxygen pose a particular challenge. We benchmarked 30 diverse density functionals against the bond dissociation enthalpies (BDE) of the 30 MO and 30 MO⁺ diatomic systems of all the 3d, 4d, and 5d metals, to test universality across the d-block as required in comparative studies. Seven functionals, B98, B97-1, B3P86, B2PLYP, TPSSh, B3LYP, and B97-2, display mean absolute errors (MAE) <30 kJ/mol. In contrast, many commonly used functionals such as PBE and RPBE overestimate M−O bonding by +30 kJ/mol and display MAEs from 48–76 kJ/mol. RPBE and OPBE reduce the over-binding of PBE but remain very inaccurate. We identify a linear relationship (p-value 7.6 ⋅ 10⁻⁵) between the precision and accuracy of DFT, i. e. inaccurate functionals tend to produce larger, unpredictable random errors. Some functionals commonly deviate from this relationship: Thus, M06-2X is very precise but not very accurate, whereas B3LYP* and MN15-L are more accurate but less precise than M06-2X. The best-performing hybrids have 10–30 % HF exchange, but this can be relieved by double hybrids (B2PLYP). Most functionals describe trends well, but errors comparing 5d to 4d/3d are ∼10 kJ/mol larger than group-wise errors, due to uncertainties in the spin-orbit coupling corrections for effective core potentials, affecting e. g. Pt/Pd or Au/Ag comparisons.     

Calculation of the Vibrationally Resolved,Circularly Polarized Luminescence of d‐Camphorquinone and (S,S)‐trans‐β‐Hydrindanone

Circularly polarized luminescence (CPL), the differential emission of left‐ and right‐handed circularly polarized light from a molecule, is modeled by using time‐dependent density functional theory. Calculations of the CPL spectra for the first electronic excited states of d‐camphorquinone and (S,S)‐trans‐β‐hydrindanone under the Franck–Condon approximation and using various functionals are presented, as well as calculations of absorption, emission, and circular dichroism spectra. The functionals B3LYP, BHLYP, and CAM‐B3LYP are employed, along with the TZVP and aug‐cc‐pVDZ Gaussian‐type basis sets. For the lowest‐energy transitions, all functionals and basis sets perform comparably, with the long‐range‐corrected CAM‐B3LYP better reproducing the excitation energy of camphorquinone but leading to a blue shift with respect to experiment for hydrindanone. The vibrationally resolved spectra of camphorquinone are very well reproduced in terms of peak location, widths, shapes, and intensities. The spectra of hydrindanone are well reproduced in terms of overall envelope shape and width, as well as the lack of prominent vibrational structure in the emission and CPL spectra. Overall the simulated spectra compare well with experiment, and reproduce the band shapes, emission red shifts, and presence or absence of visible vibrational fine structure.     

Performance of range‐separated hybrid exchange–correlation functionals for the calculation of magnetic exchange coupling constants of organic diradicals

The prediction of magnetic behavior is important for the design of new magnetic materials. Kohn–Sham density functional theory is popular for this purpose, although one should be careful about choosing the right exchange–correlation functional. Here, we perform a statistical analysis to test different range‐separated hybrid density functionals for the calculation of magnetic exchange coupling constants J of fourteen organic diradicals. Our analysis suggests that in absolute terms the MN12SX functional performs best among the series of twelve functionals studied here (including the popular B3LYP), followed by N12SX functionals along with Scuseria's HSE series of functionals. LC‐ PBE was found to be the least accurate, which is in contrast with its good performance for calculating J for transition metal complexes. The HSE family of functionals and B3LYP are the only functionals to reproduce the qualitative trends of the coupling constants correctly for the ferromagnetically coupled diradicals under study. © 2017 Wiley Periodicals, Inc.     

Quantum mechanical modeling of Zn-based spinel oxides: Assessing the structural,vibrational, and electronic properties

The structural, electronic, and vibrational properties of two leading representatives of the Zn-based spinel oxides class, normal ZnX₂O₄ (X = Al, Ga, In) and inverse Zn₂MO₄ (M = Si, Ge, Sn) crystals, were investigated. In particular, density functional theory (DFT) was combined with different exchange-correlation functionals: B3LYP, HSE06, PBE0, and PBESol. Our calculations showed good agreement with the available experimental data, showing a mean percentage error close to 3% for structural parameters. For the electronic structure, the obtained HSE06 band-gap values overcome previous theoretical results, exhibiting a mean percentage error smaller than 10.0%. In particular, the vibrational properties identify the significant differences between normal and inverse spinel configurations, offering compelling evidence of a structure-property relationship for the investigated materials. Therefore, the combined results confirm that the range-separated HSE06 hybrid functional performs the best in spinel oxides. Despite some points that cannot be directly compared to experimental results, we expect that future experimental work can confirm our predictions, thus opening a new avenue for understanding the structural, electronic, and vibrational properties in spinel oxides.     

Evaluation of range-separated hybrid density functionals for the prediction of vibrational frequencies, infrared intensities, and Raman activities

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-omegaPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.