Basis Set Effects Research Articles

Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules.

Benchmark scalar-relativistic coupled-cluster calculations for dissociation energies of the 20 diatomic molecules containing 3d transition metals in the 3dMLBE20 database ( J. Chem. Theory Comput. 2015 , 11 , 2036 ) are reported. Electron correlation and basis set effects are systematically studied. The agreement between theory and experiment is in general satisfactory. For a subset of 16 molecules, the standard deviation between computational and experimental values is 9 kJ/mol with the maximum deviation being 15 kJ/mol. The discrepancies between theory and experiment remain substantial (more than 20 kJ/mol) for VH, CrH, CoH, and FeH. To explore the source of the latter discrepancies, the analysis used to determine the experimental dissociation energies for VH and CrH is revisited. It is shown that, if improved values are used for the heterolytic C-H dissociation energies of di- and trimethylamine involved in the experimental determination, the experimental values for the dissociation energies of VH and CrH are increased by 18 kJ/mol, such that D0(VH) = 223 ± 7 kJ/mol and D0(CrH) = 204 ± 7 kJ/mol (or De(VH) = 233 ± 7 kJ/mol and De(CrH) = 214 ± 7 kJ/mol). The new experimental values agree quite well with the calculated values, showing the consistency of the computation and the measured reaction thresholds.

Testing the CP-correction procedure with different DFT methods on H-bonding complexes of κ-carrabiose with water molecules.

Interaction of water molecules with κ-carrabiose disaccharide, within three H-bonding complexes, was investigated. Particular interest was focused on the way with which the BSSE correction has to be performed. Two strategies were used, either performing BSSE correction during or after optimization. For this aim, several DFT-functionals (hybrid GGA and hybrid meta-GGA) and 6-31 + G* basis set were considered. The results demonstrated the uselessness of including of BSSE-CP correction during optimization for all complexes. From a structural point of view, a proper H-bonding description was obtained using the PBE0 functional for all complexes. The basis set effect on the BSSE using B3LYP functional was also investigated. The reliability of B3LYP/6-31 + G** and B3LYP/6-31++G** models for the complexes involving one or two water molecules was reported while the use of B3LYP/6-311 + G** or B3LYP/6-311++G** levels was shown to be more appropriate for larger complexes equivalent to that involving three water molecules. CP-corrected interaction energies were demonstrated to be closer to CBS-4M interaction energies than the uncorrected ones. Graphical abstract Functional and basis set effects on BSSE.

Density functional modelling studies of chloride-substituted Schiff bases as corrosion inhibitors: Optimized geometries, atomic charges, solvent and non-linear optical effects

The anti-corrosive properties, optimized geometrical structures, atomic charges, molecular electrostatic potential (MEP) surfaces and non-linear optical (NLO) effects of some chloride-substituted Schiff bases salicylaldimine (R), N-(2-chlorophenyl)salicyaldimine (2Cl–R), N-(3-chlorophenyl)salicyaldimine (3Cl–R) and N-(4-chlorophenyl)salicyaldimine (4Cl–R) have been investigated by using density functional modelling calculations. The quantum chemical parameters, such as the highest occupied molecular orbital, the lowest unoccupied molecular orbital, gap energy and other parameters, including electronegativity, global hardness, the total charges on the whole molecules and the total energies have been calculated and discussed to obtain information about the relationships between the molecular and electronic structures of the studied inhibitors and their experimental corrosion inhibition efficiencies. The linear polarizability (α), and the firstorder hyperpolarizability (β) have been also predicted by the density functional theory (DFT) with different base sets 6-31G(d), 6-31+G(d,p), 6-31++G(d,p), 6-311+G(d) and 6-311++G(d,p) for investigating the effects of basis sets on the NLO properties.

Accuracy of Coupled Cluster Excitation Energies in Diffuse Basis Sets.

We present a comprehensive statistical analysis on the accuracy of various excited state Coupled Cluster methods, accentuating the effect of diffuse basis sets on vertical excitation energies of valence and Rydberg-type states. Many popular approximate doubles and triples methods are benchmarked with basis sets up to aug-cc-pVTZ, with high level EOM-CCSDT results used as reference. The results reveal a serious deficiency of CC2 linear response and CIS(D) techniques in the description of Rydberg states, a feature not shown by the EOM-CCSD(2) and EOM-CCSD variants. The CC3 theory proves to be an accurate choice among the iterative approximate triples methods, while the novel perturbation-based CCSD(T)(a)* variant turns out to be the best way to include the effect of triple excitations in a noniterative way.

Probing Electronic Wave Functions of Sodium-Doped Clusters: Dyson Orbitals, Anisotropy Parameters, and Ionization Cross-Sections.

We apply high-level ab initio methods to describe the electronic structure of small clusters of ammonia and dimethyl ether (DME) doped with sodium, which provide a model for solvated electrons. We investigate the effect of the solvent and cluster size on the electronic states. We consider both energies and properties, with a focus on the shape of the electronic wave function and the related experimental observables such as photoelectron angular distributions. The central quantity in modeling photoionization experiments is the Dyson orbital, which describes the difference between the initial N-electron and final (N-1)-electron states of a system. Dyson orbitals enter the expression of the photoelectron matrix element, which determines total and partial photoionization cross-sections. We compute Dyson orbitals for the Na(NH3)n and Na(DME)m clusters using correlated wave functions (obtained with equation-of-motion coupled-cluster model for electron attachment with single and double substitutions) and compare them with more approximate Hartree-Fock and Kohn-Sham orbitals. We also analyze the effect of correlation and basis sets on the shapes of Dyson orbitals and the experimental observables.

Basis set effects on the geometry of C96H24

C96H24 has D6h symmetry using the 4-31G, 6-31G, cc-pVDZ, or cc-pVTZ basis sets, but has lower symmetry if the 6-31G∗∗ or 6-311G∗∗ basis sets are used. Changing the carbon 3d exponent in the 6-31G∗∗ basis set can restore the D6h symmetry, but raises the total energy. The question of geometry vs basis set is discussed.

Benchmarking the DFT methodology for assessing antioxidant-related properties: quercetin and edaravone as case studies

The overall objective was to identify an accurate computational electronic method to virtually screen phenolic compounds through their antioxidant and free-radical scavenging activity. The impact of a key parameter of the density functional theory (DFT) approach was studied. Performances of the 21 most commonly used exchange-correlation functionals are thus detailed in the evaluation of the main energetic parameters related to the activities of two prototype antioxidants, namely quercetin and edaravone, is reported. These functionals have been chosen among those belonging to three different families of hybrid functionals, namely global, range separated, and double hybrids. Other computational parameters have also been considered, such as basis set and solvent effects. The selected parameters, namely bond dissociation enthalpy (BDE), ionization potential (IP), and proton dissociation enthalpy (PDE) allow a mechanistic evaluation of the antioxidant activities of free radical scavengers. Our results show that all the selected functionals provide a coherent picture of these properties, predicting the same order of BDEs and PDEs. However, with respect to the reference values, the errors found at CBS-Q3 level significantly vary with the functional. Although it is difficult to evidence a global trend from the reported data, it clearly appears that LC-ωPBE, M05-2X, and M06-2X are the most suitable approaches for the considered properties, giving the lowest cumulative mean absolute errors. These methods are therefore suggested for an accurate and fast evaluation of energetic parameters related to an antioxidant activity via free radical scavenging.

How Accurate is DFT for Iridium-Mediated Chemistry?

Iridium chemistry is versatile and widespread, with superior performance for reaction types such as enantioselective hydrogenation and C–H activation. In order to gain insight into the mechanistic details of such systems, density functional theory (DFT) studies are often employed. But how accurate is DFT for modeling iridium-mediated transformations in solution? We have evaluated how well DFT reproduces the energies and reactivities of 11 iridium-mediated transformations, which were carefully chosen to correspond to elementary steps typically encountered in iridium-catalyzed chemistry (bond formation, isomerization, ligand substitution, and ligand association). Five DFT functionals, B3LYP, PBE, PBE0, M06L, and M11L, were evaluated as-is or in combination with an empirical dispersion correction (D2, D3, or D3BJ), leading to 13 combinations. Different solvent models (IEFPCM and SMD) were evaluated, alongside various correction terms such as big basis set effects, counterpoise corrections, frequency scaling,...

A theoretical study of intramolecular H–bonding and metal–ligand interactions in some complexes with bicyclic guanidine ligands

The reported complexes formulated as [MnCl2(hppH)2] (1), [FeCl2(hppH)2] (2), and [NiCl2(hppH)2] (3) and a new theoretically designed example, [CuCl2(hppH)2] (4), have been used for calculations at the B3LYP/LANL2DZ/6-311G (d, p) level of density functional theory (DFT). The intramolecular hydrogen bonds (HB) NH⋯Cl could followed through their physicochemical properties such as, vibrational frequency, electronic transmission in UV–Visible spectroscopy, metal–ligand donor–acceptor interactions in NBO analysis, total energy and frontier molecular orbital energy. These properties influenced by the relationship of structure and metal–ligand electron density exchange will be discussed. The computations revealed that the stronger NH⋯Cl HB exists in complexes with longer MCl and MNimine bonds and shorter H⋯Cl bond, and vice versa that confirms the shortest and longest HBs in 4 and 3, respectively. These results agree with the second–order perturbation energies obtained by NBO analysis within charge transfer from the proton–acceptor chlorine to the p∗ orbital of the N atom. The calculated electronic absorption spectra by TD–DFT calculations show the larger Cl− to M2+ donation in 2 and 3 in comparison with 1 and 4 that confirms the stronger HB in 1 and 4 compared to 2 and 3. In order to find the basis set effect on the structure, vibrational frequencies, and electronic transitions, we use another basis set def2-TZVP includes polarization function for Mn element in complex 1. The obtained test results showed unremarkable differences between two basis sets LANL2DZ and def2-TZVP (cf. Figs. S2, S3 and Tables S1 and S2 in Supplementary Materials).

Assessment of Contemporary Theoretical Methods for Bond Dissociation Enthalpies

The density functional theory (DFT) is the most popular method for evaluating bond dissociation enthalpies (BDEs) of most molecules. Thus, we are committed to looking for alternative methods that can balance the computational cost and higher precision to the best for large systems. The performance of DFT, double-hybrid DFT, and high-level composite methods are examined. The tested sets contain monocyclic and polycyclic aromatic molecules, branched hydrocarbons, small inorganic molecules, etc. The results show that the mPW2PLYP and G4MP2 methods achieve reasonable agreement with the benchmark values for most tested molecules, and the mean absolute deviations are 2.43 and 1.96 kcal/mol after excluding the BDEs of branched hydrocarbons. We recommend the G4MP2 is the most appropriate method for small systems (atoms number≤20); the double-hybrid DFT methods are advised for large aromatic molecules in medium size (20≤atoms number≤50), and the double-hybrid DFT methods with empirical dispersion correction are recommended for long-chain and branched hydrocarbons in the same size scope; the DFT methods are advised to apply for large systems (atoms number≥50), and the M06-2X and B3P86 methods are also favorable. Moreover, the differences of optimized geometry of different methods are discussed and the effects of basis sets for various methods are investigated.

Coupled-cluster interpretation of the photoelectron spectrum of Ag3 (.).

We use the scalar relativistic ionized equation-of-motion coupled-cluster (IP-EOMCC) approaches to investigate the photoelectron spectrum of Ag3 (-), examining the effects of basis set, number of correlated electrons, level of applied theory including up to 3-hole-2-particle terms, and geometry relaxation. By employing an IP-EOMCC-based extrapolation scheme, we are able to provide an accurate interpretation and complete assignment of peaks and other key features in the experimentally observed spectra, including electron binding energies as high as about 6.5 eV.

F2 dimer: Improved intermolecular potential energy surface using ab initio calculations

AbstractA computational study on the intermolecular potential energy of 44 different orientations of F2 dimers is presented. Basis set superposition error (BSSE) corrected potential energy surface is calculated using the supermolecular approach at CCSD(T) and QCISD(T) levels of theory. The interaction energies obtained using the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets are extrapolated to the complete basis set limit using the latest extrapolation scheme. The basis set effect is checked and it is found that the extrapolated intermolecular energies provide the best compromise between the accuracy and computational cost. Among 1320 energy points of F2–F2 system covering more relative orientations, the most stable structure of the dimers was obtained with a well depth of −146.62 cm−1 that related to cross configuration, and the most unstable structure is related to linear orientation with a well depth of −52.63 cm−1. The calculated second virial coefficients are in good agreement with experimental data. The latest extrapolation scheme of the complete basis set limit at the CCSD(T) level of theory is used to determine the intermolecular potential energy surface of the F2 dimer. Comparing the results obtained by the latest scheme with those by older schemes show that the new approach provides the best compromise between accuracy and computational cost.

Density functional theory study of substituent effects on gas‐phase heterolytic Fe–O and Fe–S bond energies of m‐G‐C6H4OFe(CO)2(η5‐C5H5) and m‐G‐C6H4SFe(CO)2(η5‐C5H5)

The knowledge of accurate bond strengths is a fundamental basis for a proper analysis of chemical reaction mechanisms. Quantum chemical calculations at different levels of theory have been used to investigate heterolytic Fe–O and Fe–S bond energies of (meta‐substituted phenoxy)dicarbonyl(η5‐cyclopentadienyl) iron [m‐G‐C6H4OFp (1)] and (meta‐substituted benzenethiolato)dicarbonyl(η5‐cyclopentadienyl) iron [m‐G‐C6H4SFp (2)] complexes. In this study, Fp is (η5‐C5H5)Fe(CO)2, and G is NO2, CN, COMe, CO2Me, CF3, Br, Cl, F, H, Me, MeO, and NMe2. The results show that Tao–Perdew–Staroverov–Scuseria and Becke's power‐series ansatz from 1997 with dispersion corrections functionals can provide the best price/performance ratio and accurate predictions of ΔHhet(Fe–O)'s and ΔHhet(Fe–S)'s. The excellent linear free energy relations [r = 1.00 (g, 1e), 1.00 (g, 2b)] among the ΔΔHhet (Fe–O)'s and δΔG0 of OH bonds of m‐G‐C6H4OH or ΔΔHhet(Fe–S)'s and ΔpKa's of SH bonds of m‐G‐C6H4SH imply that the governing structural factors for these bond scissions are similar. And, the linear correlations [r = −0.97 (g, 1 g), −0.97 (g, 2 h)] among the ΔΔHhet (Fe–O)'s or ΔΔHhet(Fe–S)'s and the substituent σm constants show that these correlations are in accordance with Hammett linear free energy relationships. The inductive effects of these substituents and the basis set effects influence the accuracy of ΔHhet(Fe–O)'s or ΔHhet(Fe–S)'s. The ΔΔHhet(Fe–O)'s(g) (1) and ΔΔHhet(Fe–S)'s(g)(2) follow the capto‐dative Principle. The substituent effects on the Fe–O bonds are much stronger than those on the less polar Fe–S bonds. Insight from this work may help the design of more effective catalytic processes. Copyright © 2016 John Wiley & Sons, Ltd.

Ab initio study of reactive collisions between Rb((2)S) or Rb((2)P) and OH(-)((1)Σ(+)).

A theoretical rate constant for the associative detachment reaction Rb((2)S) + OH(-)((1)Σ(+)) → RbOH((1)Σ(+)) + e(-) of 4 × 10(-10) cm(3) s(-1) at 300 K has been calculated. This result agrees with the experimental rate constant of 2-1 (+2)×10(-10)cm(3)s(-1) obtained by Deiglmayr et al. [Phys. Rev. A 86, 043438 (2012)] for a temperature between 200 K and 600 K. A Langevin-based dynamics which depends on the crossing point between the anion (RbOH(-)) and neutral (RbOH) potential energy surfaces has been used. The calculations were performed using the ECP28MDF effective core potential to describe the rubidium atom at the CCSD(T) level of theory and extended basis sets. The effect of ECPs and basis set on the height of the crossing point, and hence the rate constant, has been investigated. The temperature dependence of the latter is also discussed. Preliminary work on the potential energy surface for the excited reaction channel Rb((2)P) + OH(-)((1)Σ(+)) calculated at the CASSCF-icMRCI level of theory is presented. We qualitatively discuss the charge transfer and associative detachment reactions arising from this excited entrance channel.

Optical and electrical properties of purpurin and alizarin complexone as sensitizers for dye-sensitized solar cells

The optical and electrical properties of two dyes purpurin (1,2,4-trihydroxy-9, 10-anthracenedione) and alizarin complexone (alizarin-3-methylimino-N,N-diacetic acid) as sensitizers for dye-sensitized solar cells were investigated by using UV–Vis spectrum, FT-IR spectrum, cyclic voltammetry and I–V (current–voltage) characteristics. In addition, electrochemical impedance spectroscopy was adopted to research the electrons transfer process between each interface of the dye-sensitized solar cell. For comparison with the experiments, the frontier molecular orbitals, vibration analysis, the total static first hyperpolarizability and driving force of electron injection were calculated by using density functional theory (DFT) with B3LYP, at 6-31G(d) basis set. Moreover, the transition properties were investigated by using time-dependent density functional theory (TD-DFT) with PBEPBE functional at 6-311+G(d,p) basis set in theory. The solvent effect and basis set effect were taken into consideration to investigate the excited state properties of the dyes. The results showed that alizarin complexone had a higher energy conversion efficiency of 0.27 % than that of purpurin (0.13 %), with higher open circuit voltage ( $$V_{oc}$$ ) of 0.45 V, higher short circuit current density ( $$I_{sc}$$ ) of 0.89 mA cm−2 and higher fill factor ( $${\text{ff}}$$ ) of 0.67, indicating that the photovoltaic characteristics of alizarin excelled that of purpurin.

Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules.

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector B at the origin of the coordinate system and by the polar vector C=∇×B, assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector A. The electronic interaction energy of these molecules in nonordered media is a cross term, coupling B and C via a¯, one third of the trace of the anapole magnetizability aαβ tensor, that is, WBC=-a¯B·C. Both A and W(BC) have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of a¯ predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.

Assessment of the basis set effect on the structural and electronic properties of organic-protected gold nanoclusters

We have investigated the structural and optical properties of five monolayer-protected gold nanoclusters with a combination of exchange–correlation functionals, namely B-PBE for the geometry relaxation and CAM-B3LYP for the time-dependent calculations. We have tested the accuracy of five different basis sets in reproducing the experimental structures of these nanoclusters, and we have found that even a rather small basis set (single zeta) can outperform a significantly larger one (double zeta) if some selected atoms are treated with polarization functions. Namely, the sulfur and phosphorous atoms of the capping thiols and phosphines usually are hypervalent when bonded to the gold inner core; therefore, polarization functions allow them significantly more structural flexibility. With the two best performing basis sets, we carried out optical calculations and found that the resulting UV–Vis profiles are largely similar, in particular the energy and orbital contributions of the optical gaps are very close. The results support the use of the small basis set proposed here to investigate larger nanoclusters with general hybrid and range-corrected hybrid functionals.

On the ultrafast charge migration dynamics in isolated ionized halogen, chalcogen, pnicogen, and tetrel bonded clusters

Here we demonstrate, compare and contrast relaxation- and correlation-driven charge migration dynamics in halogen, chalcogen, pnicogen and tetrel bonded clusters, following their vertical ionization. For this work, we have selected different isolated A–X:NH3 clusters, where A represents F, Cl, CN and NH2 substituents and X features Cl, SH, PH2 and SiH3 to exhibit specific noncovalent bonding interaction. The charge migration dynamics in these clusters is studied using the density functional theory (DFT) with the wB97XD functional and the 6-31+G(d,p) basis set. Approximately 400–600 attosecond time scale is predicted for charge migration in (1:1) AX:NH3 complexes. Effects of basis set and intermolecular distance on the ultrafast charge migration dynamics through the halogen, chalcogen, pnicogen, and tetrel bonded clusters are also discussed. This is the first report on pure relaxation- and correlation-driven charge migration dynamics in chalcogen, pnicogen and tetrel bonded clusters.

The effect of basis set and exchange-correlation functional on time-dependent density functional theory calculations within the Tamm-Dancoff approximation of the x-ray emission spectroscopy of transition metal complexes.

The simulation of X-ray emission spectra of transition metal complexes with time-dependent density functional theory (TDDFT) is investigated. X-ray emission spectra can be computed within TDDFT in conjunction with the Tamm-Dancoff approximation by using a reference determinant with a vacancy in the relevant core orbital, and these calculations can be performed using the frozen orbital approximation or with the relaxation of the orbitals of the intermediate core-ionised state included. Both standard exchange-correlation functionals and functionals specifically designed for X-ray emission spectroscopy are studied, and it is shown that the computed spectral band profiles are sensitive to the exchange-correlation functional used. The computed intensities of the spectral bands can be rationalised by considering the metal p orbital character of the valence molecular orbitals. To compute X-ray emission spectra with the correct energy scale allowing a direct comparison with experiment requires the relaxation of the core-ionised state to be included and the use of specifically designed functionals with increased amounts of Hartree-Fock exchange in conjunction with high quality basis sets. A range-corrected functional with increased Hartree-Fock exchange in the short range provides transition energies close to experiment and spectral band profiles that have a similar accuracy to those from standard functionals.

Could the description on polynuclear superhalogens by DFT be comparable with high-level ab initio results? A comparison between DFT and CCSD(T).

A systematic density functional theory study including 17 exchange-correlation functionals was performed on different types of superhalogens with high level coupled-cluster single double including perturbative triple excitations (CCSD(T)) results as the reference. The superhalogens selected here cover the ranges from mononuclear to polynuclear structures and from structures with halogen-atom ligands to those with non-halogen ligands, e.g., [MgX3](-), [Mg2X5](-), and [Mg3X7](-) (X = F, Cl, CN). It is clearly indicated that three double-hybrid functionals B2T-PLYP, B2GP-PLYP, B2K-PLYP as well as the range-separated hybrid functional ωB97X are capable of providing results which approach the accuracy at the CCSD(T) level. The basis set effect is usually moderate and, in most cases, it is enough to utilize the basis set of triple-ξ quality, e.g., Def2-TZVP. In addition, the results of the HF and MP2 method are also acceptable here, especially for polynuclear superhalogens where CCSD(T) is probably unpractical.