Evaluation of DFT methods for computing the interaction energies of homomolecular and heteromolecular dimers of monosubstituted benzene

We present density functional theory (DFT) interaction energies for the sandwich and T‐shaped conformers of substituted benzene dimers. The DFT functionals studied include TPSS, HCTH407, B3LYP, and X3LYP. We also include Hartree–Fock (HF) and second‐order Møller–Plesset perturbation theory calculations (MP2), as well as calculations using a new functional, P3LYP, which includes PBE and HF exchange and LYP correlation. Although DFT methods do not explicitly account for the dispersion interactions important in the benzene–dimer interactions, we find that our new method, P3LYP, as well as HCTH407 and TPSS, match MP2 and CCSD(T) calculations much better than the hybrid methods B3LYP and X3LYP methods do. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

A comparative study of DFT and traditional ab initio methodologies on the OsO4 molecule

The performance of different conventional ab initio methodologies and density functional procedures is compared through its application to the theoretical calculation of the bond distance and harmonic vibrational frequencies of the OsO₄ molecule. The problem of the basis set is first considered, with up to nine different basis sets being tested in calculations using the hybrid Becke3LYP density functional, and the most appropriate basis set is used in the comparison of Hartree–Fock, post‐Hartree–Fock, and density functional methods. The post‐Hartree–Fock methods analyzed are MP2, CISD, and CCSD(T), and the density functionals tested are SVWN, BLYP, BPW91, and Becke3LYP. The results show that for this particular system density functional methods perform better than do HF‐based methods with the exception of CCSD(T), which gives the best overall results. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 544–551, 2000     

A density functional study of chemical reactions

Density functional theory (DFT ) was used to study reactions involving small molecules. Relative energies of isomers and transition structures of diazene, formaldehyde, and methylenimine were determined using various DFT functionals and results were compared with MP 2 and MP 4 calculations. DFT reaction barriers were found to be consistently lower. For some reactions, such as OH + H₂→ H₂O + H, gradient-corrected functionals predict very low or nonexistent barriers. The hybrid Hartree–Fock–DFT adiabatic connection method (ACM ) often provides much better results in such cases. The performance of several density functionals, including ACM , was tested in calculations on over 100 atomization, hydrogenation, bond dissociation, and isodesmic reactions. The ACM functional provides consistently better geometries and reaction energetics than does any other functional studied. In cases where both HF and gradient-corrected DFT methods underestimate bond distances, the ACM geometries may be inferior to those predicted by gradient-corrected DFT methods. © 1995 John Wiley & Sons, Inc.     

A comparison of Hartree—Fock,MP2, and DFT results for the HCN dimer and crystal

A number of hydrogen-bond related quantities—geometries, interaction energies, dipole moments, dipole moment derivatives, and harmonic vibrational frequencies—were calculated at the Hartree—Fock, MP2, and different DFT levels for the HCN dimer and the periodic HCN crystal. The crystal calculations were performed with the Hartree—Fock program CRYSTAL92, which routinely allows an a posteriori electron-correlation correction of the Hartree—Fock obtained lattice energy using different correlation-only functionals. Here, we have gone beyond this procedure by also calculating the electron-correlation energy correction during the structure optimization, i.e., after each CRYSTAL92 Hartree—Fock energy evaluation, the a posteriori density functional scheme was applied. In a similar manner, we optimized the crystal structure at the MP2 level, i.e., for each Hartree—Fock CRYSTAL92 energy evaluation, an MP2 correction was performed by summing the MP2 pair contributions from all HCN molecules within a specified cutoff distance. The crystal cell parameters are best reproduced at the Hartree—Fock and the nongradient-corrected HF + LDA and HF + VWN levels. The BSSE-corrected MP2 method and the HF + P91, HF + LDA, and HF + VWN methods give lattice energies in close agreement with the ZPE-corrected experimental lattice energy. The (HCN)₂ dimer properties are best reproduced at the MP2 level, at the gradient-corrected DFT levels, and with the B3LYP and BHHLYP methods. © 1996 John Wiley & Sons, Inc.     

Theoretical study of the internal elimination reactions of xanthate precursors

The gas‐phase internal elimination (E_i) reaction of ethyl xanthate (CH₃‐CH₂‐S‐CS‐O‐CH₃) has been investigated by means of Hartree–Fock, second‐order Møller–Plesset, and density functional theory (DFT) using the Becke three‐parameter Lee–Yang–Parr (B3LYP) functional and the modified Perdew–Wang one‐parameter model for kinetics (MPW1K). Considerable differences between the ground‐ and transition‐state geometries and the calculated activation energies are observed from one approach to the other, which justifies first a careful calibration of the methods against the results of benchmark CCSD(T) calculations. Compared with these, DFT calculations along with the MPW1K functional are found to be an appropriate choice for describing the E_i reaction of xanthate precursors. The precursor conformation and the transition states involved in the internal conversion of xanthate precursors of cyano derivatives of ethylene, and of cis‐ and trans‐stilbene, are then characterized in detail by means of this functional. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 2023–2031, 2003     

An improved generator coordinate Hartree–Fock method applied to the choice of contracted Gaussian basis sets for first‐row diatomic molecules

Accurate Gaussian basis sets (18s for Li and Be and 20s11p for the atoms from B to Ne) for the first‐row atoms, generated with an improved generator coordinate Hartree–Fock method, were contracted and enriched with polarization functions. These basis sets were tested for B₂, C₂, BeO, CN⁻, LiF, N₂, CO, BF, NO⁺, O₂, and F₂. At the Hartree–Fock (HP), second‐order Møller–Plesset (MP2), fourth‐order Møller–Plesset (MP4), and density functional theory (DFT) levels, the dipole moments, bond lengths, and harmonic vibrational frequencies were studied, and at the MP2, MP4, and DFT levels, the dissociation energies were evaluated and compared with the corresponding experimental values and with values obtained using other contracted Gaussian basis sets and numerical HF calculations. For all diatomic molecules studied, the differences between our total energies, obtained with the largest contracted basis set [6s5p3d1f], and those calculated with the numerical HF methods were always less than 3.2 mhartree. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 15–23, 2000     

Comparative study on formamide–water complex

The hydrogen bonding of 1:1 complexes formed between formamide and water molecule have been investigated systematically using Hartree–Fock (HF), hybrid density functional theory (B3LYP), and post‐Hartree–Fock (MP2 and CCSD(T)) methods with range of basis sets 6‐31G(d), cc‐pVXZ (X = D, T, Q) and aug‐cc‐pVYZ (Y = D, T). Three stable structures are considered on the potential energy surface of formamide and water system. The optimized geometric parameters and interaction energies for various isomers at different levels are estimated. The IR frequencies, intensities, and frequency shifts are reported. This study shows that B3LYP/aug‐cc‐pVDZ method gives better performance for formamide‐water complexes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010.     

On Ethylene Polymerisation with Aluminium and Scandium Complexes: DFT and Post‐HF Calculations

Summary: The performance of Density Functional Theory (DFT) methods in predicting ethylene polymerisation and/or oligomerisation activity in selected aluminium and scandium based complexes was studied using both DFT and post‐Hartree‐Fock CCSD(T) calculations. Whereas previous reports have drawn attention to the underestimation of the barrier for the β‐hydrogen termination process for a few aluminium based species, we found that the same holds for the corresponding scandium complexes. New, however, is the observation that apart from underestimating the energy barrier connected to β‐hydrogen termination, the insertion of ethylene is also severely underestimated by the DFT methods applied compared to post‐Hartree‐Fock calculations up to the CCSD(T) level.

Structure of the diketiminate complex referred to in the text.     

Comparative study of DFT methods applied to small titanium/oxygen compounds

The performance of a number of different local and nonlocal density functional theory (DFT) methods has been investigated for some small titanium—oxygen systems. Equilibrium geometries, ionization potentials, dipole moments, atomization energies, and harmonic vibrational frequencies have been calculated for the TiO, TiO₂, and Ti₂ molecules, and the results are compared with experimental data and ab initio calculations. It is shown that most DFT methods perform much better than the ab initio Hartree—Fock (HF), second-order perturbation theory (MP2), and configuration interaction including single and double excitations (CISD) treatments. For good agreement with experimental data, gradient corrections to the exchange part of the DFT functional are needed, as well as some type of correction for the errors in the calculated energy splittings between different atomic states of titanium. Hybrid methods including a mixture of HF exchange with DFT exchange correlation do not perform as well as “pure” DFT methods for the studied systems. © 1996 John Wiley & Sons, Inc.     

EHF theory of chemical reactions V. Nature of manganese–oxygen bonds by hybrid density functional theory (DFT) and coupled‐cluster (CC) methods

Hybrid density functional theory (DFT) and post‐Hartree–Fock methods are compared by depicting potential energy curves of the O–O dissociation of hydroperoxide and the M–O dissociation of transition‐metal oxides. The former approach includes BLYP, B2LYP, B3LYP, and more general hybrid DFT methods, while the unrestricted Hartree–Fock (UHF) coulpled‐cluster (UCC) SD(T) method is considered as the latter approach. The hybrid DFT methods can reproduce the potential curve of the O–O dissociation process and the dissociation energy of HOOH by UCCSD(T). The methods are also useful for depicting potential curves of copper oxide (CuO) and manganese oxide (MnO), and reproduce the experimental M–O binding energies. The nature of Mn–O bonds in the naked Mn–O, Mn–O porphyrine system and model complexes, XH₃Mn(IV)O₂Mn(IV)H₃Y (X,Y=O,H), are examined in relation to the possible mechanisms of oxygenation reactions. It is found that the radical character of Mn–O bonds increases with the increase of the oxidation number of the Mn ion in these systems. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Kinetics and Thermodynamics of Reactions Involving Criegee Intermediates: An Assessment of Density Functional Theory and Ab Initio Methods Through Comparison with CCSDT(Q)/CBS Data

Reactions involving Criegee intermediates (CIs, R₁R₂COO) are important in atmospheric ozonolysis models. In recent years, density functional theory (DFT) and CCSD(T)-based ab initio methods are increasingly being used for modeling reaction profiles involving CIs. We obtain highly accurate CCSDT(Q)/CBS reaction energies and barrier heights for ring-closing reactions involving atmospherically important CIs (R₁/R₂ = H, Me, OH, OMe, F, CN, cyclopropene, ethylene, acetaldehyde, and acrolein). We use this benchmark data to evaluate the performance of DFT, double-hybrid DFT (DHDFT), and ab initio methods for the kinetics and thermodynamics of these reactions. We find that reaction energies are more challenging for approximate theoretical procedures than barrier heights. Overall, taking both reaction energies and barrier heights into account, only one of the 58 considered DFT methods (the meta-GGA MN12-L) attains near chemical accuracy, with root-mean-square deviations (RMSDs) of 3.5 (barrier heights) and 4.7 (reaction energies) kJ mol⁻¹. Therefore, MN12-L is recommended for investigations where CCSD(T)-based methods are not computationally feasible. For reaction barrier heights performance does not strictly follow Jacob's Ladder, for example, DHDFT methods do not perform better than conventional DFT methods. Of the ab initio methods, the cost-effective CCSD(T)/CBS(MP2) approach gives the best performance for both reaction energies and barrier heights, with RMSDs of 1.7 and 1.4 kJ mol⁻¹, respectively. All the considered Gaussian-n methods show good performance with RMSDs below the threshold of chemical accuracy for both reaction energies and barrier heights, where G4(MP2) shows the best overall performance with RMSDs of 2.9 and 1.5 kJ mol⁻¹, respectively. © 2019 Wiley Periodicals, Inc.     

Natural bond orbital‐based energy density analysis for correlated methods: Second‐order Møller–Plesset perturbation and coupled‐cluster singles and doubles

Natural bond orbital‐based energy density analysis (NBO‐EDA), which split energies into atomic and bonding contributions, is proposed for correlated methods such as coupled‐cluster singles and doubles (CCSD) and second‐order Møller–Plesset (MP2) perturbation. Applying NBO‐EDA for CCSD and MP2 to ethylene and the Diels–Alder reaction, we are successful in obtaining useful knowledge regarding electron correlation of π‐ and σ‐type orbitals, and clarifying the difference of the reaction barriers and heat of reaction calculated by CCSD and MP2. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

The computation of the potential energy surface for H2 + OH → H2O + H using ab initio and density functional theory methods

The reaction energy profile for H₂ + OH → H + H₂O was computed using HF, MP2, MP4, QCISD, G1, G2, and G2MP2 ab initio methods. In addition, the B3LYP, B3P86, B3PW91, BLYP, BP291, and SVWN density functional theory (DFT) methods were also used. All the ab initio methods, with the exception of the G series, produced much higher activation barriers and heats of reaction than the experimental values. On the other hand, the DFT methods produced negative forward and reverse barriers which were too low, with the exception of the hybrid DFT methods. The G2 ab initio method generated energies which deviated from the experimental values by ∼ 1 kcal/mol and therefore should be considered a very accurate computational method. The hybrid DFT methods produced positive forward reaction barriers with energies that were 2–4 kcal/mol lower than the experimental values. The geometries of the transition state and energies computed by the ab initio and DFT methods were compared. These results suggest that, in the hybrid exchange functional, the portion of the Slater exchange term should be increased. This may be the reason why the computed energies were too low. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 639–644, 1997     

CASCI-DFT study of the phenalenyl radical system

We present ab initio complete-active-space configuration interaction (CASCI) density functional theory (DFT) study of the phenalenyl radical systems. Our approach employed in this study is based on the assumption that one-electron per one phenalenyl unit is responsible for magnetic properties of the phenalenyl radical dimeric compounds and that the residual correlation effects can be covered by DFT correlation potential for CASCI[2,2] wavefunction. The effective exchange integrals and lowest-lying excited energies of several phenalenyl dimeric compounds are calculated by CASCI[2,2]-DFT method. The implication of the computational results are discussed in relation with those of spin unrestricted Hartree–Fock (UHF), hybrid DFT, and pure DFT, and the experimental ones.     

Theoretical study on the molecular structures of toluene,para‐fluorotoluene,para‐chlorotoluene,and 4‐methylpyridine and their sixfold internal rotational barriers

Two kinds of sixfold internal rotational configurations of toluene, para‐fluorotoluene, para‐chlorotoluene, and 4‐methylpyridine were calculated using Hartree–Fock (HF), second‐order Møller–Plesset (MP2), and Beck's three parameter hybrid functional using the LYP correlation functional (B3LYP) theory methods with various high‐level basis sets. Structures and energies were compared for different configurations. Calculations indicate that the orthogonal configuration has a local minimum while the planar configuration is a transition structure. Furthermore, geometries of the orthogonal and the planar configurations are quite similar, except for a methyl CH bond. Sixfold internal rotational barriers were calculated from the energy difference of two different configurations. For the calculated results, HF methods underestimated the rotational barriers, but MP2 calculations overestimated them. However, the density functional theory (DFT) method is a reliable method since the calculated internal rotational barriers are similar to the experimental ones. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 772–778, 2000     

Ab initio calculations for absorption and emission energies of alkali halide crystals doped with thallium

We calculate transition energies associated with optical properties of thallium doping in alkali halide crystals via an atomic cluster of minimal size where an sp‐valence‐shell impurity enters as a substitutional defect in the model crystal. Hartree–Fock (HF), density functional theory (DFT), and configuration interaction (CI) [CIS (CI with single excitation) and QCISD (single plus double and quadruple excitation)] calculations are performed to theoretically obtain the absorption and emission energies as vertical transitions evaluated at the ground and first excited‐state optimized geometries, respectively, where the optimization is carried out separately with the HF and DFT methods. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 785–790, 2000     

Design of low band gap polymers employing density functional theory—hybrid functionals ameliorate band gap problem

Band gaps in solids and excitation energies in finite systems are underestimated significantly if estimated from differences between eigenvalues obtained within the local spin density approximation (LSDA). In this article we present results on 20 small- and medium-sized π-systems which show that HOMO–LUMO energy differences obtained with the B3LYP, B3P86, and B3PW91 functionals are in good agreement with vertical excitation energies from UV-absorption spectra. The improvement is a result of the use of the exact Hartree–Fock exchange with hybrid methods. Negative HOMO energies and negative LUMO energies do not provide good estimates for IPs and EAs. In contrast to Hartree–Fock theory, where IPs are approximated well and EAs are given poorly, DFT hybrid methods underestimate IPs and EAs by about the same amount. LSDA yields reasonable EAs but poor IPs. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1943–1953, 1997     

Theoretical study of the vibrational frequencies of carbon disulfide

A benchmark comparison for different computational methods and basis sets has been presented. In this study, five computational methods (Hartree–Fock (HF), MP2, B3LYP, MPW1MP91, and PBE1PBE) along with 18 basis sets have been applied to optimize the geometry of carbon disulfide (CS₂), and further calculate the vibrational frequencies of the optimized geometries. The differences between the calculated frequencies and corresponding experimental data are used to evaluate the efficiency of each combination of computational method and basis set. The comparison of frequency difference indicates that B3LYP generally gives the best prediction of frequencies for CS₂, whereas the other two density functional theory (DFT) methods, i.e., MPW1PW91 and PBE1PBE, often give parallel results. Although MP2 predicts the frequencies with accuracy almost as good as those from DFT methods, in a particular case, HF calculation outperforms MP2 as well as MPW1PW91 and PBE1PBE for prediction of the frequency of asymmetrical stretching for CS₂. © 2013 Wiley Periodicals, Inc.     

Prediction of a Neutral Noble Gas Compound in the Triplet State

Discovery of the HArF molecule associated with H?Ar covalent bonding [Nature, 2000 , 406, 874–876] has revolutionized the field of noble gas chemistry. In general, this class of noble gas compound involving conventional chemical bonds exists as closed‐shell species in a singlet electronic state. For the first time, in a bid to predict neutral noble gas chemical compounds in their triplet electronic state, we have carried out a systematic investigation of xenon inserted FN and FP species by using quantum chemical calculations with density functional theory and various post‐Hartree–Fock‐based correlated methods, including the multireference configuration interaction technique. The FXeP and FXeN species are predicted to be stable by all the computational methods employed in the present work, such as density functional theory (DFT), second‐order Møller–Plesset perturbation theory (MP2), coupled‐cluster theory (CCSD(T)), and multireference configuration interaction (MRCI). For the purpose of comparison we have also included the Kr‐inserted compounds of FN and FP species. Geometrical parameters, dissociation energies, transition‐state barrier heights, atomic charge distributions, vibrational frequency data, and atoms‐in‐molecules properties clearly indicate that it is possible to experimentally realize the most stable state of FXeP and FXeN molecules, which is triplet in nature, through the matrix isolation technique under cryogenic conditions.