Compatibility of correlation‐consistent basis sets with a hybrid Hartree–Fock/density functional method

The present study examines the feasibility of combining the correlation‐consistent basis sets developed by Dunning and coworkers with the hybrid Hartree–Fock/density functional method B3LYP. Furthermore, extrapolation to the complete basis set (CBS) limit minimizes errors due to the presence of an incomplete basis set and can act as a rigorous test of the limitations of the B3LYP method. Equilibrium geometries, energies, and harmonic vibrational frequencies were determined for a series of well‐studied, yet computationally challenging, small inorganics and their respective ions. The results were then extrapolated to the CBS limit, where applicable, and compared to experiment. It was found that a union between the hybrid Hartree–Fock/density functional B3LYP method and Dunning's augmented correlation‐consistent basis sets gave results that were comparable to molecular orbital methods that explicitly account for electron correlation. Furthermore, the minimum basis set necessary to attain reasonable results for the systems studied was aug‐cc‐pVTZ. Upgrading to the aug‐cc‐pVQZ level and subsequent extrapolation to the CBS limit further improved the overall agreement with the experiment. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 207–216, 1999     

A Comparative Study of Hydrogen Bonding Using Density Functional Theory

The hydrogen‐bond energies of water dimer and water‐formaldehyde complexes have been studied using density functional theory (DFT). Basis sets up to aug‐cc‐pVXZ (X=D, T, Q) were used. It was found that counterpoise corrected binding energies using the aug‐cc‐pVDZ basis set are very close to those predicted with the aug‐cc‐pVQZ set. Comparative studies using various DFT functionals on these two systems show that results from B3LYP, mPW1PW91 and PW91PW91 functionals are in better agreements with those predicted using high‐level ab initio methods. These functionals were applied to the study of hydrogen bonding between guanine (G) and cytosine (C), and between adenine (A) and thy mine (T) base pairs. With the aug‐cc‐pVDZ basis set, the predicted binding energies of base pairs are in good agreement with the most elaborate ab initio results.     

Quantum‐chemistry based calibration of the alkali metal cation series (Li+Cs+) for large‐scale polarizable molecular mechanics/dynamics simulations

The alkali metal cations in the series Li⁺? Cs⁺ act as major partners in a diversity of biological processes and in bioinorganic chemistry. In this article, we present the results of their calibration in the context of the SIBFA polarizable molecular mechanics/dynamics procedure. It relies on quantum‐chemistry (QC) energy‐decomposition analyses of their monoligated complexes with representative O? , N? , S? , and Se? ligands, performed with the aug‐cc‐pVTZ(‐f) basis set at the Hartree–Fock level. Close agreement with QC is obtained for each individual contribution, even though the calibration involves only a limited set of cation‐specific parameters. This agreement is preserved in tests on polyligated complexes with four and six O? ligands, water and formamide, indicating the transferability of the procedure. Preliminary extensions to density functional theory calculations are reported.     

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     

Improving on equilibrium isotropic nuclear shielding constants

Isotropic nuclear shielding constants at the equilibrium molecular structure σ_eq and zero‐point vibrational corrections (ZPVCs) to σ_eq are evaluated using the B3LYP/aug‐cc‐pVTZ level of theory, as well as the KT2/aug‐cc‐pVTZ level of theory. Various scaling factors and systematic corrections are obtained by linear regression to experimental shielding constants. Comparisons of the scaled and systematically corrected equilibrium and vibrationally averaged shielding constants reveal that, at the 99% confidence level, the ZPVCs via second‐order perturbation theory do not improve the agreement of B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ calculated shielding constants with experiment. This holds true when the same analysis is applied to CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σ_eq of Teale et al. [Journal of Chemical Physics 2013, 138, 024111]. In addition, at the 99% confidence level, B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ scaled and systematically corrected shielding constants are found to be statistically no different from CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σ_eq. The use of scaling factors and systematic corrections could thus provide a cheaper but yet reasonably accurate alternative for the study of nuclear shielding constants of larger systems.     

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     

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.     

Spin‐orbit ZORA and four‐component Dirac–Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers

Hartree–Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange‐correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin‐orbit zeroth‐order regular approximation Hamiltonian in combination with the large Slater‐type basis set QZ4P as well as with the four‐component Dirac–Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization‐consistent basis sets aug‐pcSseg‐4 for He, Ne and Ar, aug‐pcSseg‐3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero‐point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.     

DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals for noncovalent interactions: Basis set effects and tentative applications to large noncovalent systems

Basis set effects on the DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals for noncovalent interactions have been extensively studied in this work. The cc‐pVXZ (X = D, T, Q, 5, 6) and augmented aug‐cc‐pVXZ (X = D, T, Q) basis sets are systematically tested without counterpoise (CP) corrections against the well‐known S66 database. Additionally, the basis sets of def2‐TZVPP and def2‐TZVPPD are also examined. Based on our computations, the performances of the aug‐cc‐pVQZ, cc‐pV5Z, and cc‐pV6Z basis sets are very approximate to those obtained with the def2‐QZVP basis set for both the DSD‐PBEP86‐NL and DOD‐PBEP86‐NL functionals. Note that the short‐range attenuation parameters for these two functionals were directly optimized using the def2‐QZVP basis set without CP corrections against the S66 database. Generally speaking, the cc‐pVXZ (X = D, T, Q), aug‐cc‐pVXZ (X = D, T, Q), def2‐TZVPP, and def2‐TZVPPD basis sets favor half CP correction for these two functionals. Nevertheless, the aug‐cc‐pVQZ basis set already performs well without any CP correction, especially for the DOD‐PBEP86‐NL functional. With respect to accuracy and computational cost, the cc‐pVTZ and def2‐TZVPP basis sets with half CP corrections are recommended for these two functionals to evaluate interaction energies of large noncovalent complexes.     

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     

IR Low‐Temperature Matrix and ab Initio Study on β‐Alanine Conformers

For the first time the argon‐matrix low‐temperature FTIR spectra of β‐alanine are recorded. They reveal a quite complicated spectral pattern which suggests the presence of several β‐alanine conformers in the matrix. To interpret the spectra, the eighteen β‐alanine conformers, stable in the gas phase, are estimated at the B3LYP and MP2 levels combined with the aug‐cc‐pVDZ. Ten low‐energy structures are reoptimized at the QCISD/aug‐cc‐pVDZ and B3LYP and MP2 levels by using the aug‐cc‐pVTZ basis sets. Assignment of the experimental spectra is undertaken on the basis of the calculated B3LYP/aug‐cc‐pVDZ anharmonic IR frequencies as well as careful estimation of the conformer population. The presence of at least three β‐alanine conformers is demonstrated. The detailed analysis of IR spectra points to the possible presence of five additional β‐alanine conformers.     

Comparative study of unscreened and screened molecular static linear polarizability in the Hartree–Fock,hybrid‐density functional,and density functional models

The sum‐over‐states (SOS) polarizabilities are calculated within approximate mean‐field electron theories such as the Hartree–Fock approximation and density functional models using the eigenvalues and orbitals obtained from the self‐consistent solution of the single‐particle equations. The SOS polarizabilities are then compared with those calculated using the finite‐field (FF) method. Three widely used mean‐field models are as follows: (1) the Hartree–Fock (HF) method, (2) the three parameter hybrid generalized gradient approximation (GGA) (B3LYP), and (3) the parameter‐free generalized gradient approximation due to Perdew–Burke–Ernzerhof (PBE). The comparison is carried out for polarizabilities of 142 molecules calculated using the 6‐311++G(d,p) basis set at the geometries optimized at the B3LYP/6‐311G** level. The results show that the SOS method almost always overestimates the FF polarizabilities in the PBE and B3LYP models. This trend is reversed in the HF method. A few exceptions to these trends are found. The mean absolute errors (MAE) in the screened (FF) and unscreened (SOS) polarizability are 0.78, 1.87, and 3.44 ų for the HF, B3LYP, and PBE‐GGA methods, respectively. Finally, a simple scheme is devised to obtain FF quality polarizability from the SOS polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Calculations of solid‐state 43Ca NMR parameters: A comparison of periodic and cluster approaches and an evaluation of DFT functionals

We present a computational study of magnetic‐shielding and quadrupolar‐coupling tensors of ⁴³Ca sites in crystalline solids. A comparison between periodic and cluster‐based approaches for modeling solid‐state interactions demonstrates that cluster‐based approaches are suitable for predicting ⁴³Ca NMR parameters. Several model chemistries, including Hartree–Fock theory and 17 DFT approximations (SVWN, CA‐PZ, PBE, PBE0, PW91, B3PW91, rPBE, PBEsol, WC, PKZB, BMK, M06‐L, M06, M06‐2X, M06‐HF, TPSS, and TPSSh), are evaluated for the prediction of ⁴³Ca NMR parameters. Convergence of NMR parameters with respect to basis sets of the form cc‐pVXZ (X = D, T, Q) is also evaluated. All DFT methods lead to substantial, and frequently systematic, overestimations of experimental chemical shifts. Hartree–Fock calculations outperform all DFT methods for the prediction of ⁴³Ca chemical‐shift tensors. © 2017 Wiley Periodicals, Inc.     

Study of conformational and optical rotation for the alaninamide

Six stationary points of alaninamide have been located on the potential surface energy (PES) at the B3LYP/6‐311++G(2d,2p) level of theory both in the gas phase and in aqueous solution. In the aqueous solution, to take the water solvent effect into account, the polarizable continuum model (PCM) method has been used. Accurate geometric structures and their relative stabilities have been investigated. The results show that the intramolecular hydrogen bond plays a very important role in stabilizing the global minimum of the alaninamide. Moreover, the consistent result in relative energy using high‐level computations, including the MP2 and MP3 methods with the same basis set [6‐311++G(2d,2p)], indicates that the B3LYP/6‐311++G(d,p) level may be applied to the analogue system. More importantly, the optical rotation of the optimized conformers (both in the gas phase and in aqueous solution) of alaninamide have been calculated using the density functional theory (DFT) and Hartree–Fock (HF) method at various basis sets (6‐31+G*, 6‐311++G(d,p), 6‐311++G(2d,2p) and aug‐cc‐pvdz). The results show that the selection of the computation method and the basis set in calculation has great influence on the results of the optical rotations. The reliability of the HF method is less than that of DFT, and selecting the basis set of 6‐311++G(2d,2p) and aug‐cc‐pvDZ produces relative reliable results. Analysis of the computational results of the structure parameters and the optical rotations yields the conclusion that just the helixes in molecules caused the chiral molecules to be optical active. The Boltzmann equilibrium distributions for the six conformers (both in the gas phase and in the aqueous solution) are also carried out. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Many‐body interactions of carbon monoxide cyclic oligomers: A computational study

Structural properties and energetics for the optimized carbon monoxide cyclic oligomers are analyzed at the correlated ab initio second‐order Møller–Plesset (MP2) and density functional methods (B3LYP and mPW1PW), using Dunning's cc‐pVXZ (X = D, T, Q) basis set, augmented with diffuse functions. Many‐body interactions of the stable carbon monoxide cyclic oligomers, (CO)₄ and (CO)₅ are computed at the MP2/aug‐cc‐pVTZ level. Contributions of two‐ to five‐body terms to each of these oligomers for their interaction energies, including corrections for basis set superposition error (BSSE) are investigated by using function counterpoise and its generalized version. It has been found that three‐body terms are attractive in nature and essential in order to describe the cooperative effects in the stable cyclic CO oligomers. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

An analytical approach for computing Franck‐Condon integrals of harmonic oscillators with arbitrary dimensions

We have developed an analytical approach for computing Franck‐Condon integrals (FCIs) of harmonic oscillators (HOs) with arbitrary dimensions in which the mode‐mixing Duschinsky effect is taken into account. A general formula of FCIs of HOs was obtained and was applied to study the photoelectron spectroscopy of vinyl alcohol and ovalene (C₃₂H₁₄). The equilibrium geometries, harmonic vibrational frequencies and normal modes of vinyl alcohol, ovalene, and their cations were computed at the B3LYP/aug‐cc‐pVTZ or the B3LYP/6‐31G(d) level, from which Franck‐Condon factors were calculated and photoelectron spectra were simulated. The adiabatic ionization energies of vinyl alcohol were also computed by extrapolating the CCSD(T) energies to the complete basis set limit with aug‐cc‐pVXZ (X = D, T, Q, 5). The simulated photoelectron spectra of both vinyl alcohol and ovalene are in agreement with the experiments. The computed adiabatic ionization energies of syn‐ and anti‐vinyl alcohol are in consistent with the experiment within 0.008 eV and 0.014 eV, respectively. We show, for the first time, that the analytical approach of computing FCIs is also efficient and promising for the studies of vibronic spectra of macrosystems. © 2012 Wiley Periodicals, Inc.     

Benchmarking density functionals in conjunction with Grimme's dispersion correction for noble gas dimers (Ne2, Ar2, Kr2, Xe2, Rn2)

Eleven exchange‐correlational functionals of different types corrected for dispersion by Grimme's D3 correction in conjunction with the aug‐cc‐pVTZ basis set were tested on the following noble gas (Ng) dimers: Ne₂, Ar₂, Kr₂, Xe₂, and Rn₂. For comparison, the D2 and D3BJ corrections were probed with the B3LYP functional. From post‐HF wavefunction methods, CCSD(T) theory was also included. The investigated properties involved potential energy curves, equilibrium bond distances, and interaction energies. The B3LYP‐D3, B3LYP‐D3BJ, and PBE0‐D3 functionals performed overall best for bond distances, while B3LYP‐D3 and B97‐D3 performed best for interaction energies. The importance of fortunate error cancellations was seen in the often reduced agreement with reference data upon correction for BSSE. As several functionals performed well selectively for some noble gases (and poorly for others), we also analysed the performance on the Ng₂ dimers individually and recommended DFT‐D3 functionals for the calculation of large clusters of each Ng.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Absorption,resonance, and near‐resonance Raman studies of the tetracyanoquinodimethane neutral and its monoanion in terms of density functional theory and complete active space self‐consistent field methods

The electronic structure of the 1¹B_1u and 1²B_3u excited electronic states of the tetracyanoquinodimethane (TCNQ) neutral and its charged derivative are studied within the framework of complete active space self‐consistent field (CASSCF) and Becke's three‐parameter hybrid method with Lee–Yang–Parr correlation functional (B3LYP) methods applied to the level aug‐cc‐p‐VDZ basis set. Both CASSCF/aug‐cc‐p‐VDZ and B3LYP/aug‐cc‐p‐VDZ treatments provide the ground‐state and the excited state geometries; these are then used to assess the Franck–Condon (FC) parameters in the 1¹B_1u state of the neutral TCNQ and in the 1²B_3u state of the TCNQ monoanion. The quality of numerical results is then tested on the base of available experimental near‐resonance and resonance Raman data. The studies are performed in terms of the vibronic model, which takes both FC and mode‐mixing (Dushinsky) effects into account. This somewhat simplified vibronic model leads to very good agreement between the theory and the Raman experiments concerning both neutral TCNQ and its monoanion. In particular, the calculated excitation profiles of the ν₂ = 2215 cm^?1, ν₄ = 1389 cm^?1, ν₅ = 1195 cm^?1, and ν₉ = 336 cm^?1 fundamentals are shown to be in excellent agreement with those for the TCNQ monoanion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Evaluating Shielding‐Based Ring‐Current Models by Using the Gauge‐Including Magnetically Induced Current Method

Magnetically induced current densities and integrated ring‐current strength susceptibilities have been calculated at the density functional theory (DFT) level for a test set consisting of 17 ring‐shaped molecules using the gauge‐including magnetically induced current (GIMIC) method. Reliable values for the ring‐current strengths have been obtained by performing numerical integration of the current‐density susceptibility passing a cut plane perpendicularly to the molecular ring. The current densities and ring current strengths were calculated at the DFT level using the B3LYP functional and def2‐TZVP basis sets. Current densities and ring‐current strengths have also been calculated at the Hartree‐Fock self‐consistent field (HF‐SCF) level using Dunning’s aug‐cc‐pVTZ basis sets, which allow a direct comparison with ring‐current strengths that have previously been estimated using ring‐current models based on magnetic shielding calculations. Current density calculations at both levels of theory show that the magnetic shielding based ring‐current models are not a very accurate means to estimate the magnetically induced ring current strengths, whereas they provide qualitatively the correct aromaticity trends for the studied molecules.