A density functional study of the glycine molecule: Comparison with post-Hartree–Fock calculations and experiment

The potential energy surface of un-ionized glycine has been explored with density functional theory. The performance of several nonlocal functionals has been evaluated and the results are presented in the context of available experimental information and post-Hartree–Fock quantum chemical results. The zero-point and thermal vibrational energies along with vibrational entropies play a very important role in determining the relative stability of glycine conformers; the realization of this has led to some revision and reinterpretation of the experimental results. Uncertainties in the vibrational contributions to the energy differences of several tenths of a kilocalorie/mole remain. The uncertainty in the vibrational free energy is even larger, about 1 kcal/mol. In the final analysis, we suggest that the best estimate of the electronic energy difference between the two lowest glycine conformers should be revised downward from 1.4 to 1.0 kcal/mol. Thirteen stationary points on the potential energy surface have been localized. For the majority of these, there is close agreement among various nonlocal density functionals and the post-Hartree–Fock methods. However, the second conformer (IIn), which has a strong hydrogen bond between the hydroxyl hydrogen and the nitrogen of the amine group, presents a distinct challenge. The relative energy of this conformer is extremely sensitive to the basis set, the level of correlation, or the functional used. The widely used BP86, PP86, and BP91 nonlocal functionals overestimate the strength of the hydrogen bond and predict that this conformer is the lowest energy structure. This contradicts both experiment and high-level post-Hartree–Fock studies. The adiabatic connection method (ACM) and the BLYP functional yield the correct order. The ACM method, in particular, gives energies which are in reasonable agreement with MP2, although these are somewhat low as compared with experiment. Based on this study, ACM should perform well for this type of bioorganic application, with typical errors of a few tenths of a kilocalorie/mole and only rarely exceeding 0.5 kcal/mol. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1609–1631, 1997     

Performance of density functionals for first row transition metal systems

This article investigates the performance of five commonly used density functionals, B3LYP, BP86, PBE0, PBE, and BLYP, for studying diatomic molecules consisting of a first row transition metal bonded to H, F, Cl, Br, N, C, O, or S. Results have been compared with experiment wherever possible. Open-shell configurations are found more often in the order PBE0>B3LYP>PBE approximately BP86>BLYP. However, on average, 58 of 63 spins are correctly predicted by any functional, with only small differences. BP86 and PBE are slightly better for obtaining geometries, with errors of only 0.020 A. Hybrid functionals tend to overestimate bond lengths by a few picometers and underestimate bond strengths by favoring open shells. Nonhybrid functionals usually overestimate bond energies. All functionals exhibit similar errors in bond energies, between 42 and 53 kJmol. Late transition metals are found to be better modeled by hybrid functionals, whereas nonhybrid functionals tend to have less of a preference. There are systematic errors in predicting certain properties that could be remedied. BLYP performs the best for ionization potentials studied here, PBE0 the worst. In other cases, errors are similar. Finally, there is a clear tendency for hybrid functionals to give larger dipole moments than nonhybrid functionals. These observations may be helpful in choosing and improving existing functionals for tasks involving transition metals, and for designing new, improved functionals.     

Calculation of molecular geometries,relative conformational energies,dipole moments,and molecular electrostatic potential fitted charges of small organic molecules of biochemical interest by density functional theory

Density functional theory is tested on a large ensemble of model compounds containing a wide variety of functional groups to understand better its ability to reproduce experimental molecular geometries, relative conformational energies, and dipole moments. We find that gradient-corrected density functional methods with triple-ζ plus polarization basis sets reproduce geometries well. Most bonds tend to be approximately 0.015 Å longer than the experimental results. Bond angles are very well reproduced and most often fall within a degree of experiment. Torsions are, on average, within 4 degrees of the experimental values. For relative conformational energies, comparisons with Hartree-Fock calculations and correlated conventional ab initio methods indicate that gradient-corrected density functionals easily surpass the Hartree-Fock approximation and give results which are nearly as accurate as MP2 calculations. For the 35 comparisons of conformational energies for which experimental data was available, the root mean square (rms) deviation for gradient-corrected functionals was approximately 0.5 kcal mol^?1. Without gradient corrections, the rms deviation is 0.8 kcal mol^?1, which is even less accurate than the Hartree-Fock calculations. Calculations with extended basis sets and with gradient corrections incorporated into the self-consistent procedure generate dipole moments with an rms deviation of 5%. Dipole moments from local density functional calculations, with more modest basis sets, can be scaled down to achieve roughly the same accuracy. In this study, all density functional geometries were generated by local density functional self-consistent calculations with gradient corrections added in a perturbative fashion. Such an approach generates results that are almost identical to the self-consistent gradient-corrected calculations, which require significantly more computer time. Timings on scalar and vector architectures indicate that, for moderately sized systems, our density functional implementation requires only slightly less computer resources than established Hartree-Fock programs. However, our density functional calculations scale much better and are significantly faster than their MP2 counterparts, whose results they approach. © 1995 John Wiley & Sons, Inc.     

Pi and sigma-phenylethynyl radicals and their isomers o-, m-, and p-ethynylphenyl: structures, energetics, and electron affinities

Molecular structures, energetics, vibrational frequencies, and electron affinities are predicted for the phenylethynyl radical and its isomers. Electron affinities are computed using density functional theory, -namely, the BHLYP, BLYP, B3LYP, BP86, BPW91, and B3PW91 functionals-, employing the double-zeta plus polarization DZP++ basis set; this level of theory is known to perform well for the computation of electron affinities. Furthermore, ab initio computations employing perturbation theory, coupled cluster with single and double excitations [CCSD], and the inclusion of perturbative triples [CCSD(T)] are performed to determine the relative energies of the isomers. These higher level computations are performed with the correlation consistent family of basis sets cc-pVXZ (X = D, T, Q, 5). Three electronic states are probed for the phenylethynyl radical. In C2v symmetry, the out-of-plane (2B1) radical is predicted to lie about 10 kcal/mol below the in-plane (2B2) radical by DFT methods, which becomes 9.4 kcal/mol with the consideration of the CCSD(T) method. The energy difference between the lowest pi and sigma electronic states of the phenylethynyl radical is also about 10 kcal/mol according to DFT; however, CCSD(T) with the cc-pVQZ basis set shows this energy separation to be just 1.8 kcal/mol. The theoretical electron affinities of the phenylethynyl radical are predicted to be 3.00 eV (B3LYP/DZP++) and 3.03 eV (CCSD(T)/DZP++//MP2/DZP++). The adiabatic electron affinities (EAad) of the three isomers of phenylethynyl, that is, the ortho-, meta-, and para-ethynylphenyl, are predicted to be 1.45, 1.40, and 1.43 eV, respectively. Hence, the phenylethynyl radical binds an electron far more effectively than the three other radicals studied. Thermochemical predictions, such as the bond dissociation energies of the aromatic and ethynyl C-H bonds and the proton affinities of the phenylethynyl and ethynylphenyl anions, are also reported.     

Testing the parametric two-electron reduced-density-matrix method with improved functionals: application to the conversion of hydrogen peroxide to oxywater

Parametrization of the two-electron reduced density matrix (2-RDM) has recently enabled the direct calculation of electronic energies and 2-RDMs at the computational cost of configuration interaction with single and double excitations. While the original Kollmar energy functional yields energies slightly better than those from coupled cluster with single-double excitations, a general family of energy functionals has recently been developed whose energies approach those from coupled cluster with triple excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. In this paper we test the parametric 2-RDM method with one of these improved functionals through its application to the conversion of hydrogen peroxide to oxywater. Previous work has predicted the barrier from oxywater to hydrogen peroxide with zero-point energy correction to be 3.3-to-3.9 kcal/mol from coupled cluster with perturbative triple excitations [CCSD(T)] and -2.3 kcal/mol from complete active-space second-order perturbation theory (CASPT2) in augmented polarized triple-zeta basis sets. Using a larger basis set than previously employed for this reaction-an augmented polarized quadruple-zeta basis set (aug-cc-pVQZ)-with extrapolation to the complete basis-set limit, we examined the barrier with two parametric 2-RDM methods and three coupled cluster methods. In the basis-set limit the M parametric 2-RDM method predicts an activation energy of 2.1 kcal/mol while the CCSD(T) barrier becomes 4.2 kcal/mol. The dissociation energy of hydrogen peroxide to hydroxyl radicals is also compared to the activation energy for oxywater formation. We report energies, optimal geometries, dipole moments, and natural occupation numbers. Computed 2-RDMs nearly satisfy necessary N-representability conditions.     

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.     

On the accuracy of computed excited-state dipole moments

The dipole moments of furan and pyrrole in many electronically excited singlet states have been determined using coupled cluster theory including large one-electron basis sets. The inclusion of connected triple excitations is shown to uniformly decrease the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) excitation energies by 0.04-0.24 eV, with an average reduction of 0.08 eV. Using a basis set larger than DZP (++)D (double-zeta plus polarization augmented with atom- and molecule-centered diffuse functions) uniformly increases the computed EOM-CCSD excitation energies by 0.03-0.29 eV, with an average increase of 0.20 eV. The corresponding shifts in excited-state dipole moments are more erratic. Including connected triple excitations changes the computed dipole moments by an rms amount of 0.17 au. More importantly, using a larger basis set shifts the dipole moments by an rms amount of 0.52 au, with an increase or a decrease being equally likely. The CC dipole moments are compared to those from time-dependent density functional theory (TD-DFT) computed by Burcl, Amos, and Handy [ Chem. Phys. Lett. 2002, 355, 8]. For 29 excited states of furan and pyrrole, the predicted TD-DFT dipole moments differ from the CC results by rms amounts of 1.6 au (HCTH functional) and 1.5 au (B97-1 functional). Including the asymptotic correction to TD-DFT developed by Tozer and Handy [ J. Chem. Phys. 1998, 109, 10180; J. Comput. Chem. 1999, 20, 106] reduces the rms differences for both functionals to 1.2 au. If those Rydberg excited states with very large polarizabilities are excluded, the rms differences from the CC results for the remaining 17 excited states become 1.31 au (HCTH) and 0.88 au (B97-1). For asymptotically corrected functionals and this subset of states, the rms differences from the CC results are only 0.54 au (HCTHc) and 0.34 au (B97-1c). Thus, the Tozer-Handy asymptotic correction for TD-DFT significantly improves the predictions of excited-state dipole moments. For excited states without very large polarizabilities, good agreement is achieved between excited-state dipole moments computed by coupled cluster theory and by the asymptotically corrected B97-1c density functional.     

Adiabatic corrections to density functional theory energies and wave functions

The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT.     

Behavior of density functionals with respect to basis set. 3. Basis set superposition error

The impact of basis set superposition error (BSSE) upon molecular properties determined using the density functionals B3LYP, B3PW91, B3P86, BLYP, BPW91, and BP86 in combination with the correlation consistent basis sets [cc-pVnZ, where n = D(2), T(3), Q(4), and 5] for a set of first-row closed-shell molecules has been examined. Correcting for BSSE enables the irregular convergence behavior in molecular properties such as dissociation energies with respect to increasing basis set size, noted in earlier studies, to be improved. However, for some molecules and functional combinations, BSSE correction alone does not improve the irregular convergence behavior.     

Assessment of the accuracy of density functionals for prediction of relative energies and geometries of low-lying isomers of water hexamers

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug'-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasi-perturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order M?ller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.     

Hydrogen bonding in the urea dimers and adenine–thymine DNA base pair: anharmonic effects in the intermolecular H-bond and intramolecular H-stretching vibrations

The equilibrium structures, binding energies, vibrational harmonic frequencies, and the anharmonic corrections for two different (cyclic and asymmetric) urea dimers and for the adenine–thymine DNA base pair system have been studied using the second-order Møller–Plesset perturbation theory (MP2) method and different density functional theory (DFT) exchange–correlation (XC) functionals (BLYP, B3LYP, PBE, HCTH407, KMLYP, and BH and HLYP) with the D95V, D95V**, and D95V++** basis sets. The widely used a posteriori Boys–Bernardi or counterpoise correction scheme for basis set superposition error (BSSE) has been included in the calculations to take into account the BSSE effects during geometry optimization (on structure), on binding energies and on the different levels of approximation used for calculating the vibrational frequencies. The results obtained with the ab initio MP2 method are compared with those calculated with different DFT XC functionals; and finally the suitability of these DFT XC functionals to describe intermolecular hydrogen bonds as well as harmonic frequencies and the anharmonic corrections is assessed and discussed.     

一些密度泛函方法预测电子亲和势

选取了杂化泛函B3LYP, B3PW91, O3LYP, PBE0, 以及与之相对应的GGA泛函BLYP, BPW91, OLYP和PBE, 还选取了能更好地兼顾强相互作用和弱相互作用的X3LYP泛函和在预测NMR的化学位移有较好表现的OPBE泛函, 以及两种meta-GGA泛函VSXC和TPSS, 共12种泛函, 详细地考察了这些泛函在预测EA方面的准确性.     

Effects of solvation on one- and two-photon spectra of coumarin derivatives: a time-dependent density functional theory study

We report one- and two-photon absorption excitation energies and cross sections for a series of 7-aminocoumarins using time-dependent density functional theory with various basis sets and functionals, including exchange-correlation functionals using the Coulomb-attenuating method, to evaluate their performance in the gas phase and in solvents. Except for the results of one functional, the computed one-photon excitation energies and transition dipole moments are in good agreement with experiment. The range of errors obtained from various functionals is discussed in detail. The relationship of donor and acceptor groups with the one- and two-photon resonances and intensities is also discussed.     

State-of-the-art computations of dipole moments using analytic gradients of high-level density-fitted coupled-cluster methods with focal-point approximations

Using the analytic derivatives approach, dipole moments of high-level density-fitted coupled-cluster (CC) methods, such as coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)], are presented. To obtain the high accuracy results, the computed dipole moments are extrapolated to the complete basis set (CBS) limits applying focal-point approximations. Dipole moments of the CC methods considered are compared with the experimental gas-phase values, as well as with the common DFT functionals, such as B3LYP, BP86, M06-2X, and BLYP. For all test sets considered, the CCSD(T) method provides substantial improvements over Hartree–Fock (HF), by 0.076–0.213 D, and its mean absolute errors are lower than 0.06 D. Furthermore, our results indicate that even though the performances of the common DFT functionals considered are significantly better than that of HF, their results are not comparable with the CC methods. Our results demonstrate that the CCSD(T)/CBS level of theory provides highly-accurate dipole moments, and its quality approaching the experimental results. © 2019 Wiley Periodicals, Inc.     

Multicoefficient density functional theory (MC-DFT)

We have systematically tested the performance of several pure and hybrid versions of density functional methods on different types of molecular energies by combining energies calculated using more than one basis sets. Most hybrid functionals show important performance improvement as compared to methods using only a single basis set. The results suggest that, in many cases, scaling the basis set corrections is also important for density functional theory calculation. The best method, the B1B95 functional using the cc-pVDZ/cc-pVTZ/aug-cc-pVDZ basis set combination, achieves an average accuracy of 1.76 kcal/mol on a database of 109 atomization energies, 38 hydrogen-transfer barrier heights, 38 non-hydrogen-transfer barrier heights, 13 ionization potentials, and 13 electron affinities.     

Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si)

To obtain a set of consistent benchmark potential energy surfaces (PES) for the two archetypal nucleophilic substitution reactions of the chloride anion at carbon in chloromethane (S(N)2@C) and at silicon in chlorosilane (S(N)2@Si), we have explored these PESes using a hierarchical series of ab initio methods [HF, MP2, MP4SDQ, CCSD, CCSD(T)] in combination with a hierarchical series of six Gaussian-type basis sets, up to g polarization. Relative energies of stationary points are converged to within 0.01 to 0.56 kcal/mol as a function of the basis-set size. Our best estimate, at CCSD(T)/aug-cc-pVQZ, for the relative energies of the [Cl(-), CH(3)Cl] reactant complex, the [Cl-CH(3)-Cl](-) transition state and the stable [Cl-SiH(3)-Cl](-) transition complex is -10.42, +2.52, and -27.10 kcal/mol, respectively. Furthermore, we have investigated the performance for these reactions of four popular density functionals, namely, BP86, BLYP, B3LYP, and OLYP, in combination with a large doubly polarized Slater-type basis set of triple-zeta quality (TZ2P). Best overall agreement with our CCSD(T)/aug-cc-pVQZ benchmark is obtained with OLYP and B3LYP. However, OLYP performs better for the S(N)2@C overall and central barriers, which it underestimates by 2.65 and 4.05 kcal/mol, respectively. The other DFT approaches underestimate these barriers by some 4.8 (B3LYP) to 9.0 kcal/mol (BLYP).     

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.