DFT studies using supercells and projector-augmented waves for structure, energetics, and dynamics of glycine, alanine, and cysteine

A large variety of gas phase conformations of the amino acids glycine, alanine, and cysteine is studied by numerically efficient semi-local gradient-corrected density functional theory calculations using a projector-augmented wave scheme and periodic boundary conditions. Equilibrium geometries, conformational energies, dipole moments, vibrational modes, and IR optical spectra are calculated from first principles. A comparison of our results with values obtained from quantum-chemistry methods with localized basis sets and nonlocal exchange-correlation functionals as well as with experimental data is made. For conformations containing strong intramolecular hydrogen bonds deviations in their energetic ordering occur, which are traced back to different treatments of spatial nonlocality in the exchange-correlation functional. However, even for these structures, the comparison of calculated and measured vibrational frequencies shows satisfying agreement.     

A comparative quantum mechanical study of bond separation energies as a measure of cyclic conjugation

Restricted Hartree-Fock (RHF), second-order Møller-Plesset (MP2), and density functional calculations [using the Becke/Lee-Yang-Parr (B-LYP) exchange/correlation gradient-corrected functionals] employing the 6-311G(d, p) and 6-311 + + G(d, p) basis sets have been carried out to calculate isodesmic bond separation energies for reactions involving a number of representative five- and six-membered ring organic compounds. The MP2 and density functional approaches yield reasonably good energies; the density functional method agrees particularly well with experiment, exhibiting a root-mean-square error of only 2.5 kcal/mol. Ring geometries are calculated satisfactorily in all approaches but are given particularly accurately by the MP2 approach. A comparison of the B-LYP bond separation energies with several other definitions of resonance energy shows that these different approaches correlate with each other in a reasonable fashion. © 1995 John Wiley & Sons, Inc.     

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.     

Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn—Sham equation using several density functionals

The performance of four commonly used density functionals (VWN, BLYP, BP91, and Becke's original three-parameter approximation to the adiabatic connection formula, referred to herein as the adiabatic connection method or ACM) was studied with a series of six Gaussian-type atomic basis sets [DZP, 6–31G**, DZVP, TZVP, TZ2P, and uncontracted aug-cc-pVTZ (UCC)]. The geometries and dipole moments of over 100 first-row and second-row molecules and reaction energies of over 300 chemical reactions involving such molecules were computed using each of the four density functionals in combination with each of the six basis sets. The results were compared to experimentally determined values. Based on overall mean absolute theory versus experiment errors, it was found that ACM is the best choice for predictions of both energies of reaction [overall mean absolute theory versus experiment error (MATvEE) of 4.7 kcal/mol with our most complete (UCC) basis set] and molecular geometries (overall MATvEE of 0.92 pm for bond distances and 0.88° for bond angles with the UCC basis set). For routine calculations with moderate basis sets (those of double-ζ type: DZP, 6–31G**, and DZVP) the DZVP basis set was, on average, the best choice. There were, however, examples of reactions where significantly larger basis sets were required to achieve reasonable accuracy (errors ≤ 5 kcal/mol). For dipole moments, ACM, BP91, and BLYP performed comparably (overall MATvEE of 0.071, 0.067, and 0.059 debye, respectively, with the UCC basis set). Basis sets that include additional polarization functions and diffuse functions were found to be important for accurate density functional theory predictions of dipole moments. © 1997 by John Wiley & Sons, Inc.     

Theoretical and experimental study of the structure and vibration spectra of 4,4′-carbonyl-di-morpholine

4,4′-Carbonyl-di-morpholine was synthesized and characterized by X-ray diffraction, the FTIR and NMR spectra. The extended MO calculations using density functional theory (DFT) and self-consistent field molecular orbital Hartree-Fock theory were carried out. The results of the calculations were compared with experimental data. The experimental and calculated results were supported each other. The performance of a hybrid B3LYP density functional was compared with the ab initio restricted Hartree-Fock method. With the basis sets of the 6-311G** quality, the DFT calculated bond lengths, dipole moments and harmonic vibrations were predicted in a very good agreement with available experimental data.     

Molecular dynamics simulation of liquid water: hybrid density functionals

The structure, dynamical, and electronic properties of liquid water utilizing different hybrid density functionals were tested within the plane wave framework of first-principles molecular dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calculations of the structural and bonding properties of the water dimer and cyclic water trimer. Liquid water simulations were performed at the state point of 350 K at the experimental density. Simulations included three different hybrid functionals, a meta-functional, four gradient-corrected functionals, and the local density and Hartree-Fock approximations. It is found that hybrid functionals are superior in reproducing the experimental structure and dynamical properties as measured by the radial distribution function and self-diffusion constant when compared to the pure density functionals. The local density and Hartree-Fock approximations show strongly over- and understructured liquids, respectively. Hydrogen bond analysis shows that the hybrid functionals give slightly smaller average numbers of hydrogen bonds than pure density functionals but similar hydrogen bond populations. The average molecular dipole moments in the liquid from the three hybrid functionals are lower than those of the corresponding pure density functionals.     

Performance of molecular orbital methods and density functional theory in the computation of geometries and energies of metal aqua ions

Geometries and energies of various metal aqua ions have been computed with Hartree-Fock (HF), single-reference second-order perturbation theory according to M?ller and Plesset (MP2), complete active space self-consistent field (CAS-SCF) methods, multi-configurational quasi-degenerate second-order perturbation theory (MCQDPT2), and density functional theory (DFT), whereby for the latter the most widely used functionals BLYP, B3LYP, LDA ("local density approximation"), and another functional (SOP) exhibiting Slater exchange, have been investigated. The geometries as well as the energies are sensitive to the computational method, results of which can lead to different conclusions. The geometries of certain reactants, products, intermediates, or transition states cannot be obtained with all of the above-mentioned computational methods: in some cases, the structures are very poor, exhibiting large errors in the bond parameters, and in others, the targeted species cannot be calculated at all. The different computational techniques do not always predict the same coordination number of a given aqua ion or the same preferred water exchange mechanism. Inaccuracies arising from inadequate basis sets are also discussed.     

A challenge for density functional theory: the XONO and XNO2 (X=F, Cl, and Br) molecules

The equilibrium geometries, harmonic frequencies, dipole moments, infrared intensities, and relative energies of the cis-XONO, trans-XONO, and XNO₂ (X=F, Cl, and Br) have been investigated using four functionals in common use in Kohn-Sham density functional theory (DFT) calculations. Two of the functionals include non-local or gradient correction terms, while the other two also incorporate some exact Hartree-Fock exchange and are labeled hybrid functionals. The quality of the results obtained from the functionals is determined by comparison to previously published high-level coupled-cluster calculations. The hybrid functionals perform better for prediction of the equilibrium geometries, where the two gradient corrected functionals yield qualitatively incorrect molecular structures for cis-FONO and cis-ClONO. None of the functionals perform well in predicting all six harmonic frequencies, showing that the correlation between equilibrium geometries and harmonic frequencies is not as strong for these DFT methods as it is for conventional wavefunction ab initio methods, such as coupled-cluster theory. Results from the various functionals generally come into better agreement with each other and also with the coupled-cluster results moving down the periodic table. Received: 12 February 1997 / Accepted: 25 March 1997     

An assessment of pure,hybrid, meta,and hybrid‐meta GGA density functional theory methods for open‐shell systems: The case of the nonheme iron enzyme 8R–LOX

The performance of a range density functional theory functionals combined in a quantum mechanical (QM)/molecular mechanical (MM) approach was investigated in their ability to reliably provide geometries, electronic distributions, and relative energies of a multicentered open‐shell mechanistic intermediate in the mechanism 8R–Lipoxygenase. With the use of large QM/MM active site chemical models, the smallest average differences in geometries between the catalytically relevant quartet and sextet complexes were obtained with the B3LYP^* functional. Moreover, in the case of the relative energies between ⁴II and ⁶II , the use of the B3LYP^* functional provided a difference of 0.0 kcal mol^–1. However, B3LYP^± and B3LYP also predicted differences in energies of less than 1 kcal mol^–1. In the case of describing the electronic distribution (i.e., spin density), the B3LYP^*, B3LYP, or M06‐L functionals appeared to be the most suitable. Overall, the results obtained suggest that for systems with multiple centers having unpaired electrons, the B3LYP^* appears most well rounded to provide reliable geometries, electronic structures, and relative energies. © 2012 Wiley Periodicals, Inc.     

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.     

Small basis sets for calculations of barrier heights, energies of reaction, electron affinities, geometries, and dipole moments

Beginning with the MIDI! basis set (also called MIDIX), we introduce the MIDIX+, MIDIY, and MIDIY+ basis sets. Using correlated ab initio and hybrid density functional theory, we compare their performance to that of several existing basis sets for electronic structure calculations. The new basis sets are tested with databases of 358 energies of reactions, 44 barrier heights, 31 electron affinities, 18 geometries, and 29 dipole moments. The MIDI!, MIDIX+, MIDIY, and MIDIY+ basis sets are shown to be cost-efficient methods for calculating relative energies, geometries, and dipole moments. The MIDIX+ basis is shown to be particularly efficient for calculating electron affinities of large molecules.Contribution to the Jacopo Tomasi Honorary Issue     

Gaussian-3 and related methods for accurate thermochemistry

In this paper, we present an overview of Gaussian-3 (G3) theory, a composite technique that employs a sequence of ab initio molecular orbital calculations to derive a total energy of a given molecular species. This method provides accurate energies of molecular systems for the calculation of enthalpies of formation, ionization potentials, electron affinities, proton affinities, etc. Also covered in this review are several variants of G3 theory including one based on scale factors (G3S) and an extended version (G3X) that uses improved geometries and larger Hartree-Fock basis sets. Finally, the G3/99 test set of accurate experimental data that is used for critical assessment is described. Overall, G3 theory has a mean absolute deviation from experiment of 1.07 kcal mol⁻¹ for the G3/99 test set and G3S theory has a similar accuracy of 1.08 kcal mol⁻¹. G3X theory is significantly more accurate with the mean absolute deviation from experiment decreasing from 1.07 kcal mol⁻¹ (G3) to 0.95 kcal mol⁻¹ (G3X). The scaled version of G3X theory shows a similar improvement. Received: 23 January 2002 / Accepted: 7 April 2002 / Published online: 4 July 2002     

The role of errors related to DFT methods in calculations involving ion pairs of ionic liquids

Ionic liquids (ILs) play a key role in many chemical applications. As regards the theoretical approach, ILs show added difficulties in calculations due to the composition of the ion pair and to the fact that they are liquids. Although density functional theory (DFT) can treat this kind of systems to predict physico–chemical properties, common versions of these methods fail to perform accurate predictions of geometries, interaction energies, dipole moments, and other properties related to the molecular structure. In these cases, dispersion and self‐interaction error (SIE) corrections need to be introduced to improve DFT calculations involving ILs. We show that the inclusion of dispersion is needed to obtain good geometries and accurate interaction energies. SIE needs to be corrected to describe the charges and dipoles in the ion pair correctly. The use of range–separated functionals allows us to obtain interaction energies close to the CCSD(T) level. © 2017 Wiley Periodicals, 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.     

DNA base trimers: empirical and quantum chemical ab initio calculations versus experiment in vacuo

A complete scan of the potential‐energy surfaces for selected DNA base trimers has been performed by a molecular dynamics/quenching technique using the force field of Cornell et al. implemented in the AMBER7 program. The resulting most stable/populated structures were then reoptimized at a correlated ab initio level by employing resolution of the identity, Møller–Plesset second‐order perturbation theory (RI‐MP2). A systematic study of these trimers at such a complete level of electronic structure theory is presented for the first time. We show that prior experimental and theoretical interpretations were incorrect in assuming that the most stable structures of the methylated trimers corresponded to planar systems characterized by cyclic intermolecular hydrogen bonding. We found that stacked structures of two bases with the third base in a T‐shape arrangement are the global minima in all of the methylated systems: they are more stable than the cyclic planar structures by about 10 kcal mol^?1. The different behaviors of nonmethylated and methylated trimers is also discussed. The high‐level geometries and interaction energies computed for the trimers serve also as a reference for the testing of recently developed density functional theory (DFT) functionals with respect to their ability to correctly describe the balance between the electrostatic and dispersion contributions that bind these trimers together. The recently reported M052X functional with a polarized triple‐zeta basis set predicts 11 uracil trimer interaction energies with a root‐mean‐square error of 2.3 kcal mol^?1 relative to highly correlated ab initio theoretical calculations.     

Electrostatic interactions in molecular mechanics (MM2) calculations via PEOE partial charges I. Haloalkanes

The PEOE (partial equalization of orbital electronegativity) procedure has been modified slightly and reparametrized for haloalkanes to calculate partial atomic charges suitable for evaluation of dipole moments and electrostatic energies in conjunction with molecular mechanics (MM2) calculations. Dipole moments of 66 haloalkanes are calculated with an average absolute deviation of 0.14 D from experimental values. The conformational energies of 40 compounds have been calculated and the agreement with experimental data is generally good and compares well with calculations by the IDME (induced dipole moment and energy) method. In addition, carbon and proton charges correlate well with C-1s core binding energies and ¹H-NMR (nuclear magnetic resonance) shifts for halomethanes. The most striking benefit of treating electrostatics through a set of partial charges compared to the standard MM2 bond dipole approach is demonstrated by calculations on 1,4-disubstituted cyclohexanes, for which standard MM2 fails to predict the most stable conformation.     

Conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete

The conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero-point vibrational energies are computed for all pertinent molecular systems using SCF theory, second-order perturbation theory, and density functional theory and employing the correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ. Single-point fourth-order perturbation theory, CCSD, and CCSD(T) calculations employing the cc-pVTZ and the cc-pVQZ basis sets are computed using the MP2/cc-pVTZ and MP2/cc-pVQZ optimized geometries, respectfully, to ascertain the contribution of higher order correlation. Three DFT functionals, B3LYP, wB97XD, and M06-2X, are employed to determine whether they can yield results similar to those obtained at the CCSD(T) level.     

Extension of the PDDG/PM3 and PDDG/MNDO semiempirical molecular orbital methods to the halogens

The new semiempirical methods, PDDG/PM3 and PDDG/MNDO, have been parameterized for halogens. For comparison, the original MNDO and PM3 were also reoptimized for the halogens using the same training set; these modified methods are referred to as MNDO' and PM3'. For 442 halogen-containing molecules, the smallest mean absolute error (MAE) in heats of formation is obtained with PDDG/PM3 (5.6 kcal/mol), followed by PM3' (6.1 kcal/mol), PDDG/MNDO (6.6 kcal/mol), PM3 (8.1 kcal/mol), MNDO' (8.5 kcal/mol), AM1 (11.1 kcal/mol), and MNDO (14.0 kcal/mol). For normal-valent halogen-containing molecules, the PDDG methods also provide improved heats of formation over MNDO/d. Hypervalent compounds were not included in the training set and improvements over the standard NDDO methods with sp basis sets were not obtained. For small haloalkanes, the PDDG methods yield more accurate heats of formation than are obtained from density functional theory (DFT) with the B3LYP and B3PW91 functionals using large basis sets. PDDG/PM3 and PM3' also give improved binding energies over the standard NDDO methods for complexes involving halide anions, and they are competitive with B3LYP/6-311++G(d,p) results including thermal corrections. Among the semiempirical methods studied, PDDG/PM3 also generates the best agreement with high-level ab initio G2 and CCSD(T) intrinsic activation energies for S(N)2 reactions involving methyl halides and halide anions. Finally, the MAEs in ionization potentials, dipole moments, and molecular geometries show that the parameter sets for the PDDG and reoptimized NDDO methods reduce the MAEs in heats of formation without compromising the other important QM observables.     

Quantum-chemical study of the molecular forms of vanillin

Equilibrium structural parameters, dipole moments, relative energies, vibration spectra, and ionization potentials of various conformers of benzoid (B), p- and o-quinoid (Q), and deprotonated anionic forms of vanillin in a vacuum and in a polarizable medium with dielectric properties of water were calculated by the quantum-chemical method (U)B3LYP/cc-pVTZ. The intramolecular hydrogen bond in free vanillin benzoid molecule B1 is characterized by the energy of 4 kcal mol⁻¹ and by the barrier of cleavage 8 kcal mol⁻¹ that correspond to the conformational transition B1 → B2. The energy of the optimal p-quinoid conformer (Q1) is 22 kcal mol⁻¹ larger than the energy of B1 in a vacuum and 15 kcal mol⁻¹ in water. The p-quinoid forms greatly exceeds the benzoid forms by dipole moment, electrophilicity, and nucleophilicity. The structure calculated for the anion is intermediate between benzoid and p-quinoid forms, and the calculated energy of polarization stabilization in water is 57 kcal mol⁻¹.     

On geometries of stacked and H-bonded nucleic acid base pairs determined at various DFT, MP2, and CCSD(T) levels up to the CCSD(T)/complete basis set limit level

The geometries and interaction energies of stacked and hydrogen-bonded uracil dimers and a stacked adeninecdots, three dots, centeredthymine pair were studied by means of high-level quantum chemical calculations. Specifically, standard as well as counterpoise-corrected optimizations were performed at second-order Moller-Plesset (MP2) and coupled cluster level of theory with single, double, and perturbative triple excitations [CCSD(T)] levels with various basis sets up to the complete basis set limit. The results can be summarized as follows: (i) standard geometry optimization with small basis set (e.g., 6-31G(*)) provides fairly reasonable intermolecular separation; (ii) geometry optimization with extended basis sets at the MP2 level underestimates the intermolecular distances compared to the reference CCSD(T) results, whereas the MP2/cc-pVTZ counterpoise-corrected optimization agrees well with the reference geometries and, therefore, is recommended as a next step for improving MP2/cc-pVTZ geometries; (iii) the stabilization energy of stacked nucleic acids base pairs depends considerably on the method used for geometry optimization, so the use of reliable geometries, such as counterpoise-corrected MP2/cc-pVTZ ones, is recommended; (iv) the density functional theory methods fail completely in locating the energy minima for stacked structures and when the geometries from MP2 calculations are used, the resulting stabilization energies are strongly underestimated; (v) the self-consistent charges-density functional tight binding method, with inclusion of the empirical dispersion energy, accurately reproduces interaction energies and geometries of dispersion-bonded (stacked) complexes; this method can thus be recommended for prescanning the potential energy surfaces of van der Waals complexes.