TPSS Functionals Research Articles

The effect of density functional and dispersion interaction on structure and bonding analysis of uranium(VI) nitride complex [NU{N(CH2CH2NSiMe3)3}]: A theoretical study

Geometry and bonding energy analysis of uranium(VI) nitride complex [NU{N(CH2CH2NSiMe3)3}] were investigated with the DFT, DFT-D3 and DFT-D3(BJ) methods using density functionals (BLYP, BP86, PW91, PBE, revPBE and TPSS). The BLYP functional yields a UN bond distance of 1.788 Å for the model complex [NU{N(CH2CH2NSiMe3)3}] which is in close agreement with the experimental value of the UN bond distance of 1.799(7) Å for [NU{N(CH2CH2NSiiPr3)3}]. The calculated Mayer bond order (2.95) and Gopinathan–Jug bond order (3.18) indicate that the UN bond in this complex is essentially UN triple bonds. The electrostatic interaction is significantly smaller than the covalent bonding. The bond dissociation energy (BDE) is largest for the functional PBE and smallest for the functional TPSS. The DFT-D3 dispersion corrections are 5.3 kcal/mol (BLYP) and 5.0 kcal/mol (TPSS).

Conformational study of the structure of 18-thiacrown-6

Conformational analysis was performed for 18-thiacrown-6 (18t6) using the CONFLEX method and the MMFF94s force field. Computations were performed for some of the low energy conformations at the HF, B3LYP, CAM-B3LYP, M06, M06L, M062x, M06HF and MP2 levels. The computations were also performed using the DFT-D3 method along with the TPSS and PBE functionals. The study predicted a new C2 conformation as the ground state conformation of 18t6. This new C2 conformation is more stable than the experimentally known solid state conformation by 4.7kcal/mol at the MP2/6-311G** level. This conformation has all of the SCCS dihedral angles adopt exodentate structure. However, the experimentally known conformation of the solid phase has two of the SCCS dihedral angles violating this exodentate rule. It was concluded that for 18t6 stability a linear dihedral SCCS angle requirement is more important than a gauche CSCC dihedral angle requirement.

Electric field gradients of transition metal complexes: Basis set uncontraction and scalar relativistic effects

The basis set dependence of density functional theory computed electric field gradients (EFG) in 3d transition metal compounds is assessed. Uncontraction of basis sets at the metal atom is crucial for a correct description of its EFG. Original and revised TPSS functionals and their hybrid variants perform best for our test set of experimental gas phase-determined nuclear quadrupole coupling constants. Recent range-separated hybrid functionals that perform well for the difficult case of CuCl, do not perform well for our larger test set. Relativistic effects for the latter, evaluated using the Douglas-Kroll-Hess and zero-order regular approximations, are found to be small.

Comparison of pure and hybrid DFT functionals for geometry optimization and calculation of redox potentials for iron nitrosyl complexes with “μ-SCN” bridging ligands

The geometry and electronic structure of neutral molecules and mono-anions of iron nitrosyl complexes with “µ-SCN” bridging ligands [(¼-SC7H4SN)Fe(NO)2]2 (I) and [(µ-SC2H3N4)Fe(NO)2]2 (II) were studied using the density functional theory: pure functionals BP86, OLYP, OPBE, TPSS, PW91 and hybrid functionals B3LYP, B1B95, B3PW91 along with 6-311++G**//6-31G*. For geometry optimization, the pure functionals are more appropriate than the hybrid functionals. For mono-anions, pure functionals favor the doublet over the quartet state by 8.0–13.9 kcal/ mol, whereas hybrid functionals yield quartet spin state of these anions to be more stable. The redox potentials of complexes I and II have been computed by DFT and compared with experimental results obtained from cyclic voltammetry method. The calculated redox potentials for I and II with pure functionals (especially BP86) are close to the experimental values, whereas those obtained by using hybrid functionals significantly deviate from the experiment.

Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions.

The nonlocal, electron density dependent dispersion correction of Vydrov and Van Voorhis (Vydrov, O. A.; Van Voorhis, T. J. Chem. Phys.2010, 133, 244103), termed VV10 or DFT-NL, has been implemented for structural optimizations of molecules. It is tested in combination with the four (hybrid)GGA density functionals TPSS, TPSS0, B3LYP, and revPBE38 for inter- and intramolecular noncovalent interactions (NCI) and compared to results from atom-pairwise dispersion corrected DFT-D3. The methods are applied to a wide range of different problems, namely the S22 and S66 test sets, large transition metal complexes, water hexamer clusters, hexahelicene, and four other difficult cases of intramolecular NCI. Critical interatomic distances are computed remarkably accurately by both dispersion corrections compared to theoretical or experimental reference data and inter- and intramolecular interactions are treated on equal footing. The methods can be recommended as reliable and robust tools for geometry optimizations of large systems in which long-range dispersion forces are crucial.

Accuracy of Several Wave Function and Density Functional Theory Methods for Description of Noncovalent Interaction of Saturated and Unsaturated Hydrocarbon Dimers.

The proper description of noncovalent complexes is a notoriously difficult problem, especially for complexes dominated by the dispersion energy. Accurate and reliable results can be obtained using computationally demanding methods such as the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction (CCSD(T)), close to the complete basis set (CBS) limit. The sizes of the noncovalent complexes of interest, however, often exceed the computational capability of available computer facilities and software. Computationally efficient yet accurate and reliable theoretical methods are highly desired. In this work, we assembled a small test set of noncovalent complexes of un/saturated a/cyclic hydrocarbon (HC) dimers in order to inspect the accuracy and reliability of several routinely used low-order scaling wave function (WFT) and density functional theory (DFT) methods. The test set comprises dispersion dominated complexes of two different monomer types, saturated and unsaturated. The unsaturated systems are relatively well populated in one of the most popular training data sets for noncovalent complexes, the S22 set of Jurečka et al. The opposite is true for saturated systems, for which rather poor performance of "approximate" methods has been observed. From the results shown is this work, it is clear that unsaturated, e.g., π···π stacked, covalent complexes are described more accurately on average. With the exception of a few "balanced methods", such as MP2C, MP2.5, SCS-/SCS(MI)-CCSD, or DFT-D3 with the TPSS and PBE functionals, a simultaneous description of saturated and unsaturated HCs introduces serious errors (i.e., more than 1 kcal/mol).

The Boron conundrum: the case of cationic clusters B n + with n = 2–20

We investigate the molecular and electronic structure and thermochemical properties of the cationic boron clusters B n + with n = 2–20, using both MO and DFT methods. Several functionals are used along with the MP2, G3, G3B3, G4, and CCSD(T)/CBS methods. The latter is the high accuracy reference. While the TPSS, TPSSh, PW91, PB86, and PBE functionals show results comparable to high-accuracy MO methods, both BLYP and B3LYP functionals are not accurate enough for three-dimensional (3D) structures. A negligible difference is observed between the B3LYP, MP2, and CCSD(T) geometries. A transition between 2D and 3D structures occurs for this series at the B16 +–B19 + sizes. While smaller clusters B n + with n ≤ 15 are planar or quasi-planar, a structural competition takes place in the intermediate sizes of B 16–19 + . The B20 + cation has a 3D tubular shape. The standard heats of formation are determined and used to evaluate the cluster stability. The average binding energy tends to increase with increasing size toward a limit. All closed-shell species B n + has an aromatic character, but an enhanced stability is found for B5 + and B13 + whose aromaticity and electron delocalization are analyzed using the LOL technique.

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps.

Density functional theory study of CO2 capture with transition metal oxides and hydroxides

We have used density functional theory (DFT) employing several different exchange-correlation functionals (PW91, PBE, PBEsol, TPSS, and revTPSS) coupled with lattice dynamics calculations to compute the thermodynamics of CO(2) absorption/desorption reactions for selected transition metal oxides, (TMO), and hydroxides, TM(OH)(2), where TM = Mn, Ni, Zn, and Cd. The van't Hoff plots, which describe the reaction equilibrium as a function of the partial pressures of CO(2) and H(2)O as well as temperature, were computed from DFT total energies, complemented by the free energy contribution of solids and gases from lattice dynamics and statistical mechanics, respectively. We find that the PBEsol functional calculations are generally in better agreement with experimental phase equilibrium data compared with the other functionals we tested. In contrast, the formation enthalpies of the compounds are better computed with the TPSS and revTPSS functionals. The PBEsol functional gives better equilibrium properties due to a partial cancellation of errors in the enthalpies of formation. We have identified all CO(2) capture reactions that lie on the Gibbs free energy convex hull as a function of temperature and the partial pressures of CO(2) and H(2)O for all TMO and TM(OH)(2) systems studied here.

The keto-enol equilibrium in substituted acetaldehydes: focal-point analysis and ab initio limit

High-level ab initio electronic structure calculations up to the CCSD(T) theory level, including extrapolations to the complete basis set (CBS) limit, resulted in high precision energetics of the tautomeric equilibrium in 2-substituted acetaldehydes (XH2C-CHO). The CCSD(T)/CBS relative energies of the tautomers were estimated using CCSD(T)/aug-cc-pVTZ, MP3/aug-cc-pVQZ, and MP2/aug-cc-pV5Z calculations with MP2/aug-cc-pVTZ geometries. The relative enol (XHC = CHOH) stabilities (ΔE e,CCSD(T)/CBS) were found to be 5.98 ± 0.17, −1.67 ± 0.82, 7.64 ± 0.21, 8.39 ± 0.31, 2.82 ± 0.52, 10.27 ± 0.39, 9.12 ± 0.18, 5.47 ± 0.53, 7.50 ± 0.43, 10.12 ± 0.51, 8.49 ± 0.33, and 6.19 ± 0.18 kcal mol−1 for X = BeH, BH2, CH3, Cl, CN, F, H, NC, NH2, OCH3, OH, and SH, respectively. Inconsistencies between the results of complex/composite energy computations methods Gn/CBS (G2, G3, CBS-4M, and CBS-QB3) and high-level ab initio methods (CCSD(T)/CBS and MP2/CBS) were found. DFT/aug-cc-pVTZ results with B3LYP, PBE0 (PBE1PBE), TPSS, and BMK density functionals were close to the CCSD(T)/CBS levels (MAD = 1.04 kcal mol−1).

Searching for Computational Strategies to Accurately Predict pKas of Large Phenolic Derivatives

Twenty-two reaction schemes have been tested, within the cluster-continuum model including up to seven explicit water molecules. They have been used in conjunction with nine different methods, within the density functional theory and with second-order Møller-Plesset. The quality of the pKa predictions was found to be strongly dependent on the chosen scheme, while only moderately influenced by the method of calculation. We recommend the E1 reaction scheme [HA + OH(-) (3H2O) ↔ A(-) (H2O) + 3H2O], since it yields mean unsigned errors (MUE) lower than 1 unit of pKa for most of the tested functionals. The best pKa values obtained from this reaction scheme are those involving calculations with PBE0 (MUE = 0.77), TPSS (MUE = 0.82), BHandHLYP (MUE = 0.82), and B3LYP (MUE = 0.86) functionals. This scheme has the additional advantage, compared to the proton exchange method, which also gives very small values of MUE, of being experiment independent. It should be kept in mind, however, that these recommendations are valid within the cluster-continuum model, using the polarizable continuum model in conjunction with the united atom Hartree-Fock cavity and the strategy based on thermodynamic cycles. Changes in any of these aspects of the used methodology may lead to different outcomes.

Genetic algorithm density functional theory study of crown ether–dibenzylammonium [2]pseudorotaxanes

Five [2]pseudorotaxanes built from the interaction of a dibenzylammonium cation with five different crown ethers have been investigated by means of high-level ab initio quantum chemical computations. A genetic algorithm has been applied to determine a series of energetically low-lying equilibrium structures for each [2]pseudorotaxane. Different sources for binding interactions such as [N +–H⋯O] and aromatic interactions ( π⋯ π stacking) are displayed by the optimised structures. In the framework of the genetic algorithm, the equilibrium structures were determined at the level of density functional theory using the meta-GGA (meta generalised gradient approximation) functional TPSS. Subsequent single-point-energy calculations at the level of second-order Møller–Plesset perturbation theory (MP2) in a large basis set (def2-TZVPP) as well as subsequent spin-component-scaled MP2 geometry optimisations were carried out. Binding energies are reported including counterpoise corrections for the basis set superposition error (BSSE) and fragment deformation energies. For two of the five systems studied theoretically, 1:1 complexes (that is, [2]pseudorotaxanes) were identified experimentally by means of 1H NMR spectroscopy, albeit with a very weak association constant for the [2]pseudorotaxane built from dibenzylammonium and the macrocyclic 12,14-diketo-benzo-25-crown-8 molecule.

Using Nonempirical Semilocal Density Functionals and Empirical Dispersion Corrections to Model Dative Bonding in Substituted Boranes.

Dative bonds to substituted boranes represent a challenge for the approximate exchange-correlation functionals typically used in density functional theory (DFT). Accurately modeling these bonds with DFT has usually required highly parametrized functionals, large admixtures of exact exchange, or computationally expensive double hybrids. This work shows that the nonempirical semilocal PBEsol functional, and the nonempirical semilocal PBE and TPSS functionals augmented with empirical interatomic dispersion corrections, accurately treat several representative problems in dative bonding. These methods typically surpass the MPW1K "kinetics" global hybrid previously recommended for dative bonds. This work also provides additional insights into the accuracy of the parametrized M06 functionals and indicates some deficiencies of the B97-D functional relative to PBE-D and TPSS-D. Applications to frustrated Lewis pairs illustrate the potential of these methods.

The Accuracy of Geometries for Iron Porphyrin Complexes from Density Functional Theory

Iron porphyrin complexes are cofactors in many important proteins such as cytochromes P450, hemoglobin, heme peroxidases, etc. Many computational studies on these systems have been done over the past decade. In this study, the performance of some of the most commonly used density functional theory functionals is evaluated with regard to how they reproduce experimental structures. Seven different functionals (BP86, PBE, PBE0, TPSS, TPSSH, B3LYP, and B97-D) are used to study eight different iron porphyrin complexes. The results show that the TPSSH, PBE0, and TPSS functionals give the best results (absolute bond distance deviations of 0.015-0.016 A), but the geometries are well-reproduced by all functionals except B3LYP. We also test four different basis sets of double-zeta quality, and we find that a combination of double-zeta basis set of Schafer et al. on the iron atom and the 6-31G* basis set on the other atoms performs best. Finally, we remove the porphyrin side chains and increase the basis set size systematically to see if this affects the results. We show that basis sets larger than double-zeta quality are not necessary to get accurate geometries, and nonaromatic side chains do not affect the geometries.

Interaction energy and the shift in OH stretch frequency on hydrogen bonding for the H2O → H2O, CH3OH → H2O, and H2O → CH3OH dimers

The ability to use calculated OH frequencies to assign experimentally observed peaks in hydrogen bonded systems hinges on the accuracy of the calculation. Here we test the ability of several commonly employed model chemistries--HF, MP2, and several density functionals paired with the 6-31+G(d) and 6-311++G(d,p) basis sets--to calculate the interaction energy (D(e)) and shift in OH stretch fundamental frequency on dimerization (delta(nu)) for the H(2)O --> H(2)O, CH(3)OH --> H(2)O, and H(2)O --> CH(3)OH dimers (where for X --> Y, X is the hydrogen bond donor and Y the acceptor). We quantify the error in D(e) and delta(nu) by comparison to experiment and high level calculation and, using a simple model, evaluate how error in D(e) propagates to delta(nu). We find that B3LYP and MPWB1K perform best of the density functional methods studied, that their accuracy in calculating delta(nu) is approximately 30-50 cm(-1) and that correcting for error in D(e) does little to heighten agreement between the calculated and experimental delta(nu). Accuracy of calculated delta(nu) is also shown to vary as a function of hydrogen bond donor: while the PBE and TPSS functionals perform best in the calculation of delta(nu) for the CH(3)OH --> H(2)O dimer their performance is relatively poor in describing H(2)O --> H(2)O and H(2)O --> CH(3)OH.

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

AbstractDensity functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (MS = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being MS = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, gav, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about −7 cm−1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

Bonding analysis for sterically uncongested simple aurocarbons CnAum

The title series of simple model aurocarbons, CAu4, C2Au2, C2Au4, C2Au6, and C6Au6, is investigated using density functional theory with TPSS and B3LYP functionals and the second-order Møller–Plesset perturbation theory, with the latest Karlsruhe basis sets. The vibrational frequencies and the 0 K thermodynamical properties are calculated. The bonding mechanism is also investigated. For C2Aun the calculated MP2 formation energy suggests increased stabilization with increasing n, due to the Au–Au aurophilic pair interactions.

Accurate interaction energies at density functional theory level by means of an efficient dispersion correction

This paper presents an approach for obtaining accurate interaction energies at the density functional theory level for systems where dispersion interactions are important. This approach combines Becke and Johnson's [J. Chem. Phys. 127, 154108 (2007)] method for the evaluation of dispersion energy corrections and a Hirshfeld method for partitioning of molecular polarizability tensors into atomic contributions. Due to the availability of atomic polarizability tensors, the method is extended to incorporate anisotropic contributions, which prove to be important for complexes of lower symmetry. The method is validated for a set of 18 complexes, for which interaction energies were obtained with the B3LYP, PBE, and TPSS functionals combined with the aug-cc-pVTZ basis set and compared with the values obtained at the CCSD(T) level extrapolated to a complete basis set limit. It is shown that very good quality interaction energies can be obtained by the proposed method for each of the examined functionals, the overall performance of the TPSS functional being the best, which with a slope of 1.00 in the linear regression equation and a constant term of only 0.1 kcal/mol allows to obtain accurate interaction energies without any need of a damping function for complexes close to their exact equilibrium geometry.

Testing the performance of density functionals for the calculation of energetic properties of complex-forming radical-molecule reactions

The performance of some popular and some more recent density functional methods for the calculation of energies of stationary points on the potential surfaces of radical-molecule reactions was examined. The functionals studied are B3-LYP, BH&H, BH&H-LYP, MPW1K, MPWB1K, TPSS, TPSSh, BB1K, M05 and M05-2X, in conjunction with nine different AO basis sets. The reaction energies, barrier heights and the relative energies of the pre-and post-reaction complexes were compared with those obtained at the CCSD(T)/CBS limit for the reactions of OH radicals with HOOH and CH3OOH. Very poor barrier heights are provided by the B3-LYP, TPSS and TPSSh functionals. The best overall performance was obtained with the BB1K, MPW1K and MPWB1K functionals. In these reactions all of the studied functionals provide converged results only if they are used with large basis sets like aug-cc-pVTZ and def2-TZVP. The data show that before relying on a functional for a specific reaction, it is desirable to make some test calculations on the performance. The same functional can predict some relative energies very well and some others very poorly even in systems including chemically similar reactants.

Water-driven structural evolution of the polar MgO (111) surface: An integrated experimental and theoretical approach

We report an experimental and theoretical analysis of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}\text{\ensuremath{-}}R30\ifmmode^\circ\else\textdegree\fi{}$ and $2\ifmmode\times\else\texttimes\fi{}2$ reconstructions on the MgO (111) surface combining transmission electron microscopy, x-ray photoelectron spectroscopy, and reasonably accurate density functional calculations using the meta-generalized gradient approximation functional TPSS [Tao, Perdew, Staroverov, and Scuseria, Phys. Rev. Lett. 91, 146401 (2003)]. The experimental data clearly show that the surfaces contain significant coverages of hydroxyl terminations, even after UHV annealing, and as such cannot be the structures which have been previously reported. For the $2\ifmmode\times\else\texttimes\fi{}2$ surfaces a relatively simple structural framework is detailed which fits all the experimental and theoretical data. For the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ there turn out to be two plausible structures and neither the experimental nor theoretical results can differentiate between the two within error. However, by examining the conditions under which the surface is formed we describe a kinetic route for the transformation between the different reconstructions that involves mobile hydroxyl groups and protons, and relatively immobile cations, which strongly suggests only one of the two $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structures.