TPSS Functionals Research Articles

Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals

We explore the simplification of widely used meta-generalized-gradient approximation (mGGA) exchange-correlation functionals to the Laplacian level of refinement by use of approximate kinetic energy density functionals (KEDFs). Such deorbitalization is motivated by the prospect of reducing computational cost while recovering a strictly Kohn-Sham local potential framework (rather than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been rather successful in solid simulations proves to be inadequate for deorbitalization but we produce other forms which, with parametrization to Kohn-Sham results (not experimental data) on a small training set, yield rather good results on standard molecular test sets when used to deorbitalize the meta-GGA made very simple, TPSS, and SCAN functionals. We also study the difference between high-fidelity and best-performing deorbitalizations and discuss possible implications for use in ab initio molecular dynamics simulations of complicated condensed phase systems.

Spin states of Mn(III) meso-tetraphenylporphyrin chloride assessed by density functional methods.

The present work assessed several exchange-correlation functionals (including GGA, meta-GGA and hybrid functionals), in combination with a variety of basis sets and effective core potentials (ECP) for their ability to predict the ground spin state of Mn(III) meso-tetraphenylporphyrin chloride complex, labeled Mn(III)TPPCl, for which experimental data support the quintet high spin state. Geometry optimization of Mn(III)TPPCl was performed for three possible spin states (singlet state, LS; triplet state, IS; and quintet state, HS) at the TPSSh level using the LANL2DZ ECP for Mn and the 6-311G(d) basis set for C, N, Cl and H. Afterwards, single-point energy calculations were conducted by applying 18 exchange-correlation functionals (BLYP, B3LYP, PW91, BPW91, BP86, OLYP, OPBE, OPW91, O3LYP, PBE0, PBEh1PBE, HSEH1PBE, TPSS, TPSSh, M06L, M06, M062X and M06HF). The influence of the basis set for the metal center was assessed using a smaller group of functionals and varying between the Pople basis set 6-31G(d), its newer formulation m6-31G(d) and the larger Def2-QZVP basis set. All functionals in combination with Pople basis sets predict the quintet state as the ground spin state. In addition, the BLYP, BP86, BPW91, PW91, PBEh1PBE, TPSS and TPSSh functionals predicted the IS lying at most ~60kJmol-1 above the HS, which agrees with the reference data. Results including Def2-QZVP basis set were inconsistent, since only BLYP and B3LYP predict HS as the ground spin state. The recommended methodology for the treatment of such systems seems to be exchange-correlations functionals with few or none Hartree-Fock exchange and modest size basis sets. Graphical Abstract MnTPPCl molecule and the energy ordering of its spin states assessed by 18 functionals.

Theoretical studies of hydrazine detection by pure and Al defected MgO nanotubes

Density Functional Theory (DFT) and time dependent density functional theory (TD-DFT) calculations using PBE and TPSS functionals have been performed to investigate the effects of the adsorption of hydrazine (N2H4) on the structural and optoelectronic features of the pure and Al defected MgO nanotubes. The calculated results for hydrazine/MgO systems reveal no remarkable changes with respect to optical and electronic features of the pure MgO after interactions. Consequently, the Al substitutions with Mg atoms placed in the middle and end sites have shown significant changes in values of the frontier molecular orbital space distribution and ground state dipole moment of states V and VII after interaction with hydrazine compared to those of hydrazine adsorbed onto pure MgO nanotubes. The quantum molecular descriptor and TD-DFT calculations show that electrons transfer from the HOMO orbitals of Al-defected MgO nanotubes to LUMO, LUMO-1 and LUMO-2 orbitals of hydrazine. This study indicates for sensor applications that Al-defected-MgO nanotubes (states X and Z) are more likely to facilitate the hydrazine detection compared to pure MgO nanotubes.

Benchmarking Density Functionals for Chemical Bonds of Gold

Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply density functionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark against 51 experimental bond enthalpies of AuX systems and seven additional polyatomic and cationic molecules. Twelve density functionals were tested, covering meta functionals, hybrids with variable HF exchange, double-hybrid, dispersion-corrected, and nonhybrid GGA functionals. The defined benchmark data set probes all types of bonding to gold from very electronegative halides that force Au+ electronic structure, via covalently bonded systems, hard and soft Lewis acids and bases that either work against or complement the softness of gold, the Au2 molecule probing gold's bond with itself, and weak bonds between gold and noble gases. Zero-point vibrational corrections are relatively small for Au-X bonds, ∼ 11-12 kJ/mol except for Au-H bonds. Dispersion typically provides ∼5 kJ/mol of the total bond enthalpy but grows with system size and is 10 kJ/mol for AuXe and AuKr. HF exchange and LYP correlation produce weaker bonds to gold. Most functionals provide similar trend accuracy, though somewhat lower for M06 and M06L, but very different numerical accuracy. Notably, PBE and TPSS functionals with dispersion display the smallest numerical errors and very small mean signed errors (0-6 kJ/mol), i.e. no bias toward over- or under-binding. Errors are evenly distributed versus atomic number, suggesting that relativistic effects are treated fairly; the mean absolute error is almost halved from B3LYP (45 kJ/mol) to TPSS and PBE (23 kJ/mol, including difficult cases); 23 kJ/mol is quite respectable considering the diverse bonds to gold and the complication of relativistic effects. Thus, studies that use DFT with effective core potentials for gold chemistry, with no alternative due to computational cost, are on solid ground using TPSS-D3 or PBE-D3.

Performance of a nonempirical density functional on molecules and hydrogen-bonded complexes.

Recently, Tao and Mo derived a meta-generalized gradient approximation functional based on a model exchange-correlation hole. In this work, the performance of this functional is assessed on standard test sets, using the 6-311++G(3df,3pd) basis set. These test sets include 223 G3/99 enthalpies of formation, 99 atomization energies, 76 barrier heights, 58 electron affinities, 8 proton affinities, 96 bond lengths, 82 harmonic vibrational frequencies, 10 hydrogen-bonded molecular complexes, and 22 atomic excitation energies. Our calculations show that the Tao-Mo functional can achieve high accuracy for most properties considered, relative to the local spin-density approximation, Perdew-Burke-Ernzerhof, and Tao-Perdew-Staroverov-Scuseria functionals. In particular, it yields the best accuracy for proton affinities, harmonic vibrational frequencies, hydrogen-bond dissociation energies and bond lengths, and atomic excitation energies.

Theoretical analysis of TcO3(OH), TcS3(OH) and TcSe3(OH)

TcO3 + and TcO3(OH) along with their S and Se analogs, TcS3 +, TcSe 3 + ,TcS3(OH) and TcSe3(OH), have been analyzed employing the hybrid meta-GGA functional TPSS. Charge, geometry, frontier orbital analysis based on the optimized structure have been done as a function of type of an atom bonded to Tc. The effect of addition of OH− group to TcS3 +, TcSe 3 + and TcO3 + on geometrical and electronic properties is discussed. Rotational barrier of the O–H bond for title molecules are calculated and discussed.

Peptide Hydration Phenomena through a Combined Quantum Chemical and Bottom-Up Approach

Abstract The M06-2X, TPSS, and B3PW91 density functionals and the classical ab initio MP2 method were used to study microsolvation around the protonated trialanine, Ala3H+. All adopted electronic structure approaches show the formation of wires or compact ring clusters of water molecules strongly bonded to peptidic polar groups through hydrogen bonds with hydration energy ranging from − 93 to –66 kcal mol –1. Independently from the adopted electronic structure methods, explicit water molecules favor peptidic chain with the polyproline II (PPII) conformation, thus the electronic energy stability order of the four unfolded conformers follows the sequence: PPII-PPII > β-PPII ∼ PPII-β > β-β, while entropy favors the reversed order. The delicate balance of electronic energy (or enthalpy) and entropy modulated by the temperature accounts for the change in abundance of the PPII and β conformations experimentally observed. The proposed bottom-up approach has been developed following the energetically dominant polar groups of peptide and water dipoles interactions. The intrapeptide dipole decoupling, caused by the β → PPII transformation, and the consequent greater dipole coupling with water molecules provide a rational base to explain the energy gain due to the explicit water coordination to PPII residues.

Influence of the Density Functional and Basis Set on the Relative Stabilities of Oxygenated Isomers of Diiron Models for the Active Site of [FeFe]-Hydrogenase

A series of different density functional theory (DFT) methodologies (24 functionals) in conjunction with a variety of six different basis sets (BSs) was employed to investigate the relative stabilities in the oxygenated isomers of diiron complexes that mimic the active site of [FeFe]-hydrogenase: (μ-pdt)[Fe(CO)2L][Fe(CO)2L'] (pdt = propane-1,3-dithiolate; L = L' = CO (1); L = PPh3, L' = CO (2); L = PMe3, L' = CO (3); L = L' = PMe3 (4). Although the enzyme may have a variety of possible sites for oxygenation, the model complexes would necessarily be oxygenated at either the diiron bridging site (μ-O) or at a sulfur (SO). Previous DFT studies with both B3LYP and TPSS functionals predicted a more stable μ-O isomer, whereas only the SO isomer was observed experimentally (J. Am. Chem. Soc. 2009, 131, 8296-8307). Here, further calculations reveal that the relative stabilities of the SO and μ-O isomers are extremely sensitive to the choice of the functional, moderately sensitive to the S basis set, but not to the Fe basis set. The relative free energies [Gsolv(μ-O) - Gsolv(SO)] range from +10 to -60 kcal/mol, a range much larger than what would have been expected on the basis of the previous DFT results. Benchmarking of these results against coupled cluster with single and double excitation calculations, which predict that the SO isomer is favored, shows that the best performing functionals are BP86 and PBE0, while B97-D, M05, and SVWN overestimate and B2PLYP, BH&HLYP, BMK, M06-HF, and M06-2X underestimate the energy differences. Most of the variation occurs with the μ-O isomer and appears to be associated with a functional's ability to predict the strength of the Fe-Fe bond in the reactant. With respect to the S basis set, it appears that the S═O bond is sensitive to the nature of the d polarization functions available on the S atom. The S seems to need a d function more diffuse than the d orbital optimized to provide polarization for the S atom alone; that is, S seems to need a d orbital that has strong overlap with the O atom's valence 2p. Other basis functions and the relative position of the PR3 (R = Ph and Me) substituent groups have smaller influences on the free energy differences.

Theoretical study on the reaction mechanism of carbon dioxide reduction to methanol using a homogeneous ruthenium(II) phosphine catalyst

Quantum-chemical calculations using the density functional TPSS were carried out for the catalytic reduction of carbon dioxide to methanol using a ruthenium catalyst and hydrogen gas. Preparation of the active species as well as the catalytic cycle were modeled on the quantum-chemical level with solvent effects included by means of a continuum solvation model. Outer as well as inner sphere mechanisms were considered to gain insight into the details of carbon dioxide reduction using a ruthenium(II) catalyst. The overall Gibbs free reaction energy for CO2+3 H2→MeOH+H2O is computed to be −13.0kJ/mol. The highest reaction barrier (112.4kJ/mol) is found for the outer sphere hydrogen transfer from the active ruthenium species to carbon dioxide via a five-membered transition state structure.

C–Cl Bond Activation on Au/Pd Bimetallic Nanocatalysts Studied by Density Functional Theory and Genetic Algorithm Calculations

The C–Cl bond activation by Au/Pd bimetallic alloy nanocatalysts has been investigated with regard to the oxidative addition of chlorobenzene (PhCl). Fifteen stable structures of the Au10Pd10 nanocluster (NC) obtained by a genetic algorithm were examined by DFT calculations using the M06-L, TPSS, and B3LYP functionals. Triplet states of cage-like C1 and Cs structures are found to be relevant reflecting the quasi-degenerate nature of the Pd moiety, while several other low-lying structures and spin states may also contribute to the oxidative addition. For all examined cluster structures, the oxidative addition step is exothermic, and internal conversion and/or spin crossing are expected to occur as several states are close in energy and geometry. Based on an energetic analysis of a model system consisting of the Au10Pd10 NC surrounded by four poly(n-vinylpyrrolidone) (PVP) molecules, the PVP units activate the system as electron donors and stabilize it. While a neutral NC model overestimates the energy barr...

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species.

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized-gradient approximation (GGA), nonlocal correlation, meta-GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised-RPBE, vdW-DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW-DF and meta-GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of -2.62 and -1.1% for the N-N stretching and Rh-H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh-H and N-N stretching modes from the bulk phonons and by solving one- and two-dimensional Schrödinger equation associated with the Rh-H, Rh-N, and N-N potential energy we calculated the anharmonic correction for N-N and Rh-H stretching modes as -31 cm(-1) and -77 cm(-1) at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments.

Complex formation of Sn(II) with glycine: An IR, DTA/TGA and DFT investigation

The novel Sn(Gly)2⋅H2O complex compound has been synthesized and characterized by TGA, IR and Raman spectroscopy. Molecular spectroscopy and ab initio simulation have given the evidence of glycine molecule being coordinated to Sn(II) as bidentate chelating ligand by oxygen atom of carboxyl group and nitrogen atom of amino group. Water molecule is bonded with amino and carboxylic groups by hydrogen bonds in the out sphere. The M06, TPSS, TPSSm, TPSSh and revTPSS density functionals have been tested for calculation of structural and vibrational data. The vibrational assignment of experimental IR and Raman and simulated spectra has been carried out. The TPSS and TPSSm density functionals and Def2-TZVP basis set have provided the most accurate results.

Communication: double-hybrid functionals from adiabatic-connection: the QIDH model.

A new approach stemming from the adiabatic-connection (AC) formalism is proposed to derive parameter-free double-hybrid (DH) exchange-correlation functionals. It is based on a quadratic form that models the integrand of the coupling parameter, whose components are chosen to satisfy several well-known limiting conditions. Its integration leads to DHs containing a single parameter controlling the amount of exact exchange, which is determined by requiring it to depend on the weight of the MP2 correlation contribution. Two new parameter-free DHs functionals are derived in this way, by incorporating the non-empirical PBE and TPSS functionals in the underlying expression. Their extensive testing using the GMTKN30 benchmark indicates that they are in competition with state-of-the-art DHs, yet providing much better self-interaction errors and opening a new avenue towards the design of accurate double-hybrid exchange-correlation functionals departing from the AC integrand.

Benchmarking quantum chemical methods for the calculation of molecular dipole moments and polarizabilities.

The calculation of molecular electric moments, polarizabilities, and electrostatic potentials is a widespread application of quantum chemistry. Although a range of wave function and density functional theory (DFT) methods have been applied in these calculations, combined with a variety of basis sets, there has not been a comprehensive evaluation of how accurate these methods are. To benchmark the accuracy of these methods, the dipole moments and polarizabilities of a set of 46 molecules were calculated using a broad set of quantum chemical methods and basis sets. Wave function methods Hartree-Fock (HF), second-order Møller-Plesset (MP2), and coupled cluster-singles and doubles (CCSD) were evaluated, along with the PBE, TPSS, TPSSh, PBE0, B3LYP, M06, and B2PLYP DFT functionals. The cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, aug-cc-pVTZ, and Sadlej cc-pVTZ basis sets were tested. The aug-cc-pVDZ, Sadlej cc-pVTZ, and aug-cc-pVTZ basis sets all yield results with comparable accuracy, with the aug-cc-pVTZ calculations being the most accurate. CCSD, MP2, or hybrid DFT methods using the aug-cc-pVTZ basis set are all able to predict dipole moments with RMSD errors in the 0.12-0.13 D range and polarizabilities with RMSD errors in the 0.30-0.38 Å(3) range. Calculations using Hartree-Fock theory systematically overestimated dipole moments and underestimate polarizabilities. The pure DFT functionals included in this study (PBE and TPSS) slightly underestimate dipole moments and overestimate polarizability. Polarization anisotropy and implications for charge fitting are discussed.

Quantum chemical approaches to the explanation of differences in NO-donor activity of iron-sulfur nitrosyl complexes

The geometries and electronic structures of iron-sulfur nitrosyl complexes with azaheterocyclic thiols with μ-SCN bridging ligands, [Fe2(SCN4Ph)2(NO)4] (1) and [Fe2(SCN4Me)2(NO)4] (2), were calculated within the framework of the density functional theory (DFT) with the BP86, TPSS, B3LYP, and OPBE functionals in order to explain differences in their NO-donor activities. Chemical bonding in the complexes was analyzed using the NBO approach, according to Mulliken, and using the Voronoi scheme. NBO analysis of complex 1 revealed a strong interaction between orbitals of the lone electron pairs of the Fe atom and the antibonding orbitals of the Fe-N bond which leads to strengthening of the Fe-NO bond. In complex 2, the Fe-NO bond is more polar than in complex 1.

On the Innocence of Bipyridine Ligands: How Well Do DFT Functionals Fare for These Challenging Spin Systems?

The electronic structures of a number of iron, cobalt, vanadium, and titanium complexes with the 2,2'-bipyridine (bpy) ligand were considered using the multireference CASSCF and NEVPT2 methods. Many of these systems have been studied in the past using B3LYP and were then found to contain the bpy ligand as a radical anion. For many of the cases, this is contradicted by our multireference calculations. While there are instances where the ligand is indeed a radical anion, in many cases it remains neutral and is involved in backbonding from the metal center. For those cases where CASSCF is too costly, a number of DFT functionals, including the newer double-hybrid functionals, were evaluated against the CASSCF data. It was found that nonhybrid functionals, especially those containing the kinetic energy density τ, were the best at predicting the electronic nature of the complexes. The τ-HCTH and HCTH functionals were the top performers, correctly predicting eleven out of eleven test cases and with the lowest mean unsigned errors (MUE, 7.6 and 7.8 kcal·mol(-1), respectively); the M06-L, N12, BLYP, PBE, and TPSS functionals also did well, while B3LYP had significant problems.

Dispersion interactions with density functional theory: Bonding description of V–NS bond in vanadium–thionitrosyl complex [(nacnac)(OAr)V(NS)

Dispersion corrected quantum chemical calculations of the complex [(nacnac)(OAr)V(NS)] were investigated at DFT, DFT-D3 and DFT-D3(BJ) level using BP86, PBE, revPBE, PW91 and TPSS functionals. The V–NS bond has essentially multiple bond character. The V–NS bond is relatively stronger than the calculated V–NO bond in the complex [(nacnac)(OAr)V(NO)]. The thionitrosyl ligand is stable in doublet state while [V(nacnac)(OAr)] fragment is stable in quartet state. The V–NS bond dissociation energies considering either doublet or quartet states of the interacting fragments vary in the order 77.2 (revPBE)<82.1 (BP86)<87.1 (PW91). The dispersion interaction energy has significant contribution to the V–NS bond dissociation energy. The dispersion corrections with DFT-D3 methods are smaller than the corresponding DFT-D3(BJ). The V–NS bond has a larger covalent character than the ionic character.

Complex formation of Sn(II) with l-cysteine: An IR, DTA/TGA and DFT Investigation

The novel complex of Sn(II) with l-cysteine (L-H2Cys) has been synthesized and characterized by elemental analysis, TGA and IR spectroscopy. Vibrational assignment and DFT/PBE0/def2-TZVP ab initio simulation give evidence of cysteine molecule being coordinated to Sn(II) as three-dentate chelating N,O,S-donor ligand. The four Perdew density functionals TPSS, PBE0, PBE, TPSSh have been tested to provide consistency of simulated and experimental IR spectra, the best result is provided by unweighted Hartree-Fock density functionals (PBE, TPSS). On the contrary, the Hartree-Fock weighted functionals (PBE0, TPPSh) provide the most accurate geometry optimization. Unharmonic frequencies are obtained via ab initio vibrational self-consistent field (PT2-VSCF) calculations at DFT/TPSS/Def2-TZVP level, the vibrational assignment of IR spectra has been carried out.

Structure and bonding energy calculations of nitrosyl, thionitrosyl and selenonitrosyl complexes [(PNP)Ir(NX)]+ (X = O, S, Se): A DFT study

Structure and bonding analyses of the complexes [(PNP)Ir(NX)]+ (X=O, S, Se; PNP=N(CHCHPMe2)2) were investigated at the DFT, DFT-D3 and DFT-D3(BJ) levels using BP86, BLYP, PBE, revPBE and TPSS functionals. The Ir–NX bond in the thionitrosyl complex is longer than that in the nitrosyl and selenonitrosyl complexes, which is consistent with the observed trend for their experimental values. The Ir–NX bond has essentially IrNX double bond character, which supports the σ-donor and π-acceptor abilities of the [NX]+ ligands. The non-covalent P–NX distances decrease in the order DFT>DFT-D3>DFT-D3(BJ). The Ir–NX bond has a larger covalent character (85.7, 75.9 and 74.6%). Dispersion interactions between the metal and [NX]+ fragments are in the range 3.2–5.5kcal/mol (BP86), 3.2–5.4kcal/mol (BLYP), 1.9–3.1kcal/mol (PBE), 3.5–5.5kcal/mol (revPBE) and 2.6–3.8kcal/mol (TPSS), which are smaller than the corresponding DFT-D3(BJ) dispersion corrections 4.9–8.6kcal/mol (BP86), 5.2–7.9kcal/mol (BLYP), 2.7–4.0kcal/mol (PBE), 5.3–7.6kcal/mol (revPBE) and 2.7–5.2kcal/mol (TPSS). The dispersion corrected DFT (DFT-D3 and DFT-D3(BJ)) methods provide quite an accurate estimate of the dispersion energy, which can be judged by the observation that the experimental and optimized Ir–NX bond distances are consistent with the most accurate dispersion corrected DFT-D3(BJ) bond dissociation energy of Ir–NX bonds.

Accurate Structure and Bonding Description of the Transition Metal-Disulfur Monoxide Complexes [(PMe3)2M(S2O)] (M= Ni, Pd, Pt): Grimme Dispersion Corrected DFT Study

Geometry and bonding energy analysis of M–S2O bonds in the metal-disulfur monoxide complexes [(PMe3)2M(S2O)] of nickel, palladium, and platinum were investigated at DFT, DFT-D3, and DFT-D3(BJ) methods using three different functionals (BP86, PBE, and TPSS). The TPSS/DFT-D3(BJ) yields better geometry, while the BP86 geometry is least accurate for studied complexes. The geometry of platinum complex optimized at TPSS/DFT-D3(BJ) level is in excellent agreement with the available experimental values. The M–S bonds are shorter than the M–S(O) bonds. The Mayer bond orders suggest the presence of M–S and M–S(O) single bonds. Both the M–S and M–S(O) bond lengths vary with the density functionals as TPSS-D3(BJ) < TPSS < PBE < BP86. The Hirshfeld charge distribution indicates that the overall charge flows from metal fragment to [S2O]. The Ni–S2O bond has greater degree of covalent character than the ionic. The contribution of dispersion interactions is large in computing accurate bond dissociation energies between the interacting fragments. The BDEs are largest for the functional TPSS and smallest for the functional BP86. The DFT-D3 dispersion corrections to the BDEs between the metal fragments [(PMe3)2M] and ligand fragment [(S2O)] for the TPSS functional are in the range 7.1–7.3 kcal·mol–1, which are smaller than the corresponding DFT-D3(BJ) dispersion corrections (9.4–10.6 kcal·mol–1).