Hybrid GGA Functionals Research Articles

Evaluating the Chemical Reactivity of DFT-Simulated Liquid Water with Hydrated Electrons via the Dual Descriptor.

Modeling the various properties of liquid water, particularly its reactivity, has been a longstanding challenge for simulation methods. Recently, ab initio simulations based on density functional theory (DFT) have come to the fore as tenable methods for calculating the properties and reactivity of water, with varying degrees of success for different exchange-correlation functionals. In particular, hybrid-GGA and meta-GGA functionals have been shown to reproduce many of the structural, dynamical, and energetic properties of water to a high degree of accuracy relative to their computational cost. Here, we show that the dual descriptor (DD) measure of nucleophilicity and electrophilicity, which is sometimes used to elucidate organic chemistry reaction mechanisms, can also be used to characterize the reactivity of DFT-simulated liquid water. The DD is especially apt for understanding the reactivity of excess electrons with water as its calculation explicitly involves adding and removing an excess electron from a reference system. We use the DD to explore the reactivity of water simulated using three different DFT functionals: the LDA functional (LDA), a hybrid-GGA functional (PBE0), and a hybrid meta-GGA functional (SCAN0). Using the DD, we show that the SCAN0 functional with the standard 25% Hartree-Fock exchange produces simulated liquid water with many regions that are far more reactive than either PBE0 or LDA. To understand the implications of these highly reactive regions, we then add a strong nucleophile in the form of an excess electron and find that although PBE0 and LDA predict stable hydrated electrons, the excess electron reacts nearly instantaneously with SCAN0 water via proton abstraction to form a hydrogen atom and hydroxide ion. We show that the DD provides the ability to not only predict whether or not liquid water will react with a hydrated electron but also which particular waters will be involved solely from analyzing pure water configurations generated with each functional. We rationalize this result in terms of the known trap-seeking behavior of injected hydrated electrons, which are able to find the most electronegative region in bulk water. These results highlight the utility of the dual descriptor as a fast and interpretable method for investigating condensed-phase reactivity with excess electrons.

BSE@GW Prediction of Charge Transfer Exciton in Molecular Complexes: Assessment of Self-Energy and Exchange-Correlation Dependence.

The Bethe-Salpeter equation using the GW approximation to the self-energy (BSE@GW) is a computationally attractive method for studying electronic excitation from first principles within the many-body Green's function theory framework. We examine its dependence on the underlying exchange-correlation (XC) approximation as well as on the GW approximation for predicting the charge transfer exciton formation at representative type-II interfaces between molecular systems of tetrachloro-1,2-benzoquinone (TCBQ) and acene derivatives. For the XC approximation, we consider several widely used generalized gradient approximation (GGA) and hybrid GGA functionals. For the GW self-energy approximation, we examine the recently proposed renormalized singles approach by Yang and coauthors [J. Phys. Chem. Lett. 2019, 10 (3), 447-452; J. Chem. Theory Comput. 2022, 18, 7570-7585] in addition to other commonly employed approximated GW schemes. We demonstrate a reliable prediction of the charge transfer exciton within the BSE@GW level of theory.

Photoredox matching of earth-abundant photosensitizers with hydrogen evolving catalysts by first-principles predictions.

Photoredox properties of several earth-abundant light-harvesting transition metal complexes in combination with cobalt-based proton reduction catalysts have been investigated computationally to assess the fundamental viability of different photocatalytic systems of current experimental interest. Density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations using several GGA (BP86, BLYP), hybrid-GGA (B3LYP, B3LYP*), hybrid meta-GGA (M06, TPSSh), and range-separated hybrid (ωB97X, CAM-B3LYP) functionals were used to calculate relevant ground and excited state reduction potentials for photosensitizers, catalysts, and sacrificial electron donors. Linear energy correction factors for the DFT/TD-DFT results that provide the best agreement with available experimental reference results were determined in order to provide more accurate predictions. Among the selection of functionals, the B3LYP* and TPSSh sets of correction parameters were determined to give the best redox potentials and excited states energies, ΔEexc, with errors of ∼0.2eV. Linear corrections for both reduction and oxidation processes significantly improve the predictions for all the redox pairs. In particular, for TPSSh and B3LYP*, the calculated errors decrease by more than 0.5V against experimental values for catalyst reduction potentials, photosensitizer oxidation potentials, and electron donor oxidation potentials. Energy-corrected TPSSh results were finally used to predict the energetics of complete photocatalytic cycles for the light-driven activation of selected proton reduction cobalt catalysts. These predictions demonstrate the broader usefulness of the adopted approach to systematically predict full photocycle behavior for first-row transition metal photosensitizer-catalyst combinations more broadly.

Theoretical DFT Investigation of Structure and Electronic Properties of η5-Cyclopentadienyl Half-Sandwich Organochalcogenide Complexes

For the first time, an extensive theoretical comparative study of the electronic structure and spectra of the η5-cyclopentadienyl half-sandwich [(Cp)(EPh3)], E = Se, Te) organochalcogenides was carried out using direct space electronic structure calculations within hybrid, meta, and meta-hybrid DFT GGA functionals coupled with double-ζ polarized 6-31G* and correlation-consistent triple-zeta cc-pVTZ-pp basis sets. The absence of covalent bonding between the cyclopentadienyl (Cp) ligands and Te/Se coordination centers was revealed. It was found that the chalcogens are partially positively charged and Cp ligands are partially negatively charged, which directly indicates a visible ionic contribution to Te/Se-Cp chemical bonding. Simulated UV–Vis absorption spectra show that all complexes have a UV-active nature, with a considerable shift in their visible light absorption due to the addition of methyl groups. The highest occupied molecular orbitals exhibit π-bonding between the Te/Se centers and Cp rings, although the majority of the orbital density is localized inside the Cp π-system. The presence of the chalcogen atoms and the extension of π-bonds across the chalcogen-ligand interface make the species promising for advanced photovoltaic and light-emitting applications.

Unraveling actinide-actinide bonding in fullerene cages: a DFT versus ab initio methodological study.

Actinide-actinide bonding poses a challenge for both experimental and theoretical chemists because of both the scarcity of experimental data and the exotic nature of actinide bonding due to the involvement and mixing of actinide 7s-, 6p-, 6d-, and particularly 5f-orbitals. Only a few experimental examples of An-An bonding have been reported so far. Here, we perform a methodological study of actinide-actinide bonding on experimentally known Th2@C80 and U2@C80 systems. We compared selected GGA, meta-GGA, hybrid-GGA and range-separated hybrid-GGA functionals with the results obtained using a multireference CASPT2 method, which we consider as a reference point. We show that functionals such as BP86, PBE or TPSS perform well for predicting geometries, while range-separated hybrids are superior in the description of the chemical bonding. None of the tested functionals were deemed reliable regarding the correct electronic spin ground state. Based on the results of this methodological study, we re-evaluate selected previously studied diactinide fullerene systems using more reliable protocol.

Benchmarking of Density Functionals for Z-Azoarene Half-Lives via Automated Transition State Search

Molecular photoswitches use light to interconvert from a thermodynamically stable isomer into a metastable isomer. Photoswitches have been used in photopharmacology, catalysis, and molecular solar thermal (MOST) materials because of their spatiotemporal activation. Visible-light-absorbing photoswitches are especially attractive because low-energy light minimizes undesired photochemical reactions and enables biological applications. Ideal photoswitches require well-separated absorption spectra for both isomers and long-lived metastable states. However, predicting thermal half-lives with density functional theory is difficult because it requires locating transition structures and chosing an accurate model chemistry. We now report EZ-TS; by automatically calculating activation energies for the thermal Z → E isomerization. We used 28 density functionals [local spin density approximation, generalized gradient approximation, meta-GGA, hybrid GGA, and hybrid meta-GGA] and five basis sets [6-31G(d), 6-31+G(d,p), 6-311+G(d,p), cc-pVDZ, and aug-cc-pVDZ]. The hybrid GGA functionals performed the best among all tested functionals. We demonstrate that the mean absolute errors of 14 model chemistries approach chemical accuracy.

Evaluation of density functional theory for a large and diverse set of organic and inorganic equilibrium structures.

Density functional theory (DFT) has been extensively benchmarked for energetic properties; however, less attention has been given to equilibrium structures and the effect of using a certain DFT geometry on subsequent energetic properties. We evaluate the performance of 52 contemporary DFT methods for obtaining the structures of 122 species in the W4-11-GEOM database. This dataset includes a total of 246 unique bonds: 117 H─X, 65 X─Y, 49 X═Y, and 15 XY bonds (where X and Y are first- and second-row atoms) and 133 key bond angles: 96 X-Y-H, 22 X-Y-Z, and 15 H-X-H angles. The reference geometries are optimized at the CCSD(T)/jul-cc-pV(n+d)Z level of theory (n= 5, 6). The performance of DFT is evaluated in conjunction with the Def2-nZVPP (n= T, Q), cc-pV(T+d)Z, and jul-cc-pV(T+d)Z basis sets. The root-mean-square deviations (RMSDs) over the bond distances of the best performing functionals from each rung of Jacob's Ladder are 0.0086 (SOGGA11), 0.0088 (τ-HCTH), 0.0059 (B3LYP), 0.0054 (TPSSh), and 0.0032 (DSD-PBEP86) Å. We evaluate the effect of the choice of the DFT geometry on subsequent molecular energies calculated with W1-F12 theory. Geometries obtained with GGA and MGGA methods result in large RMSDs in the subsequent W1-F12 energies; however, six hybrid GGA functionals (B3LYP, B3P86, mPW3PBE, B3PW91, mPW1LYP, and X3LYP) result in an excellent performance with RMSDs between 0.25 and 0.30 kJ mol-1 relative to the CCSD(T)/CBS reference geometries. The B2GP-PLYP and mPW2-PLYP DHDFT methods result in near-CCSD(T) accuracy with RMSDs of 0.11 and 0.10kJ mol-1 , respectively.

What Types of Chemical Problems Benefit from Density-Corrected DFT? A Probe Using an Extensive and Chemically Diverse Test Suite.

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange–correlation (XC) functionals (PBE, BLYP, TPSS, and SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation, HF-DFT is highly beneficial, particularly at low HF exchange percentages. This is especially true for noncovalent interactions where the electrostatic component is dominant, such as hydrogen and halogen bonds: for π-stacking, HF-DFT is detrimental. For subsets with significant nondynamical correlation (i.e., where a Hartree–Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals—consistent with Grimme’s proposal of the PBE38 functional—HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4) as the use of HF orbitals greatly mitigates the error at 25% for barrier heights. Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that for HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree–Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorially optimized empirical range-separated hybrids ωB97X-V and ωB97M-V.

Toward a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming

Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems, and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the static correlation in DFT when frontier orbitals are degenerate by the means of using a semidefinite programming (SDP) approach to minimize the system energy as a function of the N-representable, non-idempotent 1-electron reduced density matrix. While showing greatly improved singlet-triplet gaps for local density approximation and generalized gradient approximation (GGA) functionals, the SDP procedure reveals flaws in modern meta and hybrid GGA functionals, which show no major improvements when provided with an accurate electron density.

Benchmark studies on protonated benzene (BZH+) and water (Wn, n = 1–6) clusters: a comparison of hybrid DFT with MP2/CBS and CCSD(T)/CBS methods

The selection of a suitable density functional theory (DFT) method is critical to study the interfacial interactions between the protonated species and water clusters at the carbon surface. The interfacial interactions are crucial for the stability of complexes with the support of various kinds of noncovalent interactions. To model this environment, we consider excess proton with benzene [i.e., protonated benzene (BZH+)] and water clusters using high-level electronic structure calculations. These clusters were stabilized by different kinds of noncovalent interactions at the interface. Modeling these clusters is challenging as high-level electronic structure calculations are expensive, whereas less expensive DFT-based methods are inconsistent. Thus, in the present study, we have chosen various hybrid DFT functionals (such as B3LYP, PBE0, M05-2X, M06-2X, and M11) to study the geometries, energetics, and the importance of interfacial interactions. Furthermore, these methods performance is validated by using MP2/CBS and CCSD(T)/CBS approaches. It is found that the selected functionals are reliable to predict the structure, but the energetics of these clusters are varied. Also, each one of these methods has its own advantage in certain aspects. Scrutiny of result reveals that hybrid GGA (PBE0) and hybrid meta-GGA (M11) functionals are more consistent for the structure and stability with the benchmark obtained from MP2/CBS and CCSD(T)/CBS approaches. Besides, our benchmark report states that the selected DFT method can be suitable for the following individual interactions; (1) PBE0 suited for O–H+···O, O–H+···π and C–H+···O interactions, (2) M05-2X more suited for O–H···π, C–H···O, and (3) B3LYP method highly favor for the O–H+···O interactions (i.e., proton transfer). Overall, PBE0/aVTZ method has an excellent correlation with MP2/CBS and CCSD(T)/CBS methods based on our analysis using the mean signed error and correlation coefficient (r) analyses.

NLO properties of a triphenlyguanidine salt: The importance of pseudo-symmetry

Using a combined experimental and computational approach, we were able to trace the quasi-vanishing of the second-order nonlinear optical (NLO) properties of a newly synthesized organic salt, bis(triphenylguanidinium) l-malate, to the pseudo-centrosymmetry of its structure. The employed experimental techniques were single crystal X-ray diffraction to determine the structure, “open-aperture” Z-scan technique to measure the nonlinear absorption, Kurtz and Perry powder method and Maker fringes techniques for second- and third-harmonic generation. The molecular hyperpolarizability tensors (β and γ) were calculated within Density Functional Theory (DFT) and the macroscopic second- and third-order susceptibility tensors were estimated by combining the supermolecule approach with the oriented gas model. The calculations performed with global hybrid GGA and range-separated functionals reproduced the correct order of magnitude of the observed second- and third-order susceptibilities.

Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?

The development of approximate exchange-correlation functionals is critical for modern density functional theory. A recent analysis of atomic systems suggested that some modern functionals are straying from the path toward the exact functional because electron densities are becoming less accurate while energies are becoming more accurate since the year 2000. To investigate this trend for more chemically relevant systems, the electron densities in the bonding regions and the atomization energies are analyzed for a series of diatomic molecules with 90 different functionals. For hybrid generalized gradient approximation functionals developed since the year 2000, the errors in densities and atomization energies are decoupled; the accuracy of the energies remains relatively consistent while the accuracy of the densities varies significantly. Such decoupling is not observed for generalized gradient and meta-generalized gradient approximation functionals. Analysis of electron densities in bonding regions is found to be important for the evaluation of functionals for chemical systems.

Excitation spectra of Ag3–DNA bases complexes: A benchmark study

Assessment of different ab initio and TDDFT methods was studied for calculation of the excitation energies of the complexes of pyrimidine bases with positively charged Ag3+ clusters. Performance of CIS, CIS(D), CC2, ADC(2), MP2, and TDDFT techniques with the use of different hybrid–GGA and meta–hybrid–GGA functionals and basis sets is studied. We found that M06–2X functional shows good accuracy in comparison with the ADC(2) ab initio method and that the geometry optimization approach can strongly affect the excitation spectra of the complexes. Our results may have important implications for further studies of ligand–stabilized silver nanoclusters.

In search of the best DFT functional for dealing with organic anionic species.

Quantum chemical computational methods are thought to have problems in dealing with unstable organic anions. This work assesses the ability of different Density Functional Theory (DFT) functionals to reproduce the electron affinity and reduction potential of organic compounds. The performance of 23 DFT functionals was evaluated by computing the negative electron affinities (from 0 eV to -3.0 eV) and reduction potentials in acetonitrile (from 0 to -2.7 V). In general, most of the hybrid GGA functionals work fine in the prediction of electron affinities, BPW91, B3PW91 and M06 being the best in each class of functionals (pure, hybrid and meta-GGA functionals, respectively). On the other hand, the ab initio post-Hartree-Fock methods, MP2 and coupled-cluster (CCSD(T)), as well as the double hybrid functionals, B2PLYP and mPW2PLYP, usually fail. For compounds with EAs lower than -1.75 eV, a method for stabilizing the anion, based on solvation with the IEFPCM model, was employed. In this case, BPW91, PBE0 and M06-HF could be the recommended option for the pure, hybrid and meta-GGA functionals, respectively. The situation improves for the evaluation and prediction of redox potentials. In this case the performance of the DFT functionals is better, in part because the solvent assists in the stabilization of the anions. Nevertheless, there is a systematic bias in the calculation of absolute redox potentials, which could be corrected by using a redox partner that helps by the cancellation of errors. In this case, the hybrid and meta-GGA functionals B3PW91, PBE0, TPSSh and M06 are also among the best for computing redox potentials with a mean absolute deviation (MAD) lower than 0.13 V.

Performance of some DFT functionals with dispersion on modeling of the translational isomers of a solvent-switchable [2]rotaxane

The balances of interactions were studied by computational methods in the translational isomers of a solvent switchable fullerene-stoppered [2]rotaxane (1) manifesting unexpected behavior, namely that due to favorable dispersion interactions the fullerene stopper becomes the second station upon change of the solvent. For comparison, another system, a pH switchable molecular shuttle (2), was also examined as an example of prevailing electrostatic interactions. Tested for 1 were five global hybrid Generalized Gradient Approximation functionals (B3LYP, B3LYP-D3, B3LYP-D3BJ, PBEh1PBE and APFD), one long-range corrected, range-separated functional with D2 empirical dispersion correction, ωB97XD, the Zhao-Truhlar's hybrid meta-GGA functional M06 with double the amount of nonlocal exchange (2X), and a pure functional, B97, with the Grimme's D3BJ dispersion (B97D3). The molecular mechanics method qualitatively correctly reproduced the behavior of the [2]rotaxanes, whereas the DFT models, except for M06-2X to some extent, failed in the case of significant dispersion interactions with participation of the fulleropyrrolidine stopper (rotaxane 1). Unexpectedly, the benzylic amide macrocycle tends to adopt preferentially ‘boat’-like conformation in most of the cases. Four hydrogen bonds interconnect the axle with the wheel for the translational isomer with the macroring at the succinamide station (station II), whereas the number of hydrogen bonds vary for the isomer with the macroring at the fulleropyrrolidine stopper (station I) depending of the computational model used. The B3LYP and the PBEh1PBE results show strong preference of station II in the gas phase and in the model solvent DMSO. After including empirical dispersion correction, the translational isomer with the macroring at station I has the lower energy with B3LYP, both in the gas phase and in DMSO. The same result, but with higher preference of station I, was estimated with APFD, ωB97XD and B97D3. Only M06-2X presented qualitatively correct behavior for the relative stability of the two translational isomers, namely, slight preference of station II for the isolated molecule and higher relative energy of the same isomer with the model solvent DMSO. The electrostatic interactions in 2 have the decisive contribution both when the macroring is positioned at the dipeptide residue for the neutral form, and at the N-benzylalanine fragment after protonation, and the observed behavior of the [2]rotaxane is correctly reproduced by the methods used.

Prediction of molecular properties and spectroscopic profile of Riluzole with different functionals (B3LYP, M06-2X, MPWLYP): A combined theoretical and experimental study

Comprehensive investigation of molecular geometry and electronic structure of Riluzole (6-(trifluoromethoxy)benzothiazol-2-amine) in ground as well as in the first excited state has been carried out. The stable conformers of the title compound have been determined from the 3D potential energy scan calculated at DFT/B3LYP, by varying selected dihedral angles, responsible for conformational flexibility. The most stable conformers were further optimized to obtain ground state structure using pure GGA (MPWLYP), hybrid GGA (B3LYP) and meta-hybrid GGA (M06-2X) functionals. Detailed vibrational analysis has been done for the structure obtained at B3LYP as it corresponds to the minimum energy structure. Experimental FT-IR and FT-Raman spectra were compared with theoretical spectral data. Dipole moment, polarizability, first static hyperpolarizability has been calculated at different functionals used in the study. Natural bond orbital (NBO) analysis has been done to study the stability of the compound arising from charge delocalization. UV–Vis spectrum of the title compound was also recorded and electronic properties such as frontier orbitals and band gap energies were calculated by TD-DFT approach.

Critical Analysis of Cluster Models and Exchange-Correlation Functionals for Calculating Magnetic Shielding in Molecular Solids.

Calculations of the principal components of magnetic-shielding tensors in crystalline solids require the inclusion of the effects of lattice structure on the local electronic environment to obtain significant agreement with experimental NMR measurements. We assess periodic (GIPAW) and GIAO/symmetry-adapted cluster (SAC) models for computing magnetic-shielding tensors by calculations on a test set containing 72 insulating molecular solids, with a total of 393 principal components of chemical-shift tensors from 13C, 15N, 19F, and 31P sites. When clusters are carefully designed to represent the local solid-state environment and when periodic calculations include sufficient variability, both methods predict magnetic-shielding tensors that agree well with experimental chemical-shift values, demonstrating the correspondence of the two computational techniques. At the basis-set limit, we find that the small differences in the computed values have no statistical significance for three of the four nuclides considered. Subsequently, we explore the effects of additional DFT methods available only with the GIAO/cluster approach, particularly the use of hybrid-GGA functionals, meta-GGA functionals, and hybrid meta-GGA functionals that demonstrate improved agreement in calculations on symmetry-adapted clusters. We demonstrate that meta-GGA functionals improve computed NMR parameters over those obtained by GGA functionals in all cases, and that hybrid functionals improve computed results over the respective pure DFT functional for all nuclides except 15N.

Molecular Excitation Energies from Time-Dependent Density Functional Theory Employing Random-Phase Approximation Hessians with Exact Exchange.

Molecular excitation energies have been calculated with time-dependent density-functional theory (TDDFT) using random-phase approximation Hessians augmented with exact exchange contributions in various orders. It has been observed that this approach yields fairly accurate local valence excitations if combined with accurate asymptotically corrected exchange-correlation potentials used in the ground-state Kohn-Sham calculations. The inclusion of long-range particle-particle with hole-hole interactions in the kernel leads to errors of 0.14 eV only for the lowest excitations of a selection of three alkene, three carbonyl, and five azabenzene molecules, thus surpassing the accuracy of a number of common TDDFT and even some wave function correlation methods. In the case of long-range charge-transfer excitations, the method typically underestimates accurate reference excitation energies by 8% on average, which is better than with standard hybrid-GGA functionals but worse compared to range-separated functional approximations.

Bulk Properties of Transition Metals: A Challenge for the Design of Universal Density Functionals.

Systematic evaluation of the accuracy of exchange-correlation functionals is essential to guide scientists in their choice of an optimal method for a given problem when using density functional theory. In this work, accuracy of one Generalized Gradient Approximation (GGA) functional, three meta-GGA functionals, one Nonseparable Gradient Approximation (NGA) functional, one meta-NGA, and three hybrid GGA functionals was evaluated for calculations of the closest interatomic distances, cohesive energies, and bulk moduli of all 3d, 4d, and 5d bulk transition metals that have face centered cubic (fcc), hexagonal closed packed (hcp), or body centered cubic (bcc) structures (a total of 27 cases). Our results show that including the extra elements of kinetic energy density and Hartree-Fock exchange energy density into gradient approximation density functionals does not usually improve them. Nevertheless, the accuracies of the Tao-Perdew-Staroverov-Scuseria (TPSS) and M06-L meta-GGAs and the MN12-L meta-NGA approach the accuracy of the Perdew-Burke-Ernzerhof (PBE) GGA, so usage of these functionals may be advisable for systems containing both solid-state transition metals and molecular species. The N12 NGA functional is also shown to be almost as accurate as PBE for bulk transition metals, and thus it could be a good choice for studies of catalysis given its proven good performance for molecular species.

Performance of Density Functional Methods. Some Difficult Cases for Small Systems Containing Cu, Ag, or Au

Twenty-six density functional theory (DFT) methods were tested in conjunction with three different effective core potentials (ECPs) and their corresponding valence basis sets, for studying the behavior of DFT methods in small systems containing Cu, Ag, or Au where it is well-known that some functionals fail. The DFT results were compared with those obtained with post Hartree-Fock methods: second-order many-body perturbation theory (MP2), coupled cluster singles-doubles (CCSD), and coupled cluster singles-doubles with perturbative triples, CCSD(T). Calculations were carried for M3 (M = Cu, Ag, Au); M4(-), (M = Cu, Ag) and [H2O-Cu](+2). The comparison of the DFT calculated values with the Post Hartree-Fock values showed that, in general, all generalized gradient approximation (GGA) type functionals fail to describe these systems. The hybrid GGA functionals (H-GGA) showed a better behavior; however, when the Lee-Yang-Parr (LYP) exchange-correlation functional was used, wrong results were obtained. The results with the hybrid meta (HM-GGA) functionals, as in the case of H-GGAs, showed that, to obtain similar results to MP2 or CCSD(T), it is necessary to have a high Hartree-Fock exchange percentage. Spurious results obtained with the H-GGA or HM-GGA methods can be eliminated increasing the Hartree-Fock exchange percentage in the H-GGA or HM-GGA type functionals. Among the different functionals tested, the BB1K and MPWB1K functionals showed the best agreement with the MP2 and CCSD(T) results.