Benchmark calculations on the adiabatic ionization potentials of M-NH(3) (M=Na,Al,Ga,In,Cu,Ag)

The ground states of the M-NH(3) (M=Na,Al,Ga,In,Cu,Ag) complexes and their cations have been studied with density functional theory and coupled cluster [CCSD(T)] methods. The adiabatic ionization potentials (AIPs) of these complexes are calculated, and these are compared to results from high-resolution zero-electron kinetic energy photoelectron spectroscopy. By extrapolating the CCSD(T) energies to the complete basis set (CBS) limit and including the core-valence, scalar relativistic, spin-orbit, and zero-point corrections, the CCSD(T) method is shown to be able to predict the AIPs of these complexes to better than 6 meV or 0.15 kcal/mol. 27 exchange-correlation functionals, including one in the local density approximation, 13 in the generalized gradient approximation (GGA), and 13 with hybrid GGAs, were benchmarked in the calculations of the AIPs. The B1B95, mPW1PW91, B98, B97-1, PBE1PBE, O3LYP, TPSSh, and HCTH93 functionals give an average error of 0.1 eV for all the complexes studied, with the B98 functional alone yielding a maximum error of 0.1 eV. In addition, the calculated metal-ammonia harmonic stretching frequencies with the CCSD(T) method are in excellent agreement with their experimental values, whereas the B3LYP method tends to underestimate these stretching frequencies. The metal-ammonia binding energies were also calculated at the CCSD(T)/CBS level, and are in excellent agreement with the available experimental values considering the error limits, except for Ag-NH(3) and Ag(+)-NH(3), where the calculations predict stronger bond energies than measured by about 4 kcal/mol, just outside the experimental error bars of +/-3 kcal/mol.     

Thermochemical kinetics of hydrogen-atom transfers between methyl, methane, ethynyl, ethyne, and hydrogen

Saddle point properties of three symmetric and one asymmetric hydrogen transfer and the energy of reaction of the asymmetric reactions are investigated in the present work. These reactions were calculated by various density functionals, many of which were developed in recent years, by coupled cluster theory, and by multicoefficient correlation methods based on wave function theory. Instead of comparing calculated results to "semi-experimental" values, we compared them to very accurate theoretical values (e.g., to values obtained by the Weizmann-1 method). Coupled cluster theory and the multicoefficient correlation methods MC-QCISD/3 and MCQCISD-MPW are very accurate for these reactions with mean unsigned errors below 0.94 kcal/mol. Diagnostics for multireference character add additional reliability to these results. The newly developed hybrid density functional M06-2X shows very good performance for these reactions with a mean unsigned error of only 0.77 kcal/mol; the BHandHLYP, MPW1K, and BB1K density functionals, can also predict these reactions well with mean unsigned errors less than 1.42 kcal/mol.     

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.     

Rozen's epoxidation reagent, CH3CN.HOF: a theoretical study of its structure, vibrational spectroscopy, and reaction mechanism

Rozen's epoxidation reagent, CH(3)CN.HOF, and a prototype epoxidation reaction employing it, have been subjected to an extensive ab initio and density functional study. Its anharmonic force field reveals a very strong red shift for the OH stretch and a strong blue shift for the HOF bend, in semiquantitative agreement with experiment. The very strong hydrogen bond (8.20 kcal/mol at the W1 level) not only serves to stabilize the reactant but also considerably lowers the barrier height for epoxidation of ethylene. Moreover, the reaction byproduct HF is found to act autocatalytically. The OH moiety acquires HO(+) character in the transition state. Our W1 benchmark data for the reaction profile allow the performance of various DFT functionals to be assessed. In general, "kinetics" functionals overestimate barrier heights, the BMK functional less so than the others. The B1B95 and TPSS33B95 meta-GGA functionals both perform very well, whereas general-purpose hybrid GGAs underestimate barrier heights. The simple PBE0 functional does reasonably well.     

Accurate pK(a) calculations for carboxylic acids using complete basis set and Gaussian-n models combined with CPCM continuum solvation methods

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(s)(H(+)), was combined with a value for G(gas)(H(+)) of -6.28 kcal/mol to calculate pK(a) values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pK(a) values accurate to less than half a pK(a) unit.     

A new database and benchmark of the bond energies of noble-gas-containing molecules

We have developed a new database of structures and bond energies of 59 noble-gas-containing molecules. The structures were calculated by CCSD(T)/aug-cc-pVTZ methods and the bond energies were obtained using the CCSD(T)/complete basis set method. Many wavefunction-based and density functional theory methods have been benchmarked against the 59 accurate bond energies. Our results show that the MPW1B95, B2GP-PLYP, and DSD-BLYP functionals with the aug-cc-pVTZ basis set excel in predicting the bond energies of noble-gas molecules with mean unsigned errors (MUEs) of 2.0 to 2.1 kcal/mol. When combinations of Dunning's basis sets are used, the MPW1B95, B2GP-PLYP, DSD-BLYP, and BMK functionals give significantly lower MUEs of 1.6 to 1.9 kcal/mol. Doubly hybrid methods using B2GP-PLYP and DSD-BLYP functionals and MP2 calculation also provide satisfactory accuracy with MUEs of 1.4 to 1.5 kcal/mol. If the Ng bond energies and the total atomization energies of a group of 109 main-group molecules are considered at the same time, the MPW1B95/aug-cc-pVTZ single-level method (MUE = 2.7 kcal/mol) and the B2GP-PLYP and DSD-PLYP functionals with combinations of basis sets or using the doubly hybrid method (MUEs = 1.9-2.2 kcal/mol) give the overall best result.     

Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions

This paper develops two new hybrid meta exchange-correlation functionals for thermochemistry, thermochemical kinetics, and nonbonded interactions. The new functionals are called PW6B95 (6-parameter functional based on Perdew-Wang-91 exchange and Becke-95 correlation) and PWB6K (6-parameter functional for kinetics based on Perdew-Wang-91 exchange and Becke-95 correlation). The resulting methods were comparatively assessed against the MGAE109/3 main group atomization energy database, against the IP13/3 ionization potential database, against the EA13/3 electron affinity database, against the HTBH38/4 and NHTBH38/04 hydrogen-transfer and non-hydrogen-transfer barrier height databases, against the HB6/04 hydrogen bonding database, against the CT7/04 charge-transfer complex database, against the DI6/04 dipole interaction database, against the WI7/05 weak interaction database, and against the new PPS5/05 pi-pi stacking interaction database. From the assessment and comparison of methods, we draw the following conclusions, based on an analysis of mean unsigned errors: (i) The PW6B95, MPW1B95, B98, B97-1, and TPSS1KCIS methods give the best results for a combination of thermochemistry and nonbonded interactions. (ii) PWB6K, MPWB1K, BB1K, MPW1K, and MPW1B95 give the best results for a combination of thermochemical kinetics and nonbonded interactions. (iii) PWB6K outperforms the MP2 method for nonbonded interactions. (iv) PW6B95 gives errors for main group covalent bond energies that are only 0.41 kcal (as measured by mean unsigned error per bond (MUEPB) for the MGAE109 database), as compared to 0.56 kcal/mol for the second best method and 0.92 kcal/mol for B3LYP.     

Benchmarking the performance of time-dependent density functional methods

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.     

Oxidative addition of the fluoromethane C-F bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for two reaction pathways (oxidative insertion, OxIn, and S(N)2) for oxidative addition of the fluoromethane C-F bond to the palladium atom and have used this to evaluate the performance of 26 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing these reactions. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods (HF, MP2, CCSD, CCSD(T)) in combination with a hierarchical series of seven Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -5.3 (-6.1) kcal/mol for the formation of the reactant complex, 27.8 (25.4) kcal/mol for the activation energy for oxidative insertion (OxIn) relative to the separate reactants, 37.5 (31.8) kcal/mol for the activation energy for the alternative S(N)2 pathway, and -6.4 (-7.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.4-2.7 kcal/mol and errors in activation energies ranging from 0.3 to 2.8 kcal/mol. The B3LYP functional compares very well with a slight underestimation of the overall barrier for OxIn by -0.9 kcal/mol. For comparison, the well-known BLYP functional underestimates the overall barrier by -10.1 kcal/mol. The relative performance of these two functionals is inverted with respect to previous findings for the insertion of Pd into the C-H and C-C bonds. However, all major functionals yield correct trends and qualitative features of the PES, in particular, a clear preference for the OxIn over the alternative S(N)2 pathway.     

Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.     

Benchmarking of density functionals for the kinetics and thermodynamics of the hydrolysis of glycosidic bonds catalyzed by glycosidases

In recent years, there has been an increased interest in understanding the enzymatic mechanism of glycosidases resorting mostly to DFT and DFT/MM calculations. However, the performance of density functionals (DFs) is well known to be system and property dependent. Trends drawn from general studies, despite important to evaluate the quality of the DFs and to pave the way for the development of new DFs, may be misleading when applied to a single specific system/property. To overcome this issue, we carried out a benchmarking study of 40 DFs applied to the geometry optimization and to the electronic barrier height (E _Barrier) and electronic energy of reaction (E _R) of prototypical glycosidase‐catalyzed reactions. Additionally, we report calculations with SCC‐DFTB and four semiempirical MO methods applied to the same problem. We have used a universal molecular model for retaining glycosidases, comprising only a 22‐atoms system that mimics the active site and substrate. High accuracy reference geometries and energies were calculated at the CCSD(T)/CBS//MP2/aug‐cc‐pVTZ level of theory. Most DFs reproduce the reference geometries extremely well, with mean unsigned errors (MUE) smaller than 0.05 Å for bond lengths and 3° for bond angles. Among the DFs, wB97X‐D, CAM‐B3LYP, B3P86, and PBE1PBE have the best performance in geometry optimizations (MUE = 0.02 Å). Conversely, semiempirical MO and SCC‐DFTB methods yielded less accurate geometries (MUE between 0.09 and 0.17 Å). The inclusion of D3 correction has a small, but still relevant, influence in the geometry predicted by some DFs. Regarding E _Barrier, 11 DFs (MPW1B95, CAM‐B3LYP, M06 ‐ 2X, PBE1PBE, wB97X ‐ D, B1B95, BMK, MN12 – SX, M05, M06, and M11) presented errors below 1 kcal.mol^?1, in relation to the reference energy. Most of these functionals belong to the family of hybrid functionals (H‐GGA, HH‐GGA, and HM‐GGA), which shows a positive influence of HF exchange in the determination of E _Barrier. The inclusion of D3 correction has not affected significantly the E _Barrier and E _R. The use of geometries at the accurate but expensive MP2/aug‐cc‐pVTZ level of theory has a small, albeit not insignificant, influence in the E _Barrier when compared with energies calculated with geometries determined with the DFs (usually a few tenths of kcal.mol^?1, with exceptions). In general, semiempirical MO methods and DFTB are associated with larger errors in the determination of E _Barrier, with unsigned errors from 6.9 to 24.7 kcal.mol^?1.     

Assessment of new meta and hybrid meta density functionals for predicting the geometry and binding energy of a challenging system: the dimer of H2S and benzene

Noncovalent interactions of a hydrogen bond donor with an aromatic pi system present a challenge for density functional theory, and most density functionals do not perform well for this kind of interaction. Here we test seven recent density functionals from our research group, along with the popular B3LYP functional, for the dimer of H 2S with benzene. The functionals considered include the four new meta and hybrid meta density functionals of the M06 suite, three slightly older hybrid meta functionals, and the B3LYP hybrid functional, and they were tested for their abilities to predict the dissociation energies of three conformations of the H 2S-benzene dimer and to reproduce the key geometric parameters of the equilibrium conformation of this dimer. All of the functionals tested except B3LYP correctly predict which of the three conformations of the dimer is the most stable. The functionals that are best able to reproduce the geometry of the equilibrium conformation of the dimer with a polarized triple-zeta basis set are M06-L, PWB6K, and MPWB1K, each having a mean unsigned relative error across the two experimentally verifiable geometric parameters of only 8%. The success of M06-L is very encouraging because it is a local functional, which reduces the cost for large simulations. The M05-2X functional yields the most accurate binding energy of a conformation of the dimer for which a binding energy calculated at the CCSD(T) level of theory is available; M05-2X gives a binding energy for the system with a difference of merely 0.02 kcal/mol from that obtained by the CCSD(T) calculation. The M06 functional performs well in both categories by yielding a good representation of the geometry of the equilibrium structure and by giving a binding energy that is only 0.19 kcal/mol different from that calculated by CCSD(T). We conclude that the new generation of density functionals should be useful for a variety of problems in biochemistry and materials where aromatic functional groups can serve as hydrogen bond acceptors.     

Polyfunctional methodology for improved DFT thermochemical predictions

Statistical error distributions for enthalpies of formation as predicted by 18 different density functionals have been analyzed using a test set of 675 molecules. Systematic errors, dependent on the number of valence electrons, have been identified for some functionals. A simple empirical correction makes a significant improvement in the prediction error for these single functionals. Linear combinations of enthalpy estimates from different density functionals are identified that exploit the error correlations among the functionals and allow for further improvements in the accuracy of thermodynamic predictions. A good compromise between accuracy and computational efforts is achieved by the BLUE (best linear unbiased estimator) combination of three functionals, B3LYP, BLYP, and VSXC (polyfunctional 3 or PF3). The PF3 method has a mean absolute deviation (MAD) from experiment of 2.4 kcal/mol on the G3 set of 271 molecules. This can be compared to the MAD of 4.9 kcal/mol for B3LYP and 1.2 kcal/mol for the more costly G3 method. On the larger set of 675 molecules, the MAD for PF3 is 3.0 kcal/mol. Opportunities for further improvements in the accuracy of this method are discussed.     

Assessment of density functionals for pi systems: Energy differences between cumulenes and poly-ynes; proton affinities, bond length alternation, and torsional potentials of conjugated polyenes; and proton affinities of conjugated Shiff bases

Woodcock et al. [J. Phys. Chem. A 2002, 106, 11923] pointed out that no density functional was able to obtain the correct sign of the relative energies of the allene and propyne isomers of C3H4 and that density functional theory (DFT) predicts that poly-ynes are insufficiently stabilized over cumulenes for higher homologues. In the present work, we show that the recent M05 density functional predicts the correct ordering of allene and propyne and gives a mean unsigned error (MUE) of only 1.8 kcal/mol for the relative energies of the two isomers of C3H4, C5H4, and C7H4. Two other recent functionals, M05-2X and PWB6K, also give reasonably low MUEs, 2.7 and 3.0 kcal/mol, respectively, as compared to 6.2 kcal/mol for the popular B3LYP functional. Another challenging problem for density functionals has been a tendency to overpolarize conjugated pi systems. We test this here by considering proton affinities of conjugated polyenes and conjugated Schiff bases. Again M05-2X performs quite well, with MUEs of 2.1 and 3.9 kcal/ mol, respectively, as compared to 5.8 and 5.9 kcal/mol for B3LYP. Averaged over the three problems, M05-2X has a MUE of 3.0 kcal/mol, the BMK functional of Boese et al. has an MUE of 3.2 kcal/mol, and M05 has an MUE of 5.1 kcal/mol. Twenty-two other tested functionals have MUEs of 5.2-8.1 kcal/mol averaged over the three test problems. Both M05 and M05-2X do quite well, compared to other density functionals, for torsion potentials in butadiene and styrene, and M05 does very well for bond length alternation in conjugated polyenes. Since the M05 functional has broad accuracy for main group and transition metal chemistry and M05-2X has broad accuracy for main group chemistry, we conclude that significant progress is being made in improving the performance of DFT across a wide range of problem types.     

Ab initio, density functional theory, and continuum solvation model prediction of the product ratio in the S(N)2 reaction of NO2(-) with CH3CH2Cl and CH3CH2Br in DMSO solution

The reaction pathways for the interaction of the nitrite ion with ethyl chloride and ethyl bromide in DMSO solution were investigated at the ab initio level of theory, and the solvent effect was included through the polarizable continuum model. The performance of BLYP, GLYP, XLYP, OLYP, PBE0, B3PW91, B3LYP, and X3LYP density functionals has been tested. For the ethyl bromide case, our best ab initio calculations at the CCSD(T)/aug-cc-pVTZ level predicts product ratio of 73% and 27% for nitroethane and ethyl nitrite, respectively, which can be compared with the experimental values of 67% and 33%. This translates to an error in the relative DeltaG* of only 0.17 kcal mol(-1). No functional is accurate (deviation <0.5 kcal mol(-1)) for predicting relative DeltaG*. The hybrid X3LYP functional presents the best performance with deviation 0.82 kcal mol(-1). The present problem should be included in the test set used for the evaluation of new functionals.