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.     

Lattice Boltzmann simulation of two-sided lid-driven flow in a staggered cavity

In this article, the lattice Boltzmann method is employed in order to explore incompressible fluid flow inside a two-sided lid-driven staggered cavity. Results of the lattice Boltzmann simulation for antiparallel motion of lids are compared with the data from existing literature. For parallel motion of lids, the characteristics of flow pattern for a variety of Re numbers (50–3200) are presented. An asymmetric steady-state flow pattern for parallel motion of lids is obtained.     

Splitting multiple bonds: A comparison of methodologies on the accuracy of bond dissociation energies

A benchmarking of different quantum chemical methodologies for the splitting of multiply bonded systems is presented, with an emphasis on quantitative reproduction of experimentally determined dissociation energies. New benchmark full configuration interaction (FCI) calculations are presented for nitrogen and acetylene, and comparisons are made between various methods with both the FCI results and with experiment in an effort to understand qualitatively and quantitatively how well these different methods cope with the bond‐breaking process. It is found that the multireference methods fare well, but are sometimes slowly convergent with respect to the size of the basis set, and in particular the angular momenta of the polarization functions. Single‐reference (SR) wavefunction‐based methods perform poorly against full CI, while CCSD(T) is reasonably accurate for comparison with experiment. Density functional theory with hybrid functionals have very quick basis‐set convergence, and offer reliable estimates of bond dissociation energies. Spin‐restricted SR wavefunctions are found to be poor for such systems, while unrestricted wavefunctions give reasonably good energies, but with severe spin contamination. © 2013 Wiley Periodicals, Inc.     

Study of Cl−(H2O)n (n = 1–4) using basin‐hopping method coupled with density functional theory

Cl^?(H₂O)_n (n = 1–4) clusters were investigated using a basin‐hopping (BH) algorithm coupled with density functional theory (DFT). Structures, energetics, thermodynamics, vertical detachment energies, and vibrational frequencies were obtained from high‐level ab initio calculations. Through comparisons with previous theoretical and experimental data, it was demonstrated that the combination of the BH method and DFT could accurately predict the global and local minima of Cl^?(H₂O)_n (n = 1–4). Additionally, to optimize larger Cl^?(H₂O)_n (n > 4) clusters, several popular density functionals as well as DF‐LMP2 (Schütz et al., J. Chem. Phys. 2004, 121, 737) (second‐order Møller‐Plesset perturbation theory using local and density fitting approximations) were tested with appropriate basis sets through comparisons with MP2 optimized results. DF‐LMP2 will be used in future studies because its overall performance in describing the relative binding energies and the geometrical parameters of Cl^?(H₂O)_n (n = 1–4) was outstanding in this study. © 2013 Wiley Periodicals, Inc.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

Reliable radical stabilization energies from diffusion Monte Carlo calculations

We assess the performance of variational (VMC) and diffusion (DMC) quantum Monte Carlo methods for calculating the radical stabilization energies of a set of 43 carbon-centered radical species. Even using simple single-determinant trial wavefunctions, both methods perform exceptionally well, with mean absolute deviations from reference values well under the chemical accuracy standard of 1 kcal/mol. In addition, the use of DMC results in a highly concentrated spread of errors, with all 43 results within chemical accuracy at the 95% confidence level. These results indicate that DMC is an extremely reliable method for calculating radical stabilization energies and could be used as a benchmark method for larger systems in future.     

Benchmark approach to search of cost-effective and accurate density functional for homolytic cleavage of C─Mg bond of Grignard reagent

Grignard reactions are of importance in organic chemistry for the synthesis β-keto esters and diethyl malonate, alcohols, aldehydes or ketones, monocarboxylic acids, and other organometallic compounds. Generally, the heterolytic dissociation of C─Mg bond in Grignard reagent is the key step in these reactions. Recently, homolytic cleavage of the C─Mg bond in Grignard reagents has been reported in the preparation of stable radicals. These reactive species react with other compounds, which result in the formation of hydrocarbons and their derivatives. Therefore, the study of homolytic cleavage of C─Mg bonds is quite vital to better understand the kinetics and thermodynamics of these reactions. In the current study, a benchmark approach is adopted to find a cost-effective and accurate density functional (DF) for bond dissociation energies measurement of the C─Mg bond of Grignard reagents. Twenty-nine DFs from 13 density functional theory (DFT) classes with three types of basis sets (Pople' 6-31G(d) and 6-311G(d), Dunning's aug-cc-pVDZ, and Karlsruhe' def2-SVP basis sets) are implemented for the measurement of dissociation energies of the C─Mg bond. Theoretical dissociation energy values are compared with experimental reported values of the C─Mg bond of selected Grignard reagents. TPSSTPSS of the meta-GGA class with 6-31G (d) basis set gave accurate results, and its Pearson's correlation is 0.95. SD, root mean square deviation, and mean unsigned error of this method are 2.36 kcal mol⁻¹, 2.33 kcal mol⁻¹, and −0.46 kcal mol⁻¹, respectively. TPSSTPSS of the meta-GGA class is a one-electron, self-interaction, error-free Tao-Perdew-Staroverov-Scuseria functional that performed better with the 6-31G(d) basis set.     

Sextic centrifugal distortion constants: interplay of density functional and basis set for accurate yet feasible computations

Quantum-chemical calculations assist the analysis of laboratory spectra, and often provide the only means to determine spectroscopic data that cannot be accessed experimentally. Accurate predictions of vibrational and rotational spectroscopic parameters are required for applications in the field of high-resolution molecular spectroscopy. While the accuracy issue of the quantum-chemical calculation of vibrational properties and of equilibrium structures has been addressed in the literature, the same is not true for centrifugal distortion constants that however play an essential role for the interpretation of remote sensing data. In this work, the performance of several model chemistries, rooted mainly in density functional theory, in computing sextic centrifugal distortion constants is assessed employing a benchmark set of molecules of both atmospheric and astrochemical relevance. The Jensen’s (aug-)pcs-n basis sets, different flavours of Dunning’s triple-ζ basis sets and the SNSD basis set, are employed in conjunction with different functionals, and their predictions are benchmarked against experimental and theoretical data at the coupled cluster level of theory. This study also demonstrates the reliability of the calculation of sextic centrifugal distortion constants within the Gaussian16 rev. B.01 program package. Reliable predictions of the sextic centrifugal distortion constants for the gauche- and trans-conformers of ethyl-mercaptan are also presented.