Validating additive correction schemes against gradient-based extrapolations

The use of additive correction schemes to obtain structures and vibrational frequencies of increasingly larger molecules is becoming more common. Such approaches, based on the cubic extrapolation formula applied directly to the quantity of interest, have been successfully validated only at the highest levels of computational accuracy: for coupled cluster methods with comparably large basis sets. Here, a systematic validation of geometries and vibrational frequencies is carried out, including more affordable and relevant levels of theory, such as the Møller-Plesset perturbation theory applied with smaller basis sets. Comparisons of such additive schemes against the more rigorous gradient-based extrapolation are presented. The cbs () routine of the open-source quantum-chemistry package Psi4 has been extended for this purpose. The results confirm that geometries and frequencies of covalently bound species obtained with additive correction schemes are in an excellent agreement with the results of gradient-based extrapolations. However, when applied to systems involving noncovalent interactions, the errors due to such schemes are significantly larger. In general, we propose the application of gradient-based extrapolations, as they incur no extra cost compared to additive schemes.     

Exact solutions of the generalized Navier– Stokes equations for benchmarking

The generalized Navier– Stokes equations for incompressible viscous flows through isotropic granular porous medium are studied. Some analytical classic solutions of the Navier– Stokes equations are generalized to the case of the considered equations. Obtained solutions of generalized equations reduce to classic ones as porosity effect disappears. Average velocity of generalized solutions is calculated and evaluated in two limiting regimes of flow. In the shallow conduit, the generalized flow rate approximates the free (without porous medium) flow rate and in the case of removed boundaries this approaches Darcy's law. The use of the derived exact solutions for benchmarking purposes is described. Copyright © 2002 John Wiley & Sons, Ltd.     

Electrolyte Effects on the Electrocatalytic Performance of Iridium-Based Nanoparticles for Oxygen Evolution in Rotating Disc Electrodes

Proton exchange membrane water electrolysers are very promising renewable energy conversion devices that produce hydrogen from sustainable feedstocks. These devices are mainly limited by the sluggish kinetics of the oxygen evolution reaction (OER). Ir-based nanoparticles are both reasonably active and stable for the OER in acidic media. The electrolyte composition and the pH may play a crucial role in electrocatalysis, yet they have been widely overlooked for the OER. Herein, we present a study on the effects of the composition and concentration of the electrolyte on commercial Ir black nanoparticles using concentrations of 0.05 M, 0.1 M and 0.5 M of both sulphuric and perchloric acid. The results show an important effect of the electrolyte composition on the catalytic performance of the Ir nanoparticles. The concentration of H₂SO₄ interferes on the oxidation of Ir and decreases the catalytic performance of the catalyst. HClO₄ does not show strong interferences in the electrochemistry of Ir. Higher catalytic performances are observed in HClO₄ electrolytes in comparison to H₂SO₄ with little effect of the concentration of HClO₄.     

Density functional theory and CCSD(T) evaluation of ionization potentials,redox potentials,and bond energies related to zirconocene polymerization catalysts

Quantum-mechanical-based computational design of molecular catalysts requires accurate and fast electronic structure calculations to determine and predict properties of transition-metal complexes. For Zr-based molecular complexes related to polyethylene catalysis, previous evaluation of density functional theory (DFT) and wavefunction methods only examined oxides and halides or select reaction barrier heights. In this work, we evaluate the performance of DFT against experimental redox potentials and bond dissociation enthalpies (BDEs) for zirconocene complexes directly relevant to ethylene polymerization catalysis. We also examined the ability of DFT to compute the fourth atomic ionization potential of zirconium and the effect the basis set selection has on the ionization potential computed with CCSD(T). Generally, the atomic ionization potential and redox potentials are very well reproduced by DFT, but we discovered relatively large deviations of DFT-calculated BDEs compared to experiment. However, evaluation of BDEs with CCSD(T) suggests that experimental values should be revisited, and our CCSD(T) values should be taken as most accurate.     

Verification of Euler/Navier–Stokes codes using the method of manufactured solutions

The method of manufactured solutions is used to verify the order of accuracy of two finite‐volume Euler and Navier–Stokes codes. The Premo code employs a node‐centred approach using unstructured meshes, while the Wind code employs a similar scheme on structured meshes. Both codes use Roe's upwind method with MUSCL extrapolation for the convective terms and central differences for the diffusion terms, thus yielding a numerical scheme that is formally second‐order accurate. The method of manufactured solutions is employed to generate exact solutions to the governing Euler and Navier–Stokes equations in two dimensions along with additional source terms. These exact solutions are then used to accurately evaluate the discretization error in the numerical solutions. Through global discretization error analyses, the spatial order of accuracy is observed to be second order for both codes, thus giving a high degree of confidence that the two codes are free from coding mistakes in the options exercised. Examples of coding mistakes discovered using the method are also given. Copyright © 2004 John Wiley & Sons, Ltd.     

Multiphase Thermohaline Convection in the Earth’s Crust: II. Benchmarking and Application of a Finite Element – Finite Volume Solution Technique with a NaCl–H2O Equation of State

We present the benchmarking of a new finite element – finite volume (FEFV) solution technique capable of modeling transient multiphase thermohaline convection for geological realistic p-T-X conditions. The algorithm embeds a new and accurate equation of state for the NaCl–H₂O system. Benchmarks are carried out to compare the numerical results for the various component-processes of multiphase thermohaline convection. They include simulations of (i) convection driven by temperature and/or concentration gradients in a single-phase fluid (i.e., the Elder problem, thermal convection at different Rayleigh numbers, and a free thermohaline convection example), (ii) multiphase flow (i.e., the Buckley–Leverett problem), and (iii) energy transport in a pure H₂O fluid at liquid, vapor, supercritical, and two-phase conditions (i.e., comparison to the U.S. Geological Survey Code HYDROTHERM). The results produced with the new FEFV technique are in good agreement with the reference solutions. We further present the application of the FEFV technique to the simulation of thermohaline convection of a 400°C hot and 10 wt.% saline fluid rising from 4 km depth. During the buoyant rise, the fluid boils and separates into a high-density, high-salinity liquid phase and a low-density, low-salinity vapor phase.     

Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.     

A method for obtaining benchmark Navier–Stokes solutions

A refinement to an established method for obtaining benchmark Navier–Stokes solutions is presented. Pressure and body forces are derived explicitly such that the momentum equations are satisfied. The problem is reduced to determining a streamfunction in separation of variables form that describes a desired flow pattern. Examples based upon the well‐known shear flow cavity are presented. Copyright © 1999 John Wiley & Sons, Ltd.