Validation of Methods for Computational Catalyst Design: Geometries, Structures, and Energies of Neutral and Charged Silver Clusters

We report a systematic study of small silver clusters, Ag_<i>n</i>, Ag_<i>n</i>⁺, and Ag_<i>n</i>^–, <i>n</i> = 1–7. We studied all possible isomers of clusters with <i>n</i> = 5–7. We tested 42 exchange–correlation functionals, and we assess these functionals for their accuracy in three respects: geometries (quantitative prediction of internuclear distances), structures (the nature of the lowest-energy structure, for example, whether it is planar or nonplanar), and energies. We find that the ingredients of exchange–correlation functionals are indicators of their success in predicting geometries and structures: local exchange–correlation functionals are generally better than hybrid functionals for geometries; functionals depending on kinetic energy density are the best for predicting the lowest-energy isomer correctly, especially for predicting two-dimensional to three-dimenstional transitions correctly. The accuracy for energies is less sensitive to the ingredient list. Our findings could be useful for guiding the selection of methods for computational catalyst design

Thermodynamics of Metal Nanoparticles: Energies and Enthalpies of Formation of Magnesium Clusters and Nanoparticles as Large as 1.3 nm

The major obstacle that prevents reliable electronic structure studies of nanoparticles is the rapid increasing computational cost for benchmark calculations using coupled-cluster methods. We show that a CCSD­(T) scheme with an MP2/CBS correction can reproduce accurate cohesive energies for magnesium clusters, and this scheme is much less computationally demanding than other reliable methods, so it is applied to Mg_<i>n</i> with <i>n</i> up to 19, which enters the realm of nanoparticles. (The diameters of all Mg clusters <i>n</i> ≥ 11 are >1 nm). With the extended benchmark data, we validate exchange–correlation functionals into the nanoparticle regime and use the two best-validated functionals to calculate the enthalpy of formation of Mg₂₈, with a diameter of 1.30 nm. We also calculated the enthalpy of formation of all Mg clusters and nanoparticles from Mg₂ to Mg₁₉. This kind of reliable thermodynamic data on size-selected metal nanoparticles has been hard to come by, either experimentally or theoretically, but it is badly needed to support applications in catalysis, electrochemistry, and other technologies

Atomic Oxygen Recombination at Surface Defects on Reconstructed (0001) α‑Quartz Exposed to Atomic and Molecular Oxygen

The surface chemistry of silica is strongly affected by the nature of chemically active sites (or defects) occurring on the surface. Here, we employ quantum mechanical electronic structure calculations to study an uncoordinated silicon defect, a non-bridging oxygen defect, and a peroxyl defect on the reconstructed (0001) surface of α-quartz. We characterized the spin states and energies of the defects, and calculated the reaction profiles for atomic oxygen recombination at the defects. We elucidated the diradical character by analyzing the low-lying excited states using multireference wave function methods. We show that the diradical defects consist of weakly coupled doublet radicals, and the atomic oxygen recombination can take place through a barrierless process at defects. We have delineated the recombination mechanism and computed the formation energy of the peroxyl and non-bridging oxygen defects. We found that key recombination reaction paths are barrierless. In addition, we characterize the electronically excited states that may play a role in the chemical and physical processes that occur during recombination on these surface defect sites

Density Functional Theory of the Water Splitting Reaction on Fe(0): Comparison of Local and Nonlocal Correlation Functionals

Metal clusters have broad applicability in catalysis due to their unique reactivity and chemical selectivity, and density functional theory has become an important method for understanding catalysis and attempting to design better catalysts. In the present paper, a main focus is on the correlation part of the exchange-correlation functional, and we tested the reliability of the Kohn–Sham density functional theory with local correlation functionals and with the nonlocal random phase approximation (RPA) correlation functional for the water splitting reaction on monatomic Fe(0) and, by implication, for transition-metal-catalyzed reactions more generally. We computed four barrier heights and six energies of reaction in the catalytic mechanism. If the results are judged by deviation from CCSD­(T) calculations, it is found that many modern exchange-correlation (xc) functionals (about half of the functionals tested) with local correlation perform better than those using RPA nonlocal correlation; for example, the PWB6K, B97-3, ωB97X-D, MPW1K, M06-2X, and M05-2X hybrid xc functionals with local correlation have overall mean unsigned deviations of 1.9 kcal/mol or less from the CCSD­(T) results, in comparison to a mean unsigned deviation of 3.5 kcal/mol for EXX-RPA@PBE. We also find significant differences between the predictions for catalysis at the Fe(100) surface. This work provides guidance and challenges for future theoretical investigations of transition-metal catalysis

Size-Dependent Ligand Quenching of Ferromagnetism in Co₃(benzene)_<i>n</i> ⁺ Clusters Studied with X‑ray Magnetic Circular Dichroism Spectroscopy

Cobalt–benzene cluster ions of the form Co₃(bz)_<i>n</i> ⁺ (<i>n</i> = 0–3) were produced in the gas phase, mass-selected, and cooled in a cryogenic ion trap held at 3–4 K. To explore ligand effects on cluster magnetic moments, these species were investigated with X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) spectroscopy. XMCD spectra yield both the spin and orbital angular momenta of these clusters. Co₃ ⁺ has a spin magnetic moment of μ_S = 6 μ_B and an orbital magnetic moment of μ_L = 3 μ_B. Co₃(bz)⁺ and Co₃(bz)₂ ⁺ complexes were found to have spin and orbital magnetic moments identical to the values for ligand-free Co₃ ⁺. However, coordination of the third benzene to form Co₃(bz)₃ ⁺ completely quenches the high spin state of the system. Density functional theory calculations elucidate the spin states of the Co₃(bz)_<i>n</i> ⁺ species as a function of the number of attached benzene ligands, explaining the transition from septet to singlet for <i>n</i> = 0 → 3