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

Abstract

We report a systematic study of small silver clusters, Ag n , Ag n + , and Ag n − , n = 1−7. We studied all possible isomers of clusters with n = 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 threedimenstional 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.

Regium bonds between Mn clusters (M = Cu, Ag, Au and n = 2–6) and nucleophiles NH3 and HCN

“…There are points of confirmation of other aspects of our results. For example, the optimal shapes of our clusters agree with previous findings 46,47 that also found the state with lowest spin multiplicity to be most stable. Our general range of regium bond energies fit in with earlier calculations, 27,45,49,51 albeit for somewhat different clusters and bases.…”

“…All of these geometries are planar, a characteristic which is confirmed by DFT, as well as available literature data. 46,47,81 In all of these clusters the ground electronic state is that with the lowest possible spin state, viz. singlet for Mn (n= 2, 4 and 6) and doublet for M3 and M5.…”

“…Similar geometries have been reported previously for the Ag3 trimer. 46,47,81 The origin of the structure of the Ag3 trimer has been explained in terms of the Jahn−Teller effect. 46 The tetramers take the shape of a rhombus with all four peripheral distances equal to one another, and with R2 separating the two vertices of the rhombus, with R2 < R1.…”

Assessment of interaction-strength interpolation formulas for gold and silver clusters

“…the generalized gradient approximation (GGA) 65 or the meta-GGA's. 66 This is an efficient approach, 25,26,33,35,37,38,48,49,[67][68][69] but in various cases it has also shown limited accuracy, especially in the not so rare case when it is necessary to discriminate between isomers with rather similar energies (for example in the prediction of the two-to three-dimensional crossover in gold and silver clusters 38,50 ). However, unlike in the case of main group molecular calculations, the use of hybrid functionals, which include a fraction of exact exchange, is not able to provide a systematic improvement.…”

“…Instead, it often leads to a worsening of the results. 38,69 The origin of this problem possibly traces back on the too simplicistic idea of mixing a fixed fraction of exact exchange with a semilocal approximation.…”