Nanoclusters and nanoalloys of group 13 elements (B, Al, and Ga): benchmarking of methods and analysis of their structures and energies

Abstract

We investigated the structural and energetic properties of nanoclusters and nanoalloys composed of group 13 elements (B, Al, and Ga) up to a cluster size of 12. We conducted a...

A reinvestigation of the boron cluster B15+/0/−: a benchmark of density functionals and consideration of aromaticity models

“…39 Although the T1 value of 0.04 for 1a remains significantly lower as compared to the T1 values of the B 2 , B 3 or B 4 species (>0.08), 18 the energy of 1a is not included in our benchmarking survey. Incidentally, we also notice some inconsistency in the previous T1 value for the triplet dimer B 2 ; while Khatun 17 reported a value of 0.042, Liu 18 gave that of 0.072. We recheck this discrepancy and find the Liu's report to be highly questionable.…”

“…Consequently, we select the relative energies obtained from CCSD(T) calculations with PBE/6-311+G(d) geometries as reference for subsequent benchmark computations. The benchmarking study incorporates several additional functionals, including the TPSSh, PBE0 and HSE06 that have extensively been demonstrated to be suitable for boron; the M06 and BPBE as proposed by Khatun et al ; 17 the popular B3LYP functional which has repeatedly been shown to be unsuitable for energy exploration in the context of boron clusters, and the VSXC, B1B95 and B2PLYPD3 that were suggested by Liu et al 18 We would emphasize that double-hybrid functionals such as the B2PLYPD3 are computationally expensive; a substantial computational resource of 500 GB of disk space needs to be allocated for a single calculation on B 15 using the latter functional.…”

“…Conversely, the B1B95 and M06 apparently overestimate the stability of 3D structures as compared to planar counterparts. As a matter of fact, on the basis of M06/def2SVP calculations, Khatun et al 17 drew a significantly erroneous conclusion that the global minimum of the B 12 cluster is a 3D structure, even though the C 3v quasi-planar structure has long been established to be its lowest-energy isomer. 5,44,45…”

“…Within a noticeably short period, two consecutive publications have recently reported benchmarks for the study of relative energies based on reference molecules with exceedingly high spin contamination in their unrestricted solutions. The first publication by Khatun et al 17 was conducted on the series of small triatomic clusters B 3 , Al 3 and Ga 3 . Subsequently, the paper by Liu et al 18 focused on the pure boron clusters B n with n = 1–4.…”