Structures and relative stability of medium- and large-sized silicon clusters. VI. Fullerene cage motifs for low-lying clusters Si39, Si40, Si50, Si60, Si70, and Si80

Abstract

We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si 39 , Si 40 , Si 50 , Si 60 , Si 70 , and Si 80 . We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si 39 , we examined six endohedral fullerene structures using all six homolog C 34 fullerene isomers as cage motifs. We found that the Si 39 constructed based on the C 34 ͑C s :2͒ cage motif results in a new leading candidate for the lowest-energy structure whose energy is appreciably lower than that of the previously reported leading candidate obtained based on unbiased searches ͑combined with tight-binding optimization͒. The C 34 ͑C s :2͒ cage motif also leads to a new candidate for the lowest-energy structure of Si 40 whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C 34 ͑C 1 :1͒. Low-lying structures of larger silicon clusters Si 50 and Si 60 are also obtained on the basis of preconstructed endohedral fullerene structures. For Si 50 , Si 60 , and Si 80 , the obtained low-energy structures are all notably lower in energy than the lowest-energy silicon structures obtained based on an unbiased search with the empirical Stillinger-Weber potential of silicon. Additionally, we found that the binding energy per atom ͑or cohesive energy͒ increases typically Ͼ10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion ͑or the minimal requirement͒ to identify low-lying silicon clusters with size larger than Si 50 .

Competitive diamond‐like and endohedral fullerene structures of Si70

“…From the DFT-BLYP calculations, the Si 10 @Si 50 endohedral fullerene is the most stable isomer consistent with the BLYP result reported in ref. 19 , which is 0.671 eV more stable than the diamond-like isomer (Fig. 3).…”

“…At the BLYP level, the diamond-like isomer is 0.605 eV lower in energy than the Si 14 @Si 56 , which is a fullerene with an optimal stuffing/cage ratio, whereas the Si 12 @Si 58 reported in ref. 19 is the second lowest energy endohedral fullerene. At the PBE level, the present lowest energy isomer is an endohedral fullerene Si 16 @Si 54 .…”

Reexamine structures and relative stability of medium-sized silicon clusters: Low-lying endohedral fullerene-like clusters Si30–Si38

“…For references, the binding-en- ergies of the lowest-lying clusters Si 39 and Si 40 (see Ref. [19]) are also included in Table 2 and plotted in Figs. 1(a)-(c).…”

“…Top candidates (isomers with large binding energies) are identified from this screening calculation. Next, additional constrained searches are performed by using the basin-hopping (BH) method combined with DFT geometry optimization [19,26]. The obtained lowest-energy clusters are classified into three groups: one according to the binding energies computed based on the PBE functional, the second according to the binding energies based on the BLYP functional, and the third according to the mean PBE/BLYP binding energies.…”

Atomistic Modelling of Si Nanoparticles Synthesis

“…The FF parameters have been optimized in order to reproduce a training-set (t-set) of properties (i.e., energies and geometries) derived from quantum chemical (QC) calculations on selected model systems. Few experimental measurements of dissociation/ionization energies and mobilities of the ionized structures are available in the literature [21][22][23][24], whereas geometries and electronic structures of small silicon clusters have been studied extensively by QC approaches over the last few years [25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”