TY - JOUR

T1 - 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

AU - Yoo, Soohaeng

AU - Shao, N.

AU - Zeng, X. C.

N1 - Funding Information:
We are grateful to valuable discussions with Professor Th. Frauenheim, Professor B.C. Pan, Professor J. Zhao, and Professor R.L. Zhou. This work is supported by grants from the DOE (DE-FG02-04ER46164), NSF (CHE-0427746), the Nebraska Research Initiative, and by the Research Computing Facility at University of Nebraska-Lincoln. Table I. Optimal core-filling@cage combinations for low-lying endohedral fullerene clusters Si 39 and Si 40 shown in Fig. 1 . The binding energy per atom was calculated at the PWP-DFT level of theory with two GGA functionals. The boldface denotes the lowest-energy isomer (isomers whose binding energy is within 4 meV /atom from the lowest-energy isomer are also highlighted in bold). Optimal core-filling@cage combination [homolog fullerene cage] Binding energy (eV/atom) PBE BLYP si39-1a Si 5 @ Si 34 [ C 34 ( C s : 2 ) ] 3.959 3.364 si39-1b Si 5 @ Si 34 [ C 34 ( C 2 : 5 ) ] 3.950 3.357 si39-1c Si 5 @ Si 34 [ C 34 ( C 3 v : 6 ) ] 3.942 3.366 si39-1d Si 5 @ Si 34 [ C 34 ( C s : 3 ) ] 3.938 3.358 si39-1e Si 5 @ Si 34 [ C 34 ( C 2 : 4 ) ] 3.938 3.350 si39-1f Si 5 @ Si 34 [ C 34 ( C 2 : 1 ) ] 3.929 3.359 si39 (Ref. 18 ) Si 5 @ Si 34 [ C 34 ( C s : 2 ) ] 3.941 3.362 si39 (Ref. 17 ) Si 5 @ Si 34 ( C 34 has a seven-member ring) 3.939 3.365 si40-1a Si 6 @ Si 34 [ C 34 ( C s : 2 ) ] 3.966 3.364 si40-1b Si 6 @ Si 34 [ C 34 ( C 2 : 5 ) ] 3.962 3.365 si40-1c Si 6 @ Si 34 [ C 34 ( C 2 : 4 ) ] 3.949 3.356 si40-1d Si 6 @ Si 34 [ C 34 ( C s : 3 ) ] 3.946 3.357 si40-1e Si 6 @ Si 34 [ C 34 ( C 3 v : 6 ) ] 3.944 3.349 si40-1f Si 6 @ Si 34 [ C 34 ( C 2 : 1 ) ] 3.938 3.350 si40 (Ref. 21 ) Si 6 @ Si 34 ( C 34 has a seven-member ring) 3.955 3.353 si40 (Ref. 12 ) Si 6 @ Si 34 [ C 34 ( C 3 v : 6 ) ] 3.943 3.359 si 40 - 1 a ′ (Ref. 17 ) Si 4 @ Si 36 [ C 36 ( D 3 h : 13 ) ] 3.928 3.372 Table II. Optimal core-filling@cage combinations for low-lying endohedral fullereen clusters Si 50 , Si 60 , Si 70 , and Si 80 shown in Fig. 2 . The binding energy per atom was calculated at the PWP-DFT level of theory with two GGA functionals. The boldface denotes the lowest-energy isomer (isomers whose binding energy is within 4 meV /atom from the lowest-energy isomer are also highlighted in bold). Optimal stuffing cage combination [homologfullerene cage] Binding energy (eV/atom) PBE BLYP si50-1a Si 8 @ Si 42 [ C 42 ( D 3 : 45 ) ] 3.988 3.393 si50 (Ref. 12 ) Si 8 @ Si 42 [ C 42 ( C 1 : 39 ) ] 3.954 3.364 si50 (Ref. 21 ) Si 10 @ Si 40 ( C 40 has a seven-member ring) 3.950 3.361 si 50 - 1 a ′ Si 6 @ Si 44 [ C 42 ( D 2 : 75 ) ] 3.938 3.400 si60-1a Si 12 @ Si 48 [ C 48 ( C 2 : 199 ) ] 3.998 3.395 si60-1b Si 12 @ Si 48 [ C 48 ( C 2 : 171 ) ] 3.996 3.386 si60 (Ref. 22 ) Si 12 @ Si 48 [ C 48 ( C 2 : 199 ) ] 3.993 3.388 si60 (Ref. 21 ) Si 12 @ Si 48 [ C 48 ( D 2 : 169 ) ] 3.987 3.379 si 60 - 1 a ′ Si 10 @ Si 50 [ C 50 ( D 3 : 270 ) ] 3.977 3.421 si70-1a Si 14 @ Si 56 [ C 56 ( D 2 : 916 ) ] 4.011 3.427 si 70 - 1 a ′ Si 12 @ Si 58 [ C 58 ( C 3 v : 1205 ) ] 4.007 3.430 si80-1a Si 16 @ Si 64 [ C 64 ( D 2 : 1998 ) ] 4.025 3.451 si 80 - 1 a ′ Si 16 @ Si 64 [ C 64 ( D 2 : 1988 ) ] 4.024 3.452 Table III. Lowest-lying or low-lying isomers obtained from BH global search on the basis of the SW potential model. SW Si 39 , Si 40 , and Si 50 are the predicted global minima, whereas SW Si 60 , Si 70 , and Si 80 are the best local minima obtained from this study. The (classical) potential energy per atom V ∕ n is given in the dimensionless unit. We also reoptimized the isomers at the DFT-PBE and DFT-BLYP levels of theory and calculated the corresponding binding energy per atom (eV). The bold highlights the binding energies per atom of low-lying cluster of Si 70 . SW Point group V ∕ n DFT/PBE DFT/BLYP Si 39 ( Si 5 @ Si 34 ) C 1 − 1.6079 3.919 3.352 Si 40 ( Si 4 @ Si 36 ) C 2 v − 1.6104 3.921 3.363 Si 50 ( Si 8 @ Si 42 ) C 3 − 1.6408 3.961 3.389 Si 60 ( Si 12 @ Si 48 ) C 1 − 1.6584 3.979 3.382 Si 70 ( Si 14 @ Si 56 ) C 1 − 1.6715 4.011 3.433 Si 80 ( Si 16 @ Si 64 ) C 1 − 1.6860 4.002 3.428 Table IV. Calculated HOMO-LUMO gaps for low-lying endohedral fullerene clusters Si 40 , Si 50 , Si 60 , Si 70 , and Si 80 . The geometric optimization is performed at the PWP-DFT level of theory with the PBE functional. The HOMO-LUMO gaps are calculated based on the B 3 LYP ∕ 6 – 31 G ( d ) single-point calculation. HOMO-LUMO gap (eV) Si40-1a 1.25 Si 40 - 1 a ′ 0.90 Si50-1a 1.42 si 50 - 1 a ′ 1.36 Si60-1a 1.12 Si 60 - 1 a ′ 1.36 Si70-1a 0.84 Si 70 - 1 a ′ 1.25 Si80-1a 0.74 Si 80 - 1 a ′ 1.01 FIG. 1. Geometries of low-lying endohedral silicon fullerene clusters Si 39 and Si 40 . The core-filling atoms are in blue and the outer cage atoms are in yellow. The corresponding homolog carbon fullerene cages (gray) are also displayed. FIG. 2. Geometries of low-lying endohedral silicon fullerene clusters (a) Si 50 , (b) Si 60 , and (c) Si 70 and Si 80 . The core-filling atoms are in blue and the outer cage atoms are in yellow. The corresponding homolog carbon fullerene cages (gray) are also displayed. FIG. 3. Geometries of lowest-lying SW silicon clusters SW Si 39 , Si 40 , and Si 50 , as well as the low-lying SW Si 60 , Si 70 , and Si 80 . The core-filling atoms are in blue and the outer cage atoms are in yellow. The corresponding homolog carbon fullerene cages (gray) are also displayed where the four, seven, and eight members are highlighted in red. FIG. 4. Binding energies per atom (eV/atom) of the lowest-energy endohedral silicon fullerenes highlighted (in bold) in Tables I and II . The squares represent PBE binding energies while the circles represent BLYP binding energies. The two horizontal dashed lines represent cohesive energies of the bulk silicon from PBE and BLYP calculations, respectively.

PY - 2008

Y1 - 2008

N2 - We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si39, Si40, Si50, Si60, Si70, and Si80. We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si39, we examined six endohedral fullerene structures using all six homolog C34 fullerene isomers as cage motifs. We found that the Si39 constructed based on the C34 (Cs:2) 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 optimization). The C34 (Cs:2) cage motif also leads to a new candidate for the lowest-energy structure of Si40 whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C34 (C1:1). Low-lying structures of larger silicon clusters Si50 and Si60 are also obtained on the basis of preconstructed endohedral fullerene structures. For Si50, Si60, and Si80, 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 energy) increases typically > 10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion (or the minimal requirement) to identify low-lying silicon clusters with size larger than Si50.

AB - We performed a constrained search, combined with density-functional theory optimization, of low-energy geometric structures of silicon clusters Si39, Si40, Si50, Si60, Si70, and Si80. We used fullerene cages as structural motifs to construct initial configurations of endohedral fullerene structures. For Si39, we examined six endohedral fullerene structures using all six homolog C34 fullerene isomers as cage motifs. We found that the Si39 constructed based on the C34 (Cs:2) 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 optimization). The C34 (Cs:2) cage motif also leads to a new candidate for the lowest-energy structure of Si40 whose energy is notably lower than that of the previously reported leading candidate with outer cage homolog to the C34 (C1:1). Low-lying structures of larger silicon clusters Si50 and Si60 are also obtained on the basis of preconstructed endohedral fullerene structures. For Si50, Si60, and Si80, 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 energy) increases typically > 10 meV with addition of every ten Si atoms. This result may be used as an empirical criterion (or the minimal requirement) to identify low-lying silicon clusters with size larger than Si50.

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U2 - 10.1063/1.2841080

DO - 10.1063/1.2841080

M3 - Article

C2 - 18345897

AN - SCOPUS:40849114849

SN - 0021-9606

VL - 128

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

IS - 10

M1 - 104316

ER -