Structures and stability of medium-sized silicon clusters. III. Reexamination of motif transition in growth pattern from Si15 to Si20

Abstract

It has been established from experiments that stable medium-sized ionic clusters Si 15 -Si 20 are prolate in shape. Density-functional theories ͑DFTs͒ also predict that nearly all low-lying neutral clusters in this size range are prolate in shape. Moreover, most of them are built onto two generic structural motifs, either the tricapped-trigonal-prism ͑TTP͒ Si 9 motif or the six/six Si 6 /Si 6 ͑sixfold-puckered hexagonal ring Si 6 plus six-atom tetragonal bipyramid Si 6 ͒ motif. However, it appears that the exact location of the TTP-to-six/six motif transition is dependent on the functional ͑e.g., PBE or BLYP͒ used in the DFT calculations. Here, we present total-energy calculations for two series of clusters ͑one series containing six/six motif and the other containing the TTP motif͒ in the size range of Si 16 -Si 20 . The calculations were based on all-electron DFT methods with a medium ͓6-311G ͑2d͔͒ and a large ͑cc-pVTZ͒ basis sets, as well as coupled-cluster single and double substitutions ͑including triple excitations͒ ͓CCSD͑T͔͒ method with a modest ͑cc-pVDZ͒ basis set. In the DFT calculations, two popular hybrid density functionals, the B3LYP and PBE1PBE, were selected. It is found that the B3LYP total-energy calculations slightly favor the six/six motif, whereas the PBE1PBE calculations slightly favor the TTP motif. The CCSD͑T͒ total-energy calculations, however, show that isomers based on the six/six motif are energetically slightly favorable in the size range of Si 16 -Si 20 . Hence, the TTP-to-six/six motif transition is more likely to occur at Si 16 .

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

“…The homolog fullerene cage of the former Si 40 structure is C 34 ͑C 3v :6͒, whereas that of the latter is C 36 ͑D 3h :13͒ ͑Table I͒. As shown in previous studies, 13,17 the PBE functional favors more compact clusters, whereas the BLYP functional favors clusters having a larger fullerene cage and less core-filling atoms.…”

“…Moreover, we have found that the PBE functional favors more compact silicon clusters ͑in terms of energy ranking͒ whereas the BLYP functional favors clusters having less core-filling atoms. 13,17 We thus present results of binding energies based on the two functionals, namely, the PBE and BLYP.…”

“…On the other hand, this approach is capable of producing competitive candidates for the lowlying clusters, as has been demonstrated for smaller silicon clusters Si N in the size range of N = 15-30. 13,17 In view of several previous studies ͑using various unconstrained global search methods͒ confirming that fullerenes are viable structural motifs to build low-lying medium-sized silicon clusters, here, we further examine fullerene-based structural motifs for constructing medium-to large-sized low-lying silicon clusters. To this end, we have performed a series of constrained ͑biased͒ searches using carbon fullerenes as cage motifs to seek low-lying silicon clusters of Si 50 Si 39 and Si 40 as testing bed.…”

“…[1][2][3][4][5][6][7] Over the past few years, medium-sized endohedral silicon fullerenes have received increasing attention [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] largely because of the advancement of global optimization methods and their application to medium-sized silicon clusters. [23][24][25][26][27] Numerous theoretical studies of lowest-energy structures of medium-sized clusters Si N ͑N = 25-40 and 45͒ have shown that beyond the size N = 29, spherical-like compact structures are more stable than elongated structures 9,13,15,16,20 and that the carbon fullerene cages are likely to be generic cage motifs for a class of lowlying spherical-like clusters. 9,14,[16][17][18]20,21 An empirical rule for determining optimal "stuffing@cage" combination for endohedral silicon fullerenes has been proposed.…”

Energies and lifetimes of electrons and excitons in Si20modeled by many-body Green’s function theory

“…Two stable geometric configurations of Si 20 have been reported in literatures, one with the C 3v symmetry (Fig. 2a) 32,33 and the other with the C 2h symmetry (Fig. 2b) 34 .…”