Structural reciprocity effect in binary silicon–bismuth clusters

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Abstract

It is shown by density functional theory using doubly polarized basis sets that the lower energy structures of silicon–bismuth clusters Bi4Si2 and Bi2Si4 have the same overall geometry and symmetry and can be formally obtained from each other by mutual substitution and optimization or by direct Bi-substitution to the corresponding neutral Si6 cluster. Such ‘structural reciprocity’, which is attributed to the fluxionality of Si6 cluster and the similarity of Bi and Si electronegativities, can be generally true for other pairs of Bi–Si clusters to a lesser degree, and could be remotely related with the metal–semiconductor transition in Bi–Si alloys.

Graphical abstract

Structural relationship between Bi2Si4 and Bi4Si2 clusters.

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Introduction

The elemental silicon clusters have been extensively studied over the past two decades [1], [2], [3], [4], [5], [6], [7] due to their added importance for nanoscience and nanotechnology on top to their fundamental scientific importance. In recent years their study has been intensified in view of the current miniaturization trends in electronic devices which are pushing towards molecular scales. For the same reason, mixed metal–silicon clusters (adsorbed or embedded) have attracted special attention [8], [9], [10], [11], [12], [13], [14]. Semimetals such as bismuth (which is the heaviest group V semimetal), could be also very interesting in this respect, and this why their study is pursued here. In addition to bismuth significance for thermoelectric applications, bismuth nanoparticles have high electron mobility and potential for inducting a semiconductor transition with decreasing crystallite size [15], [16]. Both Bi-rich and Si-rich regions of interest have been examined in the literature. Many studies have been performed on the doping of bismuth with group IV elements (Si, Ge, Sn, and others) which reveal a profound effect of doping on its transport properties (see Refs. [15], [16], [17]). Also, Bi adsorption on Si, Ge, Sn surfaces has been well studied over the last decade (see Refs. [15], [18]). Yet, there have been only few studies on binary Bi–Si (or Bi–Ge, or Bi–Sn) clusters, until recently [15], [19], [20], [21]. Recently, Sun et al. [15] have examined experimentally and theoretically neutral and anionic clusters of the form BinSim0, −1 (and similarly for Bi–Ge and Bi–Sn clusters) with n + m  6; while more recently Li et al. [19] and Zdetsis [20] have studied dibismuthic clusters of the form Bi2Si5 and Bi2Sin−2 (with n = 3–12) respectively. Dibismuthic clusters of the form Bi2Sn10 have been also studied by the present author [20] in the context of the ‘boron connection’ isolobal analogy [20], [21], [22], [23]. This analogy allows the structural and electronic correlation between [19], [20], [21], [22], [23] Sin2−, (BnHn)2− dianions, C2Bn−2Hn, and Sin−2C2H2 clusters, which can be extended to [20] Sin−2Bi2 clusters. This last step involves the 2BH1−  2CH  2Bi isoelectronic substitution involving 5 valence electrons. The same substitution is behind the schematical formation of bisboranes from boranes or carboranes [19], [20], [21]. The advantage of invoking such isoelectronic and isolobal analogies is the exploitation of the well known and well tested powerful structural and stability principles, as well as electron counting rules developed for boranes and carboranes [24], [25], [26], [27], in the study of such (seemingly very different) molecular systems. Through this analogy it was illustrated that the structures of Bi2Sin−2 clusters are obtained from the structure of the corresponding Sin2− dianions by simple Bi  Si substitution [19], [20]. It was verified [19], [20] for instance, that Bi2Si5 has the same pentagonal dipyramidal structure as Si72−, and Si5C2H2 which are similar and isolobal [20] to (BH)72−, (BH)5C2H2, and (BH)5Bi2.

For Bi2Si4 however, it was found [20] that in addition to the low energy structures obtained from Si62− dianion, there were even lower energy structures (and among them the lowest) related to the Si6 neutral cluster rather than the Si62− dianion. This was attributed [20] to the fluxionality of the Si6 cluster [6], [7] and in part to the similarity of the Bi and Si electronegativities. If we want to test and/or push further this interpretation, we must examine the structural (and electronic) properties of the ‘reciprocal’ cluster Bi4Si2. This is the starting and main point of the present investigation. As we can see below in Section 3, the low energy structures of the Bi4Si2 cluster are indeed ‘reciprocal’ to those of Bi2Si4, and both of them are obtained in a ‘complementary’ way from the same basic structure(s).

Section snippets

Method of calculation

The geometry optimizations (symmetry constrained and unconstrained) and single point calculations for all structures were performed within the density functional theory (DFT), using the hybrid exchange and correlation functional of Becke-Lee, Parr and Yang (B3LYP) [28] and the triple-ζ valence doubly polarized (TZV2P) basis sets [29]. These basis sets, implemented in the TURBOMOL program package [30] under the label def-TZVPP, and def2-TZVPP are comparable to 6-311G(2df) quality. The initial

Results and discussion

The lower energy structures of Bi4Si2, Bi2Si4 and Si6 clusters (including the lowest) are shown in Fig. 1.

In this figure the energetical ordering is indicated by numbers below the structures. The reference structure in both cases (zero of energy) is the one which is isolobal to the corresponding carborane (and bisborane) or the corresponding hydrogenated silicon carbon cluster [22], [23] (see top and bottom rows of Fig. 2). For Bi2Si4 the lowest and second lowest reference structures (i.e.

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