The group 14 cationic clusters by encapsulation of coinage metals X 10 M + , with X = Ge, Sn, Pb and M = Cu, Ag, Au: Enhanced stability of 40 valence electron systems Truong Ba Tai a , Hue Minh Thi Nguyen b , Minh Tho Nguyen a,c,⇑ a Department of Chemistry, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium b Center for Computational Science and Faculty of Chemistry, National University of Education, Hanoi, Viet Nam c Institute for Computational Science and Technology (ICST), Thu Duc, HoChiMinh City, Viet Nam article info Article history: Received 4 October 2010 In final form 6 December 2010 Available online 17 December 2010 abstract The coinage metal encapsulated group 14 cationic clusters X 10 M + (X = Ge, Sn, Pb and M = Cu, Ag, Au) are investigated using quantum chemical calculations. While Cu- and Au-doped clusters have similar stabil- ity, Ag-doped counterparts are less stable. The D 4d global minima have large frontier orbital gaps and binding energies, and are magic clusters of 40 valence electrons that satisfy the jellium shell model. The concept of doubly spherical aromaticity, based on the number of 2(N + 1) 2 p and r valence electrons, is proposed to account for the enhanced stability. Predictions are in good agreement with experiment for available X 10 Cu + clusters. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Metal (M) encapsulated group 14 element clusters continue to attract much attention in part due to their peculiarly high stabil- ity and symmetrical shape. Several experimental and theoretical investigations on the M@X n clusters (M = metal elements, X = Si, Ge, Sn, Pb) have been performed to gain a better understanding of their bonding nature, spectroscopic properties, and also effect of various dopants on the pure cages [1–6]. For instance, Kumar and Kawazoe reported theoretical studies on divalent-metal doped X n M clusters, with n = 8–12 and 14, X = Si, Ge, Sn and M = Be, Mg, Zn, Cd and Mn [7,8]. A theoretical investigation on smaller metal encapsulated clusters of these elements X 10 M (X = Si, Ge, Sn, Pb and M = Ni, Pd, Pt) was performed subse- quently by these authors [9], with a comparison to the earlier re- sults on the X 10 Co  clusters. The structural and electronic properties of the metal doped germanium clusters MGe n (M = Hf, W, Os, Ni, Zn and n = 10, 12) were also calculated by Lu and Nagasausing using DFT calculations [10]. Recently, Lie- vens et al. [11] proposed a general principle for designing highly symmetrical stable clusters, that is based on both the three- dimensional aromatic stability and the close-packing structures. From experimental photoelectron spectroscopy results and DFT calculations of MSn  12 with M = Ti, V, Cr, Fe, Co, Ni, Cu, T, Nb, Gd, Hf, Ta, Pt, Au, Wang et al. [12] found that stannaspherene can trap any transition metal atom or f-block element to form a new class of endohedral caged clusters. These authors con- cluded that while transition metal dopants increase the stability of the silicon- and germanium-based clusters, empty cages of tin (Sn) are stable systems that rather exhibit similarities with car- bon fullerenes. Compared to the metal encapsulated clusters containing 12 background atoms M@X 12 , the 10-atom clusters M@X 10 have received much less attention. The main reason for this is probably the size of the X 10 cages, which are relatively smaller, and endo- encapsulation is therefore less favorable. Recently Lievens et al. [13] performed a mass spectrometric stability investigation of a large series of metal doped group IVA clusters MX n , including X = Si, Ge, Sn, Pb and M = Cr, Mn, Cu, Zn. Their experimental results interestingly revealed that copper – group 14 element mixed clus- ters X n Cu (X = Ge, Sn and Pb) exhibit remarkably high abundance at size of n = 10. Consequently, the systems such as CuGe þ 10 , CuSn 0;þ 10 and CuPb 0;þ 10 were established to be the species with enhanced stability. However the reasons for such behavior have not been fully understood yet. Let us note that earlier theoretical reports usually focused on a few systems having certain sizes but without available experimental results. In an attempt to gain more insights into the 10-atoms clusters of group 14, we set out to carry out a systemic investigation on the clus- ters with impurity X 10 M + , in which X = Ge, Sn, Pb and M = Cu, Ag, Au. The search for the low-lying isomers of clusters is carried out using a stochastic searching method. As the experimental studies on silver- or gold-doped group 14 clusters are not available, it is of interest to predict the properties of the corresponding higher homologues, and thereby to have additional confirmation for the effects of impurities on the caged clusters. 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.12.021 ⇑ Corresponding author at: Department of Chemistry, Katholieke Universiteit Leuven, B-3001 Leuven, Belgium. Fax: +32 16 32 79 92. E-mail address: minh.nguyen@chem.kuleuven.be (M.T. Nguyen). Chemical Physics Letters 502 (2011) 187–193 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett