An 18-Electron System Containing a Superheavy Element: Theoretical Studies of Sg@Au 12 Guo-Jin Cao, †,§ W. H. Eugen Schwarz,* ,§,∥ and Jun Li* ,§ † Key Laboratory of Chemical Biology and Molecular Engineering of the Education Ministry, Institute of Molecular Science, Shanxi University, Taiyuan 030006, China § Department of Chemistry and Key Laboratory of Organic Optoelectronics and Molecular Engineering, Ministry of Education, Tsinghua University, Beijing 100084, China ∥ Physical and Theoretical Chemistry, University of Siegen, Siegen 57068, Germany * S Supporting Information ABSTRACT: M@Au 12 cage molecules (M = transition element from group 6) are interesting clusters with high-symmetric structure and significant stability. As the heavier homologue of W is 106 Sg, it is interesting to pinpoint whether the Sg@Au 12 cluster is also stable. Geometric and electronic structures and bonding of various Sg@Au 12 isomers were investigated with density functional theory (PW91, PBE, B3LYP) and wave function theory (MP2, CCSD(T)) approaches. The lowest-energy isomer of Sg@Au 12 has icosahedral symmetry with significant Sg(6d)−Au(6s) covalent-metallic interaction and is comparable to the lighter homologues (M = Mo, W), with similar binding energy, although Sg follows (as a rare case) the textbook rule “ns below (n − 1)d”. The 12 6s valence electrons from Au 12 and the six 7s6d ones from Sg can be viewed as an 18e system below and above the interacting Au 5d band, forming nine delocalized multicenter bond pairs with a high stability of ∼0.8 eV of bond energy per each of the 12 Sg−Au contacts. Different prescriptions (orbital, multipole-deformation, charge-partition, and X-ray-spectroscopy based ones) assign ambiguous atomic charges to the centric and peripheral atoms; atomic core-level energy shifts correspond to some negative charge shift to the gold periphery, more so for Cr@Au 12 than for Sg@Au 12 or Au@Au 12 . 1. INTRODUCTION Bohr had invented electronic orbits in nuclear atoms in 1913, and he derived the respective energy level patterns and maximum occupation numbers within that theoretical frame- work from experimental data until 1923. 1,2 Earlier, though in a purely empirical manner, Langmuir 3 had formulated atomic 8-, 18-, and 32-electron rules, which were further developed by Sidgewick, Mingos, Pyykkö , and others up to recent times. 4−6 Many examples are found in the field of transition metal complexes; see the textbooks of inorganic chemistry, for example. 7 Systems with a slightly broken spherical symmetry, such as highly symmetric transition metal complexes or atomic clusters, may have slightly broken atom-like one-particle level schemes resembling stable s 2 -p 6 ,s 2 -p 6 -d 10 , or s 2 -p 6 -d 10 -f 14 type shells for 8, 18, or 32 electrons, respectively. As Pyykkö 6 had pointed out, not all s-p-d or s-p-d-f subshells must act stabilizing or be (partially) localized on the central atom. We also note that the 18e noble gas shells of Kr and Xe are of d 10 - s 2 -p 6 type. Pyykkö 6,8,9 had discussed the relevance of the 18e rule for metal clusters of type M′@M n such as M′@Au 12 , where M′ with [(n - 1)d,ns] 6 outer shell means an element with six valence electrons from group 6 of the periodic system, and the 12 Au atoms contribute their 12 loose outer valence electrons. The first experimental observation of icosahedral W@Au 12 and Mo@Au 12 clusters was reported by Wang et al. 17 in 2002 following Pyykkö ’s theoretical prediction earlier that year. As usual, the atomic radii increments increase down the group (values of Fluck 10 / Pyykkö , 11 respectively): Cr ≈ 125/ 122, Mo ≈ 136/138, W ≈ 137/137, and Sg ≈ 132/143 pm. The values suggested for Au show a larger discrepancy of 144/ 124 pm; see also refs 12 and 15. The two radii of Au resemble those of the lightest versus the heaviest group 6 elements, namely, Cr and Sg. Seaborgium is the heaviest of all elements where simple chemistry may still be possible: the 270±1 Sg isotopes have lifetimes of ∼2 min. Various halo−oxo−hydroxo and carbonyl complex species of Sg (of even shorter-lived isotopes) in the gaseous and liquid phase have been reported as similar to Sg’s lighter homologues. 13 Concerning the effective atomic radii of Sg, the open question is whether W < Sg or W > Sg. W < Sg seems more reasonable because the Dirac−Fock radii of both the p-core and d-valence shells of Sg are 11.5% larger than those of W, 14 although Fricke advocated W ≈ Sg. 15 Sg exhibits even larger relativistic effects than those of the celebrated Au, 16 such as large 6p core and 6d valence spin−orbit splittings, 6d self- consistent relativistic expansion and destabilization, and 7s direct relativistic stabilization and contraction. The question arises, in which direction Sg@Au 12 might deviate from well- investigated W@Au 12 . 8,9,17,18 Gold atoms and gold clusters have recently gained increased interest in chemistry and material science, since they can act as Received: February 13, 2015 Article pubs.acs.org/IC © XXXX American Chemical Society A DOI: 10.1021/acs.inorgchem.5b00356 Inorg. Chem. XXXX, XXX, XXX−XXX