The question of the highest possible coordination number for an atom is addressed as this is related to the Gregory-Newton problem of kissing hard spheres.[1] Using first-principles quantum chemical simulations we show that the interaction of Pb 2+ with He atoms results in remarkably stable PbHe 15
2+with 15 atoms in the first coordination sphere forming a Frank-Kasper polyhedron.[2] The PbÀHe distances do not change significantly by subsequent filling of the first coordination shell as one expects for a hard-sphere model. Such high coordination numbers have been proposed only in liquid simulations so far. [3] The problem of how many spheres (N max , called the kissing number or Newton number) of a given radius R can be packed around a unit sphere in n dim dimensions is called the generalized Gregory-Newton problem. In three dimensions, if all spheres have the same radius, the answer is well known: N max = 12.[1] The extension to general dimensions (with the exception of n dim = 1, 2, 3, 8, and 24), or the kissing-number problem of spheres with radius R on a unit sphere, remains unsolved. [1] In chemistry N max corresponds to the maximum coordination number of ligands interacting with a central atom, as pointed out as early as 1875 by Günther.[4] Herein we assume that the ligands do not interact strongly with each other. Hence this excludes systems like M@C 60 , which would have N max = 60 but are better described as an atom trapped in a fullerene cage.It is well known that regular icosahedral structures with N = 12 in the first coordination sphere are particularly stable and are found, for example, in rare-gas clusters and in a number of metallic clusters.[ . [7] In the solid state, coordination numbers up to N max = 12 (hexagonal closed packing and face-centered cubic) are realized, and high coordination numbers usually imply denser packing. In liquid-metal simulations, coordination numbers as high as 16 or higher have been postulated but only for a very short timeframe. [3,8] In binary intermetallic alloys local coordination numbers of 14, 15, and even 16 are predicted; prime examples are FriaufLaves phases in MgZn 2 or MgNi 2 .[9] Frank and Kasper showed that the frequent use of icosahedral coordination will occur in conjunction with coordination numbers higher than 12 stabilized by the surrounding matrix.[2]Herein we take a different approach. We look for a single molecule MX N in the gas phase of high coordination number N which can be experimentally verified. We choose a large positively charged central atom, M = Pb
2+, and a very small ligand, X = He. Both atoms have reasonably small polarizabilities (a He = 1.38 au [10] and a Pb 2+ = 14.1 au [11] ), and therefore fit the hard-sphere model quite well. The ionization potential of Pb + (15.03 eV) is much smaller than that of He (24.58 eV).[12] Hence, Pb
2+ÀHe does not undergo a Coulomb explosion and there is no (or minimal) charge transfer from He to Pb 2+ . Hence the Pb 2+ -He interaction V(R) is mainly of charge-induced-dipole (CID) nature [Eq. (1) with ...