Browsing by Author "Trombach L"

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    From sticky-hard-sphere to Lennard-Jones-type clusters
    (American Physical Society, 2018-04-24) Trombach L; Hoy RS; Wales DJ; Schwerdtfeger P
    A relation M_{SHS→LJ} between the set of nonisomorphic sticky-hard-sphere clusters M_{SHS} and the sets of local energy minima M_{LJ} of the (m,n)-Lennard-Jones potential V_{mn}^{LJ}(r)=ɛ/n-m[mr^{-n}-nr^{-m}] is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both m and n and increases exponentially with increasing cluster size N for N≳10. While the map from M_{SHS}→M_{SHS→LJ} is noninjective and nonsurjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to N=13, and most of the missing structures correspond to energetically unfavorable minima even for fairly low (m,n). Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.
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    Gregory-Newton problem for kissing sticky spheres
    (American Physical Society, 2018-09-28) Trombach L; Schwerdtfeger P
    All possible nonisomorphic arrangements of 12 spheres kissing a central sphere (the Gregory-Newton problem) are obtained for the sticky-hard-sphere (SHS) model and subsequently projected by geometry optimization onto a set of structures derived from an attractive Lennard-Jones (LJ) type of potential. It is shown that all 737 derived SHS contact graphs corresponding to the 12 outer spheres are (edge-induced) subgraphs of the icosahedral graph. The most widely used LJ(6,12) potential has only one minimum structure corresponding to the ideal icosahedron where the 12 outer spheres do not touch each other. The point of symmetry breaking away from the icosahedral symmetry towards the SHS limit is obtained for general LJ(a,b) potentials with exponents a,b R+. Only if the potential becomes very repulsive in the short range, determined by the LJ hard-sphere radius σ, are symmetry-broken solutions observed.