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π-π Interaction in Fullerenes
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
Lemi Turker, Caglar Celik Bayar
Carbon nanorings are commonly related to π-conjugated hydrocarbon macrocycle structures such as [n]cycloparaphenylene, [n]cycloparaphenyleneacetylene and its derivatives (Yuan et al., 2014). Those carbon nanorings that are used as potential supramolecular elements in their own right also serve as well-defined model compounds for studying concave π-supramolecular interactions. Interestingly, quite stable host-guest complexes can be formed with carbon nanorings and fullerenes via convex-concave π-π interactions. Moreover, the filling of the interior space of the carbon nanorings with nanoscale materials results in novel nano-hybrid with interesting properties and unique functions, which may be very different from the individual components. Supramolecular nanocavities capable of encapsulating large molecules, such as C60 fullerene are also possible (Park et al., 2008). In this kind of supramolecular systems, the hosts have a window large enough for a guest to enter but which can also serve as an exit door. π-π interactions are one of the non-covalent interactions which give rise to the flexibility of the host-guest molecule besides other complementary interactions such hydrogen bonding, van der Waals interactions and/or weak metal-ligand interactions (Park et al., 2008).
Sum of characteristic polynomial coefficients of cycloparaphenylene graphs as topological index
Published in Molecular Physics, 2020
Swapnadeep Mondal, Bholanath Mandal
A cycloparaphenylene (CPP) is cylindrical shaped compound composed of phenyl rings para-connected to each other. A weighted cycloparaphenylene (CPP) graph with hexagonal rings and with each edge of weight , shown in Figure 2(b), will have vertices. On symmetry plane fragmentation [1–3,27–29], such a graph results in a cycle of alternant edge weights () with of () vertices and number ethylene units with edge weight of each. For such systems, the cyclic chains of alternant edge weights () will have their analogues with increment or decrement of 4 vertices, i.e. or . Thus it is convenient to express CP (and hence the CP coefficients) of a cycle of N vertices in terms of that of and vertices in order to express CP coefficients of CPP graph. For this purpose we need to first express the CP coefficients [21] of alternant edge-weighted linear chain () of vertices in terms of that of and vertices and that can be accomplished using Equation (1) as follows.