Digitalizing Structure–Symmetry Relations at the Formation of Endofullerenes in Terms of Information Entropy Formalism

Abstract

Information entropy indices are widely used for numerical descriptions of chemical structures, though their applications to the processes are scarce. We have applied our original information entropy approach to filling fullerenes with a guest atom. The approach takes into account both the topology and geometry of the fullerene structures. We have studied all possible types of such fillings and found that information entropy (ΔhR) and symmetry changes correlate. ΔhR is negative, positive or zero if symmetry is increased, reduced or does not change, respectively. The ΔhR value and structural reorganization entropy, a contribution to ΔhR, are efficient parameters for the digital classification of the fullerenes involved into the filling process. Based on the calculated values, we have shown that, as the symmetry of the fullerene cage becomes higher, the structural changes due to the filling it with a guest atom become larger. The corresponding analytical expressions and numerical data are discussed.

Stability and Electronic Properties of Mixed Rare-Earth Tri-Metallofullerenes YxDy3-x@C80 (x = 1 or 2)

“…It should be noted that the symmetry of this fullerene is lowered to due to the Jahn–Teller symmetry reduction. The cage obtains its highest symmetry only when filled with metals [ 48 ]. To ascertain whether Y 2 Dy@C 80 and YDy 2 @C 80 also adopt this particular fullerene cage, we conducted DFT calculations.…”

On the origin of the combinatorial complexity of the crystal structures with 0D, 1D, or 2D primary motifs

“…Even non-periodic host-guest inclusion systems such as endofullerenes demonstrate a clear dependence of the host's combinatorial complexity on the presence of the guest. 57 Such combinations as molecules/chains, molecules/layers, chains/layers, chains/ framework, and interpenetrating frameworks 58 are also possible in chemistry, but the symmetry of a net binding the primary building units, in fact, comes down to G 3 3 , G 2 2 , or G 1 1 and is determined by the least dimensionality of a primary motif included in the structure. A generalized abbreviation for primary motifs with diverse dimensionality (molecules, chains, layers, framework) could be "b.u."…”

“…Even non-periodic host–guest inclusion systems such as endofullerenes demonstrate a clear dependence of the host's combinatorial complexity on the presence of the guest. 57 Such combinations as molecules/chains, molecules/layers, chains/layers, chains/framework, and interpenetrating frameworks 58 are also possible in chemistry, but the symmetry of a net binding the primary building units, in fact, comes down to G 3 3 , G 2 2 , or G 1 1 and is determined by the least dimensionality of a primary motif included in the structure. A generalized abbreviation for primary motifs with diverse dimensionality (molecules, chains, layers, framework) could be “b.u.” (building unit), and the dimensionality (dim) could be indicated by a superscript H U ′′ = H ( v 1 , v 2 , …, v U ′′ )where U ′′ is the total number of symmetrically independent building units of all dimensionalities, v 1 , v 2 , …, v U ′′ are corresponding to the reduced cell in 3D, and H dim edge is estimated separately according to eqn (14) and taking into account the dimensionality (dim) of the net.…”