Computational Exploration of Xe Dimers Inside Fullerene Cages

Abstract

A systematic analysis for the determination of the optimum fullerene cage for encapsulation of xenon dimers was carried out using density functional theory and activation strain analysis. Our calculations indicate that tubular-like fullerenes are better candidates for the encapsulation of xenon atoms. However, the tubular-like structure should have at least a diameter that is proportional to the van der Waals radius of encapsulated atoms. Our calculations indicate that the smallest fullerene that can stabilize the encapsulation of the xenon dimers in an energetically favorable dimeric state is Xe₂@C₁₂₀ ([10,0] C₁₂₀-D_5h(10766)). When going to higher order fullerenes, the dispersion interaction will dominate over all other interactions. However, the additional space provided by the tubular-like fullerene leads to elongation of the distance between the encapsulated xenon atoms, thus hampering the formation of a xenon-xenon chemical bond.

1

Topology of fullertubes, with an example shown on the right, in which case cap A and cap B consist of 30 carbon atoms (C₃₀) and an armchair tube (5,5) with 10 atoms in each ring in the middle. Overall, this leads to the general formula C₃₀ + C₃₀ + C_10n for the total number of carbons.

2

Computed (electronic) binding energies (pink, dotted line) obtained at the S12g-D3/TZ2P level and Xe–Xe distances (purple, solid line) of Xe₂-encapsulated EF plotted against the number of atoms in the fullerenes. For reference, the optimized distance (S12g-D3/TZ2P) for the Xe–Xe van der Waals dimer is 4.445 Å.

3

Activation strain analysis and EDA of the interaction energy between fullerenes (Isomer number in the parentheses) and Xe monomer (a,b) and Xe₂ dimer (c,d). Decomposition of total energy into preparation and interaction (a,c) and of interaction energy into Pauli repulsion, electrostatic interactions, orbital interactions, and dispersion energy (b,d).

4

Computed MDC-d charge on Xe₂ (pinkish, dotted line) and GJ bond order index (BODSEP) (purple, solid line) obtained at the S12g-D3/TZ2P level of Xe₂-encapsulated EF plotted against the number of atoms in the fullerenes.

5

EDA of the interaction energy between the Xe₂ dimer and the fullertubes. Decomposition of total energy into strain/preparation and interaction (top) and of interaction energy into Pauli repulsion, electrostatic interactions, orbital interactions, and dispersion energy (bottom). Energy values plotted are the saturated value of energy at the different fullertube families plotted against the radius of the fullertube ( $\frac{a\sqrt{3}}{2\pi }\sqrt{n^2+m^2+nm}$ , a = 1.44).