Localization of the valence electron of endohedrally confined hydrogen, lithium and sodium in fullerene cages

The localization of the valence electron of $H$, $Li$ and $Na$ atoms enclosed by three different fullerene molecules is studied. The structure of the fullerene molecules is used to calculate the equilibrium position of the endohedrally atom as the minimum of the classical $(N+1)$-body Lennard-Jones potential. Once the position of the guest atom is determined, the fullerene cavity is modeled by a short range attractive shell according to molecule symmetry, and the enclosed atom is modeled by an effective one-electron potential. In order to examine whether the endohedral compound is formed by a neutral atom inside a neutral fullerene molecule $X@C_{N}$ or if the valence electron of the encapsulated atom localizes in the fullerene giving rise to a state with the form $X^{+}@C_{N}^{-}$, we analyze the electronic density, the projections onto free atomic states, and the weights of partial angular waves

Fullerene graphs of small diameter

A fullerene graph is a cubic bridgeless plane graph with only pentagonal and hexagonal faces. We exhibit an infinite family of fullerene graphs of diameter $\sqrt{4n/3}$, where $n$ is the number of vertices. This disproves a conjecture of Andova and \v{S}krekovski [MATCH Commun. Math. Comput. Chem. 70 (2013) 205-220], who conjectured that every fullerene graph on $n$ vertices has diameter at least $\lfloor \sqrt{5n/3}\rfloor-1$

Fusion mechanism in fullerene-fullerene collisions -- The deciding role of giant oblate-prolate motion

We provide answers to long-lasting questions in the puzzling behavior of fullerene-fullerene fusion: Why are the fusion barriers so exceptionally high and the fusion cross sections so extremely small? An ab initio nonadiabatic quantum molecular dynamics (NA-QMD) analysis of C$_{60}$+C$_{60}$ collisions reveals that the dominant excitation of an exceptionally "giant" oblate-prolate H$_g(1)$ mode plays the key role in answering both questions. From these microscopic calculations, a macroscopic collision model is derived, which reproduces the NA-QMD results. Moreover, it predicts analytically fusion barriers for different fullerene-fullerene combinations in excellent agreement with experiments

Fullerene graphs have exponentially many perfect matchings

A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.Comment: 7 pages, 3 figure

2-Resonant fullerenes

A fullerene graph $F$ is a planar cubic graph with exactly 12 pentagonal faces and other hexagonal faces. A set $\mathcal{H}$ of disjoint hexagons of $F$ is called a resonant pattern (or sextet pattern) if $F$ has a perfect matching $M$ such that every hexagon in $\mathcal{H}$ is $M$-alternating. $F$ is said to be $k$-resonant if any $i$ ($0\leq i\leq k$) disjoint hexagons of $F$ form a resonant pattern. It was known that each fullerene graph is 1-resonant and all 3-resonant fullerenes are only the nine graphs. In this paper, we show that the fullerene graphs which do not contain the subgraph $L$ or $R$ as illustrated in Fig. 1 are 2-resonant except for the specific eleven graphs. This result implies that each IPR fullerene is 2-resonant.Comment: 34 pages, 25 figure