Quantum Bound States in a C–C60 System

Abstract

We investigate the quantum mechanical system of a carbon "test atom" in the proximity of a C60 molecule, both inside and outside the fullerene "cage". Two sets of bound states are found to exist, a deeply bound set inside the cage and another weakly bound set outside it. Tunnelling between these regions is highly unlikely to happen because of the extreme height and width of the potential barrier. However, we predict that a layer of atoms could be adsorbed onto C60 by forming a quantum mechanical bound state, with the adsorbed atoms being concentrated above the "panels" of the buckyball, consistent with "bucky onions" observed experimentally. Until now analysis of such fullerene systems has been via classical mechanics, but a quantum approach reveals new insights. BackgroundSince 1970, when Henson proposed the buckminsterfullerene structure [1], major strides have been made in the field. The compound was first identified by Iijima in 1980 [2] and synthesized in 1985 [3], the latter work resulting in the 1996 Nobel Prize for Chemistry. Fullerenes have attracted wide interest over the past 30 years, for both fundamental and practical reasons, in fields as diverse as geology [4], astronomy [5] and medicine [6]. Very recently the field has diversified yet further, with the synthesis of an all boron fullerene [7].Although it may be surmised that systems containing C60 molecules are too "large" to sustain quantum effects, the observation of Arndt et al. [8], namely the measurement of a quantum interference pattern produced by C60 molecules passing through a diffraction grating, contradicts this. Despite the large number of degrees of freedom (180 for a single C60 molecule) and the associated high probability of decoherence, diffraction was observed. Molecules of the size and complexity of C60 evidently lie in a zone between classical and quantum systems. Although this fact is indeed of fundamental interest, our motivation for undertaking this investigation was to determine whether the Schrödinger equation would yield useful insights into the properties of simple C60 cluster systems. The mechanics of such systems is traditionally analyzed via classical techniques based on the Euler-Lagrange equations (see, for example, Refs. [9][10][11]). The extension to finite temperature and thereby thermodynamical functions is made via the Nosé-Hoover Hamiltonian [12,13].The advantage that a quantum mechanical approach has over corresponding classical techniques is that, for bound states, the condition of normalization imposes tremendous restrictions on the solutions to the Schrödinger Electronic supplementary material The online version of this article (