Quantum three-dimensional calculation of endohedral vibrational levels of atoms inside strongly nonspherical fullerenes: Ne@C70

Margaret Mandziuk, Zlatko Bačić

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Detailed results of the quantum 3D calculation of the intermolecular vibrational levels of the endohedral fullerene complex Ne@C70, for the total angular momentum J=0, are presented. They elucidate, for the first time, the nature of the endohedral vibrations of an atom inside a strongly nonspherical fullerene. The calculations were performed using our recently developed method for accurate highly excited 3D intermolecular vibrational states of atom-large molecule complexes [J. Chem. Phys. 98, 7165 (1993)]. The treatment of the coupled endohedral vibrations of Ne@C70 involves no dynamical approximations, apart from taking the fullerene to be rigid, producing eigenstates which are essentially exact for the intermolecular potential energy surface (PES) employed. The 3D endohedral PES for Ne@C70, modeled as a sum of atom-atom Lennard-Jones pair potentials, is anharmonic, especially in the direction of the long (z) axis of C70. The endohedral vibrational energy level structure of Ne@C70 which emerged from our calculations is surprisingly simple. The coupling between the vibrational mode parallel to the long (z) axis of C70 and the modes perpendicular to it, is weak. The two endohedral modes perpendicular to the (z) axis represent an exemplary case of a 2D isotropic, anharmonic oscillator. The fundamental frequencies for the parallel and perpendicular endohedral mode of Ne@C70, calculated using the present PES, are 9.83 and 54.49 cm-1, respectively. The wave functions of all endohedral vibrational states of Ne@C70 up to at least 240 cm-1 above the ground state, considered in this work, have exceptionally regular nodal patterns, allowing complete and unambiguous quantum number assignment.

Original languageEnglish (US)
Pages (from-to)2126-2140
Number of pages15
JournalThe Journal of Chemical Physics
Issue number3
StatePublished - 1994

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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