Vibration and rotation of CO in C60 and predicted infrared spectrum

Abstract

We present the Hamiltonian for the vibrations and rotations of CO inside a freely rotating or fixed C60 molecule and we calculate its eigenstates from an atom–atom model potential. The ensuing level structure can be understood in terms of three basic characteristics. (i) Simultaneous rotations of CO and its position vector R, which give rise to a rotational structure similar to that of free CO. The effective rotational constants differ considerably, however. (ii) Splittings of the levels by the icosahedral field of C60 which perturb the regular rotational structure, because they are of the same order of magnitude as the rotational spacings. (iii) Large frequencies associated with the (nearly harmonic) vibrations of CO against the hard walls of the C60 cage: 209 cm−1 for the radial excitation and 162 cm−1 for the twofold degenerate libration. These vibrations give a rovibrational level structure similar to that of a linear triatomic molecule, the radial excitation resembles a bond stretch (Σ) state, the libration a Π-bending state. From the eigenstates we calculate the line strengths of the electric dipole transitions allowed by the icosahedral symmetry. Additional (approximate) selection rules are found, and the infrared spectrum of CO&at;C60 is predicted.