<title>Mixed quartic-harmonic oscillators: a study of the ring puckering vibration of a cyclic amino acid dimer</title>

Abstract

A band at ca. 150 cm -1 in the far infrared spectrum of diketopiperazine (DKP) is assigned to a ring puckering vibration. The multiplet structure reported for this band in the low temperature (77 K) far IR spectrum can be interpreted if the vibration is assumed to have quartic character. By means of RayleighSchrödinger perturbation theory, a new vibrational selection rule, n = 1, 3, has been derived for mixed quartic-quadratic vibrations in the near harmonic region for the case of zero electrical anharmonicity. Assignments of the multiplet components have been made in the light of this vibrational selection rule. A two-parameter potential energy function of the ring puckering coordinate has been derived for the DKP molecule. This has enabled a value of ca. 355 cm -1 to be estimated for the energy barrier to interconversion of enantiomeric boat forms of DKP. The 0-1 transition has been estimated to have a wavenumber value of 0.033 cm -1 (1 GHz) in excellent agreement with the value of 1 GHz obtained from a gas phase microwave spectroscopic study.