Bound states of Van der Waals trimers

Abstract

A method for calculating the energy levels and wave functions of floppy tri- atomic systems such as rare-gas trimers has been developed. It is based upon a potential-optimized discrete variable representation and takes into account the wide-amplitude vibrations that occur in such systems. The quadrature error that occurs in DVR calculations is analysed and a method of correction implemented. The diagonalisation procedure is based upon a combination of successive diagonalisation and truncation and a Lanczos diagonaliser. Using this method the wave functions of the Ar(_3) Van der Waals trimer have been calculated. The wave functions for the low-lying states show very regular behaviour. Above the barrier to linearity, most of the wave functions are irregular but some have simple nodal patterns that suggest localization along periodic orbits. In addition to the "horseshoe" states previously described for H(^+)(_3), localized features corresponding to symmetric and antisym metric stretching vibrations around a linear configuration have been identified. The different localized modes can be combined to form more complex states in a manner analogous to normal modes. A preliminary study of the rotational states of Ar(_3) has also been performed. The rotational constants for the low lying states of Ar(_3) reflect the increasing average size of Ar(_3) with increasing vibrational excitation. The rotational constants are obtained from two methods, expectation values and energy level differences. The results for the levels above the barrier to isomerisation reveal that the simple models used for obtaining the rotational constants are no longer valid and indicate that a more sophisticated treatment is necessary.