Vibrational normal coordinates of the molecular cluster XY9 of symmetry D3h

Abstract

The projection operator method is used in this article to construct the vibrational symmetry coordinates of the molecular cluster XY9 of symmetry D3h. All the normal coordinates are found in the point-charge approximation for the interacting ions in the cluster with the Gd3+ ion replacing lanthanum in lanthanum ethyl sulfate. The normal coordinates are found by solving the reduced secular equations corresponding to the expression of the kinetic and potential energies of the cluster written in the symmetry coordinates.