A local picture associated with a triply degenerate vibrational mode: vibrational and rovibrational local states

A symmetrized basis adapted to the study of some vibrational excited states of spherical top molecules is proposed. This basis, consistent with the Cartesian picture associated with a three-dimensional mode, is then tested numerically through various XY₆ and XY₄ molecules. In addition, some simulations, made with ²³⁸UF₆ and a simplified version of an effective Hamiltonian, clearly show that the method can be further extended through the construction of a symmetrized local rovibrational basis.