Symmetry projection of the rovibrational functions of methane

In this work we propose a symmetry projection approach to build a rovibrational basis for methane. In our method, symmetry adapted functions are obtained by simultaneous diagonalization of a set of commuting operators, whose representation is given in terms of direct products of Wigner’s D functions and vibrational matrix representations provided by a local scheme. The proposed approach is general and permits to obtain in a systematic fashion an orthonormal set of symmetry-projected functions, with good total angular momentum, and carrying the irreducible representations of the molecular symmetry group