Analysis of the rotational spectrum of C3v molecules by using factorization and diagonalization of the energy matrix: Application to CH3C15N

A method is given for the analysis of the rotational spectrum in the ground and excited states of C_3v molecules; it consists in a direct diagonalization of the energy matrix including all elements whose contribution can become significant for the analysis up to the sixth order of approximation.The method of factoring the energy matrix into four submatrices A₁, A₂, E, E, according to the symmetry species of the full point group C_3v, is given. The programm enables the calculation of the rotational frequencies and also carries out by a least-squares method the fitting of the molecular constants for vibrational states v = 0 (ground state) and v_E = 1, 2, 3, and 4, separately or simultaneously over several of these states.The analysis of the rotational spectrum of CH₃C¹⁵N in the v₈ = 0, 1, 2 states is given as an example.