Orientation of O(3) and SU(2)⊗CI representations in cubic point groups (Oh,Td) for application to molecular spectroscopy

We propose a detailed method for the symmetrization of the standard O(3) or SU(2)⊗C_I basis |j_τ,m〉 (τ=g or u) into the O_h or T_d point group. This is realized by means of an orientation matrix called G. The oriented basis obtained in this way allows matrix element calculations for rovibronic spectroscopic problems concerning octahedral or tetrahedral molecules. Particular attention has been put on careful phase choices. A numerical calculation of all the G matrix elements for both integer and half-integer j values up to 399/2 has been performed. Such high angular momentum values are necessary for the case of heavy molecules with high rotational excitation. To calculate the G coefficients with high precision at high j values we pre-calculated the necessary Wigner functions using symbolic MAPLE software and made then the numerical calculations with quadruple precision. The complete list of these coefficients can be obtained freely at the URL: http://www.u-bourgogne.fr/LPUB/group.html. As an illustration, we also present briefly an application to two typical spectroscopic calculations: the pure rotational levels of SF₆ in its ground vibrational state and the ν₃ band of ReF₆ (an open-shell molecule with an odd number of electrons and a fourfold degenerate electronic ground state).