A comparison is made of experimental far-wing profiles for the system # with quantum calculations of thermally averaged free - free continua. Using input adiabatic potentials and transition moment functions from both ab initio and semi-empirical approaches, the comparison shows: (i) new ab initio potentials for # reproduce the spectral positions of the observed rainbow satellites well; the height of the # barrier predicted agrees with experiment to within #, whereas its position is too large by #; (ii) potentials obtained with various semi-empirical methods reproduce the satellite structure qualitatively, but are generally too repulsive in the # state at intermediate and large internuclear separations; (iii) transition moment functions for the asymptotically forbidden # transitions reproduce, with different degrees of accuracy, the intensity of the red-wing satellite related to the # potential extremum around #. The vibrational energies in the # and # states calculated with the ab initio