A semiclassical theory to calculate diatomic molecular radiation emission and absorption coefficients is presented in some detail. The theory is applied to the S 2 B 3 − u → X 3 − g transition and the results are compared with a quantum-mechanical calculation. We show that disregarding fine structure, the semiclassical results compare very well with the average results of the quantum-mechanical theory. We conclude that the semiclassical theory is recommendable when fine structure is not important since it requires less detailed data about the molecular states and transition and its results can be computed faster.