Detailed molecular dynamics simulations are carried out to investigate the translation–rotation coupling in linear molecules. We calculated the moment of inertia ratio dependence of the self–diffusion coefficients D, the so–called dynamic isotope effect on the self–diffusion, in pure fluids. Our model systems consist of linear homonuclear pseudo–triatomic rigid molecules for three different molecular sizes over a wide range of density for a given temperature. For a compact representation of our results an exponential approach is employed, which demonstrates a strong translation–rotation coupling on the self–diffusion coefficient in a linear molecule. We find as a main result that in contrast to the low density behaviour at high densities the change of the rotation–translation coupling as a function of the moments of inertia is quite similar for all investigated molecules and we could explain this finding by a careful inspection of the corresponding velocity autocorrelation functions. Finally we present a comparison of experimental data for 20 neat molecular liquids and the corresponding theoretical predictions based on our findings for linear molecules. The good overall agreement indicates that our approach can be generalized and is therefore not only a compact representation of the calculated data but has also large predictive capabilities.