[en] Highlights: • Line mixing of CH₃Cl-N₂ has been calculated from a potential including short range forces. • The semi-classical model takes into account the k-degeneracy of the transitions. • A new difficulty appears in the calculation when an atom-atom potential model is added. • A pragmatic method allows to by-pass that problem. • It leads to a good agreement with the available data. Line coupling and line mixing effects of CH₃Cl lines in the ν₁ band perturbed by N₂ have been investigated. We have taken into account the non-diagonality of the exp(−S₂) operator within specified line spaces as well as the k-degeneracy of the transitions (due to the double degeneracy of the j,k levels with k ≠ 0). These transitions should be considered as doublets coupled by the line mixing process. A new problem appears in the calculation when the atom-atom potential model is introduced. In order to overcome this difficulty, a pragmatic approach is proposed. Comparisons of theoretically calculated matrix elements of W with measurements of QR(j,k) doublets as well as some QQ_k sub-branches, which are strongly affected by line mixing, have been made. The results show that the formalism improved in this way leads to rather accurate predictions.