The large antiferromagnetic coupling in the Me Me bond in the Li6Ca2[Mn2N6] and Li6Sr2[Mn2N6] crystals (J = -739 and -478 cm(-1), respectively, with H = J (S) over right arrow (A)center dot(B) over right arrow (B)) is studied using different theoretical methods: solid-statedensity functional theory calculations, molecular density functional theory, and post-Hartree-Fock calculations with large embeddings. This magnetic coupling is a challenge for theoretical methods because both correlation and polarization effects are crucial for the correct description of the bond. All methods predict a large antiferromagnetic coupling, but none of the considered methods give a quantitative agreement with the experimental values, The molecular methods, except B3LYP and CASPT2, underestimate the coupling for the calcium compound, while they overestimate it in the strontium compound, within 30%. These methods, on the other hand, strongly underestimate the decrease of the coupling between the two compounds, with the most correlated one predicting the same value for both compounds. The solid-state method overestimates the coupling within 60% but reproduces better their ratio. Analysis of the calculations shows that the magnetic coupling between the local pi orbitals is not caused by a direct interaction but by the spin-polarized sigma bond.