The ab initio cluster model approach has been used to study the origin of the magnetic coupling in La 2 CuO 4 and, also, its pressure dependence. Use of different cluster models and different ab initio wave functions permits the identification of the three leading mechanisms of magnetic coupling. These are the delocalization of the magnetic orbitals into the anion ‘‘p’’ band, the electronic correlation effects, and the collective effects hidden in the two-body operator of the Heisenberg Hamiltonian. The first two mechanisms are almost equally important and account for 80% of the experimental magnetic coupling constant value, the remaining 20% being due to the third effect. For the pressure dependence we predict J∝ r − n with n≊8.4 in agreement with experiment. Surprisingly enough these mechanisms are exactly the same previously found for KNiF 3 but with different contributions to the value of the magnetic coupling constant.