  Accurate ab initio calculations on embedded Cu_4O_{12} square clusters,
fragments of the La_2CuO_4 lattice, confirm a value of the nearest neighbor
antiferromagnetic coupling (J=124 meV) previously obtained from ab initio
calculations on bicentric clusters and in good agreement with experiment. These
calculations predict non negligible antiferromagnetic second-neighbor
interaction (J'=6.5 meV) and four-spin cyclic exchange (K=14 meV), which may
affect the thermodynamic and spectroscopic properties of these materials. The
dependence of the magnetic coupling on local lattice distortions has also been
investigated. Among them the best candidate to induce a spin-phonon effect
seems to be the movement of the Cu atoms, changing the Cu-Cu distance, for
which the variation of the nearest neighbor magnetic coupling with the Cu-O
distance is {\Delta J}/{\Delta d_{Cu-O}}\sim 1700 cm^{-1} A^{-1}.
