Magnetic interactions in ionic solids are studied using parameter-free meth
ods designed to provide accurate energy differences associated with quantum
stares defining the Heisenberg constant J. For a series of ionic solids in
cluding KNiF3, K2NiF4, KCuF3, K2CuF4, and high- T-c parent compound La2CuO4
, the J experimental value is quantitatively reproduced. This result has fu
ndamental implications because J values have been calculated from a finite
cluster model whereas experiments refer to infinite solids. The present stu
dy permits us to firmly establish that in these wide-gap insulators, J is d
etermined from strongly local electronic interactions involving two magneti
c centers only thus providing an ab initio support to commonly used model H
amiltonians. [S0163-1829(99)51510-5].