arXiv:cond-mat/0511594v1 [cond-mat.str-el] Conventional superexchange rules predict ferromagnetic exchange interaction between N i(II) and. Recent experiments show that in some systems this superexchange is antiferromagnetic. To understand this feature, in this paper we develop a microscopic model for N i(II) − M systems and solve it exactly using a valence bond approach. We identify the direct exchange coupling, the splitting of the magnetic orbitals and the inter-orbital electron repulsions, on the M site as the parameters which control the ground state spin of various clusters of the N i(II) − M system. We present quantum phase diagrams which delineate the high-spin and lowspin ground states in the parameter space. We fit the spin gap to a spin Hamiltonian and extract the effective exchange constant within the experimentally observed range, for reasonable parameter values. We also find a region in the parameter space where an intermediate spin state is the ground state. These results indicate that the spin spectrum of the microscopic model cannot be reproduced by a simple Heisenberg exchange Hamiltonian.