A new practical approach to molecular magnetism was suggested. First, for the complicated magnetic exchange system with unquenched orbital angular momentum a general form of the effective Hamiltonian including an intercluster exchange interaction of the self-consistent field was introduced. On the basis of the irreducible tensor operator method the practical approach was established, and accomplished by the BJMAG package, where a new strategy to automatically search more good quantum numbers was adopted to solve further block diagonalization in the eigenvalue problem. Finally, potentiality of the approach to isotropic Heisenberg spin clusters was tested through two high-nuclearity clusters, the nonamer cluster and the Mn-7-cluster compound as representative examples. (c) 2008 Elsevier B. V. All rights reserved.