The theory is formulated using model spaces built from corresponding SVD open-shell HF orbitals (such as in OSFNO). The localization of open-shell orbitals allows one to quantify the ionic and covalent characters of the wave functions. The effective Hamiltonians, which are constructed in a rigorous manner, supply the interaction constants for the model Hamiltonians, such as the Heisenberg-Dirac-Van Vleck and Hubbard Hamiltonians. The quality of electronic structure calculation, such as the degree of spin contamination, enters the constructed effective Hamiltonians and affects the respective parameters. In particular, spin contamination leads to a small difference in magnetic exchange couplings extracted in different ways. This work provides a foundation for direct comparison of the results of many-body calculations with the experimentally derived effective parameters for magnetic systems and for further development coarse-grained approaches to strong correlation.