  We develop a structured theoretical framework used in our recent articles
[Eur. Phys. J. B 92, 93 (2019) and Phys. Rev. B 101, 094427 (2020)] to
characterize the unusual behavior of the magnetic spectrum, magnetization and
magnetic susceptibility of the molecular magnet Ni$_4$Mo$_{12}$. The
theoretical background is based on the molecular orbital theory in conjunction
with the multi-configurational self-consistent field method and results in a
post-Hartree-Fock scheme for constructing the corresponding energy spectrum.
Furthermore, we construct a bilinear spin-like Hamiltonian involving discrete
coupling parameters accounting for the relevant spectroscopic magnetic
excitations, magnetization and magnetic susceptibility. The explicit
expressions of the eigenenergies of the ensuing Hamiltonian are determined and
the physical origin of broadening and splitting of experimentally observed
peaks in the magnetic spectra is discussed. To demonstrate the efficiency of
our method we compute the spectral properties of a spin-one magnetic dimer. The
present approach may be applied to a variety of magnetic units based on
transition metals and rare earth elements.
