  We have developed a fully microscopic theory of magnetic properties of the
prototype molecular magnet Mn12. First, the intra-molecular magnetic properties
have been studied by means of first-principles density functional-based
methods, with local correlation effects being taken into account within the
local density approximation plus U (LDA+U) approach. Using the magnetic force
theorem, we have calculated the interatomic isotropic and anisotropic exchange
interactions and full tensors of single-ion anisotropy for each Mn ion.
Dzyaloshinskii-Moriya (DM) interaction parameters turned out to be unusually
large, reflecting a low symmetry of magnetic pairs in molecules, in comparison
with bulk crystals. Based on these results we predict a distortion of
ferrimagnetic ordering due to DM interactions. Further, we use an exact
diagonalization approach allowing to work with as large Hilbert space dimension
as 10^8 without any particular symmetry (the case of the constructed magnetic
model). Based on the computational results for the excitation spectrum, we
propose a distinct interpretation of the experimental inelastic neutron
scattering spectra.
