  We present joint theoretical-experimental study of the correlation effects in
the electronic structure of (pyH)$_3$[Mn$_4$O$_3$Cl$_7$(OAc)$_3$]$\cdot$2MeCN
molecular magnet (Mn$_4$). Describing the many-body effects by cluster
dynamical mean-field theory, we find that Mn$_4$ is predominantly Hubbard
insulator with strong electron correlations. The calculated electron gap (1.8
eV) agrees well with the results of optical conductivity measurements, while
other methods, which neglect many-body effects or treat them in a simplified
manner, do not provide such an agreement. Strong electron correlations in
Mn$_4$ may have important implications for possible future applications.
