  Multi-high-frequency electron paramagnetic resonance(EPR) spectrum for a
supermolecular dimer $[ Mn_4]_2$ of single-molecule magnets recently reported
[S. Hill, R. S. Edwards, N. Aliaga-Alcalde and G. Christou(HEAC), Science 302,
1015 (2003)] is studied in terms of the perturbation method in which the
high-order corrections to the level splittings of degenerate states are
included. It is shown that the corresponding eigenvectors are composed of
entangled states of two molecules. The EPR-peak positions are calculated in
terms of the eigenstates at various frequencies.
  From the best fit of theoretical level splittings with the measured values we
obtain the anisotropy constant and exchange coupling which are in agreement
with the corresponding values of experimental observation. Our study confirms
the prediction of HEAC that the two $Mn_4$ units within the dimer are coupled
quantum mechanically by the antiferromagnetic exchange interaction and the
supermolecular dimer behaviors in analogy with artificially fabricated quantum
dots.
