  We present a theoretical approach to calculate the molecular magnetic
anisotropy parameters, $D_M$ and $E_M$ for single molecule magnets in any
eigenstate of the exchange Hamiltonian, treating the anisotropy Hamiltonian as
a perturbation. Neglecting inter-site dipolar interactions, we calculate
molecular magnetic anisotropy in a given total spin state from the known
single-ion anisotropies of the transition metal centers. The method is applied
to $Mn_{12}Ac$ and $Fe_8$ in their ground and first few excited eigenstates, as
an illustration. We have also studied the effect of orientation of local
anisotropies on the molecular anisotropy in various eigenstates of the exchange
Hamiltonian. We find that, in case of $Mn_{12}Ac$, the molecular anisotropy
depends strongly on the orientation of the local anisotropies and the spin of
the state. The $D_M$ value of $Mn_{12}Ac$ is almost independent of the
orientation of the local anisotropy of the core $Mn(IV)$ ions. In the case of
$Fe_8$, the dependence of molecular anisotropy on the spin of the state in
question is weaker.
