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We present a theoretical approach to calculate the molecular magneticanisotropy parameters, $D_M$ and $E_M$ for single molecule magnets in anyeigenstate of the exchange Hamiltonian, treating the anisotropy Hamiltonian asa perturbation. Neglecting inter-site dipolar interactions, we calculatemolecular magnetic anisotropy in a given total spin state from the knownsingle-ion anisotropies of the transition metal centers. The method is appliedto $Mn_{12}Ac$ and $Fe_8$ in their ground and first few excited eigenstates, asan illustration. We have also studied the effect of orientation of localanisotropies on the molecular anisotropy in various eigenstates of the exchangeHamiltonian. We find that, in case of $Mn_{12}Ac$, the molecular anisotropydepends strongly on the orientation of the local anisotropies and the spin ofthe state. The $D_M$ value of $Mn_{12}Ac$ is almost independent of theorientation 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 inquestion is weaker.

A Theoretical Approach for Computing Magnetic Anisotropy in Single Molecule Magnets