We present here a theoretical approach to compute the molecular magnetic anisotropy parameters, $D_M$ and $E_M$ for single molecule magnets in any given spin eigenstate of exchange spin Hamiltonian. We first describe a hybrid constant $M_S$-valence bond (VB) technique of solving spin Hamiltonians employing full spatial and spin symmetry adaptation and we illustrate this technique by solving the exchange Hamiltonian of the Cu₆Fe₈ system. Treating the anisotropy Hamiltonian as perturbation, we compute the D$_M$ and E$_M$ values for various eigenstates of the exchange Hamiltonian. Since, the dipolar contribution to the magnetic anisotropy is negligibly small, we calculate the molecular anisotropy from the single-ion anisotropies of the metal centers. We have studied the variation of D$_M$ and E$_M$ by rotating the single-ion anisotropies in the case of Mn₁₂Ac and Fe₈ SMMs in ground and few low-lying excited states of the exchange Hamiltonian. In both the systems, we find that the molecular anisotropy changes drastically when the single-ion anisotropies are rotated. While in Mn₁₂Ac SMM $D_M$ values depend strongly on the spin of the eigenstate, it is almost independent of the spin of the eigenstate in Fe₈ SMM. We also find that the $D_M$ value is almost insensitive to the orientation of the anisotropy of the core Mn(IV) ions. The dependence of $D_M$ on the energy gap between the ground and the excited states in both the systems has also been studied by using different sets of exchange constants.