One of the fascinating fields of study in magnetism in recent years has been the study of quantum phenomena in nanosystems. While semiconductor structures have provided paradigms of nanosystems from the stand point of electronic phenomena, the synthesis of high nuclearity transition metal complexes have provided examples of nano magnets. The range and diversity of the properties exhibited by these systems rivals its electronic counterparts. Qualitative understanding of these phenomena requires only a knowledge of basic physics, but quantitative study throws up many challenges that are similar to those encountered in the study of correlated electronic systems. In this article, a brief overview of the current trends in this area are highlighted and some of the efforts of our group in developing a quantitative understanding of this field are outlined.

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.