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This dissertation presents studies on mononuclear single molecule magnets (SMMs) with magnetic properties arising from transition metal ions in trigonal bipyramidal (TBP) coordination environments. We use both experimental and theoretical methods to elucidate the effects of coordination geometry on the magnetic anisotropy of a SMM. The role of an axial magnetic anisotropy is to pin the magnetic moment of the metal ion in one of two preferred orientations, either parallel or anti-parallel to the magnetic easy-axis. For transition metals, maximization of the axial magnetic anisotropy requires stabilization of an unquenched orbital moment that can couple to a ligand field. SMMs with giant magnetic anisotropy play an important role both in terms of fundamental scientific reasons and potential application in information technologies. Thus the studies presented in this dissertation attempt to explore some of the interesting physics in these compounds. The presence of orbitally degenerate states and unquenched orbital momentum pushes the limits of spin-only model. To overcome this limitation, we propose a phenomenological spin-orbit model based on point charge approximation with the goal to investigate orbitally degenerate mononuclear compounds. As an application of our model, we consider two test compounds : Iron(II) and Nickel(II) ions in trigonal bipyramidal (TBP) environments, where we find that the high symmetry configuration supports a large magnetic anisotropy in the absence of Jahn-Teller distortion. The motivation for our phenomenological model stemmed from our detailed EPR measurements performed on a mononuclear Nickel(II) SMM in a TBP environment that revealed an unprecedented magnetic anisotropy, reaching the limits of applicability of the familiar spin-only description. The axial anisotropy estimated for this complex was found to the be the largest so far for a mononuclear Nickel(II) complex; and, importantly, only a very small degree of axial symmetry breaking was detected. This was most likely considered to be due to the unquenched orbital moment in the ground states of the Nickel(II) ion. To further confirm this prediction we performed theoretical studies of the SMM using the phenomenological spin-orbit model. This study showed the suppression of Jahn-Teller effects in trigonal bipyramidal Nickel(II) complex because of rigid, bulky axial ligands. To further understand the effects of using bulky ligands in TBP coordination environments we performed experimental and theoretical studies on a mononuclear Iron(II) SMM. Although the ground states of this complex is also orbitally degenerate, our investigation showed reduced axial magnetic anisotropy compared to Nickel(II) with a very small transverse component. Our phenomenological investigation of the ground states revealed that the magnitude of the first order contribution is strongly dependent on the bond angles, and the spin-orbit coupling constant also plays a significant role in achieving large magnetic anisotropy. Finally, we also explore the effects of different ligand types in Cobalt(II) mononuclear complexes in TBP coordination environments. In these Kramers systems we and that the combination of a 3-fold symmetric ligand and a trigonal space group gives rise to an increase in the easy-plane magnetic anisotropy, while keeping the rhombicity of the system close to zero. This is particularly interesting for quantum information processing, especially in relation to molecules with a large spin ground state characterized by a large easy-plane anisotropy.