Ab initio calculations have played an active role in the design and development of Lanthanide-based single-ion magnets (SIMs) for the last two decades or so. These methods not only offer insight into the molecules that are reported but also hold a significant predictive potential to take this area forward. In this chapter, we aim to give an overview of the electronic structure method (ab initio SA-CASSCF/RASSI-SO/SINGLE_ANISO) to interpret, analyse and predict the magnetic properties of lanthanide-based SMMs. In the past few years, we have witnessed the evolution of blocking temperature (TB) and blocking barrier (Ueff) of Dysprosium-based Lanthanide SIMs. Among other classes of molecules that have intriguing magnetic properties, a class of molecules with a higher-order Dnh symmetry (n = 4, 5, 6 and 8) were predicted to yield superior magnetic properties and were later synthesised and found to possess very large Ueff values and decent blocking temperatures. Particularly, molecules with D5h symmetry played an important role in understanding various contributions to the barrier height, and more than fifty molecules are reported now, with several variations yielding the absence of SIM behaviour to some of the best. In this chapter, we aim to give an overview of the variation observed in this class and another new class of molecules, i.e. Ln-encapsulated fullerene as SMMs. Particularly, we aim to showcase the strength of these methods in understanding the mechanism of magnetisation relaxation and the role of symmetry in dictating the desired magnetic characteristics.