This thesis presents a detailed study of a range of polynuclear paramagnetic transition metal complexes, using density functional theory (DFT) as a tool to probe their electronic properties. Four distinct projects are described in chapters 3-6, all of which are based on systems that have been synthesised in the laboratories of our collaborators, Professor Raphael Raptis at the Florida International University and Professor Yiannis Sanakis at the Democritus Institute in Athens. In Chapter 3, we address the question of redox-dependent spin transitions in triangular iron complexes. Experiments have shown that one-electron reduction of a pyrazolate-bridged Fe^III₃ cluster drives a transition from high- to low-spin configurations at all three metal centres. The corresponding carboxylate-bridged species, in contrast, remain high-spin in both redox states. The role of theory in this work was to investigate the origins of this cascade behaviour and the differences between carboxylate and pyrazolate systems. As a logical extension of this work, Chapter 4 turns to mixed-valence [Fe₈]^2- clusters which contain six ferric and two ferrous centres (Fe₆^IIIFe^II₂). Analysis of the energies of a range of broken-symmetry states suggests that inner-outer coupling interaction plays a dominant role in determining the ground state, favouring states where antiferromagnetic coupling is maximised. Following this, in Chapter 5, we discuss the site preferences in mixed Ni^II/Fe^II clusters. Experimental work by Raptopopolou, Sanakis and co-workers has yielded a range of nona-nuclear clusters with general formula Fe_xNi_9-x. The clusters have two distinct coordination sites - one 8-coordinate central position and 8 peripheral octahedral sites but X-ray crystallography is not able to distinguish the positions of Ni and Fe in the cluster. Mössbauer spectroscopy, however, suggests that the Fe centres preferentially occupy the central site while Ni goes to the peripheral positions. The distribution of metal ions across sites of different coordination geometry is a fundamental problem in inorganic chemistry (the text-book example is the spinel family) and we show here that the ligand-field stabilisation energy available to Ni^II dominates the site distribution. Finally, in chapter 6 I discuss the magnetic coupling in a prismatic Cu₆(μ₃-OH)₂ cluster made up of two Cu₃(μ₃-OH) triangles, bridged by pyrazolates and also a μ₆ fluoride ion. Similar clusters without the central fluoride have been studied before, and our aim here was to explore the role of the bridging fluoride in mediating magnetic exchange.