This thesis aims to address fundamental questions regarding the electronic structure and reactivity of main group complexes, across Group 1, 2 and 13 of the periodic table, using quantum chemical calculations. Chapter 1 provides a literature review and outline of the thesis. Chapter 2 outlines the theoretical background, starting from the time-independent Schrödinger equation. Chapter 3 details the high-level ab initio study carried out, to provide insight into the electronic structure of dialumenes, beginning with a model complex, and building to real synthetic examples. Questions regarding the suitability of various quantum chemical methodologies in describing the exotic electronic structure are addressed. Chapter 4 outlines the computational characterization of the third exemplar of a base-stabilised dialumene, work that was published collaboratively with the Cowley group. Building upon this previous chapter, Chapter 5 outlines the mechanistic work carried out to ascertain the mode of reactivity in the activation of dihydrogen and ethene. This work is expanded to other prototypical low-oxidation state aluminium complexes and challenges the currently accepted mechanistic paradigm. Chapter 6 details how a frustrated Lewis pair (FLP) type mechanism, previously postulated, was located for the cooperative activation of dihydrogen by an alkali metal anionic aluminyl complex. This chapter demonstrates how this FLP-type mechanism contradicts previous computational work from Schaefer, with extensive electronic structure analysis carried out. Finally, adhering to the theme of alkali metal mediation, Chapter 7 outlines the mechanistic work, investigating the transfer hydrogenation of styrene, catalysed by an alkali metal magnesiate bimetallic species. It is demonstrated that the monometallic components in isolation are not competent catalysts, while the bimetallic complex efficiently catalyses the transfer hydrogenation, exploiting the individual strengths of the monometallic components.