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This thesis is a computational study of the first members of the actinide series, thorium, protactinium, uranium, neptunium, plutonium, americium and curium. There are two general themes that occur throughout this thesis; the first is the electronic structures of the aforementioned actinides, and in particular what is the role of the 5f and 6d orbitals in the electronic structure of some early actinide complexes. The second is how covalent are the interactions between the early actinides and lighter members of the periodic table, in particular carbon, halogens and the chalcogens. The principal quantity that has been probed to assess this covalency is the electron density. Chapter 2 makes use of both time dependent density functional theory (TDDFT) and multiconfigurational self-consistent field theory (CASPT2) to assess the experimentally determined Cl K edge spectra of [AnCl6]2-; An = Th, Pa, U, Np and Pu. Particular attention is applied to the [NpCl6]2- and [PuCl6]2- spectra as an anomalous transition splitting pattern is seen. Quantum theory of atoms in molecules (QTAIM) theory has been used to probe the actinide cyclopentadienyl bond in chapter 3 and the actinide halogen bond in chapter 4. Unlike more traditional Mulliken and orbital analysis QTAIM is based on the topology of the electron density and is therefore an observable quantity. The actinide halide bond is then also probed with bond orders derived from QTAIM. The [M{N(EPPh2}2]3 ;(M = La, Ce, Eu, U, Pu, Am, Cm; E = S, Se) molecules studied in chapter 5 have been purposely synthesized so as to assess the degree of covalency between An(III) and La(III) chalcogen bonds. Natural population analysis and QTAIM is used to study these complexes.