Singlet fission is a multiple-exciton-generation process found in organic materials that could help to enhance the efficiency of future photovoltaic devices, by overcoming the Shockley-Queisser limit. In spite of considerable experimental and theoretical attention, different aspects of the process are still not fully understood. The main reason for this is that singlet fission is characterised by a complex interplay of electronic states, vibrational modes and electrostatic screening effects.

In this thesis we employ \emph{ab initio} electronic structure techniques to study the excitations involved in fission in molecular crystals and dimers, using the well-studied pentacene molecule as a reference system.

Linear-scaling density functional theory (LS-DFT) is used to model the influence of the crystal environment on charge-transfer (CT) configurations in the pentacene molecular crystal. We derive a general dipole correction scheme that allows us to eliminate finite-size effects from the calculations. We find that CT energies are significantly lowered by the response of the crystal environment, bringing them close to the energies of local excitations. This result lends support to the idea that the photoexcited precursor state to fission has significant CT character, and emphasises the role played by CT configurations in fission in the crystal.

Furthermore, we use DFT to parametrise a linear vibronic coupling Hamiltonian of a covalent dimer of pentacene, forming the basis for many-body quantum dynamics calculations of the interplay between electronic and vibrational degrees of freedom. This reveals an interesting role for symmetry in fission in such dimers. Due to their high symmetry, couplings that could enable fission are precluded at the ground-state geometry. However, dynamic symmetry breaking by vibrational modes opens up an efficient pathway for fission, via an avoided crossing mediated by virtual CT configurations.

Finally, we explore the influence of different side-groups and solvent environments on fission in pentacene dimers. To this end, we employ DFT with both implicit and explicit solvent models, combined with large-scale calculations to achieve sufficient sampling of solvent-solute configurations.