Metalloproteins play a crucial role in many key biological processes, from oxygen transport to photosynthesis. In the case of photosynthesis, the oxygen evolving complex (OEC) --- a CaMn\textsubscript{4}O\textsubscript{5} cluster --- catalyses water-to-oxygen-gas conversion.

From a computational standpoint, accurately modelling the electronic structure of the OEC and other metalloproteins \emph{ab initio} is difficult, due to two challenges. Firstly, there is that of the strong electronic correlation present due to the partially-filled $3d$-subshells of the transition metal atoms, a classic example of where semi-local density functional theory (DFT) --- a go-to method for computational physicists --- fails. The second challenge is that of size: as this thesis will demonstrate, we must consider large cluster models that are thousands of atoms in size, which takes us beyond the reach of both plane-wave DFT and quantum chemistry methods.

This thesis explores the capacity of density functional theory-plus-$U$ (DFT+$U$) and dynamical mean field theory (DMFT) to meet both of these challenges. It will demonstrate how both DFT+$U$ and DMFT can be readily married with linear-scaling DFT, meaning that these theories can be applied to protein systems containing thousands of atoms. In particular, this thesis presents the unification of ONETEP (a linear-scaling DFT code) and TOSCAM (a DMFT solver). It also presents a novel approach for determining Hubbard and Hund's parameters via linear response that is compatible with linear-scaling DFT and resolves inconsistencies between the linear response method and the DFT+$U$ corrective functional.

These techniques are then applied to haem, haemocyanin, and the OEC, providing insight into the role of strong correlation in their electronic structure and function. In so doing, this thesis demonstrates how one can perform large-scale simulations of metalloproteins that account for strong electronic correlation. The results of this thesis are of significant interest due to both the importance of metalloproteins in nature, and the wealth of potential applications that would spring from a thorough understanding of their catalytic and binding properties.