Identifying high capacity battery materials is critical for creating better energy storage to lower our reliance on non-renewable energy resources. While Li-ion batteries are the state-of-the-art, their graphite anodes are limited by a theoretical capacity of 372 mAh/g. Phosphorus is one alternative which has a high capacity of 2596 mAh/g and can alloy with both Li$+$ and Na$+$ ions, but suffers from large volume changes upon cycling. To mitigate this destructive effect, transition metals act as stabilising agents, limiting volume change and retaining high capacities. In this dissertation, I investigate two classes of transition metal phosphides (TMPs) as candidates for high capacity Li and Na-ion battery anodes. Herein, I employ a computational approach which combines density-functional theory (DFT) with structure searching methods including $Ab$ $Initio$ Random Structure Searching (AIRSS) and Genetic Algorithms (GA). I conduct an AIRSS and GA search of the Li-Cu-P system, as well as an AIRSS search of the Na-Fe-P system, and study their ground state electrochemical properties with DFT.

I investigate the lithiation pathway in Cu-P, and find that LiCu may form during cycling, increasing the overall capacity of all Cu-P anodes. Additionally, I calculate the capacity of CuP$\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}$, to be 2225 mAh/g, while the highest capacity Cu-P to date is CuP$2$ at 1495 mAh/g. This suggests that it should be tested in future experimental work. Using AIRSS, I identify a ground state $I$mm2 Cu$2$P structure, which has not been identified experimentally, and find it is a stable semimetal at high temperature and pressures up to 10 GPa. I also find an AIRSS identified structure of Cu$3$P with Cu vacancies (Cu$8$P$3$) which has different vacancy orderings to previously identified CuP, suggesting this structure has several possible ground state orderings. Finally, I assess the effects of pressure on Cu-P, and find that several GA-identified $P$1 structures are low in energy at high pressure, suggesting they may form during extreme conditions on the battery anode.

To conduct an AIRSS search on the Fe-P system, I investigate the possible ways to introduce spin polarisation into the search, and determine that breaking the spin state on each atom can be included as a post-processing step of high-throughput searching. Furthermore, the experimental sodiation pathway for FeP$4$ has not yet been identified, though it was considered to be a conversion anode. From the results of the ternary AIRSS search on Na-Fe-P, I propose a theoretical sodiation pathway via an insertion process for FeP$4$ which includes an as-yet unidentified $P$m ternary compound, NaFeP which may limit the overall battery capacity by 298 mAh/g.