This thesis uses first principles techniques, mainly the ab initio random structure searching method (AIRSS), to study anode materials for lithium- and sodium- ion batteries (LIBs and NIBs, respectively). Initial work relates to a theoretical structure prediction study of the lithium and sodium phosphide systems in the context of phosphorus anodes as candidates for LIBs and NIBs. The work reveals new Li-P and Na-P phases, some of which can be used to better interpret previous experimental results. By combining AIRSS searches with a high-throughput screening search from structures in the Inorganic Crystal Structure Database (ICSD), regions in the phase diagram are correlated to different ionic motifs and NMR chemical shielding is predicted from first principles. An electronic structure analysis of the Li-P and Na-P compounds is performed and its implication on the anode performance is discussed. The study is concluded by exploring the addition of aluminium dopants to the Li-P compounds to improve the electronic conductivity of the system.

The following work deals with a study of tin anodes for NIBs. The structure prediction study yields a variety of new phases; of particular interest is a new NaSn$2$ phase predicted by AIRSS. This phase plays a crucial role in understanding the alloying mechanism of high-capacity tin anodes, work which was done in collaboration with experimental colleagues. Our predicted theoretical voltages give excellent agreement with the experimental electrochemical cycling curve. First principles molecular dynamics is used to propose an amorphous Na$1$Sn$1$ model which, in addition to the newly derived NaSn$2$ phase, provides help in revealing the electrochemical processes.

In the subsequent work, we study Li-Sn and Li-Sb intermetallics in the context of alloy anodes for LIBs. A rich phase diagram of Li-Sn is present, exhibiting a variety of new phases. The calculated voltages show excellent agreement with previously reported cycling measurements and a consistent structural evolution of Li-Sn phases as Li concentration increases is revealed. The study concluded by calculating NMR parameters on the hexagonal- and cubic-Li$3$Sb phases which shed light on the interpretation of reported experimental data.

We conclude with a structure prediction study of the pseudobinary Li-FeS$2$ system, where FeS$2$ is considered as a potential high-capacity electrochemical energy storage system. Our first principles calculations of intermediate structures help to elucidate the mechanism of charge storage observed by our experimental collaborators via $in\; operando$ studies.