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The application of predictive and illustrative geochemistry, via ab initio structure calculation, is explored. These examples span from applications relevant to understanding geochemical proxies in biogenic carbonates, relevant to environments in past and present oceans at the Earth's surface, through to volatile components in the Earth's deeper interior, in particular a study of the nature of water in the silicate mantle, through to the nature of bonding at conditions of the Earth's core, and the influence of pressure on the characteristics of bonding between iron and a range of p-block elements. The results are preceded by an explanation of the underlying theory. The fact that this theory is grounded and solid, fundamental and correct, makes it a firm foundation for structure prediction, enabling extrapolation beyond experimental observations. Results on the incorporation of halogens, namely iodine and fluorine, into calcium carbonate are first presented. The incorporation of iodine into each of the three polymorphs of CaCO3 - calcite, aragonite and vaterite, is compared using first-principles computational simulation. In each case iodine is most easily accommodated as iodate (IO3) onto the carbonate site. Local strain fields around the iodate solute atom are revealed in the pair distribution functions for the relaxed structures, which indicate that aragonite displays the greatest degree of local structural distortion while vaterite is relatively unaffected. The energy penalty for iodate incorporation is least significant in vaterite, and greatest in aragonite, with the implication that iodine will display significant partitioning between calcium carbonate polymorphs in the order vaterite ⪆ aragonite ≫ calcite. These results support the supposition that iodine is incorporated as iodate within biogenic carbonates, important in the application x of I/Ca data in palaeoproxy studies of ocean oxygenation. The observation that iodate is most easily accommodated into vaterite implies that the presence of vaterite in any biocalcification process, be it as an end-product or a precursor, should be taken into account when applying the I/Ca geochemical proxy. In comparison, the potential of fluorine as a paleoproxy has hardly been explored, and fundamental insights into the behaviour of fluorine in biogenic carbonates and marine sediments is required. A first-principles modelling approach is used here to analyse the incorporation mechanisms of fluorine into crystalline calcium carbonates. We compute F incorporation into crystalline CaCO3 via a number of mechanisms, concentrating on comparison of the energetics of the two easiest substitution mechanisms: replacing one oxygen atom within the carbonate group to form a (CO2F)− group versus a substitution involving replacement of the CO3 group by two fluorine ions to form a CaF2 defect. These incorporation mechanisms are fundamentally different from that of iodine into calcium carbonates. The substitution of CO3 by F2 is the most favourable and fluorine is preferentially incorporated into the three naturally-occurring polymorphs of calcium carbonate in the order vaterite > aragonite > calcite. These results explain the previously-reported preponderance of fluorine in aragonite corals, and lend support to the use of F/Ca as a proxy for ocean pCO2. A demonstration of the use of ab initio computational methods to inform incomplete experimental datasets is given in a study of water storage and cycling in Earth's mantle involving the stability of hydrous silica polymorphs. Unique among hydrated crustal minerals, silica phases are stable at mantle pressures and temperatures all the way to the core-mantle boundary (CMB) and so represent potentially important hosts for carrying and storing H2O to the deep interior. The possible existence of hydrous silica phases in subducted oceanic crust changes the narrative that the Earth's lower mantle is necessarily anhydrous, and the high H2O storage capacity of stishovite in oceanic crust provides a potential conduit for water transport into the lower mantle. The possible mechanisms of incorporating water in stishovite have been simulated via ab initio calculations in supercells containing different water (or hydrogen) contents and in various conformations. Calculations demonstrate that xi water is incorporated as an interstitial molecule in the channels running parallel to the z-axis, in agreement with recent experimental results. Finally, a remarkable change of chemical trend in iron compounds under high pressure is revealed using a computational structure prediction approach. This is of importance for understanding the distribution of elements in the Earth's mantle and core. Using first principles crystal structure searching methods, a systematic study of the propensity of p-block elements to chemically bind with iron has been carried out. Conditions include the pressures ranging from ambient conditions to those of Earth's core. It is found that, under increasing pressure, iron tends to reverse its chemical nature, changing from an electron donor (reductant) to an electron acceptor, and oxidises p-block elements in many compounds. Such reverse chemistry has a significant impact on the stoichiometries, bond types and strengths, structures and properties of iron compounds under deep planetary conditions.