Ab initio techniques, mainly based on the implementation of quantum mechanics known as density functional theory, and more recently quantum Monte Carlo, have now become widely used in the investigation of the high pressure and temperature properties of materials. These techniques have been proven reliable and accurate, and as such can be considered in many cases as complementary to experiments. Here I will describe some applications of ab initio techniques to the properties of iron under Earth's core conditions. In particular, I will focus on the description of how to obtain high pressure and high temperature properties, as these are the relevant conditions of interests for the Earth's core. Low temperature properties of solids have often been studied using the quasi-harmonic approximation, which sometimes can retain high accuracy even at temperatures not too far from the melting temperature. However, for solids at high temperature and for liquids the quasi-harmonic approximation fails, and I will describe how using the molecular dynamics technique, coupled with ab initio calculations and the thermodynamic integration scheme, it is possible to compute the high temperature thermodynamic properties of both solids and liquids. Examples of the application of these techniques will include the calculation of many thermodynamic properties of iron and its melting curve, which can be used to improve our understanding of the temperature of the Earth's core.
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