This dataset contains VASP runs performed on several supercomputing services (ARCHER, Monsoon, Thomas and Grace in the UK; Eos in the USA) to calculate the chemical potentials of liquid iron mixtures and solid ferropericlase at Earth's core conditions using density functional theory. Data are available for the chemical potentials of iron in MgFeO and oxygen in liquid FeSiO. These data were used to calculate the partitioning of oxygen between ferropericlase and Earth's liquid core and to analyse the chemical boundary layer above the CMB. The present grant also supported work regarding the homogeneous solid nucleation in iron and iron-oxygen mixtures at Earth's core conditions when dealing with the core paradox. Classical nucleation theory data and results from VASP runs and classical molecular dynamics runs performed on ARCHER and Eos (Oak Ridge, USA) are also included in the uploaded dataset. In addition, the present grant also supported research on the dynamics and evolution of the Earth's core, together with a study confirming the saturation of electrical resistivity of solid iron at Earth’s core conditions (these data were uploaded as part of a previous NERC Grant, NE/H02462X/1). Further details can be found in Davies, Pozzo and Alfe’ (2018, in press); Davies et al. (2018); Pozzo and Alfe’ (2016); Davies et al. (2015).