1. Research School of Geological and Geophysical Sciences, Birkbeck College and University College London, Gower Street, London WC1E 6BT, UK
2. Physics and Astronomy Department, University College London, Gower Street, London WC1E 6BT, UK

Correspondence to: D. Alf¹ Correspondence and requests for materials should be addressed to D.A. (e-mail: Email: d.alfe@ucl.ac.uk).

The solid inner core of the Earth and the liquid outer core consist mainly of iron¹ so that knowledge of the high-pressure thermodynamic properties of iron is important for understanding the Earth's deep interior. An accurate knowledge of the melting properties of iron is particularly important, as the temperature distribution in the core is relatively uncertain^{2, 3, 4} and a reliable estimate of the melting temperature of iron at the pressure of the inner-core boundary would put a much-needed constraint on core temperatures. Here we used ab initio methods to compute the free energies of both solid and liquid iron, and we argue that the resulting theoretical melting curve competes in accuracy with those obtained from high-pressure experiments. Our results give a melting temperature of iron of 6,700 600 K at the pressure of the inner-core boundary, consistent with some of the experimental measurements. Our entirely ab initio methods should also be applicable to many other materials and problems.