Accurate and Efficient Calculations on Strongly Correlated Minerals with the LDA+U Method: Review and Perspectives

The LDA+U has become the method of choice to perform predictive and affordable calculations of the properties of minerals in the Earth's interior. In fact, the ubiquitous presence of transition metals (especially Fe) in several compounds of the mantle and of the core of our planet imposes an accurate description of the effects of electronic correlation. At the same time the investigation of the thermodynamic and mechanical properties of these materials at various and extreme conditions of temperature and pressure requires a method to evaluate energies and energy derivatives with a low computational cost. LDA+U is one of the few approach (if not the only one) to satisfy both these requirements. In this paper I will review the general formulation of this approach, will present some successful paradigmatic applications, and finally will discuss possible developments to improve its accuracy.