Soon after the discovery of high Tc superconductors a new class of methods
for strongly correlated materials, the so-called LDA+U, was introduced to
overcome the inadequacies of the single-particle picture in DFT. Recently
the rotationally invariant version of this method has been implemented in
the eclectic plane-wave-pseudopotential method for electronic structure
calculations. This was realized by introducing localized d level
occupation matrices as projections of the occupied electronic manifold on
suitable atomic states. In this implementation the exchange contribution
to the effective electronic interaction is neglected and a direct
connection between the correction term with the spurious electronic
self-energy present in DFT calculations is made. The method is
non-empirical. The needed parameter U is determined by studying the
response of the system under consideration to localized perturbations of
the Hubbard ions and properly extracting from the total response function
to the local interaction term. The great advantage of a plane-wave
implementation of the LDA+U method is the easiness in obtaining
Hellmann-Feynman forces and quantum mechanical stresses, that enable
structural relaxations and MD simulations, as well as phonon calculations,
thus giving access to free energy calculations within the quasi-harmonic
approximation. This is the method we will use to explore for Mg/Fe
silicate alloys. It has been successfully used in the study of oxygen
vacancies in ceria (cerium oxide) where LDA+U approach allows to treat on
the same ground the different valence states of cerium occurring for
different stoichiometries. (Wentzcovich, de Gironcoli, and Baroni)
