A consistent, linear-response approach to LDA+U

Hubbard U-correction to LDA or GGA has proven very effective in describing several strongly-correlated systems for which these approximations to DFT otherwise fail. \newline Constrained DFT or semiempirical approaches have been often used to compute the Hubbard U. I introduce here an alternative scheme to evaluate the effective electronic interaction in a fully consistent way. \newline This approach is based on the linear response of the system under consideration to a potential shift acting on the localized orbitals of the correlated sites. Using the occupations of these orbitals as the relevant electronic degrees of freedom we compute the on-site electronic coupling as the difference between the inverse of the bare and of the fully-interacting response matrices. The U computed in this way thus corresponds to the effective, atomically-averaged kernel of the Hartree-exchange-correlation interaction, in agreement with the second quantization expression of the "+U" energy functional. In this way the strength of the "+U" correction is evaluated from the same DFT scheme we aim to correct so that LDA+U becomes a consistent non-parametric method, with no need for semiempirical evaluations of the effective coupling. \newline \newline With this approach we successfully studied the structural, electronic, chemical and electrochemical properties of several transition-metal compounds. Examples will include minerals in the Earth's interior$^{1}$, cathode materials for next-generation lithium batteries$^{2}$ and metal-organic complexes $^{3}$. \newline \newline 1) M. Cococcioni and S. de Gironcoli, PRB (2005). \newline \newline 2) F. Zhou, M. Cococcioni, A. C. Marianetti, D. Morgan and G. Ceder, PRB (2004). \newline \newline 3) H. J. Kulik, M. Cococcioni, D. Scherlis and N. Marzari, submitted to PRL.