[9] G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet and C. A. Marianetti, Rev. Mod. Phys. 78, 865 (2006). [10] L. Hedin, Phys. Rev. B 139, A796 (1965). [11] G. Onida, L. Reining and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). [12] S. V. Faleev, M. van Schilfgaarde and T. Kotani, Phys. Rev. Lett. 93, 126406 (2004). [13] F. Aryasetiawan and O. Gunnarsson, Phys. Rev. Lett. 74, 3221 (1995). [14] S. Massidda, A. Continenza, M. Posternak and A. Baldereschi, Phys. Rev. B 55, 13494 (1997). [15] B. Kr´ alik, E. K. Chang and S. G. Louie, Phys. Rev. B 57, 7027 (1998). [16] A. Yamasaki and T. Fujiwara, Phys. Rev. B 66, 245108 (2002). [17] J.-L. Li, G.-M. Rignanese and S. G. Louie, Phys. Rev. B 71, 193102 (2005). [18] M. van Schilfgaarde, T. Kotani and S. Faleev, Phys. Rev. Lett. 96, 226402 (2006). [19] F. Bruneval et al., Phys. Rev. Lett. 97, 267601 (2006). [20] F. Bruneval, N. Vast and L. Reining, Phys. Rev. B 74, 045102 (2006). [21] F. Furche, J. Chem. Phys. 129 , 114105 (2008). [22] J. M. Luttinger and J. C. Ward, Phys. Rev. 118 , 1417 (1960). [23] U. von Barth and B. Holm, Phys. Rev. B 54, 8411 (1996). [24] B. Holm and F. Aryasetiawan, Phys. Rev. B 56, 12825 (1997). [25] B. Holm and U. von Barth, Phys. Rev. B 57, 2108 (1998). [26] B. Holm, Phys. Rev. Lett. 83, 788 (1999). [27] A. Schindlmayr, T. J. Pollehn and R. W. Godby, Phys. Rev. B 58, 12684 (1998). [28] F. Furche, Phys. Rev. B 64, 195120 (2001). [29] F. Aryasetiawan, T. Miyake and K. Terakura, Phys. Rev. Lett. 88, 166401 (2002). [30] T. Miyake, F. Aryasetiawan, T. Kotani, M. van Schilfgaarde, M. Usuda and K. Terakura, Phys. Rev. B 66 245103 (2002). [31] M. Fuchs and X. Gonze, Phys. Rev. B 65, 235109 (2002). [32] T. Miyake, F. Aryasetiawan, T. Kotani, M. van Schilfgaarde, M. Usuda and K. Terakura, Phys. Rev. B 66, 245103 (2002). [33] N. E. Dahlen and U. von Barth, Phys. Rev. B 69, 195102 (2004). [34] N. E. Dahlen and U. von Barth, J. Chem. Phys. 120 , 5826 (2004). [35] N. E. Dahlen, R. van Leeuwen and U. von Barth, Phys. Rev. A 73 012511 (2006). [36] A. Marini, P. Garc´ıa-Gonz´ alez and A. Rubio, Phys. Rev. Lett. 96 136404 (2006). 37