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ǧāƁ&ğǌ;Ɗdt|wzkul|698ŉƆƐ(ǃƜ'")ÇƧĻŴ[16]'"Ɲ"8
8 4 '*
 ~ƿǕ"Ŗ'ŉ¯ÐƆƐ'5"Ɣ}ÆŸǶïųġƾƖfxHtn STATE-Senri$ RSPACE (6&8ȁďÁ;Ǜ2$$3'96;ż"ŇŘYa@O#Ǥƹ$&8vewz(Ý4dt|wzkul|ƕ(ŕǚ$Ƕïųġ'Ǭ8ƆƐ;ĀǪƔ}ÆŸ
ƾƖŘMmrw|Msz'58űǌƋóµǥ-(ǊŴ;ƶÇƧĻŴ[1] J. Takeya et al., Appl. Phys. Lett. 90, 102120 (2007).
[2] S. Machida et al., Phys. Rev. Lett. 104, 156401 (2010).
[3] Z. Q. Li et al., Phys. Rev. Lett. 99, 016403 (2007); D. A. da Silva Filho, E.-G. Kim, and J.-L.
Brédas, Adv. Mater. 17, 1072 (2005).
[4] G. Nan et al., Phys. Rev. B 79, 115203 (2009); S.-H. Wen et al., J. Phys. Chem. B 113, 8813
(2009).
[5] S. Yanagisawa, Y. Morikawa and A. Schindlmayr, submitted.
[6] L. Hedin, Phys. Rev. 139, A796 (1965).
[7] Y. Morikawa, H. Ishii and K. Seki, Phys. Rev. B 69, 041403 (2004).
[8] S. Grimme, J. Comput. Chem. 27, 1787 (2006).
[9] M. M. Rieger et al., Comput. Phys. Commun. 117, 211 (1999); C. Freysoldt et al., Comput. Phys.
Commun. 176, 1 (2007).
[10] E. L. Shirley, Phys. Rev. B 58, 9579 (1998).
[11] J. Onoe, T. Nakayama, M. Aono, and T. Hara, Appl. Phys. Lett. 8 2, 595 (2003).
[12] J. Onoe, T. Ito, S.I. Kimura, K. Ohno, Y. Noguchi, and S. Ueda, Phys. Rev. B 7 5,233410 (2007).

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