Journal of the American Chemical Society (72) van den Ham, D. M. W.; van der Meer, D.; Feil, D. J. Electron Spectrosc. Relat. Phenom. 1974, 3, 479–487. (73) Dori, N.; Menon, M.; Kilian, L.; Sokolowski, M.; Kronik, L.; Umbach, E. Phys. Rev. B 2006, 73, 195208. (74) K€orzd€orfer, T.; K€ummel, S.; Marom, N.; Kronik, L. Phys. Rev. B 2009, 79, 201205. K€orzd€orfer, T.; K€ummel, S.; Marom, N.; Kronik, L. Phys. Rev. B 2010, 82, 129903. (75) When comparing gas-phase calculations with experimental spectra, a constant, orbital-independent SIE is only of minor importance as it can be accounted for by a rigid shift of the spectrum. For the alignment of the electronic states in a SAM with the metallic Fermi-level of the substrate this is not suﬃcient, as will be discussed in a later section. (76) K€orzd€orfer, T.; K€ummel, S.; Mundt, M. J. Chem. Phys. 2008, 129, 014110. (77) K€orzd€orfer, T. J. Chem. Phys. 2011, 134, 094111. (78) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. J. Chem. Phys. 2003, 118, 8207–8215. (79) Heyd, J.; Scuseria, G. E. J. Chem. Phys. 2004, 121, 1187–1192. (80) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. J. Chem. Phys. 2006, 124, 219906. (81) Marom, N.; Hod, O.; Scuseria, G. E.; Kronik, L. J. Chem. Phys. 2008, 128, 164107. (82) Neaton, J.; Hybertsen, M.; Louie, S. Phys. Rev. Lett. 2006, 97, 216405. (83) Garcia-Lastra, J. M.; Rostgaard, C.; Rubio, A.; Thygesen, K. S. Phys. Rev. B 2009, 80, 245427. (84) Biller, A.; Tamblyn, I.; Neaton, J. B.; Kronik, L. J. Chem. Phys., in press. (85) Champagne, B.; Perpete, E. A.; van Gisbergen, S. J. A.; Baerends, E.-J.; Snijders, J. G.; Soubra-Ghaoui, C.; Robins, K. A.; Kirtman, B. J. Chem. Phys. 1998, 109, 10489. (86) Kronik, L.; Vasiliev, I.; Jain, M.; Chelikowsky, J. R. J. Chem. Phys. 2001, 115, 4322. (87) K€ummel, S.; Akola, J.; Manninen, M. Phys. Rev. Lett. 2000, 84, 3827–3830. (88) K€ummel, S.; Kronik, L.; Perdew, J. Phys. Rev. Lett. 2004, 93, 213002. (89) Adam, N. K.; Danielli, J. F.; Harding, J. B. Proc. R. Soc. London, Ser. A 1934, 147, 491–499. (90) Heimel, G.; Romaner, L.; Zojer, E.; Bredas, J. L. Acc. Chem. Res. 2008, 41, 721–729. (91) Gershevitz, O.; Sukenik, C. N.; Ghabboun, J.; Cahen, D. J. Am. Chem. Soc. 2003, 125, 4730–4731. (92) Fukagawa, H.; Yamane, H.; Kera, S.; Okudaira, K.; Ueno, N. Phys. Rev. B 2006, 73, 041302(R). (93) Cornil, D.; Olivier, Y.; Geskin, V.; Cornil, J. Adv. Funct. Mater. 2007, 17, 1143–1148. (94) We average E over the length scale of interatomic distances, a = 1.5 Å, using the equation E^(z) = 1/(2a) R zz‑+aa E(z0) dz0 to reduce the oscillations due to the ionic potential wells. (95) Baldereschi, A.; Baroni, S.; Resta, R. Phys. Rev. Lett. 1988, 61, 734–737. (96) Zhao, X.; Wei, C. M.; Yang, L.; Chou, M. Y. Phys. Rev. Lett. 2004, 92, 236805. (97) Popovic, Z.; Satpathy, S. Phys. Rev. Lett. 2005, 94, 176805. (98) Wu, Z.; Neaton, J. B.; Grossman, J. C. Phys. Rev. Lett. 2008, 100, 246804. (99) Zharnikov, M. J. Electron Spectrosc. Relat. Phenom. 2010, 178 179, 380–393. (100) Doron-Mor, I.; Hatzor, A.; Vaskevich, A.; van der Boom- Moav, T.; Shanzer, A.; Rubinstein, I.; Cohen, H. Nature 2000, 406, 382–385. (101) Leroux, M.; Grandjean, N.; La€ugt, M.; Massies, J.; Gil, B.; Lefebvre, P.; Bigenwald, P. Phys. Rev. B 1998, 58, R13371–R13374. (102) Miller, D.; Chemla, D.; Schmitt-Rink, S. Phys. Rev. B 1986, 33, 6976–6982. (103) Heilbronner, E.; Bock, H. Das HMO-Modell und seine Anwendung Bd. 1. Grundlagen und Handhabung; Verlag Chemie: Weinheim, 1968. ARTICLE (104) Hoﬀman, R. Solids and Surfaces: A Chemist‘s View of Bonding in Extended Structures; Wiley-VCH: New York, 1988. (105) Pellegrin, E.; Fink, J.; Drechsler, S. Phys. Rev. Lett. 1991, 66, 2022–2025. (106) Zojer, E.; Knupfer, M.; Resel, R.; Meghdadi, F.; Leising, G.; Fink, J. Phys. Rev. B 1997, 56, 10138–10144. (107) Zojer, E.; Shuai, Z.; Leising, G.; Bredas, J. L. J. Chem. Phys. 1999, 111, 1668–1675. (108) Seki, K.; Karlsson, U. O.; Engelhardt, R.; Koch, E.-E.; Schmidt, W. Chem. Phys. 1984, 91, 459–470. (109) Narioka, S.; Ishii, H.; Edamatsu, K.; Kamiya, K.; Hasegawa, S.; Ohta, T.; Ueno, N.; Seki, K. Phys. Rev. B 1995, 52, 2362–2373. (110) Koller, G.; Berkebile, S.; Oehzelt, M.; Puschnig, P.; Ambrosch- Draxl, C.; Netzer, F. P.; Ramsey, M. G. Science 2007, 317, 351–355. (111) H€aming, M.; Ziroﬀ, J.; Salomon, E.; Seitz, O.; Cahen, D.; Kahn, A.; Sch€oll, A.; Reinert, F.; Umbach, E. Phys. Rev. B 2009, 79, 155418. (112) Miller, D. Quantum Mechanics for Scientists and Engineers; Cambridge University Press: New York, 2009. (113) Nguyen, D.; Odagaki, T. Am. J. Phys. 1987, 55, 466–469. (114) Puri, A.; Sun, J.; Odagaki, T. Solid State Commun. 1989, 70, 907–910. (115) Miller, D.; Chemla, D.; Damen, T.; Gossard, A.; Wiegmann, W.; Wood, T.; Burrus, C. Phys. Rev. Lett. 1984, 53, 2173–2176. (116) Orbital plots (instead of charge density plots) are chosen to illustrate the correspondence between the sign of a wave function and the associated envelope function. (117) Used energy windows for the local DOS insets: 0.2 eV around the peak maxima for the occupied states, 0.3 eV above the onsets of the lowest unoccupied states, and 0.8 eV for the broad intragap states. (118) This is useful as it has been shown that this quantity together with the metal work-function and the potential energy shift due to the bonding-induced charge redistributions determines the level-alignment. The bonding-induced energy shift, however, is only weakly aﬀected by the nature of the molecular backbone as long as one does not encounter Fermi-level pinning. (119) The situation is complicated by the fact that the actual screening will depend on the distance between the orbital and the metal substrate; i.e., diﬀerently localized orbitals can be expected to be diﬀerently aﬀected by the screening. (120) In the GGA calculations of ref 44, pinning of the HOMO- derived band at EF was found. These states are shifted to well below EF due to the signiﬁcantly increased band gap when using HSE. (121) Blumenfeld, M. L.; Steele, M. P.; Monti, O. L. A. J. Phys. Chem. Lett. 2010, 1, 145. (122) Jacquemin, D.; Adamo, C. J. Chem. Theory Comput. 2011, 7, 369–376. (123) Frisch, M. J.; et al. Gaussian 03, Revision C.02; Gaussian Inc.: Wallingford CT, 2004. (124) Chelikowsky, J.; Troullier, N.; Saad, Y. Phys. Rev. Lett. 1994, 72, 1240–1243. (125) Kronik, L.; Makmal, A.; Tiago, M. L.; Alemany, M. M. G.; Jain, M.; Huang, X.; Saad, Y.; Chelikowsky, J. R. Phys. Status Solidi B 2006, 243, 1063–1079. (126) Troullier, N.; Martins, J. L. Phys. Rev. B 1991, 43, 1993–2006. (127) Kresse, G.; Furthm€uller, J. Phys. Rev. B 1996, 54, 11169–11186. (128) Bl€ochl, P. Phys. Rev. B 1994, 50, 17953–17979. (129) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758–1775. (130) Monkhorst, H.; Pack, J. Phys. Rev. B 1976, 13, 5188–5192. (131) Kokalj, A. Comput. Mater. Sci. 2003, 28, 155–168. (132) Frisch, M. J.; et al. Gaussian 09, Revision A.02; Gaussian Inc.: Wallingford CT, 2009. 18645 dx.doi.org/10.1021/ja203579c |J. Am. Chem. Soc. 2011, 133, 18634–18645