Journal of the American Chemical Society localization (and anomalous polarization) of the molecular orbitals (respectively the real space representations of the associated bands), (ii) a signiﬁcant decrease of the computed band gap by up to 0.8 eV, and (iii) concomitantly, a strong impact of the collectively induced electric ﬁeld on the level alignment with the metal Fermi-level. These trends can be rationalized combin- ing the quasiband/envelope-function picture with the Quantum- Conﬁned Stark eﬀect typically observed in semiconductor quan- tum-wells under the inﬂuence of strong external ﬁelds. The peculiarity of the present systems is that here the potential energy gradient within the layer is collectively induced by the interacting polar molecular building blocks. For the sake of clarity, these eﬀects are primarily discussed for the hypothetical free-standing monolayers, but essentially prevail also when the SAMs are bonded to a metal substrate. The above considerations underline that periodically assembled molecules can display properties that hugely diﬀer from those they possess in gas phase. Therefore, when designing molecular building blocks for novel self-assembled materials and hybrid systems, collective eﬀects have to be carefully considered. This is particularly relevant when working with molecules containing polar building blocks, where electrostatic eﬀects can have a huge impact on the electronic properties. Apart from complicating the bottom-up de- sign of new systems, the presented results, however, also provide tools that can be exploited as additional handles for tuning the properties of also more complex systems than the ones dis- cussed here. As a long-term vision, one could imagine exploiting collective electrostatic eﬀects that occur as a result of monolayer formation to shift the electronic levels “by design” in various parts of extended molecules giving molecular electronics a “collectively-controlled” twist. ’ METHODS All molecular geometries were obtained by optimizations with the PBE functional using the Gaussian 03123 package and the aug-cc-pVTZ basis set. Subsequent LDA and GKLI calculations were done with the PARSEC real-space code124,125,76 and norm-conserving pseudopotentials126 and HSE06 calculations with the VASP code127 with a plane-wave basis set (kinetic energy cutoﬀ of approximately 20 Ry) and the projector augmented-wave (PAW) method.128,129 For LDA and PBE, the comparability of the eigenvalues resulting from the diﬀerent codes was carefully tested. For details on the GKLI methodol- ogy the reader is referred to the original publication.76 In the periodic calculations, a Methfessel Paxton occupation scheme with the temperature set to 100 K (0.008 62 eV) was used, and Monkhorst-Pack130 k-point grids of 8 5 1, 4 5 1, 2 5 1, 2 2 1 and 1 1 1 were chosen for the SAM packing densities of 1/ 2 , 1/ 4 , 1/ 8 , 1 /16, and 1/64, respectively. The corresponding unit cells were obtained by doubling the short lattice vector (see Figure 1b) once (θ = 1/4) and twice (θ = 1/8); θ = 1/16 was obtained by doubling the 1 1 shorter lattice vector of the cell at θ = /8, and θ = /64 by again doubling both lattice vectors. The latter was used as approximation for the isolated molecule. Even at such low packing density, ΔEvac does not vanish exactly. We have found values ΔEvac < 0.2 eV, and account for this in Figures 4, 6b, and 8b by using the reference energy E (and Elveafct in Figure 8b) also in the case of the isolated molecule. The molecular geometries were not reoptimized in the periodic calculations, and the molecules were oriented parallel to the z-axis of the unit cell (see Figure 1); this procedure facilitates an easy comparison of molecular orbitals and orbital-derived bands. To exclude spurious interaction between subsequent slabs in the z-direction, a vacuum gap of >20 Å ARTICLE was introduced together with a dipole layer within the vacuum to compensate for the net dipole moment of the slab. Orbital charge-densities Fi(z) were deﬁned as FiðzÞ ¼ Z a Z b ∑ ji, kBðx, y, zÞji, kBðx, y, zÞ dxdy 0 0 Bk in units of e/Å, with a and b being the lattice constants of the surface unit-cell and e the (positive) elementary charge. The sum is taken over all reciprocal-space vectors Bk included in the calculation. Note that the unit cell size (i.e., a and b) and the included vectors Bk diﬀer for “isolated” and periodic systems as detailed above. Fi(z) comprises the charge of a non- spin-polarized band; i.e., the area below a curve amounts to 2 electrons. Five layers of the nonrelaxed Au(111) surface in the above-used p(√3 3) unit cell were used for the calculations on the full metal/SAM systems. No geometry relaxation of the upright-standing molecules was performed, and the position of the bonded sulfur atom was determined from previous work.44 Representations of the systems were generated with XCrysDen.131 3D orbital/band charge density plots were generated at the isovalue of 0.02 e/Å3. HSE06 calculations for the orbital representations in Figure 7a and dipole moments in Figure 9 were done with Gaussian 09132 using the 6-311++G(d,p) basis set. An isovalue of 0.04 a.u. was used. ’ ASSOCIATED CONTENT bS Supporting Information. Detailed discussion of the role of self-interaction, assessment of the accuracy of DFT for molecular polarizabilities, dipole moments and energy gaps, additional information on the role of the docking group; full name, geometry and total energy of optimized molecular struc- tures, complete references 11, 123, and 132. This material is available free of charge via the Internet at http://pubs.acs.org. ’ AUTHOR INFORMATION Corresponding Author egbert.zojer@tugraz.at Present Addresses zDepartment of Physical Electronics, Tel-Aviv University, 69978 Tel-Aviv, Israel Author Contributions These ) authors contributed equally to this work. ’ ACKNOWLEDGMENT The authors thank A.M. Kelterer, O.T. Hofmann, C. Slugovc, Z.Y. Ma, and L.J. Wang for fruitful discussions, and Z.Y. Ma from the Institute of Chemistry of the Chinese Academy of Sciences also for support with the Gaussian HSE06 calculations. We thank the ZID of the TU Graz for providing computational resources. The research was largely funded by the Austrian Science Fund (FWF): P20972 N20. D.A.E. is recipient of a DOC-fellowship of the Austrian Academy of Sciences. T.K. acknowledges ﬁnan- cial support by the Alexander-von-Humboldt-Foundation. S.K. acknowledges ﬁnancial support by GRK 1640 and the German- Israeli-Foundation. L.K. acknowledges ﬁnancial support by the Israel Science Foundation, the German-Israeli-Foundation, and the Lise Meitner Minerva Center for Computational Chemistry. 18643 dx.doi.org/10.1021/ja203579c |J. Am. Chem. Soc. 2011, 133, 18634–18645