Journal of the American Chemical Society all three Qi(z) (Figure 7b, lower right panel, black curve) shows that the net polarization due to the HOMO-related quasiband essentially vanishes. This simultaneous occurrence of polariza- tion and anomalous polarization within a quasiband is fully consistent with previous ﬁndings for the eigenfunctions of quantum-wells (cf., Figure 3c).113,114,112 Whether a small polar- ization or depolarization remains within a given quasiband then depends on the details of the involved orbitals. The overall response obtained from summing over all orbitals must, of course, reﬂect a depolarization (cf., Figure 7b, lower right panel, gray curve). Interestingly, the maximum of this net cumulative transfer amounts to <0.1 electrons, which is only about 1/4 of what is observed for the HOMO alone. Bonding the SAM to the Metal Substrate: Experimentally Accessible Quantities. Attaching the monolayer to the metal substrate can conceptually be viewed as a two-step process: First a docking group needs to be attached to the terpyrimidine SAM, which then binds the layer to the metal. The attachment of the docking group has two consequences: (i) It determines in which orientation the terpyrimidines are bonded to the metal and whether they induce a work-function decrease (3Ndown) or a work-function increase (3Nup) (cf., ΔEvac in Figure 3b and ref 44). (ii) Typically, docking group orbitals will hybridize with the states of the terpyrimidines. For thiols, the latter is evident already in Figure 2c, where for the isolated molecules we find the HOMO to display π-character, as the corresponding 3N orbital (the HOMO 1) has been destabilized due to the contribution of the sulfur to the molecular π-system. As a consequence of the orbital localization in terpyrimidine (cf., Figure 4), the effect is more pronounced in 3Ndown. Consistently, there the degree of localization of the highest occupied π-state is increased by the thiol, whereas it is decreased for 3Nup. In 3Ndown, when forming a monolayer from the isolated molecules, the collectively induced ﬁeld is oriented such that it enhances the localization of the HOMO (and HOMO 1) and strongly destabilizes it relative to the average vacuum level. This results in the particularly small band gap of 2.8 eV (see left plot of Figure 8a). In the 3Nup case the highest occupied σ-type orbital experiences a similar shift as in 3Ndown, while the energetic position of the highest occupied π-state relative to E is hardly aﬀected by the collectively induced ﬁeld. This results in the gap of the 3Nup SAM being of σ π* character as in the terpyrimidine SAM (cf., Figure 8a). A similar situation is encountered also when considering isocyanide as docking group. Also, there the π- electrons of the NC group hybridize with the π-system of 3N, modifying orbital localization and the packing-density dependent shifts of the eigenenergies. A more detailed discussion is con- tained in the Supporting Information. To understand qualitatively how the collectively induced QCSE aﬀects the alignment between the molecular states and the Fermi-level, i.e., addressing question I raised in the Introduc- tion, it is useful to analyze the position of the electronic states relative to the vacuum level at the docking-group end of the SAM (Elveafct in Figure 3a) as detailed in refs 118, 61, 90, and 38. The alignment of the states relative to Elveafct for 3Ndown and 3Nup shown in Figure 8b can be understood in a straightforward manner from the schematic sketch in Figure 6a and the localiza- tion of the orbitals in the isolated molecules (Figure 2c) and the monolayers (Figure 8a). In 3Ndown, the potential energy gradient is opposite to that sketched in Figure 6a. This is, compared to Elveafct all states are shifted down in energy upon increasing the ﬁeld (i.e., increasing the packing density). The eﬀect is relatively weak for ARTICLE Figure 8. (a) DOS of 3Ndown and 3Nup SAMs at θ = 1/2, aligned at the average electrostatic energy across the SAM, E (see Figure 3a). The thick black curves are Gaussian-convolutions (σ = 0.1 eV) of the results of the calculation. The insets show band charge-densities of the frontier states, and the band gap is indicated. It is determined from the onsets of the respective nonbroadened DOS peaks. (b) Energetic shifts of the HOMO, HOMO 1, and LUMO derived bands in a SAM of 3Ndown (left) and 3Nup (right) molecules relative to the molecular eigenvalues upon increasing the SAM packing density θ. The energies are deter- mined from the onsets of the respective peaks in the DOS. They are aligned at the left vacuum energy Elveafct; the absolute molecular eigenva- lues (approximated by θ = 1/64) are 6.52 eV ( 6.57 eV), 7.02 eV ( 6.74 eV), and 3.02 eV ( 2.90 eV) for the π-HOMO, σ-HOMO, and LUMO of 3Ndown (3Nup). (c) DOS of the full metal/SAM system projected onto the molecular region (PDOS) for the 3Ndown and 3Nup SAMs, with broadening and insets as in part a.117 Only a small fraction of metal atoms is shown. The Fermi energy is indicated as gray horizontal line. the HOMO and the HOMO 1 as a result of their localization close to the docking-group end of the SAM and amounts to only ca. 0.5 eV. For the 3Nup SAM, the energy gradient is opposite to that in 3Ndown, resulting in an upward shift of all states for increasing coverage. The net shift between the isolated molecule and the θ = 1/2 SAM amounts to ca. 1.3 eV for the (SAM) HOMO 1 and the LUMO and becomes as large as 2.0 eV for the (SAM) HOMO, which is localized on the ring furthest away from the docking group end of the SAM. This already strongly suggests that the level alignment of the 3Nup and 3Ndown SAMs 18641 dx.doi.org/10.1021/ja203579c |J. Am. Chem. Soc. 2011, 133, 18634–18645