Journal of the American Chemical Society parallel orientations, but in a denser packing of one molecule per (√3 3) cell (shown in Figure 1b). Also from a practical point of view the chosen surface unit-cell is convenient as it allows an easy comparison of the various systems and between the electronic structure of isolated and assembled molecules. For consistency with previous work,44,57 where each (√3 3) cell contained two molecules in a herringbone pattern (vide supra), we denote the present full coverage as θ = 1/2. Finally, we note that in test calculations on the herringbone-packed SAM at the coverage used in ref 44 we qualitatively recover the results reported below. Determining a Suitable Computational Approach. Before discussing the electronic structure of the above-discussed SAMs, it is imperative to critically assess which of the available computa- tional approaches is most suitable for reliably predicting the quantities of interest. We expect that to be of distinct relevance also for future studies of related systems. As we aim at describing monolayers, i.e., systems that are inﬁnitely extended in two dimensions, periodic boundary con- ditions are required. Considering the size of the investigated unit cells, any approach other than DFT is computationally not aﬀordable. In spite of its great success in quantum-chemistry and physics, (semi)local DFT, however, also suﬀers from a number of shortcomings. In the present context especially the infamous self-interaction error (SIE) in (semi)local DFT, i.e., the erroneous interaction of each orbital with itself,68,69 can become particularly relevant (cf., extended discussion in the Supporting Information). This is because in pyrimidines there are close-lying σ- and π-orbitals in the vicinity of the HOMO/LUMO gap,70 72 intertwined with signiﬁcant variations in orbital localization, a scenario in which drastic failures of a (semi)local DFT-based description have been reported.73,74 In oligopyrimidines this could very well result in an incorrect prediction of the actual nature (σ vs π) of the frontier states. To estimate the possible impact of the SIE, we follow the strategy presented in ref 74, where a simple-to-evaluate predictor for the presence of a strongly orbital-dependent SIE has been proposed. For every Kohn Sham orbital, it calculates the amount of Coulomb self-repulsion that is not canceled by exchange-correlation (xc) self-attraction. To evaluate the impor- tance of self-interaction in the present systems, we performed this test for the isolated 3Nup molecule. The orbital SIEs, ei, for the HOMO 10 to HOMO (i.e., valence orbitals 36 to 46) relative to that of the HOMO, Δei:= (ei e46), are shown as solid orange circles in Figure 2a.75 The displayed values have been calculated using the local density approximation (LDA), but essentially equivalent results are obtained when using gradient- corrected (GGA) functionals. Indeed, strongly varying values of Δei are found for the high- lying orbitals, which are most important in applications. An inspection of the real-space representations of the orbital charge- densities (contained in the Supporting Information) shows that the magnitude of the SIE predictor indeed depends on the visual impression of orbital localization (while, apparently, it is not signiﬁcantly aﬀected by whether an orbital displays σ- or π- character). These results clearly emphasize the importance of using a description that is free from self-interaction. To achieve this goal, we performed a self-interaction correction (SIC) employing the generalized optimized eﬀective potential (GOEP) method76 using the Krieger Li Iafrate approximation (GKLI). The latter has been shown to accurately reproduce ARTICLE Figure 2. Self-interaction error and electronic structure of the isolated 3Nup molecule. (a) The self-interaction error of the LDA orbitals is shown (orange) together with the GKLI SIC (green) and the HSE corrections (black). All quantities are given relative to the value for the HOMO (orbital 46). (b) LDA (left) and HSE (right) orbital energies, aligned to the respective HOMO energies. The arrows link associated orbitals. (c) Absolute HSE-computed eigenenergies of 3Ndown (left panel) and 3Nup molecule (right panel), broadened by a Gaussian with σ = 0.1 eV. The insets show orbital charge-densities of the frontier states; the HOMO LUMO gap is indicated. the results of numerically far more demanding full GOEP calculations.76 The obtained relative orbital energy shifts, ΔεiGKLI = (εiGKLI εiLDA) (εGHKOLMI O εLHDOAMO), are depicted in Figure 2a as solid green squares. Besides opposite signs, we ﬁnd systematic diﬀerences between Δei and ΔεiGKLI. This is insofar expected, as there is only an approximate correlation between the SIE and its correction.77 Diﬀerent from Δei, the values ΔεiGKLI appear to be primarily sensitive to the character of an orbital; i.e., there is a common correction for all σ-states and a diﬀerent common one for all π-states irrespective of the intuitive impression of localization (see Supporting Information). Most importantly, the correction shifts the HOMO 2 up in energy by 0.59 eV, to above the LDA- HOMO, demonstrating that the SIE severely distorts the electronic structure of terpyrimidinethiols. An alternative approach to obtain improved orbital energies is the use of hybrid functionals. These, however, only partially correct for self-interaction, as they include only a fraction of exact exchange. Still (as rationalized in the Supporting Information), often good comparability with experiment and SIC or GW calculations is found for the low binding energy states. A functional which is readily applicable to both molecular and periodic systems is the Heyd Scuseria Ernzerhof screened- exchange hybrid functional, HSE06,78 80 where the long-range 18636 dx.doi.org/10.1021/ja203579c |J. Am. Chem. Soc. 2011, 133, 18634–18645