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67.Experimentally, for the pentacene adsorbed Ag(111) surface, the dimensions of the surface unit cell of high density ordered monolayer are reported to be and with an angle of (structure 1 in Ref. 31), and for the Au(111) surface, they are and with an angle of (type B in Ref. 34). They are frequently observed and, therefore, most likely the stable configurations for a monolayer structure. Recent near-edge x-ray absorption fine structure experiment suggested that the molecular plane of the first layer of pentacene on a clean Au(111) surface is tilted along the molecular short axis by about 13° [D. Kafer, L. Ruppel, and G. Witte, Phys. Rev. B 75, 085309 (2007)]
67.On the other hand, on Ag(111), the tilting of the molecular plane has not been reported. This might be the reason for the large difference in the coverage of pentacene monolayer between the two surfaces. The inclined molecular orientation makes higher packing density of the pentacene monolayer possible on Au(111). In our calculations, however, we assumed flat-lying pentacene monolayer on Au(111). We checked that the effect of the tilting of pentacene on the work function change is small provided that the molecular density is the same as the present calculation. If the molecular density becomes as high as the experimentally observed high coverage regime, the intermolecular interaction becomes larger, and therefore, the assumptions of flat-lying geometry and the linear scaling of the work function change for Au(111) become inadequate, and this maybe the reason for the overestimation of the calculated value. Actually, very recent DFT calculations of pentacene/Au(111) with inclined geometry gives better estimation of the work function change [H. Li, Y. Duan, V. Coropceanu, and J. -L. Bredas, Org. Electron. 10, 1571 (2009)]. Although we assumed the flat-lying adsorption geometry, it does not alter the main conclusion of our study, especially, discussions concerning Figs. 4 and 5.
68.For Cu(111) and Au(111), the equilibrium distance calculated by DFT-D is the same as the deduced distance in our previous paper (Ref. 11). On Cu and Au, the calculated ’s at are evaluated to be −1.09 and −1.06 eV, which are in good agreement with the experimental values of −1.05 and −1.10 eV, respectively. On the other hand, for Ag(111), the equilibrium distance calculated by DFT-D is smaller than the deduced distance in our previous paper (Ref. 11) by 0.04 nm. This discrepancy comes from the inadequate assumption of the surface molecular density of benzene on Ag(111) in our previous paper. In Ref. 11, we employed the surface molecular density of benzene on Au(111), which is higher than that on Ag(111). If the surface molecular density of benzene on Ag(111) [T. J. Rockey, M. Yang, and H. -L. Dai, J. Phys. Chem. B 110, 19973 (2006)] is employed, the calculated at is evaluated to be , being in excellent agreement with the experimental value of −0.7 eV
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69.At becomes slightly below −1.0. We have not yet obtained clear reason for this point, but we think the following fact maybe a possible origin. At , the hybridization between the pentacene and the Cu and Ag surfaces is already strong, whereas the hybridization between the pentacene and the Au surface is significantly weak (the push-back effect is dominant). Therefore, at this distance, the hybridization between the pentacene and metal substrates is not uniform on the three surfaces. At smaller than 0.24 nm, the hybridization becomes strong on the three surfaces, and converges to the unity.
70.The contribution of to the bonding interaction between pentacene and the metal substrate is not large because is much higher than LUMO by . Therefore, we did not include the state.
71.It should be noted that the present GGA underestimates a HOMO-LUMO gap, whereas it does not describe the energy shift due to a polarization of the metal substrate, which reduces the HOMO-LUMO gap [J. B. Neaton M. S. Hybertsen, and S. G. Louie, Phys. Rev. Lett. 97, 216405 (2006)]
71.The two effects tend to cancel the error in the HOMO-LUMO gap [J. M. Garcia-Lastra, C. Rostgaard, A. Rubio, and K. S. Thygesen, Phys. Rev. B 80, 245427 (2009)].
72.On Cu(111), some electrons are transferred from the Cu substrate to the LUMO of pentacene, which should increase the work function. However, the calculated work function is actually decreased. We estimated Gross Population of each orbital and found that about 1.6 electrons are transferred from the Cu surface to the LUMO state, but the HOMO and deeper levels become partially empty, and in total, only 0.4 electrons are transferred from the Cu surface to pentacene molecule. Therefore, majority of the charge transfer takes place intramolecularly, i.e., from the antibonding state of Cu and pentacene HOMO states to bonding state of Cu and pentacene LUMO state and the net charge transfer from the Cu substrate to pentacene is small. Furthermore, filling of the bonding state, which has large weight in the region between Cu and pentacene, and partially emptying of the antibonding state, which has large weight in the vacuum side of pentacene molecule, lead to polarization of pentacene molecule normal to the molecular plane, as pointed out in our previous paper (Ref. 42). This polarization induces the work function decrease even if the LUMO of pentacene becomes partially filled.

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In order to clarify factors determining the interface dipole, we have studied the electronic structures of pentacene adsorbed on Cu(111), Ag(111), and Au(111) by using first-principles density functionaltheoretical calculations. In the structural optimization, a semiempirical van der Waals (vdW) approach [S. Grimme, J. Comput. Chem.27, 1787 (2006)] is employed to include long-range vdW interactions and is shown to reproduce pentacene-metal distances quite accurately. The pentacene-metal distances for Cu,Ag, and Au are evaluated to be 0.24, 0.29, and 0.32 nm, respectively, and work function changes calculated by using the theoretically optimized adsorption geometries are in good agreement with the experimental values, indicating the validity of the present approach in the prediction of the interface dipole at metal/organic interfaces. We examined systematically how the geometric factors, especially the pentacene-substrate distance , and the electronic properties of the metal substrates contribute to the interface dipole. We found that at , the work function changes (’s) do not depend on the substrate work function, indicating that the interface level alignment is nearly in the Schottky limit, whereas at , ’s vary nearly linearly with , and the interface level alignment is in the Bardeen limit. Our results indicate the importance of both the geometric and the electronic factors in predicting the interface dipoles. The calculated electronic structure shows that on Au, the long-range vdW interaction dominates the pentacene-substrate interaction, whereas on Cu and Ag, the chemical hybridization contributes to the interaction.


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