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2009, 113, 9969–9973 Published on Web 05/14/2009
Pentacene Binds Strongly to Hydrogen-Terminated Silicon Surfaces Via Dispersion Interactions Gino A. DiLabio,*,† Erin R. Johnson,‡ and Jason Pitters† National Institute for Nanotechnology, National Research Council of Canada, 11421 Saskatchewan DriVe, Edmonton, Alberta, Canada T6G 2M9, and Department of Chemistry, Duke UniVersity, Durham, North Carolina 27708 ReceiVed: March 9, 2009; ReVised Manuscript ReceiVed: April 24, 2009
Understanding the interaction of organic molecules with clean and hydrogen-terminated silicon surfaces is important for the development of hybrid structures with interesting electronic properties. Previous theoretical work has predicted that pentacene, an important molecule for organic electronics, is bound to hydrogenterminated silicon(100)-2×1 by less than 6.5 kcal/mol and has a barrier to diffusion on the surface of ∼0.23 kcal/mol. This low barrier to diffusion is apparently supported by scanning tunneling microscopy observations. By means of density-functional theory with newly developed dispersion-correcting potentials, we predict that pentacene is bound to H-Si(100)-2×1 terraces by 17.4 kcal/mol. This strong binding is supported by evaluations of dispersion using an exchange-hole dipole model. The low binding of pentacene predicted in the previous theoretical studies is likely the result of the neglect of the contributions of silicon in the evaluation of dispersion binding. Our calculations also predict that barriers to diffusion of pentacene on H-Si(100)2×1 terraces are on the order of 2-3 kcal/mol, depending on the diffusion direction. These findings are fully consistent with the earlier scanning tunneling microscopy studies if the effects of inelastic tunneling are taken into account. The interaction of aromatic hydrocarbons with silicon surfaces is a rich area of scientific exploration. Much effort has been applied to understanding the details of the chemistry associated with the addition of simple aromatic systems to silicon. As a single illustrative example, Schwartz et al.1 reported in substantial detail experimental results for the chemisorption of styrene on clean Si(100)-2×1.2 Much of the interest in this chemistry is related to the functionalization of semiconductor surfaces for the purpose of altering electrical properties of the substrate. It has been shown experimentally3 and theoretically4 that modification of silicon surfaces through chemisorption can significantly alter the electronic properties of the substrates. Such interest has led to significant activity related to molecular control of electronic devices5 and to the creation of ordered organic nanostructures on hydrogen-terminated silicon surfaces that may have interesting electrical properties.6 One of our interests in this area is related to noncovalent interactions between hydrocarbons and hydrogen-terminated silicon. Some time ago, we showed that dispersion interactions between long-chain 1-alkenes and the hydrophobic H-Si(100)2×1 surface7 are critical for the room-temperature growth of one-dimensional organic nanostructures on the silicon surface.8 Our experimental findings were supported by hybrid densityfunctional theory (DFT) calculations, which, because of the size of our model system, was one of the only practical approaches available to us at the time. The functional that was used, * To whom correspondence should be addressed. Phone:+1-780-6411729. E-mail:
[email protected]. † National Research Council of Canada. ‡ Duke University.
10.1021/jp902126b CCC: $40.75
HCTH407,9 was chosen because it fortuitously predicts some binding in a number of small hydrocarbon dimer systems10,11 and not because it contains the correct dispersion physics. Incorporation of dispersion physics into DFT methods has been a major challenge for members of the development community, and much progress in this area has been made over the past few years.12-14 We recently introduced a different approach that largely corrects the erroneous long-range behavior of some conventional DFTs through the use of atom-centered, effective-core-like potentials.15,16 These local potentials are referred to as dispersion-correcting potentials, DCPs. The DCP approach is simple and generally applicable. It can be used with most common computational packages that can handle effective potential input (e.g., Gaussian-03)17 and can therefore exploit all of the “machinery” of these programs, namely, geometry optimizations, frequency calculations, solvation models, and so forth. An example of an input file demonstrating the use of DCPs can be found in the Supporting Information (SI). Careful benchmarking of DCPs for carbon16 and silicon18 against high-level wave function binding energies of numerous dispersion-bound dimers, including π-stacked aromatics and dimers containing silicon atoms (vide infra), demonstrated the effectiveness of the approach. This provided us with the confidence to apply DCPs to study the interaction of the model hydrocarbons methane and benzene on H-Si(100)-2×1.18 Our calculations indicate that the strongest binding between methane and H-Si(100)-2×1 occurs with the molecule over the gulley2,7 with a binding energy, BE, of 2.2 kcal/mol. The distance between the methane carbon and the silicon surface is predicted to be ∼2.9 Å. Benzene is predicted to interact most strongly 2009 American Chemical Society
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Figure 1. Top-down views of structures of pentacene with the central ring nominally over a dimer row on hydrogen-terminated silicon(100)-2×1, as determined by density-functional theory with dispersion-correcting potentials. The surfaces are represented by three rows of seven dimers in a contiguous layer. The surface H and Si atoms are shown in tube representation, the H atoms used to cap the Si back bonds are shown in wireframe representation, and atoms constituting pentacene are shown as balls and sticks Key: C ) dark gray, Si ) light gray, H ) white. Calculated binding energies (kcal/mol), average distance from dimer Si atoms (Å), and point group symmetry: (a) 17.4, 3.92, Cs; (b) 15.0, 4.12, C2V; (c) 14.6, 4.03, C2; (d) 15.1, 3.99, C2V.
Figure 2. Top-down views of structures of pentacene with the central ring nominally over a gully on hydrogen-terminated silicon(100)-2×1, as determined by density-functional theory with dispersion-correcting potentials. The surfaces are represented by one and a half rows of seven dimers on either side of the central gulley, in a contiguous layer. The surface H and Si atoms are shown in tube representation, the H atoms used to cap the Si back bonds are shown in wireframe representation, and atoms constituting pentacene are shown as balls and sticks. Key: C ) dark gray, Si ) light gray, H ) white. Calculated binding energies (kcal/mol), average distance from dimer Si atoms (Å), and point group symmetry: (a) 16.9, 3.92, C2V; (b) 14.9, 4.07, C2; (c) 14.5, 3.97, C2V.
with the silicon dimer rows. The minimum-energy configuration is one in which benzene is approximately parallel to and 4 Å above the surface, with a surface Si-H group pointing toward the center of the ring. Our calculations indicate that benzene binds to H-Si(100)-2×1 with an energy of 5.6 kcal/mol. Our calculated results appear to be inconsistent with previously reported theoretical results for the binding of pentacene on H-Si(100)-2×1. Using standard DFT methods with van der Waals correction terms containing empirical dispersion parameters for the pentacene carbon and hydrogen atoms, Tsetseris and Pantelides predicted binding energies that are less than 6.5 kcal/mol.19 Later, Ample and Joachim20 performed a similar study using a semiempirical approach corrected with van der Waals correction terms and found results that are consistent with those of Tsetseris and Pantelides. On the basis of a simple summation over point contacts, we expected the binding of pentacene to H-Si(100)-2×1 to be larger than that of benzene by a factor of 3-4,18 namely, ∼16-22 kcal/mol. Given the potential importance of pentacene in organic electronics21,22 and efforts to use silicon substrates to create pentacene thin films,21 we felt it worthwhile to resolve the discrepancy between our results and those of refs 19 and 20. We present here the results of our investigation of the noncovalent binding of pentacene to H-Si(100)-2×1 using the DCP approach. Our study is particularly timely given the recently published work by Bellec et al. in which theory and experiment were used to study pentacene orbitals on H-Si(100)-2×1.23 The scanning tunneling microscopy (STM) measurements reported
in ref 23 seem to support the authors’ theoretical data that indicate that pentacene diffusion across H-Si(100)-2×1 is facile, even at temperatures near 5 K. Calculations were performed using the PBE24 densityfunctional with 6-31+G(d,p) basis sets with C and Si DCPs.25,26 For calculations involving pentacene, two surface models were used depending on the position of the molecule on the surface. For pentacene interacting with the Si dimer row, the surface was modeled using 90 Si atoms and 126 H atoms arranged in 3 rows of 7 dimers in one contiguous layer (see Figure 1). For pentacene over the gulley, the surface was represented with 96 Si atoms and 150 H atoms. One and one-half rows of seven dimers were arranged on either side of a central gulley (see Figure 2). These two surfaces were used so that it was possible to take advantage of symmetry in most of the calculations. Si-Si “back bonds”, that is, bonds that would connect the surface Si atoms to the bulk, were capped by H atoms. Additional calculations were performed with the smaller aromatics benzene,25 naphthalene, anthracene, and tetracene. The results for these systems, which are relegated to the SI, are consistent with those that we obtain for pentacene.27 In all cases, the H-Si models were taken from a “slab” of H-Si that was optimized by a periodic boundary PBE calculation4 using the VASP program package.28 For all calculations, the positions of the atoms in the models representing H-Si(100)-2×1 were kept fixed during optimizations, and only the positions of the aromatic molecules were allowed to move. The use of a truncated model to represent the Si surface will most certainly result in predicted
Letters binding energies that are underestimates of the actual values. On the basis of our previous work,18 we expect our predicted BEs to be too low by about 10%. Relative BEs and estimates of barrier heights should be reasonably accurate because of error cancellation. The optimized structures for various orientations of pentacene on H-Si(100)-2×1 are shown in Figure 1, with the BEs and some structural information given in the caption. For these structures, the central pentacene ring is nominally over a surface dimer row. The most strongly bound complex has pentacene over one side of a dimer row; see Figure 1a. This orientation is similar to the lowest-energy arrangement of benzene on H-Si(100)2×1.18 Both pentacene and benzene preferentially interact with the surface such that Si-H groups point toward ring centers. Not obvious from Figure 1a is that the molecule is slightly bowed, with the central ring ∼0.04 Å farther than the outer rings from the plane defined by the surface Si atoms. In this orientation, the molecule is generally parallel to, and resides ∼3.9 Å above, the surface. Pentacene in this arrangement is predicted to be bound to H-Si(100)-2×1 by 17.4 kcal/mol.29,30 We reiterate that previous theoretical work has predicted pentacene to be bound to H-Si(100)-2×1 by significantly smaller energies, namely, less than 6.519 and 2.5 kcal/mol.20,23 The reason for this poor agreement is discussed below. Figure 1b-d shows orientations of pentacene in which the central ring is directly over the dimer row. In all cases, the pentacene displays some small amount of deformation from planarity, namely, ∼0.04-0.07 Å differences in C atom distances from the dimer Si atoms. This indicates that the molecule is not rigidly planar and can distort in order to better interact with the surface. Figure 1b shows the optimized structure of a pentacene aligned directly over a dimer row. This arrangement is 2.4 kcal/mol higher in energy (BE ) 15.0 kcal/ mol) than that shown in Figure 1a and is representative of a transition state (TS)-like structure connecting two minima in which pentacene is over either edge of the dimer row. In Figure 1c, the long axis of pentacene is oriented at an angle of ∼45° relative to the dimer row. The pentacene in this arrangement is bound to the surface by 14.6 kcal/mol and is only slightly higher in energy than the structure shown in Figure 1b. Figure 1d shows pentacene bound to the surface in an orientation such that the long axis of the molecule is perpendicular to the row direction. The BE for this orientation, 15.1 kcal/mol, is nearly identical to that shown in Figure 1b. The structure shown in Figure 1c is representative of a TS-like structure connecting the row-aligned structure (Figure 1b) and the perpendicular-to-row structure (Figure 1d).31 As such, the approximate barrier height of 0.4-0.5 kcal/mol for the rotation of pentacene over a dimer row indicates that this process would occur freely at room temperature. However, this process is not likely because pentacene prefers to be positioned on the edge of a dimer row (Figure 1a) rather than directly over a dimer row (Figure 1b). Figure 2 shows orientations of pentacene on H-Si(100)-2×1 that have the central ring of the molecule over a surface gulley. BEs and some structural data are provided in the figure caption. The lowest-energy orientation is shown in Figure 2a, where the pentacene has its central ring over a gulley and its long axis oriented in the perpendicular-to-row direction. Arranged in this manner, a number of surface Si-H groups point toward the centers of four of the pentacene rings, which has been determined to be particularly stabilizing (vide supra). The BE for this orientation is 16.9 kcal/mol, and the molecule lies, on average, ∼3.9 Å above the surface. Interestingly, the pentacene molecule is distorted from planarity in a manner opposite to
J. Phys. Chem. C, Vol. 113, No. 23, 2009 9971 the distortion noted in the case where the molecule is over a row, as in Figure 1a. The structure in Figure 2a has the central ring closer to the surface than the terminal rings. This finding reflects the fact that the central ring can more closely approach the Si atoms of the gulley than the terminal rings can approach the Si atoms of the dimers because of intervening surface H atoms in the latter case. Comparing the structure in Figure 2a to that in Figure 1d gives a sense of the energy profile associated with the diffusion of pentacene in the direction of its long axis when the molecule is oriented perpendicular to the dimer rows. Although the limited extent of the surfaces that we used for modeling prevent us from exploring this process in detail, it is likely that the structure shown in Figure 1d (BE ) 15.1 kcal/mol) is a TS-like structure connecting two local minima such as those shown in Figure 2a. In this case, the diffusion process described above will have a barrier of 1.8 kcal/mol. Rotation of the perpendicular-to-row structure in Figure 2a by ∼45° requires ∼2.0 kcal/mol of energy and results in the orientation shown in Figure 2b. This structure is also “bowed” away from the surface and is ∼4.1 Å above the surface. Further rotation to produce a structure where the long axis of the pentacene is aligned with the dimer row direction, namely, Figure 2c, requires an additional 0.4 kcal/mol. The reduced binding for the structure in Figure 2c (BE ) 14.5 kcal/mol) compared to that in Figure 2a reaffirms our earlier conclusions that favorable interactions are generated when Si-H groups are directed toward ring centers. The structure in Figure 2c can be compared with those in Figure 1a and b in order to obtain a sense for the diffusion of pentacene in the direction perpendicular to its long axis when the molecule is aligned in the dimer row direction. Figure 2c shows a structure representative of a TS-like structure that connects two minima like that represented in Figure 1a in a diffusion event across a gulley. The energy barrier for this process is ∼2.9 kcal/mol. Diffusion across a row, namely, 1a f 1b f 1a′,32 as described above, has a barrier of 2.4 kcal/ mol. The important point that emerges from the analyses above is that pentacene faces barriers on the order of 2-3 kcal/mol for movement across the H-Si(100)-2×1 surface.33 At room temperature, such barriers are easily surmounted, and diffusion should be quite facile. On the other hand, at very low temperatures, for example, those at which experiments to measure pentacene orbitals on H-Si(100)-2×1 were conducted (5 K),23 diffusion should be completely disabled. However, Bellec et al. reported that STM imaging of pentacene on H-Si(100)-2×1 was not possible at 5 K if the molecule was not physisorbed to the surface next to a terrace step edge.23 This inability to perform STM imaging of pentacene was supported by the very low calculated diffusion barrier of 0.23 kcal/mol (0.01 eV) that they obtained using their computational approach. We believe that the lack of agreement between our calculated barriers to diffusion and that calculated in ref 23 is related to the disagreement in binding energies of pentacene on H-Si(100)-2×1 that was described above. It is very likely that the previously reported calculated BEs of pentacene on H-Si(100)-2×119,20,23 and the barriers to its diffusion across the surface23 are too low because these previous works did not completely account for the effects of dispersion. In all three studies, the authors incorporated explicit corrections for dispersion binding through the use of van der Waals parameters. This approach is generally very good at describing dispersion interaction in a variety of systems (see, for example,
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ref 14). However, in ref 19, only the van der Waals terms for the pentacene C and H atoms were incorporated into the theoretical treatment. In refs 20 and 23, van der Waals terms for all C and H atoms, including silicon surface hydrogens, were used in the calculations. These treatments should provide a reasonable description of dispersion binding between hydrocarbon moieties19 but not between pentacene and the H-Si(100)-2×1 surface. If van der Waals parameters were not required to describe silicon-hydrocarbon interactions, conventional (i.e., not corrected for dispersion) DFT methods would be expected to treat these systems accurately. However, our recent work has shown that B971, a conventional DFT method, underestimates the BEs in conformations of the silane-methane and silane-benzene dimers by percent absolute deviations of 37 and 56, respectively, compared to high-level wave function data.18 Therefore, it is necessary to include dispersion corrections for the C and the Si atoms in order to obtain reasonable computed binding energies and diffusion barriers. We elucidate the differences between a complete dispersion treatment and one involving only the C and H atoms through the use of the exchange-hole dipole moment (XDM) approach of Becke and Johnson.12b,c,34 The minimum-energy structure shown in Figure 1a has an XDM dispersion energy of 21.4 kcal/ mol (compare the PBE/6-31+G(d,p)-DCP BE of 17.4 kcal/ mol).35 However, if only interactions between the pentacene molecule and the surface H atoms are included, the dispersion energy is reduced, by a factor of roughly 4, to 4.6 kcal/mol. This latter value is close to the binding energies obtained in previous work20,23 and clearly demonstrates the importance of including Si dispersion parameters in the calculation of pentacene binding to H-Si(100)-2×1. It remains to be explained how the STM observations of Bellec et al.23 apparently support the low calculated diffusion barriers for pentacene on H-Si(100)-2×1. The authors report that they are unable to image pentacene on H-Si terraces, a fact that implies that there is facile molecular diffusion. This led them to believe that the barriers to pentacene diffusion are very low, that is, consistent with their calculated value of 0.23 kcal/mol. Our calculated diffusion barriers of 2-3 kcal/mol correspond to lifetimes of >1080 s-1 for a pentacene molecule in a local potential energy well on H-Si(100)-2×1 at 5 K36 and are at odds with Bellec et al.’s findings. However, their experimental observations can also be explained by diffusion induced by the STM tip. It is known that the filled state imaging of the highest occupied molecular orbital (HOMO) levels of organic molecules on thin insulating films occurs through a positive ion resonance tunnel mechanism.37 That is, as the applied potential on the tip aligns with the molecule’s HOMO level, an electron tunnels from the molecule to the tip. This leaves a positive hole in the molecule which is then filled with an electron from the valence band of the substrate. With some probability, the electron can tunnel inelastically from the bulk material to the transiently positive molecular ion. This process provides energy equal to that of the inelastic event to the molecule. Under the imaging conditions used by Bellec et al. (i.e., -3 V), enough energy from inelastic tunneling events can be supplied to induce molecular diffusion (∼0.1 eV calculated herein) and even desorption of the molecule from the surface (∼0.8 eV calculated herein). This is not unexpected given that experiments of covalently bound organic molecules such as benzene and styrene, which are bound to Si surfaces by 1.1 and 1.6 eV, respectively, have been shown to displace laterally, change
Letters orientation, and desorb completely from the surface under similar imaging conditions.38,39 In other examples, inelastic tunneling in STM experiments has been used for the manipulation of atoms and molecules, including inducing lateral molecular motion (diffusion), rotation, orientation switching, desorption, and chemical bond formation and breaking.40-42 It is therefore quite likely that the mobility of the pentacene molecule on H-Si terraces observed by Bellec et al. is due to inelastic tunneling. Step-edge-bound molecules experience a larger barrier to diffusion and are therefore less likely to undergo tip-induced motion compared to terrace-bound molecules, as observed by Bellec et al. We performed additional calculations that show that pentacene at a step edge is bound by ∼2.7 kcal/mol more than pentacene on a terrace (Figure 1a). This increase in binding energy leads to a large increase in, for example, the cross-row diffusion barrier, namely, from 2.9 to 5.6 kcal/mol, and explains why pentacene is more easily observed by STM at a step edge. Note that inelastic tunneling-induced diffusion can still occur, and this has also been observed by Bellec et al. (see Figure 1 of ref 23). In summary, we have shown that PBE density-functional theory with dispersion-correcting potentials predicts that pentacene is bound on H-Si(100)-2×1 terraces by 17.4 kcal/mol. This binding is much larger than that predicted in previous theoretical works using van der Waals parameters to correct the DFT treatment. The discrepancies in pentacene binding are explained by the fact that van der Waals terms for silicon were not included in the previous studies. We have also shown that barriers to diffusion of pentacene on H-Si(100)-2×1 terraces are on the order of 2-3 kcal/mol, depending on the diffusion direction. These findings are fully consistent with previous scanning tunneling microscopy studies if the effects of tipinduced inelastic tunneling are taken into account. Acknowledgment. We are grateful to Leonidas Tsetseris (Vanderbilt University) and Iain Mackie (NINT) for helpful discussions, to Professor Pierre Boulanger (University of Alberta) for access to computational resources, and to the Program for Energy Research and Development (PERD) for financial support. Supporting Information Available: A sample input file for the Gaussian-03 program demonstrating the use of DCPs, binding energies calculated for conformers of the silane-benzene dimer using PBE/6-31+G(d,p)-DCP, a plot showing the calculated binding energy as a function of polyacene ring size, and the optimized structure for pentacene on a H-Si(100)-2×1 dimer row. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Schwartz, M. P.; Ellison, M. D.; Coulter, S. K.; Hovis, J. S.; Hamers, R. J. J. Am. Chem. Soc. 2000, 122, 8529–8538. (2) The clean Si(100)-2×1 surface has rows of dimers of Si atom that share in a strong σ-bond and a weak π-bond. The distance between dimers in a row is ∼3.85 Å, and the periodicity of the rows is ∼7.70 Å. We refer to the space between dimer rows as a “gulley”. (3) Sinha, S.; Dickie, A. J.; Wolkow, R. A. Chem. Phys. Lett. 2009, 469, 279–283. (4) Anagaw, A.; Wolkow, R. A.; DiLabio, G. A. J. Phys. Chem. C 2008, 112, 3780–3784. (5) Vilan, A.; Shanzer, A.; Cahen, D. Nature 2000, 404, 166–168. (6) Piva, P.; DiLabio, G. A.; Pitters, J. L.; Zikovsky, J.; Rezeq, M.; Dogel, S.; Hofer, W. A.; Wolkow, R. A. Nature 2005, 435, 658–661. (7) The structure of hydrogen-terminated Si(100)-2×1 is similar to that of the clean surface,2 except that the weak π-bond shared by dimer row Si atoms is replaced by σ-bonds to capping hydrogen atoms.
Letters (8) DiLabio, G. A.; Piva, P. G.; Kruse, P.; Wolkow, R. A. J. Am. Chem. Soc. 2004, 126, 16048–16050. (9) Boese, A. D.; Handy, N. C. J. Chem. Phys. 2001, 114, 5497–5503. (10) Johnson, E. R.; DiLabio, G. A. Chem. Phys. Lett. 2006, 419, 333. (11) Johnson, E. R.; Wolkow, R. A.; DiLabio, G. A. Chem. Phys. Lett. 2004, 394, 334–338. (12) (a) Johnson, E. R.; Becke, A. D. J. Chem. Phys. 2006, 124, 174104. (b) Becke, A. D.; Johnson, E. R. J. Chem. Phys. 2007, 127, 124108. (c) Becke, A. D.; Johnson, E. R. J. Chem. Phys. 2007, 127, 154108. (d) Johnson, E. R.; Becke, A. D. J. Chem. Phys. 2008, 128, 124105. (13) (a) Iikura, H.; Tsuneda, T.; Yanai, T.; Hirao, K. J. Chem. Phys. 2001, 115, 3540–3544. (b) Dion, M.; Rydberg, H.; Schro¨der, E.; Langreth, D. C.; Lundqvist, B. I. Phys. ReV. Lett. 2004, 92, 246401. (c) Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2006, 110, 13126–13130, and references therein. (d) Lin, I.-C.; Coutinho-Neto, M. D.; Felsenheimer, C.; von Lilienfeld, O. A.; Tavernelli, I.; Rothlisberger, U. Phys. ReV. B 2007, 75, 205131, and references therein. (e) Chai, J.-D.; Head-Gordon, M. J. Chem. Phys. 2008, 128, 084106. (14) (a) Grimme, S. J. Comput. Chem. 2004, 25, 1463–1473. (b) Grimme, S. J. Comput. Chem. 2006, 27, 1787–1799. (c) Antony, J.; Grimme, S. Phys. Chem. Chem. Phys. 2006, 8, 5287–5293. (15) DiLabio, G. A. Chem. Phys. Lett. 2008, 455, 348–353. (16) Mackie, I. D.; DiLabio, G. A. J. Phys. Chem. A 2008, 112, 10968– 10976. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision D.01; Gaussian, Inc.: Pittsburgh, PA, 2004. (18) Johnson, E. R.; DiLabio, G. A. J. Phys. Chem. C 2009, 113, 5681– 5689. (19) Tsetseris, L.; Pantelides, S. T. Appl. Phys. Lett. 2005, 87, 233109. (20) Ample, F.; Joachim, C. Surf. Sci. 2008, 602, 1563–1571. (21) Meyer zu Heringdorf, F.-J.; Reuter, M. C.; Tromp, R. M. Nature 2001, 412, 517–520. (22) Mattheus, C. C.; de Wijs, G. A.; de Groot, R. A.; Palstra, T. T. M. J. Am. Chem. Soc. 2003, 125, 6323. (23) Bellec, A.; Ample, F.; Riedel, D.; Dujardin, G.; Joachim, C. Nano Lett 2009, 9, 144–147. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865–3868. (25) In ref 18, we optimized silicon DCPs for use with B97126/631+G(d,p) and with carbon DCPs. For the present work, we reoptimized the Si DCP coefficients for use with PBE/6-31+G(d,p) following the approach we used in ref 18. The PBE method, as implemented in ref 17, is computationally more efficient, in terms of computational speed, than B971. The optimized coefficients for silicon are c1 )-0.00053 and c2 ) 0.00165. These coefficients were determined by minimizing the mean absolute deviations (MAD) of PBE/6-31+G(d,p)-DCP binding energies relative to high-level wave function data for six conformations each of the methanesilane and silane-benzene dimers. The high-level data were obtained by complete basis set extrapolated CCSD(T) calculations, which generally
J. Phys. Chem. C, Vol. 113, No. 23, 2009 9973 provide fairly accurate estimates of dispersion binding energies. The MADs of the BEs determined using PBE/6-31+G(d,p) with the optimized DCPs are 0.14 kcal/mol for methane-silane and 0.06 kcal/mol for silane-benzene. As a check, we calculated the BEs of benzene on the model H-Si(100)(2×1) that we used in ref 18. For four configurations of benzene on H-Si(100)-(2×1), PBE/6-31+G(d,p)-DCP predicted BEs that are 0.2-0.3 kcal/mol (4.3-5.2%) lower than the B971/6-31+G(d,p)-DCP values. This minor difference in calculated BEs was deemed to be a worthwhile tradeoff for the high speed of PBE over B971. Additional details are provided in the Supporting Information. (26) Hamprecht, F. A.; Cohen, A. J.; Tozer, D. J.; Handy, N. C. J. Chem. Phys. 1998, 109, 6264–6271. (27) Our calculated data, plotted in Figure S2 of the Supporting Information, indicate that polyacene binding to H-Si(100)-2×1 increases monotonically as a function of the number of rings in the molecule. (28) (a) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558–561. (b) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251–14269. (c) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15–50. (d) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169–11186. (e) Neugebauer, J.; Scheffler, M. Phys. ReV. B 1992, 46, 16067–16080. (29) One Reviewer correctly pointed out that previous experimental work showed that tetracene molecules in monolayers interact with the surface in an “edge-on” fashion rather than lying flat on the surface as in Figure 1a.30 We calculated that such an interaction involving a long edge of a single pentacene results in 6.8 kcal/mol of dispersion binding. However, such an edge-on arrangement allows pentacene molecules to π-stack with each other, which is favorable by ∼15.6 kcal/mol according to our calculations. Taking into account that a molecule laying flat on the surface occupies more surface area than does an edge-on molecule, it is clear that in the limit of full monolayer coverage, the edge-on orientation is preferred. (30) See, for example: Tersigni, A.; Shi, J.; Jiang, D. T.; Qin, X. R. Phys. ReV. B 2006, 74, 205326. (31) It is most likely that the potential energy curve associated with the rotation of pentacene on the surface does not smoothly increase from the row-aligned structure to this transition-state-like structure. More likely, the energy curve displays a number of shallow minima over the range of rotation angles defined by these two structures. (32) The prime is used to denote an energetically equivalent structure to that shown in Figure 1a. (33) We performed some additional calculations to explore diffusion along the row direction for pentacene bound on one edge of a dimer row. For these calculations, the structure shown in Figure 1a was translated along the dimer row in increments representing 1/10 of the dimer-dimer separation (calculated to be 3.86 Å). These calculations indicate that the barrier height for diffusion along the dimer row is 1.8 kcal/mol. (34) Similar calculations were performed in ref 18. (35) Using a very large surface consisting of 7 rows of 11 dimers each and 16 silicon layers, the dispersion energy increases to 23.6 kcal/mol. This means that the silicon surface model that we used for our calculations recovers all but ∼100 × (23.6-21.4)/23.6 ) 9.3% of the dispersion energy. (36) On the basis of a simple Arrhenius expression and using T ) 5 K, the temperature at which the STM experiments were performed in ref 18. (37) Repp, J.; Meyer, G.; Stojkoviæ, S. M.; Gourdon, A.; Joachim, C. Phys. ReV. Lett. 2005, 94, 026803. (38) Patitsas, S. N.; Lopinski, G. P.; Hul’ko, O.; Moffatt, D.; Wolkow, R. A. Surf. Sci. 2000, 457, L425-L431. (39) Pitters, J. L.; Wolkow, R. A. Nano Lett. 2006, 6, 390–397. (40) Hla, S.-W. J. Vac. Sci. Technol., B. 2005, 23, 1351–1360. (41) Ho, W. J. Chem. Phys. 2002, 117, 11033–11061. (42) Komeda, T.; Kim, Y.; Kawai, M.; Persson, N. J.; Uega, H. Science. 2002, 295, 2055–2058.
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