J. Phys. Chem. C 2007, 111, 15653-15659
15653
Exploring the Energetic Deposition of Pentacene on Pentacene through Molecular Dynamics Simulations† Joseph E. Goose and Paulette Clancy* School of Chemical and Biomolecular Engineering, Cornell UniVersity, Ithaca, New York 14853 ReceiVed: May 28, 2007; In Final Form: August 7, 2007
We use molecular dynamics simulations to explore in detail the factors affecting the behavior of an incident pentacene molecule colliding with the pentacene (010) step edge. We examine the effect of molecular orientation in conjunction with incident kinetic energy (Ei) and angle (θi) of the incoming molecule and proximity of the collision of the incoming molecule to the step edge in determining the relative contributions of fundamental mechanisms such as insertion, ejection, and interlayer transport. We find that to maximize 2D growth through experimentally controllable parameters, Ei and θi, the molecular orientation within the beam must be controlled. For θi ) 0°, when the momentum of the incident molecule is aligned along the long axis of the molecule, downward interlayer transport of the incident molecule is dominant for all hyperthermal energies. When the molecular orientation is random, higher energies must be employed to achieve the same degree of downward interlayer transport. For nonzero values of θi, the mechanism for 2D growth moves away from direct insertions, thus reducing the bias on molecular orientation.
1. Introduction Pentacene is the subject of intense current scrutiny for research into organic semiconductors because of its relatively low cost and electrical properties rivaling those of amorphous silicon.1,2 Pentacene is of potential use in devices used to create solar cells and in flexible display technologies. However, the production of devices exhibiting single-crystal electrical properties has proven challenging. The deposition of small organic molecules is notoriously sensitive to many variables such as deposition rate,3 temperature,4,5 and the nature of the substrate.6 There is considerable interest in controlling the growth modes of pentacene7,8 because of its tendency to form undesirable 3D structures that adversely affect device performance. A number of approaches have been utilized to increase the molecular ordering within the film and promote 2D morphologies such as postfabrication annealing9,10 or exploration of soluble derivatives11,12 for use in spin coating. However, one of the most successful methods has been to deposit molecules hyperthermally by accelerating the incident molecules, using an inert carrier gas, to kinetic energies of the order of a few electronvolts. This technique has been used extensively on atomic/ionic substances, such as copper13 and silicon,14 and over a large range of incident energies on the order of 100 eV, but only recently for organic molecules.15 When considering the variables involved in hyperthermal deposition, the geometry of the pentacene molecule provides a rich phase space, immediately bringing orientational and rotational aspects into the equation. The molecular-level processes that define the final morphology of the film are still little understood, but local annealing, direct insertions and increased molecular mobility are thought to play a role. Casalis et al.16 attributed the hyperthermal growth of better-quality films pentacene films on Ag(111) at low substrate temperatures (200 K) to the local annealing triggered by the †
Part of the “Keith E. Gubbins Festschrift”. * Corresponding author. Telephone: 1-607-255-6331. Fax:1-607-2559166. E-mail: pqc1@cornell. edu.
collision of the incident molecule with the surface and observed a decreasing quality of film as the substrate temperature was increased. Killampalli et al.17,18 studied the nucleation of pentacene on inert silicon dioxide-based substrates and postulated the existence of insertion events or an increased interlayer transport efficiency at higher energies. They found a critical nucleus size of 4 molecules. The same system was also studied by Wu et al.19 who found a smaller critical nucleus size of 2-3 molecules depending on the incident energy. They state that quite different growth modes can be achieved using a muchreduced deposition rate. They attributed the 2D structure observed in the submonolayer film to the increased diffusive length of a high-energy incident molecule landing on the second layer, enabling it to retain enough kinetic energy to overcome a Ehrlich Schwoebel barrier at the step edge and join the submonolayer. (The existence of a Schwoebel barrier for pentacene steps and its magnitude are unknown.) Toccoli et al.20 characterized field-effect transistors fabricated from hyperthermally deposited films on silicon dioxide and found an linear increase of field-effect mobilities with incident energies up to 6.5 eV and an improved film quality. Despite this considerable experimental scrutiny, a clear picture of the molecular processes that are thought to govern the observed rich variety of behavior remains elusive. This situation provides some impetus for a computational approach that can tease apart the various processes at play in a more controlled manner than is possible experimentally. Modeling energetic beam deposition and growth in a molecular simulation offers insight that is difficult, if not impossible, to obtain experimentally and is the focus of this paper. Jacobsen et al.21 developed a computational approach to model the energetic beam deposition of Cu on Cu by incorporating molecular dynamics simulations (for the collision) into a kinetic Monte Carlo framework (describing the diffusion events). Unfortunately, its computational complexity limited it, in practice, to the deposition of only 1-2 layers of growth of atomic species. For small organic molecules, the additional
10.1021/jp074124a CCC: $37.00 © 2007 American Chemical Society Published on Web 09/21/2007
15654 J. Phys. Chem. C, Vol. 111, No. 43, 2007 complications arising from the size and anisotropy of the molecules render this method computationally prohibitive. The local effects of the collision are typically on the order of picoseconds, whereas thermal diffusion is a continuous process occurring over the lifetime of the film. In effect, deposition events are instantaneously altering the initial configuration for which longerterm processes are taking place, but not altering their intrinsic rates due to rapid thermal equilibration. Here we examine only the local effects of the collision specific to hyperthermal deposition and leave the kinetics of the longerterm processes, inherent to all growth modes, for a separate study. The rotational and vibrational properties of organic molecules in a hyperthermal beam is of current interest to experimentalists. The supersonic expansion of a mixture of benzene molecules and a helium carrier has been shown to produce a rotationally relaxed “frisbee-like” flight of the benzene molecules under certain conditions,22 yet how these orientational factors affect the collision is unknown. Very recently, we compared experimentally measured sticking probabilities of pentacene on pentacene to those generated from a simulated system of pentacene deposition events on pentacene using molecular dynamics.23 We found that both estimates of the sticking coefficient were very similar in value. However, in that study, no attention was paid to the orientation of the molecule as it hits the surface. In this study, we investigate the role of molecular orientation when combined with varying incident energies (Ei) and angles (θi). To investigate the suggestion that fragmentation of pentacene could play a role at higher incident energies, we have complemented our MD studies with ab initio calculations to estimate the strain imposed on molecules within the system and confirm that we are not operating within a bondbreaking regime.
Goose et al.
Figure 1. Schematic of the simulated system. Bottom layer fixed in the bulk phase with all other molecules free to move. All collisions occur within the “impact zone”. Periodic boundary conditions are imposed in the x-y plane and are “infinite” in the z direction.
2. Methodology We used the nonreactive empirical MM3 potential24-26 to model the collision of pentacene molecules in the proximity of a pentacene (010) step edge using molecular dynamics. The time evolution of the system is governed by the Beeman algorithm using the TINKER software package. Each simulation was run for 10 ps; this time frame was generally found to be sufficient for the molecular collision to occur and the system to thermalize. Longer runs were made in the rarer cases where thermalization required more time. The MM3 potential was used because it is known to model organic molecules accurately, including pentacene27 in both crystalline and gaseous forms and also has a large degree of transferability. Intermolecular interactions in the MM3 model consist of dipole-dipole and van der Waals (vdW) forces, and constraints for the internal structure of the molecules are applied using “mechanical” terms such as bond stretching and bending, torsional, and out-of-plane bending contributions. A recent development in the MM3 potential included a Mo¨llerPlesset second-order self-consistent field correction for conjugated π systems (resulting in a slightly larger equilibrium Cd C bond length). In practice, the computational penalty of this correction has limited its use to systems containing 50 atoms or less. The π correction has little effect on the intermolecular interactions (the only intermolecular interactions implemented in the potential are vdW and dipole-dipole interactions), and no noticeable difference was observed in the outcome because of its inclusion in test collisions. Verlaak et al.27 developed a parametrization that works well for relaxed molecular crystals but is untested for dynamic situations. We have also compared the MM3 potential to ab initio methods for intermolecular
Figure 2. Kinetic/potential energy and temperature evolution for a typical 10 ps, Ei ) 10 eV simulation.
interactions of acenes (members of the same homologous series as pentacene). MM3 was found to predict energies similar to the much more computationally expensive MP2/6-31g(d) but orders of magnitude faster. The cohesive energy of the crystal (1.3 eV) and surface energies predicted by Northrup et al.28 using DFT methods were found to match to within a few percent results with the MM3 potential. The system shown in Figure 1 involved 6948 atoms, consisting of 121 molecules that were free to move under the influence of the intermolecular forces and a bottom layer of 72 molecules (6 × 6 unit cells) fixed in pentacene’s “bulk phase”. The system was thermalized at 300 K for 100 ps, except for the incident molecule which was relaxed to 0 K. All collisions between the single incident molecule and the surface were performed in the NVE ensemble to avoid any complications due to the velocity corrections used to scale the temperature to a desired value. This approach was validated through our observations that the incident energy dissipated rapidly among the internal energy of the molecules and not raise the system temperature more than 5 K, even transiently (Figure 2). The (010) orientation of the step edge was chosen for these studies because it has been predicted by DFT and force-field methods to be relatively stable,27-29 and reinforced by experimental evidence pointing toward its prevalence during the growth of
Energetic Deposition of Pentacene
Figure 3. Collision points generated within the impact zone (as illustrated in Figure 1) for collisions of vertically oriented molecules with the surface.
thin films of crystalline pentacene.29 In this work, the lattice parameters (a, b, and c) were 6.06 Å, 7.9 Å, and unrestricted, meaning that the (010) step edge was parallel to the short lattice parameter in the x-y plane. To justify freezing the bottom layer and thus creating a large temperature gradient in the system, pairs of simulations were examined where, in one case, the bottom layer was free to move and, in the other, fixed. A comparison of these two cases led to no significant difference in the general behavior of system (allowing for deterministic differences because of the different degrees of freedom). The distance between collision point and the plane of the fixed atoms was approximately 30 Å, which was enough to allow an efficient dissipation of the incident kinetic energy to other molecules in the system through lateral interactions. The bottom layer, when allowed to move, was found to interact very weakly with the layer above and maintained its lateral integrity throughout, resisting any great deformation in the x-y plane. This was due to the strong intralayer bonding relative to the interlayer bonding, as predicted by surface energy calculations.29 Single molecules in the bottom layer were displaced vertically from their neighbors by no more than 2 Å. 3. Results and Discussion Vertical Orientation Collisions with Velocity Normal to the Surface (θi ) 0°). The collisions of a vertically oriented molecule (as in Figure 1) were studied for 25 randomly generated collision points (Figure 3) within the target zone. At each point, five incident kinetic energies (Ei ) thermal, 1, 2, 5, and 10 eV) were supplied to the molecule directed at the surface. The final destinations of the incident molecules were recorded and are shown in Figure 4a as a function of Ei. A clear difference in behavior was noticed between the thermal molecules that preferred to dock on top of the step and hyperthermal molecules where the energetics made other destinations more likely. At hyperthermal energies, fewer than 1 in 10 molecules are left on top of the step because of transfer of molecules downward, or molecules rebounding (i.e, leaving the system through desorption). In cases where the molecule did end up in the first layer (the layer constituting the step), the vast majority of such instances occurred through a direct insertion mechanism, leading to interstitial molecule formation. Only for collisions directly on the step edge were molecules observed to fall off the step and join the layer below by overcoming the Ehrlich Schwoebel barrier.
J. Phys. Chem. C, Vol. 111, No. 43, 2007 15655 In contrast, at high energies such as Ei ) 10 eV, a significant proportion of the molecules became inserted into the second layer by “channeling” through the first layer. This occurred increasingly frequently at distances further from the step edge as the molecules in the vicinity of the collision point were more constrained by the presence of their neighbors and, consequentially, the incident molecule found it harder to move laterally. The maximum frequency of incident molecules leaving the system, a contributing factor to the experimentally measurable sticking factor, occurred at Ei ) 1 eV. The reasons for this are not obvious from Figure 4a until the exact mechanisms of ejection are examined. At Ei ) thermal, 1 and 2 eV, all incident molecules that were ejected from the system did so as a result of rebounding off the top (001) surface of the step, more than 5 Å from the step edge itself. The further from the step edge at which the collisions occurred, the more stable and therefore the more resistant the surface with respect to penetration. In this work, a “penetration” of the surface is said to occur when the center of mass of the incoming molecule passes through the (001) surface of the step. None of the molecules had sufficient energy to penetrate the molecular crystal and simply rebounded out of the system. At Ei ) 5 and 10 eV, all of the incident molecules that were subsequently ejected did manage to penetrate the surface. The molecules were then rejected by the molecules in the molecular crystal by rebounding off the layer below and being channeled back up through the crystal structure (essentially “bouncing” off the “mattress” provided by the fixed bottom layer). Random Orientation Collisions, Velocity Normal to Surface (θi ) 0°). We froze the atomic vibrations and rotational energies of the molecule and altered the orientation of the molecule as it hit the molecular surface. The collisions were carried out on the same impact zone as before but at just three collision points (a) on the step edge, (b) 5 Å from the step edge, and (c) 11 Å from the step edge. The random orientation of the molecule combined with its large long axis (approximately 14 Å) ensured that the actual point of contact of the molecule with the surface varied even though the center of mass collision trajectories remained the same. By averaging data over the three collision points, we were able to compare directly to the vertical orientation results. Figure 5 shows a quite different dependence on Ei to the vertically oriented case for the destination of the incident molecule. There is a smoother, more gradual transition across energies from the thermal case where, again, almost all molecules remain on top of the step, to the high-energy collisions where molecules are ejected from the system or are incorporated into the existing crystal structure by insertion. For Ei ) 1 eV collisions, in contrast to that for vertically aligned molecules where ejections were a disproportionately high occurrence, the random orientations reduce the number of ejections at 1 eV to fit within the general trend of an increase of ejections with increasing Ei. The angles φ and φ categorize the orientation of the molecule: φ measures the angle from verticality; thus, φ ) 0° represents a vertical molecule. φ is the angle that the molecular plane forms with the surface normal, and φ ) 90° represents a molecule lying parallel to the surface. In Figure 6, we plot the occurrence of specific “events” for all collisions at “point c”, 11 Å from the step edge and for all collisions at “point a”, on the step edge, as a function of orientation. The situation was far more varied for collisions 11 Å from the step edge (the lefthand subfigures). Figure 6a shows that all of the molecules that were able to penetrate the surface occurred where Ei ) 2 eV or above and relatively vertical (φ e 30°) in orientation or, were
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Figure 4. Destination of vertically oriented incident molecules shown in part a as a histogram for the various incident energies studied; the schematic in part b illustrates possible molecular destinations.
Figure 5. (a) Destination of randomly oriented incident molecules as a histogram for different incident energies. (b) Illustration of the three initial positions chosen for the collisions as a function of orientation. The center of mass is (a) on the step edge, (b) 5 Å, and (c) 11 Å from the step edge. The molecules are shown in the vertical position parallel to the step for clarity, 25 random orientations sharing the same center of mass are generated for each case.
displaying a leading edge to the surface (φ e 20°). As the molecules strayed from a vertical orientation, greater incident kinetic energy was needed to penetrate the surface. Figure 6c shows a concentration of vertically oriented (φ e 20°), Ei ) 1 eV molecules being ejected from the system. The same orientations that caused penetrations of the surface for Ei ) 2 eV molecules caused the Ei ) 1 eV molecules to rebound back out of the system. This can be attributed to the stiffness of the molecule as the momentum is carried along its vertical axis. The molecules did not topple over after hitting the surface, and therefore the attractive interactions with the surface were restricted to van der Waals forces between hydrogen atoms. (A simple analogy would be dropping a rigid object such as a pen onto a carpeted floor. When the pen is oriented at angles close to normal it bounces off with just the leading end having made contact with the carpet. If the pen is oriented further from normal, then the pen falls over during the collision and bounces back only after having had both ends touch the carpet.) If the initial collision could not burrow into the surface, then the reactive force dominates and the molecule is forced back off the surface. When the orientation is far enough from normal that the molecule can fall over during the collision, more of the molecule becomes exposed to the surface attractive forces and the chances of it sticking are increased. Figure 6e reinforces the finding that if molecules are vertically oriented (φ e 20°) only molecules of thermal energy will remain on top of the step edge leading to 3D growth.
Collisions on the step edge were dominated by molecules penetrating the step as reported by us earlier,23 a sort of downward funneling effect of the step edge.30,31 The distinction between direct insertion events and molecules falling down the step becomes unclear because of the disruption caused to the step by the arrival of the incident molecule. Figure 6b includes all incident molecules that were transported downward into the first layer and consists of nearly all incident hyperthermal energies and values of φ and φ except for thermal collisions. Figure 6d and f shows the only molecule leaving the system at Ei ) 5 eV and the prevalence of thermal molecules that remain on top of the step, respectively. There was no obvious orientational bias observed for collisions at the step edge. Random Orientation Collisions, Velocity Non-normal to the Surface (θi ) 30° and 60°). We studied the effect of molecular orientation on the fate of molecules with incident angles 30° and 60°. At these values of θi, the effect of molecular orientation was found not to be significant and θi itself was the far more dominant variable probably because of the relatively upright orientation of the pentacene molecules within the crystal structure. As described elsewhere,23 increasing θi was found to minimize the number of direct insertion events and lead to more ejections from the system by rebounding off the top surface. In this study, we noticed other rarer events, such as surface molecules being scattered by the incident molecule or being transported up or down a layer. These events did not occur
Energetic Deposition of Pentacene
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Figure 6. Comparison of molecules colliding 11 Å from the step edge (left-hand figures) and on the step edge (right-hand figures) for instances of molecules, (a and b) penetrating the (001) surface, (c and d) being ejected from the system, and (e and f) remaining on the surface, as a function of φ and φ. Cartoons represent the orientations at the respective corners of the graphs. Vertical molecules are found at the origin, horizontal molecules with a leading edge facing the surface at the bottom right and horizontal molecules with the molecular plane parallel to the surface are shown in the top right-hand corner. All collision points are marked for completeness. A successful occurrence of the event is marked by a colored circle representing the energy of the incident molecule.
frequently enough to warrant numerical study. Vacancy formation was also observed, but the step edge introduced too much disorder into the system to enable an accurate quantification of
vacancy formation occurrence. Estimation of the impact of vacancy formation on subsequent growth would best be studied in a separate study of bulk systems.
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Goose et al. insertion events were observed. The proximity of the collision to the step edge was also an important factor. A downward funneling mechanism at the step edge was observed for all hyperthermal energies with no particular molecular orientational bias. Ab initio calculations on distorted pentacene molecules extracted from the MD simulations confirmed that we are not operating in a bondbreaking regime where molecules would preferentially fragment upon impact. Acknowledgment. We acknowledge the financial support of the Cornell Center for Materials Research funded primarily by the National Science Foundation’s MRSEC Program. We also thank the Intel Corporation for the donation of computing resources used in this work. References and Notes
Figure 7. Internal energy of a single incident molecule with 10 eV incident kinetic energy, calculated with both the MM3 potential and MP2/6-31g(d), followed in time throughout its collision with a surface showing the molecular distortion that occurs
Single Molecule ab Initio Calculations. To test the internal strain on molecules, we extracted the trajectories of a number of molecules with high kinetic energy as they underwent a collision with the pentacene surface and examined the internal energy of each molecule. Every 0.1 ps for the first 2 ps, where the distortions were most evident (up to 30° out of plane bending), the isolated single point energies of the incident molecule were calculated using two methods, first the MM3 potential itself and second ab initio MP2 calculations using Gaussian 03.32 Although not a strictly fair comparison because of the energetic minima of the molecule for MP2/6-31g(d) calculations resulting in a slightly longer average bond length, the deviations from a planar molecule seemed to outweigh this. A typical collision trajectory is shown in Figure 7 where, for both methods of calculation, the maximum in energy occurred for the same highly distorted molecule around 1.2-1.3 ps. This maximum was an increase of 1.2 eV per molecule from the minimum configuration; thus, considering the covalent bond strength in the pentacene system is on the order of 5 eV, the impact energy is not enough to cause the internal fragmentation of the molecule. We hope to employ the reactive AIREBO potential33 in the future to test the limits of the system in this regard, but we are confident that collisions of 10 eV incident kinetic energy are not within the fragmentation regime for pentacene. 4. Conclusions We have demonstrated, through the use of molecular dynamics simulations, the effect of molecular orientation on the deposition event of a pentacene molecule colliding with the pentacene (010) step edge. For incident angle θi ) 0°, a vertical orientation of the molecule (φ e 20°) greatly enhanced direct insertions at all hyperthermal values of Ei. If direct insertion was not observed, then the incident molecule was ejected in preference to remaining on top of the step, hence promoting growth of 2D films. For randomly orientated molecules, a more gradual transition to 2D growth was observed with increasing Ei. A detailed characterization of the pentacene molecular beam is therefore necessary to determine which energy to deposit. Where more glancing angles of incidence (θi ) 30° and 60°) were used, the orientational bias was lost and very few direct
(1) Gundlach, D. J. 57th DeVice Research Conference Digest 1999, 1, 164. (2) Oana, D. J.; Jacob, B.; Thomas, T. M. P. Appl. Phys. Lett. 2004, 84, 3061. (3) Pratontep, S.; Brinkmann, M.; Nuesch, F.; Zuppiroli, L. Phys. ReV. B: Condens. Matter Mater. Phys. 2004, 69, 165201. (4) Kim, C.; Bang, K.; An, I.; Kang, C.; Kim, Y.; Jeon, D. Curr. Appl. Phys. 2006, 6, 925. (5) Minakata, T.; Imai, H.; Ozaki, M. J. Appl. Phys. 1992, 72, 4178. (6) Ruiz, R.; Nickel, B.; Koch, N.; Feldman, L. C.; Haglund, R. F.; Kahn, A.; Scoles, G. Phys. ReV. B 2003, 67, 125406. (7) Zorba, S.; Shapir, Y.; Gao, Y. Phys. ReV. B: Condens. Matter Mater. Phys. 2006, 74, 245410. (8) Meyer zu Heringdorf, F. J.; Reuter, M. C.; Tromp, R. M. Nature 2001, 412, 517-520. (9) Lloyd, M. T.; Mayer, A. C.; Tayi, A. S.; Bowen, A. M.; Kasen, T. G.; Herman, D. J.; Mourey, D. A.; Anthony, J. E.; Malliaras, G. G. Org. Electron. 2006, 7, 243. (10) Guo, D.; Ikeda, S.; Saiki, K.; Miyazoe, H.; Terashima, K. J. Appl. Phys. 2006, 99, 094502. (11) Park, S. K.; Kuo, C. C.; Anthony, J. E.; Jackson, T. N. Int. Electron DeVices Meet., Tech. Dig. 2005, 113. (12) Ostroverkhova, O.; Cooke, D. G.; Shcherbyna, S.; Egerton, R.; Tykwinski, R. R.; Anthony, J. E.; Hegmann, F. A. Phys. ReV. B 2005, 71, 035204. (13) Jahma, M. O.; Rusanen, M.; Karim, A.; Koponen, I. T.; Ala-Nissila, T.; Rahman, T. S. J. Chem. Phys. 2005, 112, 6472. (14) Rabalais, J. W.; Al-Bayati, A. H.; Boyd, K. J.; Marton, D.; Kulik, J.; Chu, W. K. Phys. ReV. B 1996, 53, 781. (15) Iannotta, S.; Toccoli, T. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 2501. (16) Casalis, L.; Danisman, M. F.; Nickel, B.; Bracco, G.; Toccoli, T.; Iannotta, S.; Scoles, G. Phys. ReV. Lett. 2003, 90, 206101. (17) Killampalli, A. S.; Schroeder, T. W.; Engstrom, J. R. Appl. Phys. Lett. 2005, 87, 033110. (18) Killampalli, A. S.; Engstrom, J. R. Appl. Phys. Lett. 2006, 88, 143125. (19) Wu, Y.; Toccoli, T.; Koch, N.; Iacob, E.; Pallaoro, A.; Rudolf, P.; Iannotta, S. Phys. ReV. Lett. 2007, 98, 076601. (20) Toccoli, T.; Pallaoro, A.; Coppede, N.; Iannotta, S.; Angelis, F. D.; Mariucci, L.; Fortunato, G. Appl. Phys. Lett. 2006, 88, 132106. (21) Jacobsen, J.; Cooper, B. H.; Sethna, J. P. Phys. ReV. B 1998, 58, 15847. (22) Pirani, F.; Cappelletti, D.; Bartolomei, M.; Aquilanti, V.; Scotoni, M.; Vescovi, M.; Ascenzi, D.; Bassi, D. Phys. ReV. Lett. 2001, 86, 5035. (23) Goose, J. E.; Killampalli, A.; Engstrom, J. R.; Clancy, P. In press. (24) Allinger, N. L.; Yuh, Y. H.; Lii, J. H. J. Am. Chem. Soc. 1989, 111, 8551. (25) Lii, J. H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 8566. (26) Lii, J. H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 8576. (27) Verlaak, S.; Steudel, S.; Heremans, P.; Janssen, D.; Deleuze, M. S. Phys. ReV. B 2003, 68, 195409. (28) Northrup, J. E.; Tiago, M. L.; Louie, S. G. Phys. ReV. B 2002, 66, 121404. (29) Drummy, L.; Miska, P.; Alberts, D.; Lee, N.; Martin, D. J. Phys. Chem. B 2006, 110, 6066. (30) Evans, J. W.; Sanders, D. E.; Thiel, P. A.; DePristo, A. E. Phys. ReV. B 1990, 41, 5410. (31) Li, M.; Evans, J. W. Phys. ReV. Lett. 2005, 95, 256101. (32) 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.;
Energetic Deposition of Pentacene 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.
J. Phys. Chem. C, Vol. 111, No. 43, 2007 15659 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 C.02; Gaussian, Inc.: Wallingford, CT, 2004. (33) Stuart, S. J.; Tutein, A. B.; Harrison, J. A. J. Chem. Phys. 2000, 112, 6472.
