Article pubs.acs.org/JPCC
Exploring the Possibility of Noncovalently Surface Bound Molecular Quantum-Dot Cellular Automata: Theoretical Simulations of Deposition of Double-Cage Fluorinated Fullerenes on Ag(100) Surface Xingyong Wang, Shuang Chen, Jin Wen, and Jing Ma* School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Key Laboratory of Mesoscopic Chemistry of MOE, Nanjing University, Nanjing 210093, P. R. China S Supporting Information *
ABSTRACT: The double-cage fluorinated fullerene (C20F18(NH)2C20F18) has been suggested to be a new kind of molecular quantum-dot cellular automata (MQCA) candidate. The possibility of noncovalently binding these candidate molecules on silver substrates is explored by molecular dynamics (MD) simulations. It is demonstrated that the candidate molecules can deposit on Ag(100) surface and form ordered MQCA arrays in both head-to-tail and side-by-side styles. The side-by-side array can keep intact even at room temperature, while the head-to-tail array shows larger thermal fluctuations. In comparison with the Ag(100) surface, ordered arrays can only be observed in the side-by-side style at low temperatures on Ag(111) surface. Density functional theory (DFT) calculations of the charge redistribution of the candidate, in response to an electrostatic driver, show that the QCA function of the candidate still maintains with the introduction of the Ag surface. In addition, a simple (Coulomb) electrostatic model is proposed to simulate the dynamical signal transmission in our MQCA wire. The transmission time is affected by the wire length as well as the long-range intercellular electrostatic interactions.
1. INTRODUCTION Quantum-dot cellular automata (QCA) is a novel alternative approach for building the next-generation microelectronic elements.1−4 In QCA, binary information is encoded in the bistable charge configuration of a cell system. QCA consists of well-organized dots, whose essential feature is to localize charge, and the quantization of the dot charge leads to the bistability. The dots can be realized in a number of ways: small metallic islands connected by tunnel junctions, electrostatically formed quantum dots in semiconductor, or redox centers in a molecule.5 The Coulomb interaction between neighboring cells provides device−device coupling for information transfer with no current flow and low power dissipation.6−9 The realization of electronic device integration and room temperature operation requires the QCA cell downscale to the molecular size,6 making the design of molecular QCA (MQCA) more appealing. Lent et al. have proposed the hydrocarbon radical cation model system and carried out extensive theoretical studies on the clocking, power dissipation, and dynamic behavior for MQCA.10−14 Several candidate systems have been proposed, including mixed-valence organometallic complexes,15−24 metal cluster carboxylates,25 zwitterionic boron− allyl complex,26 and double-cage fluorinated fullerene anions.27 To realize controllable fabrication and operation of MQCA, the molecules need to be attached to a substrate, such as a semiconductor or metal surface.6,28 Fehlner and co-workers synthesized a series of mixed-valence dinuclear organometallic Ru and Fe complexes and succeeded in binding them to © 2012 American Chemical Society
Si(111) surface and forming ordered arrays via covalent bonding.18,19 Furthermore, the deposition of such mixedvalence species on Au(111) surface and formation of straight molecular lines have been achieved, and the charge localization in a single molecule has been probed using scanning tunneling microscopy (STM).29,30 However, forming MQCA wires via the deposition of candidate molecules on the substrates still remains a challenge. Fullerene systems, such as C60 molecules, can line up in directed supramolecular arrays either on metal31 or semiconductor32 surfaces or via organic templates.33−36 The doublecage fluorinated fullerene (C20F18(NH)2C20F18) has aroused great theoretical interests,37−39 and it was suggested to be a potential MQCA candidate.27 Thus, the question arises as to whether it is possible to deposit such double-cage fullerene, which resembles the C60 molecule to some extent, on metal surfaces and form ordered QCA arrays. Recent experimental31 and theoretical40 studies demonstrated that C60 molecules could aggregate in ordered arrays on Au(111)31 or Ag(111)40 surfaces. Here, we choose Ag surface as a trial substrate and try to see whether it is possible to obtain ordered arrays of the double-cage fullerene molecules. The monomer of this molecule is called M for short. Through MD simulations, it will be demonstrated that M can deposit on Received: July 12, 2012 Revised: September 22, 2012 Published: October 23, 2012 1308
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Ag(100) surface and form both head-to-tail (H−T) and side-byside (S−S) arrays (Figure 1c). The QCA behavior of the
Figure 2. (a) M/Ag38 cluster model. (b) The binding energies (Eb) of M/Ag38 and M−/Ag38 calculated by DFT and MM with different force fields. Inset: the vdW interaction between M (M−) and the Ag38 cluster.
charged M−/Ag38 cluster was also calculated, and it is comparable to the neutral one. To further understand the nature of the nonbonded interactions, we investigated the van der Waals (vdW) contribution to the interaction between M (M−) and the Ag38 cluster, as shown in the inset of Figure 2b. The parameters of the Lennard-Jones 9−6 potential function were taken from the default values in the compass and pcff force fields. It is shown from Figure 2b that the vdW interaction dominates the nonbonded interaction between the adsorbate and the substrate. The basis set superposition error (BSSE) effect was also investigated by counterpoise method46,47 for both M/Ag38 and M−/Ag38.Because of the formidable computational costs, only the points around the minimum, i.e., d = 2.4−3.1 Å, were selected for BSSE calculations. The result is shown in the Supporting Information (Figure S1). For the M/Ag38 and M−/ Ag38 models, the minimum occurs at 2.7 and 2.6 Å, respectively, close to that (2.5 Å) without BSSE corrections. It should be mentioned that, when doing the BSSE calculations, the charge for the Ag38 cluster was set to zero. This may somewhat weaken the interaction between the two components. As expected, the BSSE corrected Eb at minimum (about −18.0 kcal/mol) is smaller than those obtained without BSSE corrections, but still shows strong physical adsorptions. Since there is no covalent bond to fix M (M−) on the Ag surface, intensive thermal motions may disturb the formation of ordered structures. Hence, temperature may be an important factor in keeping ordered QCA arrays. To investigate the influence of the molecular thermal motion on the surfacesupported packing arrays, we performed MD simulations at three different temperatures, 77, 150, and 298 K, respectively. The H−T and S−S on Ag(100) surface were represented by periodic slabs of 98.0 × 40.8 × 43.2 Å3 and 89.9 × 40.8 × 43.2 Å3, respectively. The five layers of Ag atoms were fixed during
−
Figure 1. (a) QCA cells and QCA wires constructed from e @ C20F18(NH)2C20F18. (b) QCA wires built in two different arrangements, head-to-tail (H−T) and side-by-side (S−S), respectively. (c) Models for M deposited on Ag(100) surface in two packing styles.
negatively charged M− on Ag(100) surface was revealed via density functional theory (DFT) calculations using cluster models. Moreover, the signal transmission process is simulated in our MQCA system. It will be shown that the transmission time depends on both the number of cells and the long-range intercellular electrostatic interactions.
2. COMPUTATIONAL DETAILS To simulate the packing structures of the double-cage fluorinated fullerene on silver surfaces, the molecular mechanics (MM) method was adopted. The performance of MM method depends mainly on the force field selected, so we tested two kinds of force fields, compass (condensed-phase optimized molecular potentials for atomistic simulation studies) and pcff (polymer consistent force field), by comparing the MM binding energies (Eb) of the M/Ag38 cluster with the DFT results. In DFT calculation, the M06-2X41 functional was chosen with effective core potential LANL2DZ basis sets for Ag atom and the standard 6-31G(d) basis sets for the nonmetal elements. Extra diffuse basis functions were used to describe the diffuse characteristic of the excess electron located at the center of the C20F20 cage.37,42−44 All DFT calculations were performed with the Gaussian09 program package.45 As shown in Figure 2a, both MM and DFT calculations predict the adsorption height around 2.5 Å. An obvious binding between M and the Ag38 cluster was shown by both methods, implying the possibility of fixing M on Ag surface through physical adsorptions. The binding energy for the negatively 1309
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Figure 3. Snapshots of (a) H−T and (b) S−S on Ag(100) surface given in top and side views, respectively, along with the average intercage distances and the adsorption heights.
intercage distances and the adsorption heights are also given in Figure 3. The side-by-side intercage distances for both H−T (along the y axis) and S−S (along the x axis) are about 8.2 Å, and they have similar average adsorption heights (∼2.3 Å). The much longer head-to-tail intercage distance for H−T (along the x axis) of 9.7 Å makes the array packing loose. The MD simulation for the deposition of M on Ag(111) surface was also performed. The H−T and S−S arrays on Ag(111) surface were represented by periodic slabs of 100.0 × 40.4 × 44.4 Å3 and 90.0 × 40.4 × 44.4 Å3, respectively. It is shown that, only at low temperatures, ordered arrays in the sideby-side style can be observed, with the result shown in Figures S12−S15, Supporting Information. As shown in Figure 4, the array of M on Ag(111) surface is less ordered than that on Ag(100) surface. The difference between the lattice parameters of Ag(111) and Ag(100) surfaces may render M subject to different interfacial interactions. The different Ag···Ag distances in the upmost layers give rise to different deposition orientations on two different surfaces. To further understand such difference in the interfacial interactions from DFT calculations, we selected two kinds of cluster models, Ag38 and Ag34 (Figure 4), respectively, to represent the surface structures of Ag(100) and Ag(111) and to calculate the corresponding binding energies with M. These two cluster models were cut from bulk silver. As shown in the insets of Figure 4, there were 21, 12, and 5 Ag atoms, respectively, in each layer of the Ag38 cluster; while in the Ag34 cluster, there were 19, 12, and 3 Ag atoms in each layer. The DFT calculations were carried out at the M06-2X/6-31G(d)// LANL2DZ level of theory. It can be seen that the interaction between M and Ag38 cluster is much stronger by 14.0 kcal mol−1 than the binding between M and Ag34 cluster. The H−T array has a similar result (Figure S16, Supporting Information), implying the stronger adsorption of M on Ag(100) surface than on Ag(111) surface. 3.2. QCA Function. The above MD simulations for the neutral M molecules on Ag(100) surface show a possibility of making ordered MQCA wires on the Ag substrate. However, anionic M− is the working unit in a real MQCA application. Herein, we extended the simulation from the neutral M to anionic M− on Ag(100) surface. The charge arrangement of M−
the simulations. The slab contained one single array of M (M−), and the slab size is large enough in the y direction (Figure 3) to avoid interarray interactions. All MD simulations were performed in the canonical (NVT) ensemble using the compass and pcff force fields, respectively. The temperature was controlled by the Andersen thermostat.48 The equations of the motion were integrated using the velocity Verlet algorithm49 with the time step of 1 fs. The 0.5 ns MD trajectories were collected after the equilibrium stage at every 1 ps. The Discover module in the Material Studios package50 was employed to run all the MD simulations. For the analysis of the trajectories, the intercage distance was defined as the distance between the cage centers of neighboring surface molecules. The adsorption height was estimated from the distance between the cage centers and the Ag surface, minus the cage radius. These parameters were evaluated by averaging values over all the molecules on the surface and the 0.5 ns duration. The compass and pcff force fields give similar results (see Supporting Information for details). For conciseness, we only take the results from compass force field in the following discussions.
3. RESULTS AND DISCUSSION 3.1. Packing Structures on Ag Surfaces: Ag(100) vs Ag(111). MD simulations for H−T and S−S on Ag(100) surface were carried out at three different temperatures, 77, 150, and 298 K, respectively. Ordered patterns are observed for S−S at all the three temperatures, while for H−T, the ordered arrays formed at low temperature become waved upon increasing the temperature to 298 K. In Figure 3, the selected MD snapshots at low and room temperatures for H−T and S− S show that the ordered assembly may be controlled by the M− Ag interaction and intermolecular M−M interactions. The result for 150 K is shown in Figures S3 and S6 in the Supporting Information. In S−S, the lateral intermolecular interaction cooperating with the top site adsorption leads to nearly perfect side-by-side arrays, but in H−T, the repulsive axial interaction (along the x direction) may become stronger when the temperature rises. When the temperature reaches a threshold value, such repulsion will be strong enough to cause a rotation in M in order to lower the energy, resulting in a damage to the ordered head-to-tail pattern. The average 1310
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Figure 5. Coulomb response of M−/Ag38 to the neighboring model driver. Both the head-to-tail and side-by-side packing styles are considered. The intercage charge difference (Δqcage) and the charge of the Ag38 cluster (qAg) are given. The red dot in the M− molecule (inset) represents the encapsulated excess electron.
Figure 4. Arrangement of M on both Ag(100) and Ag(111) surfaces (S−S style), along with the lattice parameters and binding energies (Eb in kcal mol−1) calculated at the energy minimum (cluster models, d = 2.5 Å) by DFT calculations.
the QCA response were denoted as M−−0 and M−−1, respectively (Figure 5). There was no driver in the M−−0 state. The intercage charge difference (Δqcage) was used to investigate the charge transfer from one cage to the other induced by the driver. The charge transfer from M− to the Ag surface (qAg) was also studied, as shown in the lower part of Figure 5. An evident intercage charge transfer is observed, showing that the charge configuration of M− can still be switched by its neighbor through Coulomb couplings, despite the interfacial charge transfer. Of course, the charge transfer from M− to the Ag surface reduces the amount of charge confined in the cage, resulting in a degradation in the QCA function of M− to some extent, compared to that in the gas phase. The further modification of the Ag(100) surface to prevent such charge transfer is desired. 3.3. Signal Transmission in MQCA Wires. When an MQCA wire is built, the signal transmission in the wire, i.e., the charge migration within each cell, needs to be investigated. An intuitive picture of charge migration in MQCA has been illustrated by several models based on ab initio calculations on the single molecule, including combining model Hamiltonian and coherence vector formalism13,14 and solving the timedependent Schrödinger equation with one-electron Hamiltonian.52,53 Similar to the dynamic treatments for Creutz−Taube complexes,52,53 herein we also studied the time-evolution of Mulliken charges of M− on the basis of unrestricted Hartree− Fock (UHF) wave functions with the minimum basis sets. The computational details are given in the Supporting Information. The dynamic behavior of M− upon the switch by a negative input charge (−0.1 e, locating 30 Å away from the cage center) is shown in Figure 6, from which one can find that the time used to complete the intercage signal transmission, tst, is about 2.5 fs in a half-cell. The time-evolution of the charge of upper cage, q(up_cage), bridge unit, q(bridge), and down cage, q(down_cage) reveal a period of about 12 fs, when the charges turn back to their initial values after signal transmission. After
was set in the way shown in Figure 1b (S−S). The partial charge of M− was taken from the natural bond orbital (NBO) charge obtained by DFT calculations in the gas phase. Although the interfacial polarization of the Ag surface can be treated in some model systems,51 this effect was ignored in the present work for simplification. The simulation result for the M−/ Ag(100) system is similar to the neutral S−S condition, as shown in the Supporting Information (Figures S17−S19), implying that the encapsulated charge will not influence the packing of M on Ag(100) surface significantly, provided that the surface polarization is not too strong. The QCA function of the charged M− in the gas phase has been demonstrated in our recent work.27 Now we try to see whether it still works on Ag(100) surface. For the DFT calculations, the same M−/Ag38 cluster model (Figure 2a) was adopted to study the binding of M− on Ag(100) surface. The distance between M− and the Ag surface was set to 2.5 Å, in accordance with the adsorption height (Figure 2a). The geometry of M− was taken as the same as that obtained previously.27 The Coulomb coupling between the neighboring molecules was investigated by checking the response of M− to a model driver, which was composed of a group of background point charges. These charges were set to be the same as the NBO partial charges of M−. The negatively charged driver simulates the electrostatic environment exerted on M− generated by a neighboring molecule. Since the intercage charge transfer in M− only involves tiny geometrical changes, only single-point energy calculations in the presence of background point charges were carried out to evaluate the QCA property of M−/Ag38 and no geometry optimizations were performed. Both the head-to-tail and side-by-side coupling modes were examined. The intermolecular distances were set in accordance with the above-mentioned MD simulation results at 77 K (Figures 3 and 5). The two states of M−/Ag38 before and after 1311
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Figure 6. (a) Computational model and (b) time-evolution of Mulliken charges of different parts of M− calculated at the UHF/STO3G level.
Figure 7. (a) Coulomb model used in MD simulation of charge migration along an MQCA wire, where the red dots denote point charges. (b) Trajectory of the charges for the 4-cell wire measured by their displacements along the y-axis (y-displacement). Inset: numbering of the charges along the transmission path.
12 fs, the next oscillation period starts, which is almost identical to the picture of the first cycle shown in Figure 6b. However, the high computational costs of ab initio electronic structure calculations prohibit their further applications to the simulation of signal transmission in a MQCA wire composed of tens or hundreds of cells. Since the charge transfer between the two cages of M− only involves negligible geometrical changes,27 herein an even more simplified model, from the viewpoint of (Coulomb) electrostatic interactions, is proposed to demonstrate the charge migration trajectories along the whole wire. As shown in Figure 7a, the point charges were used to model the encapsulated electron in M− and the intercellular couplings were also described by the Coulomb interactions between the point charges. In our MD simulations, some ghost atoms with mass of 4.0 a.m.u and with negative partial charges were taken to represent the encapsulated electron in M−. The driver was modeled by a negative charge with the fixed position (8.2 Å away from the first point charge, Figure 7a). The partial charges for the driver (qdriver) and electron in the cell (qcell) were set to −1.0 e and −0.48 e, respectively. According to our simulations, qcell cannot be too large or too small. When qcell is too large, the Coulomb repulsion between the charges is so strong that the energy barrier for the charge migration is quite high. In contrast, when qcell is too small, the Coulomb coupling between the charges is not strong enough to drive the charges to move. The charge migration was observed only when qcell was within the range of about −0.45 e to −0.50 e. A Lennard-Jones wall was also introduced to confine the motion of the charges within the cells and prevent any intercellular movement. The wall was made up of a set of neon (Ne) atoms with fixed positions, and the ghost charges were located inside this wall (Figure S20, Supporting Information). The force field parameters for the electron and wall were refitted so that the electron could only move inside the wall and mainly along the y direction. The temperature was set to 77 K, in accordance with the MD studies above for the deposition of M on Ag(100) surface. Such a low temperature also prevents violent thermal motions of the ghost charges. The MD simulations were performed in the
canonical (NVT) ensemble using pcff force field. The MD trajectories were collected at every 1 ps. The gray cage molecular backbones in Figure 7a only indicate the positions of the charges and do not explicitly appear in the simulations. In this way, we could simulate the intercage charge migration process under the inducement of the driver, i.e., the signal transmission through the wire. In order to study the length dependence of intercellular charge migration, we investigated several MQCA wires, composed of 2, 4, and 8 cells, respectively. As exemplified by the trajectory of the charges in a 4-cell wire (Figure 7b), a domino style charge migration was observed, and the signal was transmitted step by step (see Supporting Information for details about the MD simulations). The tst values for the three wires with increasing lengths were about 0.15, 0.4, and 1.5 ns, respectively. The transmission time does not increase linearly with the increasing of the number of cells, indicating that the long-range intercellular electrostatic interactions may somewhat hinder the signal transmission. In a real MQCA wire, the electrostatic coupling between cells comes mainly from molecular dipolar interaction, which is supposed to be more efficient in intercellular electrostatic signal transmission than the charge−charge interaction model. The coupling between the migrating charge and the backbone of MQCA is also neglected in our simplified Coulomb model. Thus, the real tst may be shorter than the predicted values.
4. CONCLUSIONS We have demonstrated through MD simulations that the double-cage fluorinated fullerenes, C20F18(NH)2C20F18, can form both head-to-tail and side-by-side style arrays on Ag(100) surface. Although the synthesis of this double-cage fluorinated fullerene system has not yet been reported, the single cage species C20F20 has already been synthesized.54 The successful connection of two C20F20 cages by suitable bridges will provide 1312
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a robust test of our predictions. The employment of proper templates on the Ag surface40 may also be useful to form ordered arrays. DFT calculations show that the introduction of Ag surface does not jeopardize the QCA function of M−, indicating that, deposited on an appropriately modified Ag surface, M− may be a promising MQCA candidate in future applications. In addition, a simple Coulomb model is proposed to simulate the dynamical signal transmission in our MQCA wire. We find that the transmission time is affected by the wire length as well as the long-range intercellular electrostatic interactions. Despite the considerable difficulties in the practical fabrication of MQCA, the insight gained from the surfacesupported MQCA array may be useful to design a wide range of charge-based nanoelectronic devices.
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ASSOCIATED CONTENT
S Supporting Information *
BSSE correction to Eb (Figure S1), MD simulation results for M (M−) on Ag(100) and Ag(111) surfaces at different temperatures (Table S1, Figures S2−S19), computational method on the time-evolution of Mulliken charges of M−, MD simulations for the charge migration in 2- and 8-cell MQCA wires (Figures 20−22), and complete citation for ref 45. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Basic Research Program (No. 2011CB808604) and the National Natural Science Foundation of China (No. 20825312 and 21273102). We are grateful to the High Performance Computing Centre of Nanjing University for providing the IBM Blade cluster system.
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REFERENCES
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