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J. Phys. Chem. C 2007, 111, 18912-18916
A New Class of Supramolecular Wires Bobby G. Sumpter,*,† Vincent Meunier,† Edward F. Valeev,†,‡ Andrew J. Lampkins,§ Hengfeng Li,§ and Ronald K. Castellano*,§ Computer Science and Mathematics DiVision and Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, and Department of Chemistry, P.O. Box 117200, UniVersity of Florida, GainesVille, Florida 32611 ReceiVed: August 7, 2007; In Final Form: October 17, 2007
We present an unconventional approach to the development of 1-D supramolecular wires based on the selfassembly of donor-σ-acceptor molecules. The concept is demonstrated using one class of these systems, 1-aza-adamantanetriones (AATs), that are well-characterized in terms of their solution/solid-state self-assembly and chemical manipulation. Our results show that accompanying spontaneous organization of the molecules into 1-D periodic arrays is delocalization of the frontier molecular orbitals through the saturated tricyclic cores of the monomers that span the entire system. The electronic band structure for the 1-D wire reveals significant dispersion and can be tuned from the insulating regime to the semiconducting regime by suitable chemical functionalization of the core. The theoretical understanding of this new class of supramolecular structures sets the stage for the tailored design of novel functional materials that are an alternative to those comprised of traditional π-conjugated systems.
Introduction The suitability of organic molecules for practical application in optoelectronics derives not only from their size, photophysical, and electronic properties, but also from their ability to spontaneously assemble into ordered structures.1-3 π-Conjugated systems are at the forefront of the organic electronics field due, in part, to their synthetic accessibility, tunable electronic properties with substitution and conjugation length, and predictable self-assembly into nanoscale architectures through π-stacking (often together with other noncovalent interactions).3-12 Molecules containing a donor and an acceptor group separated by an insulating spacer (donor-σ-acceptor molecules), while actively studied for use in single-molecule electronic devices since the pioneering theoretical work of Aviram and Ratner,13-15 have been largely unexplored with respect to their self-assembly and transport properties through supramolecular architectures. Herein we describe a new approach to constructing 1-D wires that have easily tunable electronic and physical properties that has emerged from experimental and theoretical studies of donor-σ-acceptor molecules. The model compounds are 1-aza-adamantanetriones (AATs, Figure 1), donor-σ-acceptor molecules that are amenable to diverse synthetic functionalization and boast through-(σ)bond interactions that have discernible chemical and structural consequences.16-21 The functional core of the molecules features a properly configured22,23 donor nitrogen atom tethered to three carbonyl acceptors by way of a saturated two-carbon spacer. Molecules like 1 and 2 (Figure 1) have been shown to aggressively self-assemble in solution and display long-range * Corresponding authors. E-mail:
[email protected] (B.G.S.);
[email protected] (R.K.C.). † Oak Ridge National Laboratory. ‡ Virginia Tech. § University of Florida.
Figure 1. Top views of the optimized structures determined for tribenzyl 1-aza-adamantanetrione 1 and triamide 1-aza-adamantanetrione 2 using DFT(LDA)/cc-pVDZ (Ph ) phenyl). Only one enantiomer of the C3-symmetric conformer is shown in each case. Hydrogen bonds are shown as black dashed lines. Atom color code: C ) gray, H ) white, N ) blue, O ) red.
order in the solid state.16,17 Recent computational work by several of the authors has identified a plausible mechanism and the driving forces (e.g., π-stacking and dipolar interactions) for their organization into 1-D periodic superstructures.24 The motif qualitatively agrees with the molecules’ organization into fibers (shown by electron microscopic analysis) and gels;16,17 more quantitative agreement has been found through comparison of experimental and simulated X-ray powder diffraction data.24 Here we report the unexpected and unprecedented electronic band structure that accompanies self-assembly of the AATs into periodic 1-D arrays. Our results show that the band gap can be tuned from the insulating to the semiconducting regime by modest structural modifications of the constituent monomers. The tunability of the electronic structure can be rationalized in terms of changes in the monomer properties and the nearestneighbor transfer characteristics. Continued recognition that electronic and transport properties akin to traditional π-conjugated materials may be accessible to alternative organic
10.1021/jp076329p CCC: $37.00 © 2007 American Chemical Society Published on Web 12/06/2007
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architectures, particularly those that spontaneously organize, should encourage new approaches to functional materials design. Computational Details All-electron quantum many-body perturbation theory (MBPT) and density functional theory (DFT) calculations were performed using the NWChem25 package. Charge-transfer parameters were evaluated with the MPQC package26 following the methodology of Valeev et al.27 For the DFT calculations, both the local density (LDA) and generalized gradient approximations (GGA) were employed. A number of different atom-centered, contracted Gaussian basis sets, including the Pople split-valence basis sets: 3-21G,28 6-31G*,29 6-311G*,29 and Dunning’s correlation consistent basis sets, cc-pVXZ30,31 and aug-cc-pVDZ,32 were used during the calculation of the self-consistent solution. The initial starting geometries for tribenzyl 1-aza-adamantanetrione 1 (61 atoms; 238 electrons) and triamide 1-azaadamantanetrione 2 (73 atoms; 304 electrons) were obtained by using DFT(LDA) with the modest basis set 3-21G in which the energetics of the conformational space defined by the substituents on the periphery of the core (all-up (toward the core), all-down (away from the core), etc.) could be efficiently examined. Once the lowest energy conformation was determined (C3-symmetric, all substituents directed upward, as shown in Figure 1), full geometry optimization was performed using the larger cc-pVDZ, cc-pVTZ, and aug-cc-pVDZ basis sets. The final optimized molecular geometry (total energy was converged to 10-7 Hartree and the rms gradient to 10-4) was used to generate a 14 × 14 × 36 Å3 box of four molecules (all of the same handedness) with random orientation and position. Ab initio (DFT/LDA/3-21G) and semiempirical molecular dynamics (AM133) were used to examine the early stages of the multimolecule self-assembly at low temperatures for up to 5 ps in the gas phase. From these simulations a dimer was extracted and subjected to full geometry optimization using DFT(LDA) with the cc-pVDZ basis set to obtain the final dimer structure and its electronic properties for comparison to the singlemolecule case. The transfer integrals were evaluated at the B3LYP/6-31+G* level using the optimized dimer geometries. Gas-phase dimer-binding energies were computed by E(binding) ) E(dimer) - E(BSSE) - E(deform) where E(dimer) is the energy of the optimized dimer and E(BSSE) is used to eliminate the basis-set superposition error (BSSE) by the counterpoise procedure as defined by E(BSSE) ) ΣiEi(ghost). Ei(ghost) is the energy of the monomer i at the geometry in the dimer with the dimer basis functions present. Finally, the energy is corrected for deformation energy E(deform) ) Σi(Ei(opt) Ei) where Ei(opt) is the energy of the optimized monomer and Ei is the energy of that monomer in its original geometry within the optimized dimer. The electronic structure of the 1-D periodic systems that are formed by self-assembly was examined using the Vienna ab initio simulation package (VASP),34,35 from which the electronic band structure, modulus, and lattice constants were obtained. The Kohn-Sham equations were solved using the projector augmented wave (PAW) approach36,37 within the frozen core approximation to describe the electron-core interaction and a plane-wave basis set. The 1D Brillouin zone was sampled using a string of 16 k-points, a sampling that was found to be sufficient to attain good numerical convergence. The basis was composed of plane-waves up to a 400 eV kinetic energy cutoff. In each case the total electronic self-consistent field (SCF) was converged to 10-5 eV/molecule. To explore the thermal stability of the periodic systems, we used first-principles DFT molecular
Figure 2. Molecular orbital description of the dimer of 1. (a) Total charge density isosurface for the gas-phase optimized dimer of 1 obtained from all-electron DFT(LDA)/cc-pVDZ calculations. (b) Charge density isosurface for the dimer HOMO (E ) -5.6 eV) showing delocalization over the tricyclic cores.
dynamics in the canonical ensemble, where the temperature of the ions was maintained with a Nose´-Hoover thermostat. Results and Discussion Identified earlier,24 the lowest-energy conformation for each of two recently synthesized molecules, tribenzyl 1-aza-adamantanetrione 1 and triamide 1-aza-adamantanetrione 2,16,17 are shown in Figure 1. Each is C3-symmetric and propeller-shaped (although chiral, only one enantiomer of each is shown). These low-energy structures agree exceptionally well with what has been observed experimentally, through both X-ray crystallographic analysis18 (the calculated bond lengths and angles agree to within 0.01 Å and 1.5° for the bond lengths and angles that describe the AAT core) and NMR spectroscopy (in solution and the solid state).16,17 Our calculations predict self-assembly of the monomers into stacked structures, shown for the dimer of 1 in Figure 2. How the symmetry and handedness of the molecules affect this process and the dimer stability has been previously discussed.24 The optimal molecule-molecule distance of the low-energy “homochiral” dimer (where both monomers are identical with respect to the arrangement of their peripheral substituents) at equilibrium is 5.1 Å with a carbonyl (from molecule R′)-tonitrogen (from molecule R) distance of 3.1 Å. Figure 2a shows the total charge density isosurface for the dimer which reveals overlap between the tricyclic cores of the two molecules and a nearly perfect alignment along a line through their centers. This line directly corresponds to the orientation of the dipoles, which is found to be 4 D for a single molecule (the dipole moment of the core alone is 4.7 D and is reduced by the substituents). The gas-phase binding energy (corrected for deformation and basisset superposition error) of the dimer is 0.58 eV (13 kcal mol-1), with a significant contribution from dipole-dipole interactions between the tricyclic cores. An additional contribution comes from three π-π interactions38,39 where the aromatic rings are oriented in a “distorted” parallel-displaced geometry with a ring-ring separation of R1 ) 3.5 Å and a lateral displacement from the face-to-face sandwich geometry of R2 ) 1.8 Å (see ref 39, Figure 1, for a description of the distances). Table 1 summarizes the electronic structure results obtained for both the single molecule of tribenzyl 1-aza-adamantanetrione 1 and its homochiral dimer. These data suggest that the mutual polarization causes electrons in one of the molecules (e.g., R; Figure 2a) to be energetically less bound as compared to the other molecule (e.g., R′) or to a single isolated molecule.
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TABLE 1: Electronic Properties of the Monomer and Dimer of 1a (1)2b parameter
1
molecule R
molecule R′
HOMO (eV) LUMO (eV) Egap (eV) B.E. N1s (eV)c B.E. N2s (eV)c B.E. N2p (eV)c partial charge (e)c
-5.80 -2.97 2.83 373.55 13.8 6.6 7.47
-5.62 -3.20 2.42 373.4 13.7 6.4 7.47
373.6 13.8 6.6 7.47
a See the Computational Details section. b See Figure 2 for illustration. c B.E. ) electron binding energy; values obtained from natural bond orbital (NBO) analysis.40
Notably, the energy levels in molecule R′ are nearly the same as in an isolated monomer. Therefore the net effect of such interactions in an infinite 1-D stack of molecules will be overall weaker bound valence electrons compared to the monomer and a narrowed band gap. We also evaluated HOMO-HOMO and LUMO-LUMO transfer integrals for the dimer using the approach of Valeev et al.27 Transfer integrals reflect the strength of the interaction between molecular systems and play a crucial role in both the band and hopping regimes. The LUMO-LUMO transfer integral (0.25 eV) is about 3 times larger than that of HOMO (Figure 2b), which indicates that electron conductance should be more robust than hole conductance. A more detailed examination reveals also a large integral, 0.47 eV, between the HOMO of molecule R and LUMO of R′. This suggests the propensity for R to donate electrons to R′. In addition, there is likely a low-lying excited state which corresponds to the intermolecular charge transfer in this direction. The “reverse” integral, between the HOMO of R′ and the LUMO of R, is about 3 times smaller, so there should not be any significant charge transfer in that direction (rectification). The intermolecular charge transfer from R to R′ is also more facile than the intramolecular transfer since the latter requires a σ-bond chargetransfer process. These results in total suggest that a selfassembled periodic system of 1 will have interesting chargetransport and optical properties. One of the most notable changes upon dimerization of 1 is reduction of the HOMO-LUMO gap by ∼0.4 eV, arising from a LUMO lowering of ∼0.21 eV and an increase of the HOMO by ∼0.19 eV (relative to the monomer). These energy changes parallel what is commonly found for π-conjugated molecular systems by increasing the conjugation length (delocalization of the HOMO or LUMO)41 but have yet, to our knowledge, to be described for self-assembled donor-σ-acceptor systems. Indeed, examination of the HOMO shows some delocalization (approximately 0.1 e computed from the NBO population analysis) through the tricyclic cores as can be seen in Figure 2b. Detailed analysis of the canonical orbitals shows that the HOMO-1 orbital is due to the lone pairs on the nitrogen atom of each molecule with an atom-atom bonding character of 40% nonbonding, 48% bonding, and 12% antibonding. The LUMO atom-atom bonding character consists of 10% nonbonding, 8% bonding, and 82% antibonding contributions and comes from the carbonyls on both molecules, but with larger coefficients (about 1.8 times) for molecule R′. The NBO method40 uses the one-electron density matrix to define the shape of the atomic orbitals in the molecular environment and to derive molecular bonds from the density between atoms. Since the NBOs do not diagonalize the Fock or Kohn-Sham operator, off-diagonal elements will be nonzero; second-order perturbation theory has shown that these off-diagonal elements give an energy that is
directly related to the stabilization energy due to that interaction. For a dimer of 1, a second-order perturbative analysis of the Fock matrix finds relatively large donor-acceptor interactions for the lone-pair electrons on the nitrogen of monomer R to the antibonding orbital on the carbonyls of R′. This is in agreement with the charge transfer integral analysis discussed above. Structural, mechanical, and electronic properties of the selfassembled 1-D stack were also probed with plane-wave periodic DFT calculations. As discussed in ref 24, the most stable arrangement is the eclipsed stack, characterized by the zero degree rotation from one monomer to the next, as in the dimer shown in Figure 2. Figure 3a shows the dependence of the total energy on the lattice distance and agrees very well with the value obtained from the dimer calculations, 5.1 Å, as does the binding energy of 0.8 eV (note this is for the two interactions between the periodic images, so half of this value gives the approximate dimer binding energy). From this curve an estimate of the bulk modulus can be obtained from a nonlinear leastsquares fit to a third-order Birch-Murnaghan equation of state.42,43 A modulus of 23 Gpa was determined (note the deformation is only along the fiber axis and the modulus is similar in magnitude to van der Waals solids like C6044), clearly indicating that the wire is reasonably rigid along the fiber axis. For tensile deformation we obtain a Young’s modulus of 10 Gpa (determined from the slope of the stress-strain curve). The electronic band structure of the periodic stack (Figure 3b) shows significant dispersion, in accordance with the transfer integral analysis, thereby indicating the delocalization of molecular-like states of the individual constituents of the assembly. This result strongly supports the supramolecular wire concept. The calculated band gap for the 1-D periodic structure is 2.3 eV, very similar to the 2.4 eV HOMO-LUMO gap determined for the dimer, a value already in the large-gap semiconductor regime. It is important to stress that by varying the substituents on the tricyclic core, it should be feasible to tune the electronic structure of these systems. Triamide 1-aza-adamantanetrione 2 illustrates this concept.16 The HOMO-LUMO gap for this molecule is calculated to be 1.9 eV, substantially lower than that of 1 (Table 1). The reduction in the HOMO-LUMO gap is attributed to significant lowering of the LUMO (∼0.7 eV) as compared to the tribenzyl system. Its origin appears to be the three weak hydrogen bonds between the carbonyls on the tricyclic core and the amide substituents (one intramolecular hydrogen bond per carbonyl group), as shown by the dashed lines in Figure 1. These hydrogen bonds have been identified in solution by 1H NMR and IR spectroscopies as reported in ref 16. Indeed, rotation of the amide substituents to break these hydrogen-bonding interactions increases the LUMO by 0.6 eV. The intramolecular hydrogen bonds thus appear as additional tunable elements toward the design of stable low-band-gap materials from 2. The computed binding energy determined from DFT(LDA) periodic plane-wave pseudopotential calculations (see Figure 4) for a homochiral dimer of 2, 0.35 eV, is reduced relative to 1 due primarily to decreased dipole-dipole interactions between the monomers. The dipole moment for 2 is significantly lowered, to 1.8 D, a consequence of its three amide dipoles opposing the core dipole in the lowest-energy conformation (Figure 1). The π-π contributions are also diminished due to less optimized phenyl-phenyl contacts (R1 ∼ 2.3 Å, R2 ∼ 3.9 Å).39 The band structure of the homochiral 1-D periodic wire of 2 (Figure 4b), like 1, shows dispersion, although to a lesser extent than that for 1. This is also in agreement with the smaller computed LUMO-LUMO transfer integral (0.16 eV). Most importantly,
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Figure 3. Evolution of electronic structure upon self-assembly of 1. (a) Total energy as a function of the lattice distance along the fiber axis. The minimum occurs at 5.1 Å in excellent agreement with the all-electron DFT calculations using atom-centered basis sets for a dimer. The binding energy of 0.8 eV for a unit cell is also in reasonable agreement with those calculations. (b) Electronic band structure determined from the DFT(LDA) periodic plane-wave pseudopotential calculations.
Figure 4. Evolution of electronic structure upon self-assembly of 2. (a) Total energy as a function of the lattice distance along the fiber axis. The minimum occurs at 5.5 Å for the eclipsed molecule orientation. (b) Electronic band structure determined from DFT(LDA) periodic plane-wave pseudopotential calculations.
the band gap in 2 is reduced to ∼ 1.5 eV, well within the semiconducting regime. Clearly, it should be possible to use the electronic structure calculations to rationally design a system that will form 1-D fibers with excellent electronic transport properties and good thermal and mechanical stability. For example, both the π-π interactions38,45 and hydrogen-bonding could be enhanced by adding an electron-withdrawing group to the phenyl rings and thus increasing structural stability and lowering the band gap. Electronic structure theory will also be key
to rationalizing the magnitude of the intermolecular transfer integrals and thus tuning the charge transport and optical properties. Organic electronics applications, for example, call for combination of the lower band gap of 2 with the larger LUMO-LUMO transfer integral of 1. On the other hand, understanding the optical properties begets the question of why the charge transfer integral in 1 is more than 20 times that of 2, but only half of the value found for the unsubstituted core. We are currently seeking better comprehension of the orbital origin of these effects.
18916 J. Phys. Chem. C, Vol. 111, No. 51, 2007 Conclusions Delocalized electronic structure that emerges upon the controlled self-assembly of organic molecules is highly sought for electronic, optoelectronic, and photonic devices. This study has shown that such behavior can accompany the 1-D periodic organization of properly functionalized donor-σ-acceptor molecules, scaffolds that appear alternative or at least complementary to traditional π-conjugated systems. High-level ab initio calculations show for a representative class of donor-σacceptor molecules, 1-aza-adamantanetriones (AATs), how a delocalized electronic structure emerges upon self-assembly into a 1-D wire. Key aspects of the emergent electronic structure phenomena can be rationalized from the analysis of a dimer of tribenzyl AAT 1. The intermolecular LUMO-LUMO transfer integral is large, indicating relatively facile electron transport, and in accordance with a significant band dispersion in the periodic 1-D stack. The band structure can be tuned from the insulating regime to the semiconducting regime by suitable functionalization of the core, in the case shown (for AAT 2) through introduction of peripheral amide groups. Our computational studies suggest that appropriate substitutents could further lower the molecular HOMO-LUMO gap while promoting self-assembly into 1-D arrays; it should therefore be possible to design fibers that have a band gap near the conducting regime. Also appearing as an attractive feature of donor-σ-acceptor molecule self-assembly is the potential to create polar materials through the head-to-tail alignment of monomers within individual columns. The consequence is directional charge transport, not generally associated with, for example, π-stacked aromatics. The idea that supramolecular wires can be conceived from alternative (saturated) organic architectures is likely to constitute an attractive additional route toward large-scale applications in the optoelectronics and molecular electronics fields. Acknowledgment. Research supported by the Center for Nanophase Materials Sciences (CNMS), sponsored by the Division of Scientific User Facilities, U.S. Department of Energy. The extensive computations were performed using the resources of the National Center for Computational Sciences at ORNL, sponsored by the Office of Science. E.F.V. was partially supported by the National Science Foundation CRIF Grant CHE-0443564 and by the start-up funding from Virginia Tech. R.K.C. acknowledges the University of Florida and the National Science Foundation (CHE-0548003) for financial support, and the CNMS User Program (CNMS2004-016 and CNMS2007-029) for resources. A.J.L. was supported by a University of Florida Alumni Graduate Fellowship. Supporting Information Available: The coordinates for the optimized geometries of the monomers and dimers. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Aviram, A.; Ratner, M. Molecular Electronics: Science and Technology (Annals of the New York Academy of Sciences); The New York Academy of Sciences: New York, 1998; Vol. 852. (2) Moliton, A. Optoelectronics of Molecules and Polymers; Springer: New York, 2006. (3) Adams, D. M.; Brus, L.; Chidsey, C. E. D.; Creager, S.; Creutz, C.; Kagan, C. R.; Kamat, P. V.; Lieberman, M.; Lindsay, S.; Marcus, R. A.; Metzger, R. M.; Michel-Beyerle, M. E.; Miller, J. R.; Newton, M. D.; Rolison, D. R.; Sankey, O.; Schanze, K. S.; Yardley, J.; Zhu, X. Y. J. Phys. Chem. B 2003, 107, 6668-6697. (4) Nguyen, T. Q.; Martel, R.; Avouris, P.; Bushey, M. L.; Brus, L.; Nuckolls, C. J. Am. Chem. Soc. 2004, 126, 5234-5242. (5) Hoeben, F. J. M.; Jonkheijm, P.; Meijer, E. W.; Schenning, A. P. H. J. Chem. ReV. 2005, 105, 1491-1546.
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