NANO LETTERS
A Donor-Nanotube Paradigm for Nonlinear Optical Materials
2008 Vol. 8, No. 9 2814-2818
Dequan Xiao,†,‡ Felipe A. Bulat,†,‡ Weitao Yang,*,† and David N. Beratan*,†,§ Departments of Chemistry and Biochemistry, Duke UniVersity, Durham, North Carolina, 27708 Received May 14, 2008; Revised Manuscript Received July 3, 2008
ABSTRACT Studies of the nonlinear electronic response of donor/acceptor substituted nanotubes suggest a behavior that is both surprising and qualitatively distinct from that in conventional conjugated organic species. We find that the carbon nanotubes serve as both electronic bridges and acceptors, leading to a donor-nanotube paradigm for the effective design of large first hyperpolarizabilities. We also find that tuning the donor orientation, relative to the nanotube, can significantly enhance the first hyperpolarizability.
Carbon nanotubes (CNTs) have been studied extensively since Iijima first observed them in 1991.1 Their unique chemical, mechanical, electronic, and optical properties have prompted studies of possible applications in virtually every scientific discipline.2-4 The usual description of CNTs as rolled-up graphene sheets explains the wide range of properties that CNTs exhibit, because of the many ways in which a two-dimensional sheet can be rolled into a nanotube. Each of these geometries is uniquely identified by the chiral vector (n,m) that describes which two points on graphene’s hexagonal lattice are brought together to form the nanotube. For example, nanotubes with an n - m value equal to a multiple of 3 are metallic, while the rest are semiconducting or insulating.2 As with electronic properties, the optical response of nanotubes, including their polarizability (R) and second hyperpolarizability (γ), has been shown to be dependent on the chiral vector (n, m).5-8 The abundance of π-electrons in CNTs could yield structures with large β values if the centrosymmetry is broken. Here, we show that endsubstituted, noncentrosymmetric nanotube segments are predicted to show large first hyperpolarizabilities, and we explore strategies to modulate β. The push-pull chromophore framework (donor-conjugated bridge-acceptor) has been a successful motif for organic nonlinear optical (NLO) materials design.9-15 CNTs are remarkable conjugated structures with abundant π-electrons, and hence they are natural candidates for conjugated bridges. Politzer et al. observed that end-substituted (6,0) carbon nanotubes are predicted to show a remarkable gradation of the molecular electrostatic potential (MEP) from * To whom correspondence should be addressed. E-mail: david.beratan@ duke.edu and
[email protected]. † Department of Chemistry. ‡ These authors contributed equally to this work. § Department of Biochemistry. 10.1021/nl801388z CCC: $40.75 Published on Web 08/12/2008
2008 American Chemical Society
one end to the other,16 in contrast to the weakly positive and very uniform potential profile displayed by unsubstituted nanotubes.17,18 The average ionization potential19 (AIP) on the molecular surface also displayed significant predicted changes along the tube. These observations suggested that a “push-pull” nanotube framework could lead to large β values, and a three-unit-cell NH2-nanotube-NO2 system showed a computed β value 9 times larger than that for paranitroaniline.16 To the best of our knowledge, there have not been further studies of related structures. Indeed, short substituted nanotubes are likely challenging to access experimentally. Recent experimental reports of short nanotube segments with well-characterized structure20,21 and dissymmetric functionalization,22 as well as the general richness of known nanotube chemistry,23,24 could pave the way for developments in NLO nanotube materials. In terms of molecular design, we will show that structures with large first hyperpolarizabilities can be designed within a framework of substituent effects described here. We examine β values of end-substituted SWNTs, considering two specific structural aspects: (i) the influence of placing electron-withdrawing or electron-donating substituents at the nanotube ends, and (ii) the influence of the substituents’ orientation, with respect to the tube. We also briefly consider the nanotube length. We find that CNTs may act as both conjugated couplers and as acceptors, making the donor-CNT motif an effective framework to establish a large NLO response. This motif is unusual from the perspective of the traditional push-pull “donor-bridge-acceptor” organic NLO paradigm. Interestingly, we also find that, as a consequence of the tube’s curvature, optimal β values appear at rather large tilt angles between the substituent and the tube’s surface. We briefly address the possibility of “clamping” two substituents using aliphatic tethers to modulate the
Table 1. Computed Static Hyperpolarizability Values of End Substituted CNTs (Partially Optimized Geometries)
Figure 1. HOMO and LUMO of end-substituted carbon nanotubes: (a) NT(6,0)-NH2 (NH2 substituent on the right end), (b) NO2-NT(6,0) (NO2 substituent on the left end), and (c) NO2NT(6,0)-NH2 (NH2 and NO2 substituents on the right and left ends, respectively).
tilt angle and maximize β. Nonresonant first-hyperpolarizability values of at least 10662 × 10-30 esu are predicted to be accessible using this donor-CNT framework with optimal substituent orientation. We shall be mainly interested in the static first hyperpolarizability along the molecular dipole moment direction, βµ )
β·µ ) |µ|
∑ βµ ∑ µ
k k
k
2
k
(1)
k
where βk ) (1/3)∑l(βkll + βlkl + βllk) and µk is the dipole moment in the kth direction. The calculations were performed for fully optimized geometries as well as for partially optimized geometries (where only the appended substituents and the capping hydrogens were allowed to relax). All of the calculations were performed using the Gaussian 03 program.25 Geometry optimizations were performed at the B3LYP/STO-3G level,26,27 and the hyperpolarizabilities were computed at the HF/6-31G* level. Density functional theory (DFT) was not used for the hyperpolarizabilities, because of its well-known deficiencies in describing the response properties of large systems.15,28,29 Effect of Donor/Acceptor Structure. The push-pull paradigm is a successful guiding principle for organic dipolar molecular NLO chromophore design. However, our tests on finite length end-substituted single-walled nanotubes (SWNTs) suggest that divergence from this paradigm may be productive, because the nanotube can serve as both polarizable bridge and acceptor. We consider a three-unit cell (6,0) carbon nanotube (72 carbon atoms) substituted with various combinations of donor and acceptor groups at opposite ends (see NT(6,0) in Figure 1). We find that when the nanotube is substituted with donor and acceptor groups at opposite ends (one NH2 and one NO2), it displays a first hyperpolarizability of approximately the same magnitude (∼300 × 10-30 esu) as when it is substituted with just an acceptor (one NO2 group). (See Table 1.) However, when the nanotube is substituted with just a donor Nano Lett., Vol. 8, No. 9, 2008
structure
βµ [× 10-30 esu]
NO2-NT(6,0) NO2-NT(6,0)-NH2 NT(6,0)-NH2 NT(6,0)-(NH2)2 NT(6,0)-[Ru(tpy)2]2+
299 330 1137 485 1206
(one NH2 group), the hyperpolarizability increases by a factor of ∼4. This trend is found for both partially and fully optimized geometries. This counter-intuitive result suggests that an end-substituted “metallic” CNT functions as both an acceptor and a bridge. Ru(II)-bis(terpyridine) ([Ru(tpy)2]2+) substituted nanotubes show a large computed β value (1206 × 10-30 esu). The [Ru(tpy)2]2+ substituent is studied here because the [Ru(tpy)2]2+ porphyrinato-zinc(II) derivatives are reported to have large nonlinear optical responses.30 To interpret these results, we performed frontier orbital analysis on NT(6,0)-NH2, NO2-NT(6,0), and NO2-NT(6,0)-NH2. Their highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) are shown in Figure 1. An electron donor is usually associated with a spatially localized HOMO, whereas an electron acceptor is associated with a spatially localized LUMO. For NT(6,0)-NH2, we find that the HOMO is localized near the NH2 group, whereas the LUMO is localized at the opposite end of the tube. Figure 1 shows that the LUMO of NO2-NT(6,0) is localized at the unsubstituted nanotube end, while the HOMO is localized on the NO2 group. Surprisingly, the NO2 group has polarized electron density from the tube, so that the NO2 acts as a donor and the tube itself is the acceptor. We also find that the HOMO of NO2-NT(6,0)-NH2 is localized near the NO2 as well. The LUMO is localized at the opposite molecular end near the NH2. The NH2 group does not alter the localization much, compared to the NO2-NT(6,0) structure. The LUMO is still localized on the terminal carbon atoms of the nanotube; the NH2 has little effect. Recent studies of the interactions between unsaturated molecules and carbon nanotubes reveal charge transfer from the covalently bonded or adsorbed π-conjugated system to the carbon nanotubes. Indeed, this charge transfer indicates that carbon nanotubes can be effective electron-transfer partners.31,32 For example, photoexcited electron transfer is observed from covalently bound phthalocyanines to the nanotube framework.33,34 Effect of the Substituent Orientation: Maximizing the NLO Response. The curvature of the nanotube’s surface, which results from the finite tube diameter, forces the sixmembered rings into a boat-like configuration, as shown in Figure 2. Consider the R-C1 bond between the tube and the substituent R, and the carbon atom across the sixmembered ring from C1 (C2). We define the tilt angle (θ) as the supplement of the R-C1-C2 angle, which serves as a measure of the substituent orientation. The tilt angle can have a large effect on the orbital overlap between the tube and the terminal substituent. The optimized geometries of endsubstituted tubes, whether the entire system or only the appended substituents were geometrically optimized, showed 2815
Figure 2. Illustration of the tilt angle θ, showing projected views of the end-substituted nanotube from the (a) top, (b) left, and (c) front viewpoints. Panel d depicts the structure of the end-substituted nanotube.
Table 2. Computed Static Hyperpolarizabilities of NT(6,0)-(NH2)2, as a Function of the Tilt Angle (θ) θ [°] 10 15 22 25 28 30 35 45
βµ [× 10-30 esu] 401 1226 9641 10662 5290 2745 751 152
that both donors and acceptors bond to the tube at an angle of ∼10°. This angle influences the π-π interactions and delocalization; therefore, we conjecture that the angle may strongly influence the first hyperpolarizability. We now evaluate the θ dependence of the hyperpolarizability of a nanotube with two amino groups at the same end (NT(6,0)(NH2)2). We choose this structure because it enables comparison with later covalently constrained donor groups (see Supporting Information). Here, we simply adjust the angle to explore its effect on the nonlinear response. First, we note that the addition of a second donor group decreases the hyperpolarizability, compared to that of the monosubstituted NT(6,0)-NH2 (see Table 1). In the optimized NT(6,0)-(NH2)2 geometry, the angle is ∼10°. The β(θ) values appear in Table 2, and the data are plotted in Figure 3. The value of βµ peaks at ∼24° and is ∼20 times larger at this angle than in the optimized geometry. The angle between π-electron units is known to tune the group interactions.38 The conjugation between moieties increases the electronic transition dipole strength, decreases the energy gap, and enhances the first hyperpolarizability, provided that asymmetry is not eliminated.11 In a related analysis of conjugated species, the Marks and Ratner groups35-37 suggested that minimizing the dihedral twist between adjacent π-conjugated moieties might enhance NLO responses. Without considering the deformation of the terminal six-membered rings, one can expect that the hyperpolarizability would be almost maximized when the linked substituent’s π-plane is aligned with the nanotube’s surface (θ ) 0°). However, we find that the maximal hyperpolarizability appears for θ ≈ 24°. This effect is a consequence of the nanotube’s curvature. For θ ≈ 25°, the 2816
Figure 3. Dependence of the hyperpolarizability on the tilt angle θ.
N-C bond is almost coplanar with the two closest C atoms. This angle leads to enhanced second-order NLO response, because the orientation strengthens the substituent-tube coupling. Frontier Orbital Analysis: A Two-State Model. We have performed frontier orbital analysis for a series of NT(6,0)-(NH2)2 structures to probe the angle effect further. The first hyperpolarizability can be linked to a frontier orbital analysis via the two-state approximation, βge ∝ ∆µge
µ2ge E2ge
,
µge ) µee - µgg
(2)
where the subscript “g” indicates the ground state and the subscript “e” indicates the charge-transfer excited state. ∆µge is the dipole moment difference, µge is the transition dipole moment, and Ege is the transition energy. A simple approximation is to represent the ground and excited states using the HOMO (H) and LUMO (L),39 respectively. The dependence of the frontier orbitals for NT(6,0)-(NH2)2 on θ is shown in Figures 4 and 5. The LUMO charge distribution shows little dependence on θ. This agrees with our expectation, because the LUMO is localized at the end of the tube opposite from where the geometry change occurs. The HOMO, however, is strongly dependent on θ. At θ ) 15°, the HOMO is localized at the tube’s end near the NH2. As the angle θ increases from 15° to 25°, the HOMO spreads
Figure 4. Schematic depictions of the LUMO for various orientations of the substituents as measured by θ: (a) 15°, (b) 22°, (c) 25°, and (d) 45°. Nano Lett., Vol. 8, No. 9, 2008
Adjusting the angle θ allows the static first hyperpolarizability to be enhanced to values as large as 10662 × 10-30 esu. The angle θ can likely be controlled using chemical modifications, such as the linking of two substituents by methylene chains. We have explored such schemes to “clamp” the substituents at larger angles with methylene tethers (see Supporting Information). The hyperpolarizability is also predicted to increase with increasing tube length for nanotubes
