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Tip-Functionalization of Finite Single Walled Carbon Nanotubes and its Impact on the Ground and Excited State Electronic Structure Anurag Sharma, Brendan J. Gifford, and Svetlana V Kilina J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b00147 • Publication Date (Web): 28 Mar 2017 Downloaded from http://pubs.acs.org on March 29, 2017

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The Journal of Physical Chemistry

Tip-Functionalization of Finite Single Walled Carbon Nanotubes and its Impact on the Ground and Excited State Electronic Structure Anurag Sharma♭, Brendan J. Gifford♯, and Svetlana Kilina♯* ♭

Department of Civil and Environmental Engineering and ♯Department of Chemistry and Biochemistry, North Dakota State University, ND 58108

Abstract: We explore the effect of capping of finite (10,5) carbon nanotube (SWCNT) with various functional groups, including methylene, ether, ester, and carboxylic derivatives, having different electron withdrawing/donating properties. Using density functional theory (DFT) and time dependent DFT (TDDFT), we found that the sp2-hybridization of the bonding atom of the capping groups and the number of such groups play the predominant role in eliminating optically inactive edge-localized mid-gap states, while withdrawing/donating properties of the functional groups is less significant. Our calculations show that two sp2-groups, like methylene derivatives, combined with hydrogens is an optimal capping scheme for (10,5) SWCNT to provide the wellopened energy gap, since sp2-groups can be placed relatively far from each other to minimize the dipole moment at the edges, while preserving conjugation of the edge according to the tube chirality. Absorption spectra demonstrate negligible effects of electron donating/withdrawing groups on the lowest optical E11 band. In contrast, the change in the bond order of the capping groups significantly changes optical spectra, resulting in red-shifted and less intensive E11 band when sp3-capping substitutes two sp2-groups. Our findings can be helpful in choosing the functional groups for tuning the optoelectronic properties of SWCNTs. In addition, a complete

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understanding of the role of tube’s capping allows for using smaller computational models making computations of a wide range of phenomena in SWNTs practical.

* Corresponding author: Svetlana Kilina (Svetlana@[email protected]) Introduction Chemical functionalization of single walled carbon nanotubes (SWCNTs) via covalent attachments or non-covalent adsorption of different molecular systems have been shown to improve tube dispersion1-3 and break their bundles,4-6 resulting in improved optical properties. Additionally, such functionalization sometimes leads to interactions selective only to a specific tube chirality and therefore generates a scheme to produce purified tube samples of a specific type7-8 with well controlled optical9-10 and electronic properties11-12. In addition to promoting the solvation and dispersion, covalent functionalization with halides, alcohols, and carboxylic groups is commonly implemented as a strategy for manipulating the intrinsic electronic properties of SWCNTs and the effects of such functionalization have been widely reported.13-15 R-COO- and R-OH- functional groups are also known for their ability to form chemical bonds to other reagents, such as metal-organic complexes,16 porphyrins,17,18 polymer chains,19-21 proteins,22 and DNA23-25 components making these functionalized SWCNTs promising candidates for applications in sensor devices, antibiotics, drug delivery systems, and other applications.5, 26-28 Covalent functionalization occurs at the sidewalls and/or open ends or tips of the SWCNTs through chemical synthesis, oxidation and acid treatments.29-31 However, due to the large strain of sp3-hybridized groups introduced in to the nanotube lattice and the corresponding low chemical reactivity of sp2-hybridized carbons in the sidewalls, SWCNTs are more


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susceptible of being functionalized on the tips or edges.32 Unfortunately, a precise control over positions and concentrations of functional groups at the nanotube surface is a challenge.29, 33 A great deal of information on position and bonding modes of functional groups at SWCNTs can be obtained from experimental methods including Transmission Electron Microscopy (TEM),34,35 and Tunnelling Spectroscopy (STS),36,37 as well as infrared38 and Raman spectroscopy39,40, and UV-Vis absorption and emission.41,42 However, these methods typically do not provide enough resolution needed for precise understanding of mechanisms of adsorptions of functional groups on SWCNTs. First principle calculations can provide detailed insights into interactions between the functional groups and nanotubes and directly identify their effects on SWCNT’s electronic and optical properties.43 Thus, Density Functional Theory (DFT) calculations with the periodic boundary conditions have been used to study the tube stability and the electronic structure of semiconducting zigzag and metallic armchair nanotubes functionalized at the side-wall with carboxylic acid, alcohol, amine, and alkyl functional groups.44 It was found that these functional groups create sp3 defects at the tube surface resulting in trap states in the band gap of a pristine nanotube, while –CH2 groups bound to metallic (9,0) SWCNT form pentagon/heptagon defects leading to opening of the band gap and a change in its metallic to semiconductor character. Time Dependent DFT (TDDFT) is a common method for calculations of optical spectra of various molecular systems.43 Applied to nanotubes, TDDFT has predicted that chemisorption of hydrogen and aryl groups at a sidewall of semiconductor SWCNTs significantly modifies the optical selection rules, so that the lowest-energy transitions become optically active.45-46 However, calculations show that such optical ‘brightening’ of the lowest state is highly sensitive to the position of the adsorbent. These predictions well agree with the recent experimental


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findings of a satellite bright emission peak in SWCNTs with sp3 defects introduced via controllable

chemical

functionalization.47

Similar

results

have

been

obtained

both

computationally and experimentally for oxygen-doped SWCNTs.48,49 It is important to note that TDDFT calculations of pristine SWCNTs50-55 and SWCNTs non-covalently56 and covalently45,46 functionalized at the sidewalls have been mostly conducted on finite-size nanotubes of about 10 nm in length with tips capped by hydrogens and CH2 groups to eliminate dangling bonds at the tube edge. However, it was reported that appearance of midgap states associated with the edges is sensitive to the ratio between H and CH2 capping groups, which, in turn, has been found to depend on the tube chirality. Unfortunately, a precise form of this dependence is still unclear and only empirical approaches have been reported in the literature.43, 53 In particular, there is still an open question why hydrogen passivation of chiral tubes does not completely open their energy gap. Besides sidewall functionalization, DFT has been used in studies of functionalization of edges of SWCNTs. In such calculations, dangling bonds at the open ends or tips of SWCNTs are saturated by carboxylic acids57-59 and alcohols.60-62 The effect of tube’s edge oxidation on the IR63 and Raman64 spectra of SWCNTs has been investigated by simulating armchair and zigzag nanotubes with −COOH, −CONH2, and −COOCH3 functional groups added at the tips. However, all these calculations have been performed for narrow-diameter zigzag and armchair SWCNTs mostly focusing on structural deformations and the strength of interactions between the SWCNT and the functional groups, while the effect of edge functional groups on the electronic structure and, in particular, on the excited state properties of chiral SWCNTs has received limiting attention, so far.


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In this paper, we provide systematic studies of several capping schemes with combinations of methylene, hydroxyl, and carboxylic groups attached to the chiral (10,5) SWCNT to understand the effect of the sp2- vs. sp3-hybridized bonding of groups with different electron withdrawing properties to the SWCNT edges. Our goal is to establish the relationships between a capping scheme and the electronic structure of the SWCNTs. With this knowledge, the capping groups can be chosen for tuning the electronic properties of SWCNTs. In addition, it helps in computations of finite size nanotubes: One can use such a capping scheme that completely eliminates all dangling bonds at the edges, so that the finite SWCNT has the electronic structure comparable to its infinite counterparts, particularly near the energy gap where optical properties originate. This finite tube approach allows for calculations of optical spectra of SWCNTs using TDDFT, which is a reasonably accurate and computationally efficient method compared to other available approaches.43 Our calculations demonstrate that the hybridization of the bonding atom of the capping groups, as well as the number of functional groups bonded through an sp2-carbon, plays the predominant role in eliminating dangling bonds responsible for the optically forbidden mid-gap states, while the precise nature and position of the functional groups is less significant.

Methodology and Computational Details Description of SWCN capping models. For investigations of the effect of edge groups on the electronic structure of SWCNTs, we model compounds of three distinct classes based on the bond order of the connectivity between the (10,5) SWCNT and the functional group, as illustrated in Scheme 1. The first class of compounds consists of two functional groups, R1 and R2, attached to the nanotube edges via the double bond (compounds 1 – 4 in Scheme 1). In this


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Class I, the atom bonded vicinal to the SWCNT on both functional groups are sp2-hybridized. In the Class II, one functional group is attached to the nanotube edge via a single bond and the other via a double bond (compounds 5 – 7 in Scheme 1). The Class III contains both functional groups interacting with the nanotube edge via only single bonds, sp3-hybridized groups (compounds 8 – 14 in Scheme 1). All other dangling bonds at the nanotube’s edges are capped by hydrogen, as illustrated in Figure 1. For the purpose of characterization of the bond lengths and charge distributions in systems we studied, it is necessary to differentiate the different carbon atoms in the SWCNT vicinal to functionalization. The notation that has been adopted for this purpose is presented in Figure 1. The carbon atom of the SWCNT to that the functional group is directly attached is labelled “C”. The two adjacent carbon atoms in SWCNT are then labelled “C1” and “C2”. These two carbon atoms are non-equivalent for any non-zigzag SWCNT as a result of distinct axis of chirality. As such, the SWCNT has three distinct types of capping connectivity. There are two connectivity types that fall along the vector A (referred to as A1 and A2, red and blue colors in Figure 1), and there is a single connectivity along the vector B (green color in Figure 1). A SWCNT with (10,5) chirality possesses precisely five bonds of each connectivity types, for a total of fifteen capping groups at each edge of the nanotube. The (10,5) SWCNTs of diameter 1.03 Å is generated using Tubegen-3.4 software.65 Fourteen different functionalization schemes (Scheme 1) are performed for the (10,5) tube of two unit cells long, resulting in a length of 23.3 Å. All fourteen structures are capped with functional groups R1 and R2 on opposing radial positions, as illustrated in Figure 1, right panel. Additionally, five geometries are generated with the methylene group as one functionalization, R1, and hydrogen as the other R2, similar to the compound 7. However, the position of R1


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functionalization in these compounds is varied such that the methylene groups are located either on opposing sides or the same side radially. Besides, the connectivity is varied to cover A1, A2, and B positions, as shown in Figure 1. We also have investigated how increasing numbers of methylene groups (from two to eight) on the edges of the SWCNT in the A1 and A2 positions affect the electronic structure of SWCNTs. This set of calculations is conducted to find an optimal scheme that could be used to eliminate the mid-gap states caused by dangling bonds at the edges of the SWCNT. Calculations of the ground state geometries and related electronic structures. All calculations are performed using Gaussian-09 software package.66 Geometries are optimized using semiempirical Austin Model 1 (AM1)67 method to obtain the lowest energy ground state structures of all the capped SWCNTs. Semiempirical methods are less computationally expensive than DFT, while giving comparative results for both pristine68 and functionalized62 SWCNTs. For instance, AM1 calculations of pristine (7,6) SWCNTs of ~10 nm in length and capped by hydrogens reproduce the subtle structure and the relevant vibrational effect in the ground and excited state dynamics of SWCNTs that have been confirmed by experimental findings51, 52, 54, 69. Based on the AM1 optimized geometries, the single-point electronic structure calculations are performed utilizing 3-21G basis sets using the hybrid density functional B3LYP and the long range corrected CAM-B3LYP functional, as incorporated into Gaussian-09 Software package. Our previous studies of pristine SWCNTs have shown that increasing the basis set from STO-3G to 3-21G and 6-31G uniformly redshifts excitation energies by about 0.15 eV at most, while further increase of the basis to 6-31G* negligibly affects the excitation energies of nanotubes.43, 53 In addition, calculations of zigzag tubes in Ref. 62 show very good agreement


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between geometries of OH-functionalized (9,0) SWCNT obtained by AM1 and by B3LYP/631G*, while B3LYP/3-21G calculations provide only 0.2-0.3% difference in bond lengths, compared to B3LYP/6-31G* results. Because extended basis sets have negligible affect on the qualitative trends in both the geometry and the electronic structure, we conclude that the 3-21G basis set is sufficient to present a useful qualitative picture of capped SWCNTs we studied. For charge distribution analysis, the natural bond orbitals (NBO) are calculated for all SWCNTs capped with different capping groups after single point energy calculation using both functionals within 3-21G basis set. Calculations of the optical spectra. The linear response TDDFT is used to analyze the excitations in capped SWCNTs, using B3LYP and CAM-B3LYP functionals and the 3-21G basis set. It has been discussed in literature43, 54, 70-71 that excitons are overbound in conjugated organic materials, including SWCNTs54, when full Hartree Fock (HF) exchange is used, while no excitonic effect (unbound free electron-hole pair) is observed when pure density functionals are used. The electron−hole interaction (an excitonic effect) can be interpreted as a competition between a long-range Coulomb attraction induced by HF exchange and local strong repulsion brought by the component of the pure density functional. As such, TD-GGA and TD-HF methods represent two extreme cases of unbound Wannier−Mott and tightly bound Frenkel excitons, respectively, whereas the moderate portion of HF exchange in hybrid functionals (e.g., TD-B3LYP or TD-PBE1PBE) recovers an intermediate case.43 Taking into account these results, we compare optical spectra obtained by hybrid density functional B3LYP (20% HF) and coulomb-attenuating method (CAM-B3LYP). CAM-B3LYP is a long-range corrected density functional that varies the HF exchange from 19% for short range interactions and up to 65% HF exchange for long range interactions, expecting to better reproduce dispersion effects.


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For these calculations, 50 singlet transitions are generated with their respective oscillator strengths for each capped SWCNT of 2 units in length. For several capping structures of Class-I, TDDFT calculations are performed for longer nanotubes of 7 and 9 lattice units in size with the total length of 8.2 nm and 10.5 nm, respectively. In these cases, the length of the tube is significantly larger than the coherent size of an exciton (1.5-2 nm), which allows for eliminating the edge effects, as compared to shorter models.43 For longer edge-functionalized (10,5) SWCNTs, 25 excited states are calculated using the same functionals and basis sets as used for calculations of shorter nanotubes. To obtain the absorption spectra profile, optical transitions are broadened by the Gaussian function with the line width parameter of 0.05 eV to reproduce thermal broadening that occur under experimental conditions. Finally, natural transition orbital (NTO)72 analysis is performed to visualize a nature of excited state in capped SWCNTs.

Results and Discussion Effect of the position of the sp2-capping group on the SWCNT’s energy gap. For all functional structures we considered, there are a number of positions on the edge of the SWCNT where a functional group can be attached. In order to verify the dependence of the electronic structure on the position of a functional group, we first have performed a series of calculations with Class II compounds, choosing the methylene group as the sp2-capping group and hydrogen as the sp3capping group. This choice is also dictated by the relatively weak electron withdrawing character of the methylene as opposed to oxygen-containing groups. Since both tube’s edges have to be functionalized, it is natural to place the methylene on either the radially opposing sides or the same across sides of the SWCNT, while also varying its connectivity along vectors A or B (A1, A2, and B positions shown in Figure 1).


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Figure 2(a) demonstrates the energy gap of the (10,5) SWCNT capped by one methylene and hydrogens (structure 7 in Scheme 1) as a function of the methylene position at the nanotube edges. It is readily seen that there is a very little effect on the electronic structure as a result of the methylene attachment at any A1 or A2 sites placed either at the opposite or the same edge positions. In addition, the energy gap of these structures is larger then those of structure 14 (Class III) with the full hydrogen passivation. However, placing the CH2 group at the B-position leads to a noticeable decrease in the HOMO-LUMO gap (by about 0.5 eV). This trend in energies is well reproduced either by semiempirical/AM1 or DFT/CAM-B3LYP approaches, with AM1 resulting in a constantly larger energy gaps (~ 2.9 eV vs. ~1.7 eV). It is well known that HF method overestimates the energy gap of molecular systems due to a lack of electronic correlations in the HF exchange.43 Such correlations are parametrically introduced in semiempirical methods. However, since the parameterization of Coulomb integrals in AM1 is not done specifically for SWCNTs, it is reasonable to expect some overestimation of the band gap energies compared to the methods including correlations from first principles, such as longrange corrected CAM-B3LYP functional. Nonetheless, a qualitative behavior of the electronic structure of SWCNTs is not sensitive to the method, which agrees with previous reports.43 The similarities in energy gaps between structures 7, with CH2 being at A1 and A2 positions, correlate to nearly identical shapes of HOMOs for these species, where electron density avoids the region of sp2 functionalization being delocalized over the entire nanotube, as can be compared in Figure 2(d). For all these structures, the HOMO predominantly has as a “spiral” form going via the central part of the nanotube away from the CH2 group on one end to the other end following the tube’s chiral vector. However, functionalization by the CH2 at Bposition (directed across the chiral vector) leads to localisation of the orbital at the tube’s edges.


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This localization results in HOMO being a trap mid-gap state, which noticeably decreases the HOMO-LUMO gap of this system. This trend is followed by LUMO and it is consistent with both DFT and AM1 calculations, as can be compared to Figure S1 in Supplemental Materials. It is important to note that the C-C bond lengths between the carbon with the methylene group and two adjacent carbon atoms at the nanotube edge exhibit resonance bonds of nearly similar lengths of ~1.46-1.47 Å for all A1 and A2-positions, Figure 2(b). This trend in C-C1 and C-C2 bonding correlates with the delocalized character of molecular orbitals in these cases. In contrast, the structure with the B-position shows more single-like (~1.46 Å) and double-like (~1.44 Å) character of adjacent C-C bonds, which explains the edge-localized character of HOMO and LUMO with a predominate contribution from the methylene group. In the compound 14, full hydrogen passivation results in even more pronounced single-like (~1.43 Å) and doublelike (~1.37 Å) bond characters of adjacent edge carbons, Figure 2(b). Although, the HOMO of 14 is not localized on edges like in the case of 7 with the methylene in B-position, the single vs. double bond character at the edges decreases the HOMO-LUMO gap of the compound 14, similarly to the compound 7 with B-positions. For all A-structures, the charge on the carbon with the functional group is slightly negative (-0.1/-0.05 a. u.), being the most negative as compared to charge on both adjacent carbons for A2-positions, while less negative than one of the adjacent carbons for A1-positions, Figure 2(c). However, B-position results on completely neutral carbon with the methylene attached, while adjacent carbons hold similar slightly negative charge as those in A1-position. Except this slight difference in the charge on the C atom with attached sp2-functional group, it is hard to see a correlation between charge distributions on carbons at nanotube edges and the trends in their energy gaps. We refer it to the averaged character of the total charge density


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distribution that is integrated over all electronic states, while the energy gap is controlled only by two specific states such as HOMO and LUMO. Number of sp2-capping groups and its effect on the energy gap of SWCNTs. In addition to the position of the capping groups, the impact of their concentration on the electronic structure is also important. To study the dependence of the SWCNT’s electronic structure on the number of sp2-hybridized groups at the nanotube edges, we functionalize up to all possible A1 and A2 type capping locations, as shown in Figure 3. For the (10,5) SWCNT, there are five A1 or A2 bonds. Therefore, for up to five methylene groups, the functionalization involves either A1 or A2 bonds only. As evidenced from Figure 2, functionalization of A1 position has a similar effect on the electronic structure as the A2 position (also see Figure S2, Supplemental Materials). Therefore, we chose A1 capping for up to five CH2 groups. B-type capping is not considered, since it provides the edge localized mid-gap states. To functionalize more than five positions along the vector A, both A1 and A2 bonds must be utilized. The largest HOMO-LUMO gap of all the functionalization schemes studied is observed for the structure with two methylene groups placed at the edge (compound 1). In our previous work,53 these capping has been shown to provide a smooth dependence of the energy gap on the length of the (10,5) SWCNT, approaching the limit of an infinite nanotube simulated by imposing 1D periodic boundary conditions. As such, the capping with two methylene groups does not introduce artifacts into the electronic structure of (10,5) SWCNT due to the capping. Functionalization of the edges of the SWCNT further with more than two sp2-hybridized groups leads to mid-gap states that significantly decrease the HOMO-LUMO gaps, Figure 3. The number of mid-gap states increases with the number of methylene groups. However, the smallest energy gap is observed in structures with 5-6 groups. It is evident from Figure 3 that the electron


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density of these mid-gap states is predominantly located near the caps of the SWCNT pointing to the edge character of these orbitals. Further increase in sp2-hybridized groups increases the energy gap approaching the values to those of three and one methylene groups. We attribute these increase in the energy gap to enhanced delocalization in HOMO and LUMO orbitals, when both A1 and A2 capping positions are involved, Figure 3. Very similar trends are obtained by AM1 calculations (Figure S3, Supplemental Materials). Interestingly, the charge and the bond lengths between the carbon with the methylene group and two adjacent carbon atoms are not sensitive to changes in the number of sp2hybridized groups (Figure S2, Supplemental Materials). For the compound 14 with full passivation by hydrogens, the HOMO and HOMO-1, as well as the LUMO and LUMO+1, are well-delocalized orbitals with two-fold degeneracy due to the symmetry of the tube structure, Figure 3. For two CH2 groups (compound 1), the HOMO and HOMO-1 / LUMO and LUMO+1 energy splitting is very small (nearly degenerate states) because of high symmetry of the edges, while the position of the sp2- groups coincide with the tube chirality along which the orbital is delocalized. However, a single CH2 group at each edge (compound 14) breaks this degeneracy resulting in significant splitting between energies of the HOMO and HOMO-1, while orbitals stay delocalized over the tube center with HOMO avoiding the CH2 group and HOMO-1 involving delocalization over the methylene groups. Such a break in degeneracy of frontier orbitals leads to decreasing of the HOMO-LUMO gap as compared to the case with two methylene groups. Addition of more than two CH2 groups makes their position being at odds with the tube chiral vector bringing edge-localization of frontier orbitals and decreasing the energy gap of the tube. As such, due to the edge symmetry and well agreement between methylene positions and the chiral angle of the nanotube, only two sp2-hybridized groups at the


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A1 or A2 positions provide an optimal capping of the (10,5) SWCNT that does not introduce edge-localized mid-gap states. Therefore, we use the same number and the same position of the capping groups as in the compound 1, while varying the R1 and R2 groups accordingly to Scheme 1, to study the effects of sp2- versus sp3-hybridized groups and their electron withdrawing/donating properties on the electronic structure of the SWCNT. Dependence of the electronic structure on the bond-order and electron withdrawing properties of the capping groups. Figure 4 compares the structural parameters and the energy gaps of (10,5) SWCNT functionalized by 14 different capping agents calculated using various methods. Other than the aforementioned difference in values of the HOMO-LUMO gap due to the variations in the HF portion in the functional and AM1 Hamiltonian, all three methods exhibit qualitatively similar behaviour with respect to the capping classes, Figure 4(a). Class I structures 1-4, with two sp2 functional groups at each tube edge, have the largest energy gap that is negligibly changing inside the class. Class II and III compounds have much smaller energy gaps, with the compounds 5-7 (class II) having slightly larger energy gap than compounds 8-11 (class III), which is the most pronounced in AM1 calculations. Decrease in the energy gap is associated with appearance of the edge-originated mid-gap states, Figure 4(d). Compounds in class III with parent groups, such as ethers (8 vs. 11), esters (9 vs. 10), and carboxylic (12 vs. 13) groups exhibit very similar electronic structures between their derivatives as compared in Figure S4, Supplemental Materials. However, ethers as the strongest electron withdrawing groups noticeably destabilizes the HOMO and LUMO in compounds 8 and 11 shifting both orbitals higher in energy than in compounds 9 and 10 with esters groups having weaker electronwithdrawing abilities. Meanwhile, relatively strong donating groups of carboxylic groups slightly stabilize both HOMO and LUMO in compounds 12 and 13. Similar trends are seen in class I


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compounds, where the strong electron donating methoxy (4) and hydroxyl (3) substitutions of the methylene groups shift the HOMO and LUMO higher in energy, as compared to the compound (1) having weak electron withdrawing methylene groups. In all cases, however, the HOMO and LUMO are shifted symmetrically, so that the energy of the HOMO-LUMO gap is insignificantly affected by the electron withdrawing or donating properties of the capping groups inside the class. Thus, the bond order of the functionalization to the nanotube capping group governs the decreasing energy gap, rather than the capping group by itself. A significant correlation between the bond order of functionalization at C and the length of C-C1 and C-C2 bonds at the edge of SWCNT is depicted in Figure 4(b). For compounds in Class I, independent on the capping group, both of these bonds exhibit a noticeable single bond like character, resulting in lengthening of these bonds. The C-C1 and C-C2 bond lengths for compounds 1-4 are nearly similar and around 1.47 Å, with a slight deviation from each other for non-equivalent R1 and R2 groups (compounds 2-4), Figure 4(b). This bond elongation and more single-bond like character of C-C1 and C-C2, as compared to the C-C bond in the central unperturbed part of the SWCNT (varying from 1.41 Å to 1.44 Å), originate from the charge distribution induced by the sp2-capping groups, as illustrated in Scheme 2(a). Thus, in Class I compounds, the carbon atom directly adjacent to the SWCNT (C) is sp2-hybridized resulting in extended conjugation from the functional group into the six-membered nanotube’s ring to which it is bonded. Electron density can be contributed through this double-like bond to the bonded “C” atom resulting in a slightly negative charge on this atom, Figure 4(c). The lone pair on the adjacent oxygen in the functional groups is able to intensify this contribution through resonance and causes a greater negative charge on “C” in compounds 2-4, while C1 and C2 atoms stay nearly neutral. More negative charge on “C” requires a sparse distribution of sp2-capping groups


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along the nanotube edge to avoid generation of a strong dipole moment, which results in edgelocalized mid-gap states. This explains why two sp2-groups is an optimal number of the capping groups to preserve well-opened energy gap, since they can be placed relatively far from each other, while preserving conjugation structure of the tube’s edge. Similar results are observed for compounds 5-7 from Class II, where the measurements are taken at the carbon with the sp2-hybridized functionalization (not shown in Figure 4). However, the carbons with the sp3-hybridized groups demonstrate more double-bond-like character for both C-C1 and C-C2 bonds in compounds 5 and 6, Figure 4(b). In contrast, For Class III compounds 8-14, a large difference in bond length between C-C1 and C-C2 is observed indicating their non-equivalence induced by the sp3-capping groups. For these cases where the bond order between the SWCNT and the functional group is a single bond, the adjacent C-C2 bond is significantly shortened, while C-C1 is close to the average resonance C-C bond in the central portion of the SWCNT, where perturbations by capping groups is negligible. A significant difference between C-C1 and C-C2 bond lengths induced by the sp3-capping groups correlates with appearance of the mid-gap states that decrease HOMO-LUMO gaps in class III compounds. Increased double-bond-like character and the difference between C-C1 and C-C2 bond lengths in compounds where an oxygen atom is bonded directly to the nanotube C atom (compounds 5, 8-11) are also associated with a significant positive charge on C, evidenced in Figure 4(c). This is because the electronegative oxygen in the capping groups is withdrawing electron density from this carbon. A slightly negative charge is observed on both C1 and C2 in these cases, likely the result of the ability of the bonded oxygen to donate electrons to portions of this conjugated ring through resonance, as illustrated in Scheme 2(b). As such, these compounds


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exhibit a strong redistribution of charges between the positively charged terminal C and the negatively charged C1 and C2, resulting in a higher dipole moment on the nanotube edge with these capping schemes. This strong dipole moment leads to stronger destabilization of both HOMO and LUMO in these compounds compared to those in oxygen free capping groups 6, 12, and 13, as can be seen in Figure S4, Supplemental Materials. However, this insignificantly affects the values of the energy gap between compounds 8-11 and 12-13, because both HOMOs and LUMOs are shifted by nearly the same energy. Overall, there is a clear correlation between the values of the energy gap, the bond-order of the capping group and the bond length difference between the carbon involved in the functionalization and its adjacent carbons at the edge of SWCNT. However, the correlation between the energy gap and the charge on these carbons is not well pronounced. We explain it by the averaged character of the total charge density distribution that is less sensitive to the local changes associated with only the HOMO and LUMO governing the energy gap. For further investigations of the differences in the electronic structure between compounds with only sp2-capping (class I) and sp3-capping (class III), we consider a few orbitals near the energy gap of representative compounds 2 (class I) and 11 (class III) shown in Figure 5. These structures differ by the methylene sp2-hybridized group (compound 2) substituting one of two hydroxyls (compound 11). For the sp2-capping, the HOMO and LUMO of the compound 2 have very similar π and π* character as the compound 1 (Figure 3) with the orbitals delocalized over the central part of the nanotube following the chiral angle of the tube and involving a minor contribution from the sp2-capping groups.

In contrast, the sp3-capping results in strong

localization of both HOMO and LUMO around the edges with a significant contribution from the capping groups. For this compound, the delocalized π and π* orbitals appear further apart from


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the HOMO-LUMO gap (HOMO-6 and LUMO+6). Thus, the sp3-capping not only introduces the edge-localized orbitals to the energy gap, but also stabilizes the π orbitals and destabilizes the π* states, so that they are noticeably shifted in their energies as compared to the π and π* orbitals (HOMO and LUMO) in compounds with the sp2-capping, Figure 4(d). Thus, not only the states near the energy gap, but also the entire electronic structure is significantly changed by the sp3capping, as compared to structures with the sp2-capping. In contrast, chemical variations in the sp2-caping groups negligibly modify the type and energy alignment of electronic states in class I compounds (see Figure S4, supplemental materials). Dependence of the absorption spectra of SWCNT on the capping scheme. Absorption spectra and oscillator strength of compounds 1, 2, 6 and 11 are presented in Figure 6. For these compounds, we also have compared the performance of B3LYP and CAM-B3LYP functionals. Overall, both methods coincide in main spectral features and provide qualitatively similar optical spectra. However, B3LYP results in red-shifted transitions as compared to CAM-B3LYP, while these shifts depend on the capping type: 0.61 eV, 0.32 eV and 0.12 eV for compounds 2, 6 and 11, respectively. This is the expected trend correlated with the decreased portion of the HF exchange in the density functional.43,

53

The variance in the redshift of each compound for

B3LYP vs. CAM-B3LYP calculations follows the trend of the energy gaps in these compounds with the largest gap for class I and the smallest gap for class III, as shown in Figure 4 (a). In all cases, a few lowest transitions have a small oscillator strength followed by the brightest transition (SB) that we associate to the main E11 band. For class II and III compounds the SB transition is red-shifted and less intense as compared to those of compounds 1 and 2 from the class I. The absorption spectra of compounds 1 and 2 exhibit very similar features (Figures 6 (c) and (d)), elucidating negligible effect of electron donating/withdrawing groups on the optical


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properties of SWNTs, due to the similar character of the molecular orbitals for all compounds within class I, as was discussed. In contrast, the change in the bond order of the capping groups has more dramatic effects on the energy alignment and oscillator strength of optical transitions, resulting in more red-shifted and less intensive E11 band with more complicated spectral shape of (10,5) nanotube when sp2-groups are changed by sp3-capping. In all species, optically active transitions with noticeable oscillator strengths have π-π* character, while optically inactive transitions with a very low or zero oscillator strength have edge-localized nature, as illustrated in NTOs shown in Figure 7. For several capping structures of Class-I, we calculate absorption spectra for longer nanotubes of ~8 nm (compound 1) and ~10 nm (compound 2) in length. In these cases, the length of the tube is significantly larger than the coherent size of an exciton (1.5-2 nm),43,54 which allows for eliminating the edge effects, as compared to shorter models. Unfortunately, we were not able to calculate longer structures from Class-II and III, because their energy gaps are nearly closed due to the edge-localized mid-gap states, interrupting conversion of the TDDFT runs. Therefore, only structures from Class-I with well-open HOMO-LUMO gap converge in TDDFT calculations. In both long structures 1 and 2, the absorption spectra are red shifted, compared to their shorter counterparts, Figure 6 (e) and (f). This is a common trend according to the increased π–conjugated length of systems.53 Additionally, the energy splitting between transitions is also decreases with the tube length resulting in a narrow and featureless E11 band. Similar to shorter tubes, a few lowest energy states are optically dark or semi-dark having negligibly small oscillator strength. However, these lowest states are much less intense than in short counterparts. This is because interactions and mixing between different excitons (optically dark and bright ones) are less pronounced in long tubes, since excitons are more localized at the


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central part of the tube (see Figure S6, Supplemental Materials) and much less affected by the tube ends as in short structures. Nonetheless, the quantitative character of spectra of short tubes well correlate with the longer ones, pointing on appropriateness of used models in these studies.

Conclusions We have studied the relationship between a capping scheme and the electronic structure of the SWCNTs, focusing on various combinations of methylene, hydroxyl, and carboxylic groups attached to the edges of (10,5) SWCNT. In particular, we consider three classes of capping scheme varying by the bond order of the connectivity between the nanotube and the functional group, e.g., the sp2- and sp3-hybridized bonding, while having different electron withdrawing properties of ligands. We have found that the hybridization of the bonding atom of the capping groups, as well as the number of functional groups bonded through an sp2-carbon, plays the predominant role in eliminating dangling bonds responsible for the optically forbidden edge-localized mid-gap states. Thus, our calculations reveal that for the (10,5) SWCNT, two sp2-groups (methylene derivatives) are required on the caps to completely open up the energy gap. In this case, the HOMO and HOMO-1 (and LUMO and LUMO+1) are nearly degenerate states because of high symmetry of the edges, while the position of the sp2-groups is such that they lie along the direction along which the orbitals are delocalized. Using only a single sp2-group decreases the energy gap, due to a significant splitting between HOMO and HOMO-1 (LUMO and LUMO-1) states as a result of symmetry breaking. Addition of more than two sp2-groups makes their position being at odds with the tube chiral vector bringing edge-localization of frontier orbitals and decreasing the energy gap. We also found that the sp2-carbon atom directly adjacent to the SWCNT has a


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slightly negative charge, due to redistribution of electron density between the functional group and the six-membered nanotube’s ring to which it is bonded. More negative charge on the sp2carbon requires a sparse distribution of sp2-capping groups along the nanotube edge to avoid generation of a strong dipole moment, which leads to edge-localized mid-gap states. This explains why two sp2-groups is an optimal number of the capping groups for (10,5) SWCNT to provide the well-opened energy gap, since they can be placed relatively far from each other, while preserving conjugation structure of the tube’s edge. Variations in electron withdrawing/donating properties of the capping groups play very little role in changing the HOMO-LUMO gaps. The strongest electron withdrawing groups (ethers) destabilizes both the HOMO and LUMO, while relatively strong donating groups (carboxyls) stabilize the frontier orbitals. In all cases, however, the HOMO and LUMO are shifted symmetrically, so that the energy of the HOMO-LUMO gap is insignificantly affected by the electron withdrawing or donating properties of the capping groups inside the class. In contrast, the bond order of functionalization at the nanotube carbon governs the energy gap decreasing, resulting in edge-localized midgap states in structures capped only by sp3-groups. Similarly, the optical spectra demonstrate negligible effects of electron donating/withdrawing groups on the lowest optical E11 band, while the change in the bond order of the capping groups significantly changes the energy alignment and oscillator strength of optical transitions, resulting in red-shifted and less intensive E11 band when two sp2-groups are changed by sp3-capping. Our results can be helpful in choosing the functional groups for tuning the optoelectronic properties of SWCNTs. In addition, our results provide a guideline in computations of finite size nanotubes: one can use such a capping scheme that completely eliminates all dangling bonds at the edges, so that the finite SWCNT has the electronic structure comparable to its infinite


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counterparts, particularly near the energy gap where optical properties originate. Such a finite tube approach allows for calculations of optical spectra of SWCNTs using TDDFT, which is a reasonably accurate and computationally efficient method compared to other available approaches. While only one (10,5) nanotube was considered in details, our preliminary calculations of other SWCNTs (not shown here) allows us to suggest that tubes having nearly the same chiral angles, like (10,5) and (8,4) with ~19o and likely (9,4) with ~18o, might have the same capping scheme (e.g., two distant sp2-hybredized groups) to completely open their bandgaps. Interestingly, nanotubes with the large chiral angles, like (5,4) with ~26o and (6,5) and (7,6) with ~27o, do not require sp2-groups, and full passivation by hydrogens is sufficient to completely open their bandgaps. Further studies are needed to explain these data, which are the subjects of our future work. Overall, our investigations are important for SWCNT modeling, because a complete understanding of the role of tube’s capping will allow for using smaller computational models and, therefore, make computations of a wide range of phenomena in SWNTs practical.

ACKNOWLEDGMENTS Authors acknowledge NSF Grant CHE-1413614 for financial support of studies of functionalized carbon nanotubes and the Alfred P. Sloan Research Fellowship BR2014-073 for partial support of studies of surface effects at interfaces of nanostructures. For computational resources and administrative support, we thank the Center for Computationally Assisted Science and Technology (CCAST) at North Dakota State University and the National Energy Research Scientific Computing Center (NERSC) allocation awards 86678, supported by the Office of Science of the DOE under contract No. DE-AC02-05CH11231. S.K. and B.G. acknowledge the


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support of the Center for Integrated Nanotechnology (CINT) computer facility at Los Alamos National Laboratory (LANL) supported by U.S. Department of Energy and Office of Basic Energy Sciences.

GRAPHICAL ABSTRACT


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SCHEMES and FIGURES

Scheme 1: Functional groups attached to the edge of the (10,5) SWNT. Class I compounds are those where both functional groups, R1 and R2, have connectivity to the SWCNT via the double bond (sp2-connectivity), Class II compounds have one connectivity via the double bond and the other via a single bond (mixed sp2-and sp3-connectivity), and Class III compounds have connectivity via single bonds (sp3-connectivity).

Scheme 2: Schematic representation of hybrid resonance structures for the different types of capping groups used as a model for the (10,5) SWCNT with various side-groups attached at the tube’s edges.


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C1 C C2

C2 C C1

Figure 1: Structural parameters for the edge-functionalized (10,5) SWCNT and different capping schemes possible for this nanotube. Positions labelled by R1 and R2 are those that are used for calculations of 14 different functional schemes shown in Scheme 1. Bonds highlighted in the same color represent the same symmetry position at the tube’s edge referred to as A1 (blue), A2 (green), and B (red).


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Figure 2: Comparison of the electronic and geometrical parameters of the (10,5) SWCNT capped only by hydrogens (compound 14), as a reference point, and by H and one CH2 group (compound 7) with the CH2 group attached at various positions (A1, A2, and B) along the nanotube edge. Position of the group at the other tube’s edge is identified either by O or S, when the CH2 groups are either at the opposite or the same sides with respect to the nanotube axis. The geometries are optimized by AM1 for all structures. (a) The energy gaps computed by AM1 and DFT using the CAM-B3LYP functional. (b) The bond lengths between the carbon atom of the SWCNT to that the CH2 group is attached (C) and the adjacent carbon atom (C1 or C2). (c) The NBO charge on C, C1, and C2 atoms of SWCNT calculated by the CAM-B3LYP. (d) Highest Occupied Molecular Orbital (HOMO) for each capping case calculated by the CAM-B3LYP. The dashed green line indicates the average bond length and charge for the central portion of the SWCNT where perturbation by capping groups is absent. There is insignificant difference between energies and orbital delocalization for either the same or opposite A-positions, while Bposition results in localization of HOMO at the edges and noticeable decreasing in the energy gap.


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Figure 3: The electronic structure of (10,5) SWNT capped by different numbers of CH2 groups along A-direction and calculated by DFT within the CAM-B3LYP functional. The number listed in the HOMO-LUMO gap of the energy diagram is the energy gap in eV. For the compound 14 with no CH2 groups at the edge (0), the HOMO and HOMO-1, as well as the LUMO and LUMO+1, are two-fold degenerate. Addition of the CH2 groups breaks this degeneracy.


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Figure 4: The electronic structure and geometrical parameters for the edge-functionalized (10,5) SWCNT optimized by AM1 method. (a) The HOMO-LUMO gap and (d) electronic levels calculated by semiempirical AM1 and DFT using CAM-B3LYP and BLYP functionals and 321G basis set. (b) Bond lengths for the AM1 optimized ground state geometry. (c) The charge on C, C1, and C2 carbons at the nanotube’s edge using NBO analysis calculated by the CAMB3LYP functional and 3-21G basis set. The dashed green line indicates the average C-C bond length and charge for the central portion of the SWCNT where perturbation by capping groups is absent.


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Figure 5: Plots of LUMO and HOMO for the (10,5) SWCNTs with functional groups 2 (Class I, sp2-capping) and 11 (Class III, sp3-capping) calculated by different methods (AM1 and CAMB3LYP), while geometries are obtained by AM1. Although AM1 results in overall more localized character of orbitals, both methods show that HOMO and LUMO are mostly localized on edges in structures with sp3-capping, while are delocalized over the central part in sp2-capped structures.


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Figure 6: Absorption spectra (in arbitrary units) of the edge-functionalized (10,5) SWCNT of several lengths. Absorption spectra of the compound 6 of class II (a), 11 of class III (b), and 1 (c) and 2 (d) of class I computed with the TDDFT/B3LYP (dotted blue lines) and TDDFT/CAMB3LYP (solid blue lines). TDDFT/B3LYP spectra are blue shifted to align the most intensive peak (SB) for both methods. Vertical red lines denote each optical transition calculated by CAMB3LYP functional with the oscillator strength shown at the right Y-axis (red), with the black arrows depicting the lowest-energy transition (S1). In four top panels (a)-(d), the nanotube is of 2 lattice units in length. In bottom panels, the nanotube is of 9 units (e) and 7 units (f) in length. SB defines the brightest transition associated with the E11 main band.


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Figure 7: Natural transition orbitals (NTOs) contributing to the lowest energy (S1) and the most bright (SB) optical transitions for the capped SWCNTs (10,5) calculated using the CAM-B3LYP functional and 3-21G basis set for capping structures 2, 6, and 11. Geometries are optimized by AM1 semiempirical approach.


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(10,5) 3.5

AM1

HOMO

2.5

CAM-B3LYP 1.5

HOMO

0.5

HOMO-LUMO gap (eV)

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0 1 2 3 4 5

Number of sp2-capping groups (methylene)


R2

Tip Functionalization of Finite Single-Walled ... - ACS Publications

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