BN Segment Doped Effect on the First ... - ACS Publications

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BN Segment Doped Effect on the First Hyperpolarizibility of Heteronanotubes: Focused on an Effective Connecting Pattern Rong-Lin Zhong, Shi-Ling Sun, Hong-Liang Xu,* Yong-Qing Qiu, and Zhong-Min Su* Institute of Functional Material Chemistry, Department of Chemistry, National & Local United Engineering Lab for Power Battery, Northeast Normal University, Changchun 130024, Jilin, People’s Republic of China S Supporting Information *

ABSTRACT: An increasing number of scientists have focused on carbon−boron-nitride heteronanotubes because of their particularly adjustable properties, as shown in many fields. In this work, four isoelectronic models (BN-n, n = 1−4) were systematically investigated to explore the crucial factor for enhancing the static first hyperpolarizibility by doping the BN segment into the carbon nanotube (CNT) with differently connecting patterns. Theoretical results show that the N-connecting pattern might increase the contribution of the BN segment to the crucial transition states, which obviously increases the occupied orbital energy while the unoccupied orbital energy is slightly influenced. Correspondingly, the transition energy of BN-1 is smaller than that of BN-2. As a result, the static first hyperpolarizability of BN-1 is 1.05 × 104 au, which is remarkably larger than the 4.37 × 102 au of BN-2. The results indicate that, compared to the B-connecting pattern, the N-connecting pattern of the BN segment linking to the conjugated CNT segment is a more efficient way to enhance the first hyperpolarizability of heteronanotubes. It is our expectation that the new knowledge about the carbon−boron-nitride heteronanotubes could provide valuable information for scientists to develop the potential nonlinear optical nanomaterials by introducing BN segments into suitable positions of CNTs.

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INTRODUCTION Single-walled carbon nanotubes (SWCNTs) have been proposed as novel nanomaterials in a wide variety of applications since Iijima first discovered them in 1991.1 The unique properties of CNTs have been shown in many fields.2 For example, it is well-known that CNTs are intrinsically either semiconducting or metallic, depending upon the chirality of the nanotubes.3 On the other hand, the single-walled boron-nitride nanotubes (SWBNNTs) are structural analogues of CNTs while they are electrical insulators with a large band gap, independent of their chirality.3,4 Recently, a large number of investigations have focused on exploring carbon−boron-nitride heteronanotubes in order to develop hybrid structures with adjustable properties.5 Generally, these heteronanotubes can be characterized as doping a BN segment into different CNT segments with control over the BN segment formation. In particular, the combination of different CNT and BNNT segments may allow the fundamental improvement for developing next-generation electronic components.6 Interestingly, Turner et al found that the highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO− LUMO) energy gap of the heteronanotubes can be significantly tuned by modifying the CNT and BNNT combinations.7 Paying further attention to the mechanism of the modification on the heteronanotubes might open new perspectives to develop their further applications in nanotechnology.3 The last two decades have witnessed progress in the design and synthesis of nonlinear optical (NLO) materials for their potential applications in laser devices.8 Up to now, many © XXXX American Chemical Society

strategies have been proposed to enhance the NLO response of organic materials, including the use of molecules with abundant π-electrons.9 The abundance of π-electrons in CNTs could yield structures with excellent NLO properties by a rational modification.10 It is worthy of note that the static first hyperpolarizability (β0) is the microcosmic parameter of the macroscopic NLO properties of materials.9b According to recent investigations, the β0 value might be properly influenced by adjusting the HOMO−LUMO energy gap of organic molecules.8e,11 We are interested in the mechanism of tuning the HOMO−LUMO energy gap and further adjusting the first hyperpolarizability by doping the BN segment into CNTs. In this work, four isoelectronic models (BN-n, n = 1−4) were systematically investigated. The BN-n models are obtained by circularly doping the BN segment into the different positions of CNTs with differently connecting patterns. This paper aims at exploring the crucial factor for enhancing the static first hyperpolarizibility of heteronanotubes. The investigation may provide a new strategy for designing high performance NLO materials by introducing BN segments into suitable positions of CNTs.

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COMPUTATIONAL DETAILS For theoretical investigations, selecting a suitable model is the key to understanding the relationship between the results and Received: March 13, 2013 Revised: April 18, 2013

A

dx.doi.org/10.1021/jp402561h | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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physical properties.12 In this work, the CNT (5, 0) segment with a suitable length (9 Å) is chosen as the basic structure (test for longer CNT segments are also shown in the Supporting Information). The geometry structures were optimized at the density functional theory (DFT) B3LYP/631G(d) level. 13 For the calculation of the (hyper)polarizabilities, traditional DFT methods (such as B3LYP) have deficiencies in describing the electronic properties of such large systems.8c,10a Recently, the new density functional Coulomb-attenuated hybrid exchange-correlation functional (CAM-B3LYP14) has been developed to overcome these limitations, and it is suitable to predict the molecular NLO properties of a large system, for example in the fullerene-dimers system15 and corresponding BNNT systems.8k In this work, a test calculation (Table S1 in the Supporting Information) shows CAM-B3LYP is adequate for our purpose. Therefore, the first hyperpolarizability was evaluated by an analytical CAMB3LYP/6-31+g(d) approach. The static first hyperpolarizability (β0) is noted as follows: β0 = (βx2 + βy2 + βz2)1/2

Table 1. Main Geometrical Parameters of BN-n (n = 1−4) Optimized at the B3LYP/6-31G(d) Level BN-1 B−N (Å) B−C N−C C−C angle-1 (deg)a angle-2 (deg) angle-3 (deg) angle-4 (deg) energy (au)

3 (β + βijj + βikk ), 5 iii

1.44 105.19 116.14 110.62 111.76 −1944.66

BN-3

BN-4

1.47 1.37 1.43 104.09 116.35 110.78 115.28 −1944.56

1.47 1.55 1.44 105.53 116.52 113.45 110.02 −1944.59

or convex in the four models. Furthermore, the energies of the four models are also shown in Table 1. It is worthy of note that the energy ranges from −1944.56 au to −1944.66 au. The maximal difference is about 63 kcal mol−1. This indicates that the electronic structures of the BN-n might be different even though the geometry is similar. The electronic properties of BN-n are listed in Table 2. Interestingly, the static first hyperpolarizability (β0) of BN-1 is 1.05 × 104 au, which is significantly larger than the 4.37 × 102 au of BN-2. Results show that the BN segment doped effect on the β0 value of CNT is dramatically dependent on the connecting pattern. In other words, compared to the B atom, the N atom of the BN segment connecting to the conjugated CNT segment is more effective to enhance the first hyperpolarizability of heteronanotubes. Correspondingly, the β0 value (1.38 × 104 au) of BN-3 is also larger than the 5.91 × 102 au of BN-4. The results indicate that the connecting pattern plays a more important role for enhancing β0 than the doped position. Furthermore, the large difference of β0 (about order of 102) between BN-1 and BN-2 caught our attention. The reasons for the origin of the difference would be unearthed, and the details are discussed as follows. To provide an understanding of the origins of the doped effects on the first hyperpolarizabilities of BN-n, first, we focused on the relative electronic spatial extent17 ⟨R2⟩. As shown in Table 2, the ⟨R2⟩ values of BN-n are the same order of magnitude, which ranges from 1.61 × 104 to 1.69 × 104 au. Correspondingly, the polarizability (α0) of BN-n ranges from 4.96 × 102 to 6.45 × 102 au. Therefore, the electronic spatial extent is more important to the polarizability rather than the first hyperpolarizability in this work. There is another approach to evaluate the first hyperpolarizability that originates from perturbation theory approaches, which express the hyperpolarizability using summation-over-states (SOS) expressions.9b,18 SOS approaches consist in evaluating energies and transition dipoles that appear in the hyperpolarizability expressions. For the first hyperpolarizability, the SOS expression reads as follows:

(1)

i, j, k = x, y, z

1.37 1.45 107.04 116.05 110.02 114.21 −1944.60

1.47 1.56

a Angle-n (n = 1−4) is the angle BNB, angle NBN, concave angle CCC, and convex angle CCC as shown in Figure 1

where βi =

BN-2

1.47

(2)

All of the calculations were performed with the Gaussian 09 program package.16

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RESULTS AND DISCUSSIONS The optimized structures of the BN-n are shown in Figure 1, and the main geometrical parameters are listed in Table 1. The

Figure 1. Optimized structures of BN-n (n = 1−4).

B−N bond length of BN-n is almost equal (about 1.47 Å). On the other hand, the B−C bond length in BN-2 is 1.56 Å, which is longer than the N−C bond length (1.37) in BN-1. However, the difference of bond length alternation (BLA) in the connecting area of BN-n is small, which indicates the topological similarity of the four models. The difference of the main angles involved in the BN/CNT segment of BN-n is also small. More specifically, the angle BNB ranges from 104.09° to 107.04° and the angle NBN ranges from 116.05° to 116.52°. Similarly, the angle CCC ranges from 110.02° to 115.28°, which is independent of whether the angle is concave

βijk ( −ωσ ; ω1 , ω2) =

∑ P−σ ,1,2 ∑ n≠0 m≠0

j k μ0in μnm μm0

(ΔEn0 − ωσ )(ΔEm0 − ω2) (3)

The quality of the computed properties depends on the level of approximation that is used to determine the ground and excited B



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Table 2. Polarizability α0 (au), First Hyperpolarizability β0 (au), Electronic Spatial Extent ⟨R2⟩ (au) of BN-n (n = 1−4) at the CAM-B3LYP/6-31+g(d) Level, Oscillator Strength f 0, and Transition Energy ΔE (eV) at the TD-CAM-B3LYP/6-31+g(d) Level βx βy βz β0 f0 ΔE Δμ 3f 0Δμ/2ΔE3 (au) α0 ⟨R2⟩

BN-1

BN-2

BN-3

BN-4

−1.05 × 104 −7.66 × 102 −2.00 1.05 × 104 0.25 1.79 1.96 1.02 × 103 6.21 × 102 1.61 × 104

−3.51 × 102 2.60 × 102 −2.60 × 101 4.37 × 102 0.10 2.28 0.83 8.99 × 101 5.69 × 102 1.69 × 104

−1.38 × 104 4.31 × 102 1.00 1.38 × 104 0.27 1.45 2.00 2.13 × 103 6.45 × 102 1.64 × 104

−5.91 × 102 0.00 −1.00 5.91 × 102 0.20 2.14 0.94 2.31 × 102 4.96 × 102 1.67 × 104

state wave functions and energies. Oudar11 proposed a twolevel expression to simplify the expressions and interpret them easily. According to the approximately two-level expression,9b,11 the β0 value is mainly dependent on three important factors: the excitation energy (ΔE), the oscillator strength ( f 0), and the difference of dipole moment between the crucial transition states (Δμ). To provide an origin understanding about the BN segment doped effects on the first hyperpolarizabilities of heteronanotubes, we focused on the transition states of these models. In this paper, the transition energies for BN-n are estimated at the TD-CAM-B3LYP/6-31+g(d) level and the results are listed in Table 2. The ΔE value of BN-1 is 1.79 eV, which is smaller than the 2.28 eV of BN-2. As shown in Table 2, the ΔE value (1.45 eV) of BN-3 is also smaller than the 2.14 eV of BN-4. Obviously, the order of ΔE3 is inversely proportional to that of the β0 values as the two-level expression. The oscillator strength of these models has also been compared at the same theory level. As shown in Table 2, the Δμ value of BN-1 is 1.96 D, which is larger than the 0.83 D of BN-2. Correspondingly, the Δμ value of BN-3 is 2.00 D, which is larger than the 0.94 D of BN-4. Therefore, the charge transfer of BN-1 and BN-3 is larger than those of BN-2 and BN-4, which like a donor−acceptor configuration. The approximate first hyperpolarizabilities from the two-state model are also listed in Table 2, which is consistent with the results of the analytical DFT method. Significantly, the excitation energy is the decisive factor in determining the β0 values of these models. In addition, the monotonic dependence of the static first hyperpolarizability on the ΔE value is shown in Figure S1 of the Supporting Information. Furthermore, we focused on analyzing the molecular orbitals of the crucial transition states of BN-n to understand the origin of these properties. From Figure 2, the crucial transition state orbitals of the BN-n are different. For BN-1 and BN-3, the BN segments contributed more to the orbitals than BN-2 and BN4. Interestingly, the occupied orbital energy is dependent on the contribution of BN segments. For example, the contribution of BN segments to the HOMO-1 of BN-1 is 15.67% (evaluated by the Aomix program19), which is larger than the 5.18% of BN-2, as shown in Table 3. As a result, the HOMO-1 energy of BN-1 is −5.16 eV, which is larger than the −7.16 eV of BN-2. As shown in Table 2, the occupied orbital energy increases with the increase of the BN segment contribution to the occupied orbitals of BN-n. Correspondingly, the transition energy of BN1 and BN-3 is smaller than that of BN-2 and BN-4. Therefore, the β0 values of BN-1 and BN-3 are remarkably larger than those of BN-2 and BN-4. Our investigation shows that adjusting the BN segment contribution to the orbitals of the

Figure 2. Crucial transitions and corresponding orbital energy (eV) of the BN-n (n = 1−4).

Table 3. BN Segment Contributions for the Crucial Transition State Orbitals of BN-n (n = 1−4) excited states ground states HOMO LUMO

BN-1

BN-2

BN-3

BN-4

38.74% 15.67% 16.22% 40.28%

8.58% 5.18% 8.26% 8.58%

40.93% 34.17% 34.17% 5.50%

8.64% 8.57% 15.77% 32.73%

crucial transition states by doping the BN segment with different connecting patterns plays a key role in enhancing the first hyperpolarizability. To get insight into the photoelectric properties of the BN-n, the total density of states (TDOS) and projected partial density of states (PDOS) have also been analyzed by using the Aomix program. 19 As plotted in Figure 3, the BN segment contribution to orbitals of the most important transition states of BN-1 and BN-3 is larger than that of BN-2 and BN-4. Obviously, the larger contributions of the BN segment might increase the occupied orbital energy while the unoccupied orbital energy is slightly influenced. This qualitatively explains C



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Figure 3. Total and partial (the BN segment and C segment) density of states (TDOS and PDOS) around the HOMO−LUMO gap.

(structures and corresponding β0 values are shown in Figure S3 in the Supporting Information). Results confirm that the connecting pattern is the key factor influencing the β0 value of BN segment doped CNTs in this work.

why the transition energies of BN-1 are smaller than those of BN-2. The natural bond orbital (NBO) charge of important atoms at the connecting area was shown in Table S2 of the Supporting Information. According to Table S2, the charge of the connecting-C atom (qC) also depends on the connecting pattern. When the N atom of the BN segment is connecting to the conjugated CNT segment, the qC is positive. However, the qC is negative when the B atom of the BN segment is connecting to the conjugated CNT segment. It is known to all that the order of electronegativity of the three atoms is as follows: B < C < N. Correspondingly, the alteration of the qC is related to the electronegativity of these atoms. For the Nconnecting pattern, the electronegativity of N is larger than that of C, so that the π-electron tends to be pulled to the BN fragment. However, for the B-connecting pattern, the electronegativity of B is smaller than that of C so that the π-electron is still at the CNT fragment. In other words, the N-connecting pattern is more conjugated (with smaller transition energy) compared to the B-connecting pattern. Therefore, the origin of these properties might significantly depend on the electronegativity of the atoms in the connecting area. The above investigations show that the BN segment contributes more to the orbitals of the crucial transition states when N atoms are connected to the conjugated CNT segment. However, the BN segment contributes little to these orbitals when B atoms are connected to the conjugated C segment. In order to validate the hypothesis, we consider two schemes. First, on the basis of BN-1 and BN-2, we enhance the components of BN segments to form BN2-1 and BN2-2 (structures are shown in Figure S2 in the Supporting Information). As expected, the β0 value of BN2-1 is 9.12 × 103 au (close to the 1.05 × 104 au of BN-1), which is significantly larger than the 2.40 × 102 au of BN2-2 (close to the 4.37 × 102 au of BN-2). Further, on the basis of BN-3 and BN4, we lengthened the conjugated CNT segment respectively

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CONCLUSIONS In summary, four isoelectronic models (BN-n) were systematically investigated to explore the crucial factor for enhancing the static first hyperpolarizibility by doping the BN segment into CNTs with differently connecting patterns. Results show that the larger contributions of the BN segment to the crucial transition states in BN-1 might obviously increase the occupied orbital energy while the unoccupied orbital energy is slightly influenced. Correspondingly, the transition energy of BN-1 is smaller than that of BN-2. As a result, the static first hyperpolrizabilities of BN-1 are remarkably larger than that of BN-2. Our investigations show that the transition property of the BN segment doped CNT is mainly dependent on the connecting pattern, which significantly influences the static first hyperpolarizabilities of corresponding carbon−boron-nitride heteronanotubes. It is our expectation that the new knowledge about the carbon−boron-nitride heteronanotubes could provide valuable information for scientists to develop the potential NLO materials by introducing BN segments into suitable positions of CNTs.

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ASSOCIATED CONTENT

* Supporting Information S

The first hyperpolarizability of BN-n (n = 1−4) by the HF method and different density functional approaches, the NBO charge of important atoms at the connecting area, the relationship between the first hyperpolarizabilities (β0) and the transition energy (ΔE) between the ground state and the crucial excited state, the electronic properties and DOS of the pristine CNT and BNNT, the optimized structures and corresponding first hyperpolarizabilities (β0) of BN2-1 and D



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BN2-2, and optimized structures in this work. 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], [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from NSFC (21003019 and 21173098), the Science and Technology Development Planning of Jilin Province (20100178 and 201201062), the Fundamental Research Funds for the Central Universities (12SSXT131), the Doctoral Fund of Ministry of Education of China (20100043120006), and the Special Grade of the Postdoctoral Foundation of China (No. 201104518).

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