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Density functional theory study of the hydrogen chemisorption of single-walled carbon nanotubes with carbon ad-dimer defect
Journal of Molecular Structure: THEOCHEM 962 (2010) 62–67
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Density functional theory study of the hydrogen chemisorption of single-walled carbon nanotubes with carbon ad-dimer defect Donglai Wang ⇑, Caihong Zhao, Guang Xin, Dongyan Hou Department of Chemistry, Anshan Normal University, Anshan 114007, China
a r t i c l e
i n f o
Article history: Received 3 May 2010 Received in revised form 9 September 2010 Accepted 10 September 2010 Available online 18 September 2010 Keywords: Density function Carbon nanotube Ad-dimer defect Hydrogenation
a b s t r a c t The structural and electronic properties of hydrogenated armchair and zigzag SWCNTs with carbon ad-dimer (CD) defect were investigated by means of the B3LYP hybrid density functional method using 6-31G* basis set. It is found that the chemisorptions of two hydrogen atoms inside and outside the CD defective SWCNTs are exothermic processes. Exohedral nanotube adsorption is energetically more favorable than endohedral adsorption. These results are in agreement with hydrogen on pristine nanotubes. The positional preference for the chemisorption of two hydrogen atoms is the same for the CD defective armchair and zigzag nanotubes. However, the reaction energy of two hydrogen atoms on the exterior sidewalls of CD defective SWCNTs is almost independent of the tube diameter. This is different from the results reported on pristine nanotubes. The calculated energy gaps indicate that the hydrogen-chemisorbed CD defective armchair tubes are always wide energy gap structures, while the hydrogen-chemisorbed CD defective zigzag tubes have significantly lower gaps. The HOMO–LUMO gap and reaction energy for the chemisorption of more hydrogen atoms on the exterior sidewalls of CD defective armchair SWCNTs were also explored. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since their discovery in 1991 [1], single-walled carbon nanotubes (SWCNTs) have attracted extensive interest all over the world due to their unique structural, mechanical, and electrical properties [2] and a variety of potential applications, such as hydrogen storage [3], chemical sensors [4], and nanobioelectronics [5], etc. The structures of carbon nanotubes could be described as a perfect graphene sheet wrapped up into a cylinder. However, the experimentally available SWCNTs are not perfect. Defects such as vacancies, pentagons, heptagons, dopants, and Stone–Wales (SW) defects are widely observed in experiment [6–9]. These defects can significantly impact the electrical, chemical, and mechanical properties of SWCNTs [10–13]. Topological defects in SWCNTs can arise from the inclusion of five- or seven-membered rings in the graphene-like carbon network. The SW defect is produced by rotating a C–C bond by 90° about its center, leading to the formation of a 5-7-7-5 ring pattern [6]. The carbon ad-dimer (CD) defect formed on a pristine nanotube by adsorption of a carbon dimer introduces two adjacent pentagons between two heptagons, i.e., the 7-5-5-7 defect [14]. With a local deformation, the nanotube with defects might be more favorable for subsequent reactions. ⇑ Corresponding author. E-mail address: [email protected] (D. Wang). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.09.015
Hydrogen atom chemisorption on the surfaces of SWCNTs has been the subject of many theoretical and experimental studies, since SWCNTs are considered as promising hydrogen storage media [15–19]. Khare et al. [16] reported that the hydrogenation of SWCNTs with atomic hydrogen and demonstrated the formation of covalent C–H bonds. Zhang et al. [17] investigated systematically the reactions between H-plasma and SWCNTs and observed ‘‘swelling” in SWCNT due to hydrogenation and confirmed C–H bond formation. Recently, Yang et al. [18] emphasized the importance of investigating the chemisorption of hydrogen at low occupancies (i.e., binding of one and two hydrogen atoms) on SWCNTs. They reported an investigation of the chemisorption of hydrogen atoms on (5,0), (7,0), (9,0) zigzag SWCNTs and a (5,5) armchair SWCNT and found that exohedral binding of hydrogen is more favorable than endohedral binding. Very recently, Dinadayalane et al. [19] used the B3LYP/6-31G(d) level of theory to study the chemisorptions of one and two hydrogen atoms on the external surface of (3,3), (4,4), (5,5), and (6,6) armchair SWCNTs and predicted that two hydrogen atoms favor binding at adjacent positions rather than at alternate carbon sites. All of the above studied are the results associated with defect-free SWCNTs. The theoretical study of the sidewall reactivity based on armchair (5,5) SWCNT in reacting with C2H4, O2, and O3 species illustrated that the central C–C bond of CD defects in SWCNT is chemically more reactive than that of perfect sites [20]. However, to our knowledge, there is no report on the chemisorption of hydrogen atoms on defectcontaining SWCNTs. What are the differences between hydrogen
D. Wang et al. / Journal of Molecular Structure: THEOCHEM 962 (2010) 62–67
adsorption in perfect and defective SWCNTs? How does the defect-containing nanotube–hydrogen interaction depend on the tube diameter and chirality? In the paper, the structural and electronic properties of armchair and zigzag carbon nanotubes with a CD defect and the chemisorption of hydrogen atoms on the surface of these nanotubes were studied through density functional theory method. 2. Computational methods The geometries of all the structures presented in the present work were fully optimized with hybrid density functional theory (DFT) at the B3LYP/6-31G* level [21,22] using the Gaussian 98 program system [23]. Twelve finite-length clusters of perfect SWCNTs terminated by hydrogen atoms were constructed as the initial structure models. Of these SWCNTs, both armchair (3,3) (4,4), (5,5), (6,6), (7,7), (8,8) and zigzag (8,0), (9,0), (10,0), (11,0), (12,0), (13,0) nanotubes were considered. For models of armchair there are seven carbon layers and there are eight carbon layers for zigzag. The carbon ad-dimer defect is created by inserting C2 into two C–C bonds across a hexagon for each of the above-mentioned pristine nanotubes. The pentagon–pentagon fusion vertexs (PPFVs) are the most active sites of the fullerene and carbon nanotube [20,24]. According to Dinadayalane et al. adjacent hydrogen adsorption is favored over alternate site adsorption for defect-free SWCNTs [19], it becomes very important to know the energy relationship between adjacent and alternate adsorption in the case of those nanotubes with defects. Here, the adsorptions of two hydrogen atoms at the C1–C2, C1–C3, C1–C4, and C2–C4 positions (Fig. 1) for each of the structures were studied. The structure models are denoted according to the hydrogen positions attached. For example, model H(1,2) means that two H atoms have been chemisorbed to atoms C1 and C2 of the nanotube structures. In the case of CD defective armchair SWCNTs, exohedral chemiadsorption 12 hydrogen atoms were also taken into consideration. The reaction energy per hydrogen atom (Er/H) addition was calculated as follows: Er/H = [ESWCNT+nH ESWCNT nEH]/n. where Er/H stands for reaction energy of per H; ESWCNT+nH denotes the total energy of the hydrogen–chemisorbed nanotube with a CD defect; n represents the number of hydrogen atoms chemisorbed; and ESWCNT and EH correspond to the energies of the CD defective nanotube and the hydrogen atom, respectively. 3. Results and discussion 3.1. Geometries The optimized structures of all the investigated CD defective SWCNT models are shown in Fig. 1. The B3LYP/6-31G* optimized
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structures of CD defective SWCNTs with two hydrogen atoms adsorbed (C1–C2, C1–C3, C1–C4, and C2–C4 positions) are given in Supplementary data. The calculated bond lengths in the defective region of all the defective nanotubes before and after addition at the B3LYP/6-31G* level are presented in Table 1. For the CD defective armchair (n,n) (n = 3–8) SWCNTs, the C1–C2 bond lengths at the pentagon–pentagon fusion have almost the same bond length (1.392–1.395 Å). The C–C bonds located between two fused pentagons and the hexagon–heptagon rings have almost the same bond length (C1–C2 and C3–C4) too, indicating the conjugation among them. Similar results are obtained for the CD defective zigzag SWCNTs. Upon two hydrogen atoms adsorption on the exterior sidewall or the interior sidewall of the CD defective SWCNTs, all the bonds in the region of hydrogen chemisorption become longer, due to the enhancement of the sp3 rehybridization. An inspection of the data provide in Table 1 shows that, for both CD defective armchair and zigzag nanotubes, the elongation of the C1–C2 bond in the exohedral H(1,2) hydrogenated structures is higher compared to the endohedral H(1,2) hydrogenated nanotubes. For all outside hydrogenated SWCNTs studied, the C1–C2 bonds in the two hydrogen atoms on the adjacent carbon sites H(1,2) are longer than in the two hydrogen atoms on the alternate positions. This increase in bond length indicates weakening of C–C bond in the region of hydrogen chemisorption. The results suggest that it seems very likely that two hydrogen atoms would attack the outer sidewall C1–C2 bond of CD defective SWCNTs. The newly formed C–H bond has a weak diameter dependence and is 1.1 Å in all cases, which is consistent with the results reported recently for the chemisorption of hydrogen atoms on pristine nanotubes by Yang et al. [18]. 3.2. Electronic properties In Table 2, the HOMO–LUMO energy gaps are reported for the CD defective and hydrogen-chemisorbed SWCNTs at the B3LYP/ 6-31G* level. The variation of the HOMO–LUMO gaps for both CD defective nanotubes before and after addition is shown in Fig. 2. The gaps for the CD defective armchair series increase with increasing tube diameter. Chemisorption of two hydrogen atoms on CD defective armchair SWCNTs in the exohedral and endohedral H(1,2) and exohedral H(1,4) types significantly increases the gap of corresponding nanotubes, implying substantial energetic stability for these SWCNTs. These features are consistent with those reported for the chemisorption of hydrogen atoms on pristine nanotubes, where hydrogenation can open up or increase the energy gap of SWCNTs [25]. On the other hand, H(1,3) and H(2,4) additions on the outer sidewalls of CD defective armchair SWCNTs except for (3,3) nanotube reduce the energy gap of corresponding nanotubes. Note that the energy gap for the exohedral
Fig. 1. Optimized structures of the CD defective (colored yellow) armchair (n,n) and zigzag (m,0) SWCNT models. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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D. Wang et al. / Journal of Molecular Structure: THEOCHEM 962 (2010) 62–67
Table 1 Selected bond lengths (in Å) obtained at the B3LYP/6-31G* level for the CD defective and hydrogen-chemisorbed SWCNTs. Structure (3,3)-CD (3,3)-CD+H(1,2), (3,3)-CD+H(1,2), (3,3)-CD+H(1,3), (3,3)-CD+H(2,4), (3,3)-CD+H(1,4), (4,4)-CD (4,4)-CD+H(1,2), (4,4)-CD+H(1,2), (4,4)-CD+H(1,3), (4,4)-CD+H(2,4), (4,4)-CD+H(1,4), (5,5)-CD (5,5)-CD+H(1,2), (5,5)-CD+H(1,2), (5,5)-CD+H(1,3), (5,5)-CD+H(2,4), (5,5)-CD+H(1,4), (6,6)-CD (6,6)-CD+H(1,2), (6,6)-CD+H(1,2), (6,6)-CD+H(1,3), (6,6)-CD+H(2,4), (6,6)-CD+H(1,4), (7,7)-CD (7,7)-CD+H(1,2), (7,7)-CD+H(1,2), (7,7)-CD+H(1,3), (7,7)-CD+H(2,4), (7,7)-CD+H(1,4), (8,8)-CD (8,8)-CD+H(1,2), (8,8)-CD+H(1,2), (8,8)-CD+H(1,3), (8,8)-CD+H(2,4), (8,8)-CD+H(1,4),
outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside
C1–C2
C2–C3
C3–C4
Structure
C1–C2
C2–C3
C3–C4
1.392 1.589 1.504 1.539 1.540 1.547 1.394 1.590 1.509 1.540 1.538 1.543 1.394 1.591 1.509 1.539 1.537 1.542 1.395 1.591 1.508 1.538 1.536 1.541 1.395 1.592 1.508 1.537 1.535 1.540 1.395 1.592 1.511 1.536 1.535 1.539
1.484 1.543 1.498 1.532 1.527 1.373 1.469 1.531 1.495 1.521 1.516 1.369 1.460 1.525 1.489 1.527 1.511 1.366 1.454 1.522 1.483 1.523 1.508 1.365 1.450 1.520 1.478 1.521 1.505 1.364 1.447 1.518 1.473 1.519 1.504 1.363
1.385 1.381 1.405 1.516 1.509 1.507 1.385 1.381 1.381 1.510 1.502 1.503 1.386 1.381 1.374 1.519 1.498 1.501 1.387 1.382 1.372 1.519 1.496 1.500 1.387 1.382 1.370 1.519 1.495 1.499 1.387 1.382 1.369 1.519 1.493 1.499
(8,0)-CD (8,0)-CD+H(1,2), outside (8,0)-CD+H(1,2), inside (8,0)-CD+H(1,3), outside (8,0)-CD+H(2,4), outside (8,0)-CD+H(1,4), outside (9,0)-CD (9,0)-CD+H(1,2), outside (9,0)-CD+H(1,2), inside (9,0)-CD+H(1,3), outside (9,0)-CD+H(2,4), outside (9,0)-CD+H(1,4), outside (10,0)-CD (10,0)-CD+H(1,2), outside (10,0)-CD+H(1,2), inside (10,0)-CD+H(1,3), outside (10,0)-CD+H(2,4), outside (10,0)-CD+H(1,4), outside (11,0)-CD (11,0)-CD+H(1,2), outside (11,0)-CD+H(1,2), inside (11,0)-CD+H(1,3), outside (11,0)-CD+H(2,4), outside (11,0)-CD+H(1,4), outside (12,0)-CD (12,0)-CD+H(1,2), outside (12,0)-CD+H(1,2), inside (12,0)-CD+H(1,3), outside (12,0)-CD+H(2,4), outside (12,0)-CD+H(1,4), outside (13,0)-CD (13,0)-CD+H(1,2), outside (13,0)-CD+H(1,2), inside (13,0)-CD+H(1,3), outside (13,0)-CD+H(2,4), outside (13,0)-CD+H(1,4), outside
1.389 1.584 1.470 1.535 1.523 1.523 1.393 1.583 1.470 1.524 1.519 1.518 1.385 1.580 1.483 1.526 1.517 1.517 1.386 1.581 1.507 1.519 1.514 1.515 1.384 1.579 1.512 1.520 1.514 1.514 1.384 1.578 1.523 1.516 1.513 1.513
1.412 1.486 1.459 1.488 1.481 1.354 1.409 1.486 1.455 1.490 1.480 1.357 1.410 1.485 1.459 1.485 1.477 1.354 1.407 1.486 1.468 1.486 1.476 1.352 1.408 1.485 1.468 1.483 1.475 1.355 1.408 1.485 1.473 1.484 1.474 1.354
1.404 1.397 1.373 1.541 1.493 1.510 1.402 1.391 1.370 1.541 1.492 1.506 1.399 1.396 1.366 1.538 1.489 1.505 1.394 1.395 1.359 1.539 1.488 1.502 1.397 1.395 1.362 1.536 1.487 1.502 1.397 1.395 1.363 1.537 1.486 1.501
Table 2 HOMO–LUMO energy gap values (in eV) obtained at the B3LYP/6-31G* level for the CD defective and hydrogen-chemisorbed SWCNTs. Structure
Defective tube
H(1,2), outside
H(1,2), inside
H(1,3), outside
H(2,4), outside
H(1,4), outside
(3,3) (4,4) (5,5) (6,6) (7,7) (8,8) (8,0) (9,0) (10,0) (11,0) (12,0) (13,0)
1.63 1.99 2.20 2.33 2.37 2.36 0.40 0.34 0.38 0.14 0.37 0.33
2.14 2.44 2.58 2.66 2.70 2.73 0.42 0.27 0.40 0.36 0.39 0.34
2.80 2.72 2.58 2.61 2.59 2.54 0.40 0.33 0.39 0.19 0.38 0.25
2.22 1.28 1.78 1.96 2.07 2.14 0.43 0.38 0.36 0.33 0.33 0.31
1.85 1.78 1.66 1.60 1.57 1.55 0.39 0.37 0.38 0.32 0.36 0.29
2.26 2.40 2.44 2.43 2.40 2.38 0.40 0.34 0.39 0.33 0.22 0.33
Fig. 2. Variation of HOMO–LUMO gaps of (n,n) and (m,0) CD defective and hydrogen-chemisorbed SWCNTs with the increase of the number (a) n and (b) m.
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H(1,2) hydrogen-chemisorbed armchair tube is proportional to tube diameter. Whereas the endohedral H(1,2) and exohedral H(1,4) hydrogen-chemisorbed armchair tubes is inversely proportional. In contrast, the CD defective zigzag series have significantly lower gaps. The gaps decrease with an odd–even oscillatory behavior, with increasing tube diameter. However, the variation in the gap is very small and hence gives little information on the meaningful trend. Upon two hydrogen atoms on the sidewalls of CD defective zigzag SWCNTs, the B3LYP/6-31G* calculations indicate that the energy gap values remain almost unaffected by chemisorption of hydrogen atoms. The energy gap variation with the increase of the number n (Fig. 2a) and m (Fig. 2b) indicates that the CD defective and hydrogen-chemisorbed armchair tubes are always wide energy gap structures, while the CD defective and hydrogen-chemisorbed zigzag tubes have significantly lower gaps and might exhibit metallic behavior. 3.3. Reaction energies of chemisorption of two hydrogen atoms Total energies and the reaction energies per hydrogen atom addition (Er/H) computed at the B3LYP/6-31G* level of theory for the CD defective and hydrogen-chemisorbed SWCNTs are present in Table 3. It can be seen that the reaction energies per hydrogen atom addition are all negative value. This implies that the addition reactions are exothermic. For both the CD defective armchair (n,n) and zigzag (m,0) SWCNTs, exohedral nanotube adsorption is energetically more favorable than endohedral adsorption, as shown in Fig. 3a and b; the reaction energies of the endo-hydrogenated CD defective SWCNTs increase with increasing tube diameter. The results are consistent with the previous reported for the chemisorption of hydrogen atoms on pristine nanotubes [18]. Upon two hydrogen atoms on the exterior sidewalls of CD defective armchair and zigzag SWCNTs, the addition of H(1,2) is thermodynamically more favored than the H(1,3), H(2,4), and H(1,4) additions regardless of the diameter and chirality of the SWCNTs considered. The addition of H(1,4) is the second positional preference. The Er/H of the H(1,2) addition is about 18–22 kcal/mol (3–10 kcal/mol) more negative than that of the H(1,4) addition for the CD defective armchair (zigzag) SWCNTs. The thermodynamically lower preference of H(1,3) and H(2,4) additions for both CD defective armchair and zigzag SWCNTs is in agreement with the results reported recently for pristine armchair-type nanotubes by Dinadayalane et al. [19]. The reaction energies of the exohedral H(1,2) for the armchair SWCNTs decrease slightly with increasing tube diameter, whereas those for the zigzag SWCNTs increase slightly except (9,0) and (12,0) SWCNTs, whose reaction energies decrease slightly. Our results indicate that tube diameter has very slight effect on the reaction energy of two hydrogen atoms on the exterior sidewalls
of CD defective SWCNTs. This is different from the results reported on pristine nanotubes [19]. The hydrogenation reaction energies (per H) of the H(1,2) addition on the exterior sidewalls of CD defective armchair SWCNTs obtained at the B3LYP/6-31G* level of theory are 89.4, 86.9, 85.1, and 83.8 kcal/mol for (3,3), (4,4), (5,5), and (6,6) SWCNTs, respectively. Compared to the hydrogenation reaction energies of two hydrogen atoms on the exterior sidewalls of pristine armchair SWCNTs obtained at the same level of theory ( 61.6 and 53.7 kcal/mol/H for 7-layer (3,3) and (4,4) SWCNTs; 64.9, 57.9, 50.0, and 42.1 kcal/mol/H for 9-layer (3,3), (4,4), (5,5), and (6,6) SWCNTs, respectively) [19,26], the reaction energies of the exo-hydrogenated CD defective armchair SWCNTs are more exothermic, meaning that the central C–C bond of CD defect in the armchair SWCNTs is more reactive than that in perfect sites. The result agrees with the previous ones [20]. The adsorptions of two hydrogen atoms at the C2–C3 and C3– C4 positions were only considered for CD defective armchair (5,5) and zigzag (9,0) nanotubes. The reaction energies are given in Fig. 4. For the CD defective armchair (5,5) nanotube, the reaction energies of 48.7 and 57.1 kcal/mol for H(2,3) and H(3,4) are 36.4 and 28 kcal/mol smaller than that of 85.1 kcal/mol for H(1,2), respectively. In the case of the CD defective zigzag (9,0) nanotube, the reaction energies of 55.6, and 60.1 kcal/mol for H(2,3) and H(3,4) are 6.6 and 2.1 kcal/mol smaller than that of 62.2 kcal/mol for H(1,2), respectively. From these results, one can clearly see that the C1–C2 sites are more reactive than the other sites. Moreover, the reactive sites in the CD defective SWCNTs are not very sensitive to the tube chirality. 3.4. Adsorption of more hydrogen atoms on the exterior sidewalls of CD defective armchair SWCNTs In the case of CD defective armchair SWCNTs, the addition of twelve hydrogen atoms only on the exterior sidewalls of SWCNTs is considered here. Fig. 5 shows the optimized geometry for twelve hydrogen atoms bonded to the CD defective (5,5) SWCNT as an example of a series of hydrogen-chemisorbed SWCNTs. The calculated bond lengths and energy values of the systems studied are given in Table 4. The calculations show that the optimized tubular structures of CD defective SWCNTs are deformed by the presence of multiply chemisorbed H atoms. The corresponding C–C bonds in the defective region of all the hydrogen-chemisorbed SWCNTs have almost the same bond length (Table 4). Compared with chemisorption of two hydrogen atoms, the chemisorption of twelve hydrogen atoms on CD defective armchair SWCNTs reduces the HOMO–LUMO gap and reaction energy of corresponding nanotubes. The reaction energies are still negative, i.e., the adsorption is favorable. The Er/H for the 12H adsorptions decreases for each
Table 3 Total energies (Etot, a.u.) and reaction energies per hydrogen atom (Er/H, kcal/mol) computed at the B3LYP/6-31G* level of theory for the CD defective and hydrogen-chemisorbed SWCNTs. Structure
(3,3) (4,4) (5,5) (6,6) (7,7) (8,8) (8,0) (9,0) (10,0) (11,0) (12,0) (13,0)
Defective tube
H(1,2), outside
Etot
Etot
1683.52149 2219.64389 2755.71912 3291.77078 3827.80704 4363.83389 2524.36315 2830.49807 3136.65207 3442.77498 3748.91213 4055.03824
1684.80695 2220.92128 2756.99095 3293.03843 3829.07177 4365.09609 2525.56899 2831.69694 3137.86146 3443.99298 3750.12411 4056.25128
H(1,2), inside Er/H 89.4 86.9 85.1 83.8 82.9 82.1 64.4 62.2 65.5 68.2 66.3 66.7
Etot 1684.53550 2220.66192 2756.75039 3292.81617 3828.86453 4364.90191 2525.46409 2831.61353 3137.78388 3443.92394 3750.06767 4056.20406
H(1,3), outside Er/H 4.2 5.5 9.6 14.1 17.9 21.2 31.5 36.1 41.2 46.6 48.6 51.9
Etot 1684.75211 2220.82432 2756.89533 3292.94817 3828.98542 4365.01274 2525.52417 2831.67073 3137.81213 3443.94850 3750.07243 4056.20019
H(2,4), outside Er/H 72.2 56.4 55.1 55.5 55.8 55.9 50.3 54.0 50.0 54.3 50.1 50.6
Etot 1684.72972 2220.82909 2756.89305 3292.93764 3828.97003 4364.99403 2525.53154 2831.67582 3137.82134 3443.95282 3750.08099 4056.20458
H(1,4), outside Er/H 65.2 57.9 54.4 52.2 51.0 50.1 52.7 55.6 52.9 55.6 52.8 52.0
Etot 1684.75125 2220.85852 2756.92484 3292.97046 3829.00301 4365.02703 2525.55082 2831.68662 3137.83829 3443.96588 3750.09092 4056.22004
Er/H 71.9 67.2 64.4 62.5 61.3 60.4 58.7 59.0 58.3 59.7 55.9 56.9
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Fig. 3. Variation of reaction energies for the chemisorption of two hydrogen atoms on the sidewalls of CD defective armchair (a) and zigzag (b) SWCNTs.
Fig. 4. B3LYP/6-31G* optimized geometries of H(2,3) and H(3,4) additions of two hydrogen atoms on the outside sidewalls of CD defective (colored yellow) armchair (5,5) and zigzag (9,0) nanotubes. The C1–C2 bond distances (in Å), HOMO–LUMO energy gap (DE) values (in eV), and the reaction energies per hydrogen atom (Er/H, kcal/mol) for hydrogen chemisorptions are given. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Optimized structures of the CD defective (colored yellow) armchair (5,5) SWCNT with twelve hydrogen atoms adsorbed on the exterior wall: (a) top view, (b) side view and (c) perspective view. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 4 Selected bond lengths (in Å) total energies (Etot), HOMO and LUMO energies, energy gaps (DE), and reaction energies per hydrogen atom (Er/H) computed at the B3LYP/6-31G* level of theory for the hydrogen-chemisorbed SWCNTs. (All energies in eV except total energies (Etot) in Hartrees and reaction energies (Er) in kcal/mol). Structure (3,3)-CD+12H, (4,4)-CD+12H, (5,5)-CD+12H, (6,6)-CD+12H, (7,7)-CD+12H, (8,8)-CD+12H,
outside outside outside outside outside outside
Formula
C1–C2
C2–C3
C3–C4
C44H24 C58H28 C72H32 C86H36 C100H40 C114H44
1.576 1.575 1.574 1.573 1.572 1.572
1.590 1.573 1.569 1.565 1.563 1.563
1.555 1.555 1.552 1.551 1.550 1.550
system. The (3,3)-CD+H(1,2), outside is 89.4 kcal/mol, whereas the (3,3)-CD+12H, outside is 63.7 kcal/mol. The (8,8)-CD+H(1,2), outside is 82.1 kcal/mol, whereas the (8,8)-CD+12H, outside is 56.4 kcal/mol. In each and every (n,n) case, the Er/H for the 12H systems are consistently 26 kcal/mol weaker in magnitude and consequently less thermodynamically stable than the 2H, outside systems.
Etot 1690.74359 2226.80140 2762.83410 3298.86689 3834.89360 4370.91586
HOMO 3.54 3.61 3.50 3.54 3.59 3.63
LUMO 2.71 2.76 2.83 2.79 2.75 2.73
DE 0.84 0.85 0.68 0.76 0.84 0.90
Er/H 63.7 60.4 58.1 57.1 56.6 56.4
4. Conclusions In summary, the structural and electronic properties of hydrogenated armchair and zigzag SWCNTs with carbon ad-dimer (CD) defect have been studied theoretically. It is found that, the chemisorptions of two hydrogen atoms on the exterior sidewalls of CD defective armchair SWCNTs are thermodynamically more stable
D. Wang et al. / Journal of Molecular Structure: THEOCHEM 962 (2010) 62–67
than the pristine nanotubes with two hydrogen atoms chemisorbed. The adsorption on the CD defective armchair SWCNTs is slightly stronger than on the CD defective zigzag ones. The addition at H(1,2) positions is more favored than addition at H(1,3), H(2,4), and H(1,4) positions for both armchair and zigzag nanotubes when two hydrogen atoms are attached to the exterior sidewalls. With the increase of the number of hydrogen atoms, the HOMO–LUMO gap and reaction energy decrease. A remarkable property of CD defective SWCNTs is that the reaction energy of hydrogen chemisorption on the exterior sidewalls of SWCNTs is almost independent of the tube diameter. This is different from the results reported on pristine nanotubes. The present results might be useful for further investigations related to the chemical functionalization of CD defective nanotubes because of the high reactivity of their exterior surface. Acknowledgement This work was supported by Department of Education of Liaoning Province (Grant No. 2009A784). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.theochem.2010.09.015. References [1] S. Iijima, Nature 354 (1991) 56. [2] M.S. Dresselhaus, G. Dresselhaus, A. Jorio, Annu. Rev. Mater. Res. 34 (2004) 247. [3] C. Liu, Y.Y. Fan, M. Liu, H.T. Cong, H.M. Cheng, M.S. Dresselhaus, Science 286 (1999) 1127. [4] J. Kong, N.R. Franklin, C.W. Zhou, M.G. Chapline, S. Peng, K.J. Cho, H.J. Dai, Science 287 (2000) 622.
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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
Density functional theory study of the hydrogen chemisorption of single-walled carbon nanotubes with carbon ad-dimer defect Donglai Wang ⇑, Caihong Zhao, Guang Xin, Dongyan Hou Department of Chemistry, Anshan Normal University, Anshan 114007, China
a r t i c l e
i n f o
Article history: Received 3 May 2010 Received in revised form 9 September 2010 Accepted 10 September 2010 Available online 18 September 2010 Keywords: Density function Carbon nanotube Ad-dimer defect Hydrogenation
a b s t r a c t The structural and electronic properties of hydrogenated armchair and zigzag SWCNTs with carbon ad-dimer (CD) defect were investigated by means of the B3LYP hybrid density functional method using 6-31G* basis set. It is found that the chemisorptions of two hydrogen atoms inside and outside the CD defective SWCNTs are exothermic processes. Exohedral nanotube adsorption is energetically more favorable than endohedral adsorption. These results are in agreement with hydrogen on pristine nanotubes. The positional preference for the chemisorption of two hydrogen atoms is the same for the CD defective armchair and zigzag nanotubes. However, the reaction energy of two hydrogen atoms on the exterior sidewalls of CD defective SWCNTs is almost independent of the tube diameter. This is different from the results reported on pristine nanotubes. The calculated energy gaps indicate that the hydrogen-chemisorbed CD defective armchair tubes are always wide energy gap structures, while the hydrogen-chemisorbed CD defective zigzag tubes have significantly lower gaps. The HOMO–LUMO gap and reaction energy for the chemisorption of more hydrogen atoms on the exterior sidewalls of CD defective armchair SWCNTs were also explored. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Since their discovery in 1991 [1], single-walled carbon nanotubes (SWCNTs) have attracted extensive interest all over the world due to their unique structural, mechanical, and electrical properties [2] and a variety of potential applications, such as hydrogen storage [3], chemical sensors [4], and nanobioelectronics [5], etc. The structures of carbon nanotubes could be described as a perfect graphene sheet wrapped up into a cylinder. However, the experimentally available SWCNTs are not perfect. Defects such as vacancies, pentagons, heptagons, dopants, and Stone–Wales (SW) defects are widely observed in experiment [6–9]. These defects can significantly impact the electrical, chemical, and mechanical properties of SWCNTs [10–13]. Topological defects in SWCNTs can arise from the inclusion of five- or seven-membered rings in the graphene-like carbon network. The SW defect is produced by rotating a C–C bond by 90° about its center, leading to the formation of a 5-7-7-5 ring pattern [6]. The carbon ad-dimer (CD) defect formed on a pristine nanotube by adsorption of a carbon dimer introduces two adjacent pentagons between two heptagons, i.e., the 7-5-5-7 defect [14]. With a local deformation, the nanotube with defects might be more favorable for subsequent reactions. ⇑ Corresponding author. E-mail address: [email protected] (D. Wang). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.09.015
Hydrogen atom chemisorption on the surfaces of SWCNTs has been the subject of many theoretical and experimental studies, since SWCNTs are considered as promising hydrogen storage media [15–19]. Khare et al. [16] reported that the hydrogenation of SWCNTs with atomic hydrogen and demonstrated the formation of covalent C–H bonds. Zhang et al. [17] investigated systematically the reactions between H-plasma and SWCNTs and observed ‘‘swelling” in SWCNT due to hydrogenation and confirmed C–H bond formation. Recently, Yang et al. [18] emphasized the importance of investigating the chemisorption of hydrogen at low occupancies (i.e., binding of one and two hydrogen atoms) on SWCNTs. They reported an investigation of the chemisorption of hydrogen atoms on (5,0), (7,0), (9,0) zigzag SWCNTs and a (5,5) armchair SWCNT and found that exohedral binding of hydrogen is more favorable than endohedral binding. Very recently, Dinadayalane et al. [19] used the B3LYP/6-31G(d) level of theory to study the chemisorptions of one and two hydrogen atoms on the external surface of (3,3), (4,4), (5,5), and (6,6) armchair SWCNTs and predicted that two hydrogen atoms favor binding at adjacent positions rather than at alternate carbon sites. All of the above studied are the results associated with defect-free SWCNTs. The theoretical study of the sidewall reactivity based on armchair (5,5) SWCNT in reacting with C2H4, O2, and O3 species illustrated that the central C–C bond of CD defects in SWCNT is chemically more reactive than that of perfect sites [20]. However, to our knowledge, there is no report on the chemisorption of hydrogen atoms on defectcontaining SWCNTs. What are the differences between hydrogen
D. Wang et al. / Journal of Molecular Structure: THEOCHEM 962 (2010) 62–67
adsorption in perfect and defective SWCNTs? How does the defect-containing nanotube–hydrogen interaction depend on the tube diameter and chirality? In the paper, the structural and electronic properties of armchair and zigzag carbon nanotubes with a CD defect and the chemisorption of hydrogen atoms on the surface of these nanotubes were studied through density functional theory method. 2. Computational methods The geometries of all the structures presented in the present work were fully optimized with hybrid density functional theory (DFT) at the B3LYP/6-31G* level [21,22] using the Gaussian 98 program system [23]. Twelve finite-length clusters of perfect SWCNTs terminated by hydrogen atoms were constructed as the initial structure models. Of these SWCNTs, both armchair (3,3) (4,4), (5,5), (6,6), (7,7), (8,8) and zigzag (8,0), (9,0), (10,0), (11,0), (12,0), (13,0) nanotubes were considered. For models of armchair there are seven carbon layers and there are eight carbon layers for zigzag. The carbon ad-dimer defect is created by inserting C2 into two C–C bonds across a hexagon for each of the above-mentioned pristine nanotubes. The pentagon–pentagon fusion vertexs (PPFVs) are the most active sites of the fullerene and carbon nanotube [20,24]. According to Dinadayalane et al. adjacent hydrogen adsorption is favored over alternate site adsorption for defect-free SWCNTs [19], it becomes very important to know the energy relationship between adjacent and alternate adsorption in the case of those nanotubes with defects. Here, the adsorptions of two hydrogen atoms at the C1–C2, C1–C3, C1–C4, and C2–C4 positions (Fig. 1) for each of the structures were studied. The structure models are denoted according to the hydrogen positions attached. For example, model H(1,2) means that two H atoms have been chemisorbed to atoms C1 and C2 of the nanotube structures. In the case of CD defective armchair SWCNTs, exohedral chemiadsorption 12 hydrogen atoms were also taken into consideration. The reaction energy per hydrogen atom (Er/H) addition was calculated as follows: Er/H = [ESWCNT+nH ESWCNT nEH]/n. where Er/H stands for reaction energy of per H; ESWCNT+nH denotes the total energy of the hydrogen–chemisorbed nanotube with a CD defect; n represents the number of hydrogen atoms chemisorbed; and ESWCNT and EH correspond to the energies of the CD defective nanotube and the hydrogen atom, respectively. 3. Results and discussion 3.1. Geometries The optimized structures of all the investigated CD defective SWCNT models are shown in Fig. 1. The B3LYP/6-31G* optimized
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structures of CD defective SWCNTs with two hydrogen atoms adsorbed (C1–C2, C1–C3, C1–C4, and C2–C4 positions) are given in Supplementary data. The calculated bond lengths in the defective region of all the defective nanotubes before and after addition at the B3LYP/6-31G* level are presented in Table 1. For the CD defective armchair (n,n) (n = 3–8) SWCNTs, the C1–C2 bond lengths at the pentagon–pentagon fusion have almost the same bond length (1.392–1.395 Å). The C–C bonds located between two fused pentagons and the hexagon–heptagon rings have almost the same bond length (C1–C2 and C3–C4) too, indicating the conjugation among them. Similar results are obtained for the CD defective zigzag SWCNTs. Upon two hydrogen atoms adsorption on the exterior sidewall or the interior sidewall of the CD defective SWCNTs, all the bonds in the region of hydrogen chemisorption become longer, due to the enhancement of the sp3 rehybridization. An inspection of the data provide in Table 1 shows that, for both CD defective armchair and zigzag nanotubes, the elongation of the C1–C2 bond in the exohedral H(1,2) hydrogenated structures is higher compared to the endohedral H(1,2) hydrogenated nanotubes. For all outside hydrogenated SWCNTs studied, the C1–C2 bonds in the two hydrogen atoms on the adjacent carbon sites H(1,2) are longer than in the two hydrogen atoms on the alternate positions. This increase in bond length indicates weakening of C–C bond in the region of hydrogen chemisorption. The results suggest that it seems very likely that two hydrogen atoms would attack the outer sidewall C1–C2 bond of CD defective SWCNTs. The newly formed C–H bond has a weak diameter dependence and is 1.1 Å in all cases, which is consistent with the results reported recently for the chemisorption of hydrogen atoms on pristine nanotubes by Yang et al. [18]. 3.2. Electronic properties In Table 2, the HOMO–LUMO energy gaps are reported for the CD defective and hydrogen-chemisorbed SWCNTs at the B3LYP/ 6-31G* level. The variation of the HOMO–LUMO gaps for both CD defective nanotubes before and after addition is shown in Fig. 2. The gaps for the CD defective armchair series increase with increasing tube diameter. Chemisorption of two hydrogen atoms on CD defective armchair SWCNTs in the exohedral and endohedral H(1,2) and exohedral H(1,4) types significantly increases the gap of corresponding nanotubes, implying substantial energetic stability for these SWCNTs. These features are consistent with those reported for the chemisorption of hydrogen atoms on pristine nanotubes, where hydrogenation can open up or increase the energy gap of SWCNTs [25]. On the other hand, H(1,3) and H(2,4) additions on the outer sidewalls of CD defective armchair SWCNTs except for (3,3) nanotube reduce the energy gap of corresponding nanotubes. Note that the energy gap for the exohedral
Fig. 1. Optimized structures of the CD defective (colored yellow) armchair (n,n) and zigzag (m,0) SWCNT models. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Table 1 Selected bond lengths (in Å) obtained at the B3LYP/6-31G* level for the CD defective and hydrogen-chemisorbed SWCNTs. Structure (3,3)-CD (3,3)-CD+H(1,2), (3,3)-CD+H(1,2), (3,3)-CD+H(1,3), (3,3)-CD+H(2,4), (3,3)-CD+H(1,4), (4,4)-CD (4,4)-CD+H(1,2), (4,4)-CD+H(1,2), (4,4)-CD+H(1,3), (4,4)-CD+H(2,4), (4,4)-CD+H(1,4), (5,5)-CD (5,5)-CD+H(1,2), (5,5)-CD+H(1,2), (5,5)-CD+H(1,3), (5,5)-CD+H(2,4), (5,5)-CD+H(1,4), (6,6)-CD (6,6)-CD+H(1,2), (6,6)-CD+H(1,2), (6,6)-CD+H(1,3), (6,6)-CD+H(2,4), (6,6)-CD+H(1,4), (7,7)-CD (7,7)-CD+H(1,2), (7,7)-CD+H(1,2), (7,7)-CD+H(1,3), (7,7)-CD+H(2,4), (7,7)-CD+H(1,4), (8,8)-CD (8,8)-CD+H(1,2), (8,8)-CD+H(1,2), (8,8)-CD+H(1,3), (8,8)-CD+H(2,4), (8,8)-CD+H(1,4),
outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside outside inside outside outside outside
C1–C2
C2–C3
C3–C4
Structure
C1–C2
C2–C3
C3–C4
1.392 1.589 1.504 1.539 1.540 1.547 1.394 1.590 1.509 1.540 1.538 1.543 1.394 1.591 1.509 1.539 1.537 1.542 1.395 1.591 1.508 1.538 1.536 1.541 1.395 1.592 1.508 1.537 1.535 1.540 1.395 1.592 1.511 1.536 1.535 1.539
1.484 1.543 1.498 1.532 1.527 1.373 1.469 1.531 1.495 1.521 1.516 1.369 1.460 1.525 1.489 1.527 1.511 1.366 1.454 1.522 1.483 1.523 1.508 1.365 1.450 1.520 1.478 1.521 1.505 1.364 1.447 1.518 1.473 1.519 1.504 1.363
1.385 1.381 1.405 1.516 1.509 1.507 1.385 1.381 1.381 1.510 1.502 1.503 1.386 1.381 1.374 1.519 1.498 1.501 1.387 1.382 1.372 1.519 1.496 1.500 1.387 1.382 1.370 1.519 1.495 1.499 1.387 1.382 1.369 1.519 1.493 1.499
(8,0)-CD (8,0)-CD+H(1,2), outside (8,0)-CD+H(1,2), inside (8,0)-CD+H(1,3), outside (8,0)-CD+H(2,4), outside (8,0)-CD+H(1,4), outside (9,0)-CD (9,0)-CD+H(1,2), outside (9,0)-CD+H(1,2), inside (9,0)-CD+H(1,3), outside (9,0)-CD+H(2,4), outside (9,0)-CD+H(1,4), outside (10,0)-CD (10,0)-CD+H(1,2), outside (10,0)-CD+H(1,2), inside (10,0)-CD+H(1,3), outside (10,0)-CD+H(2,4), outside (10,0)-CD+H(1,4), outside (11,0)-CD (11,0)-CD+H(1,2), outside (11,0)-CD+H(1,2), inside (11,0)-CD+H(1,3), outside (11,0)-CD+H(2,4), outside (11,0)-CD+H(1,4), outside (12,0)-CD (12,0)-CD+H(1,2), outside (12,0)-CD+H(1,2), inside (12,0)-CD+H(1,3), outside (12,0)-CD+H(2,4), outside (12,0)-CD+H(1,4), outside (13,0)-CD (13,0)-CD+H(1,2), outside (13,0)-CD+H(1,2), inside (13,0)-CD+H(1,3), outside (13,0)-CD+H(2,4), outside (13,0)-CD+H(1,4), outside
1.389 1.584 1.470 1.535 1.523 1.523 1.393 1.583 1.470 1.524 1.519 1.518 1.385 1.580 1.483 1.526 1.517 1.517 1.386 1.581 1.507 1.519 1.514 1.515 1.384 1.579 1.512 1.520 1.514 1.514 1.384 1.578 1.523 1.516 1.513 1.513
1.412 1.486 1.459 1.488 1.481 1.354 1.409 1.486 1.455 1.490 1.480 1.357 1.410 1.485 1.459 1.485 1.477 1.354 1.407 1.486 1.468 1.486 1.476 1.352 1.408 1.485 1.468 1.483 1.475 1.355 1.408 1.485 1.473 1.484 1.474 1.354
1.404 1.397 1.373 1.541 1.493 1.510 1.402 1.391 1.370 1.541 1.492 1.506 1.399 1.396 1.366 1.538 1.489 1.505 1.394 1.395 1.359 1.539 1.488 1.502 1.397 1.395 1.362 1.536 1.487 1.502 1.397 1.395 1.363 1.537 1.486 1.501
Table 2 HOMO–LUMO energy gap values (in eV) obtained at the B3LYP/6-31G* level for the CD defective and hydrogen-chemisorbed SWCNTs. Structure
Defective tube
H(1,2), outside
H(1,2), inside
H(1,3), outside
H(2,4), outside
H(1,4), outside
(3,3) (4,4) (5,5) (6,6) (7,7) (8,8) (8,0) (9,0) (10,0) (11,0) (12,0) (13,0)
1.63 1.99 2.20 2.33 2.37 2.36 0.40 0.34 0.38 0.14 0.37 0.33
2.14 2.44 2.58 2.66 2.70 2.73 0.42 0.27 0.40 0.36 0.39 0.34
2.80 2.72 2.58 2.61 2.59 2.54 0.40 0.33 0.39 0.19 0.38 0.25
2.22 1.28 1.78 1.96 2.07 2.14 0.43 0.38 0.36 0.33 0.33 0.31
1.85 1.78 1.66 1.60 1.57 1.55 0.39 0.37 0.38 0.32 0.36 0.29
2.26 2.40 2.44 2.43 2.40 2.38 0.40 0.34 0.39 0.33 0.22 0.33
Fig. 2. Variation of HOMO–LUMO gaps of (n,n) and (m,0) CD defective and hydrogen-chemisorbed SWCNTs with the increase of the number (a) n and (b) m.
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H(1,2) hydrogen-chemisorbed armchair tube is proportional to tube diameter. Whereas the endohedral H(1,2) and exohedral H(1,4) hydrogen-chemisorbed armchair tubes is inversely proportional. In contrast, the CD defective zigzag series have significantly lower gaps. The gaps decrease with an odd–even oscillatory behavior, with increasing tube diameter. However, the variation in the gap is very small and hence gives little information on the meaningful trend. Upon two hydrogen atoms on the sidewalls of CD defective zigzag SWCNTs, the B3LYP/6-31G* calculations indicate that the energy gap values remain almost unaffected by chemisorption of hydrogen atoms. The energy gap variation with the increase of the number n (Fig. 2a) and m (Fig. 2b) indicates that the CD defective and hydrogen-chemisorbed armchair tubes are always wide energy gap structures, while the CD defective and hydrogen-chemisorbed zigzag tubes have significantly lower gaps and might exhibit metallic behavior. 3.3. Reaction energies of chemisorption of two hydrogen atoms Total energies and the reaction energies per hydrogen atom addition (Er/H) computed at the B3LYP/6-31G* level of theory for the CD defective and hydrogen-chemisorbed SWCNTs are present in Table 3. It can be seen that the reaction energies per hydrogen atom addition are all negative value. This implies that the addition reactions are exothermic. For both the CD defective armchair (n,n) and zigzag (m,0) SWCNTs, exohedral nanotube adsorption is energetically more favorable than endohedral adsorption, as shown in Fig. 3a and b; the reaction energies of the endo-hydrogenated CD defective SWCNTs increase with increasing tube diameter. The results are consistent with the previous reported for the chemisorption of hydrogen atoms on pristine nanotubes [18]. Upon two hydrogen atoms on the exterior sidewalls of CD defective armchair and zigzag SWCNTs, the addition of H(1,2) is thermodynamically more favored than the H(1,3), H(2,4), and H(1,4) additions regardless of the diameter and chirality of the SWCNTs considered. The addition of H(1,4) is the second positional preference. The Er/H of the H(1,2) addition is about 18–22 kcal/mol (3–10 kcal/mol) more negative than that of the H(1,4) addition for the CD defective armchair (zigzag) SWCNTs. The thermodynamically lower preference of H(1,3) and H(2,4) additions for both CD defective armchair and zigzag SWCNTs is in agreement with the results reported recently for pristine armchair-type nanotubes by Dinadayalane et al. [19]. The reaction energies of the exohedral H(1,2) for the armchair SWCNTs decrease slightly with increasing tube diameter, whereas those for the zigzag SWCNTs increase slightly except (9,0) and (12,0) SWCNTs, whose reaction energies decrease slightly. Our results indicate that tube diameter has very slight effect on the reaction energy of two hydrogen atoms on the exterior sidewalls
of CD defective SWCNTs. This is different from the results reported on pristine nanotubes [19]. The hydrogenation reaction energies (per H) of the H(1,2) addition on the exterior sidewalls of CD defective armchair SWCNTs obtained at the B3LYP/6-31G* level of theory are 89.4, 86.9, 85.1, and 83.8 kcal/mol for (3,3), (4,4), (5,5), and (6,6) SWCNTs, respectively. Compared to the hydrogenation reaction energies of two hydrogen atoms on the exterior sidewalls of pristine armchair SWCNTs obtained at the same level of theory ( 61.6 and 53.7 kcal/mol/H for 7-layer (3,3) and (4,4) SWCNTs; 64.9, 57.9, 50.0, and 42.1 kcal/mol/H for 9-layer (3,3), (4,4), (5,5), and (6,6) SWCNTs, respectively) [19,26], the reaction energies of the exo-hydrogenated CD defective armchair SWCNTs are more exothermic, meaning that the central C–C bond of CD defect in the armchair SWCNTs is more reactive than that in perfect sites. The result agrees with the previous ones [20]. The adsorptions of two hydrogen atoms at the C2–C3 and C3– C4 positions were only considered for CD defective armchair (5,5) and zigzag (9,0) nanotubes. The reaction energies are given in Fig. 4. For the CD defective armchair (5,5) nanotube, the reaction energies of 48.7 and 57.1 kcal/mol for H(2,3) and H(3,4) are 36.4 and 28 kcal/mol smaller than that of 85.1 kcal/mol for H(1,2), respectively. In the case of the CD defective zigzag (9,0) nanotube, the reaction energies of 55.6, and 60.1 kcal/mol for H(2,3) and H(3,4) are 6.6 and 2.1 kcal/mol smaller than that of 62.2 kcal/mol for H(1,2), respectively. From these results, one can clearly see that the C1–C2 sites are more reactive than the other sites. Moreover, the reactive sites in the CD defective SWCNTs are not very sensitive to the tube chirality. 3.4. Adsorption of more hydrogen atoms on the exterior sidewalls of CD defective armchair SWCNTs In the case of CD defective armchair SWCNTs, the addition of twelve hydrogen atoms only on the exterior sidewalls of SWCNTs is considered here. Fig. 5 shows the optimized geometry for twelve hydrogen atoms bonded to the CD defective (5,5) SWCNT as an example of a series of hydrogen-chemisorbed SWCNTs. The calculated bond lengths and energy values of the systems studied are given in Table 4. The calculations show that the optimized tubular structures of CD defective SWCNTs are deformed by the presence of multiply chemisorbed H atoms. The corresponding C–C bonds in the defective region of all the hydrogen-chemisorbed SWCNTs have almost the same bond length (Table 4). Compared with chemisorption of two hydrogen atoms, the chemisorption of twelve hydrogen atoms on CD defective armchair SWCNTs reduces the HOMO–LUMO gap and reaction energy of corresponding nanotubes. The reaction energies are still negative, i.e., the adsorption is favorable. The Er/H for the 12H adsorptions decreases for each
Table 3 Total energies (Etot, a.u.) and reaction energies per hydrogen atom (Er/H, kcal/mol) computed at the B3LYP/6-31G* level of theory for the CD defective and hydrogen-chemisorbed SWCNTs. Structure
(3,3) (4,4) (5,5) (6,6) (7,7) (8,8) (8,0) (9,0) (10,0) (11,0) (12,0) (13,0)
Defective tube
H(1,2), outside
Etot
Etot
1683.52149 2219.64389 2755.71912 3291.77078 3827.80704 4363.83389 2524.36315 2830.49807 3136.65207 3442.77498 3748.91213 4055.03824
1684.80695 2220.92128 2756.99095 3293.03843 3829.07177 4365.09609 2525.56899 2831.69694 3137.86146 3443.99298 3750.12411 4056.25128
H(1,2), inside Er/H 89.4 86.9 85.1 83.8 82.9 82.1 64.4 62.2 65.5 68.2 66.3 66.7
Etot 1684.53550 2220.66192 2756.75039 3292.81617 3828.86453 4364.90191 2525.46409 2831.61353 3137.78388 3443.92394 3750.06767 4056.20406
H(1,3), outside Er/H 4.2 5.5 9.6 14.1 17.9 21.2 31.5 36.1 41.2 46.6 48.6 51.9
Etot 1684.75211 2220.82432 2756.89533 3292.94817 3828.98542 4365.01274 2525.52417 2831.67073 3137.81213 3443.94850 3750.07243 4056.20019
H(2,4), outside Er/H 72.2 56.4 55.1 55.5 55.8 55.9 50.3 54.0 50.0 54.3 50.1 50.6
Etot 1684.72972 2220.82909 2756.89305 3292.93764 3828.97003 4364.99403 2525.53154 2831.67582 3137.82134 3443.95282 3750.08099 4056.20458
H(1,4), outside Er/H 65.2 57.9 54.4 52.2 51.0 50.1 52.7 55.6 52.9 55.6 52.8 52.0
Etot 1684.75125 2220.85852 2756.92484 3292.97046 3829.00301 4365.02703 2525.55082 2831.68662 3137.83829 3443.96588 3750.09092 4056.22004
Er/H 71.9 67.2 64.4 62.5 61.3 60.4 58.7 59.0 58.3 59.7 55.9 56.9
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D. Wang et al. / Journal of Molecular Structure: THEOCHEM 962 (2010) 62–67
Fig. 3. Variation of reaction energies for the chemisorption of two hydrogen atoms on the sidewalls of CD defective armchair (a) and zigzag (b) SWCNTs.
Fig. 4. B3LYP/6-31G* optimized geometries of H(2,3) and H(3,4) additions of two hydrogen atoms on the outside sidewalls of CD defective (colored yellow) armchair (5,5) and zigzag (9,0) nanotubes. The C1–C2 bond distances (in Å), HOMO–LUMO energy gap (DE) values (in eV), and the reaction energies per hydrogen atom (Er/H, kcal/mol) for hydrogen chemisorptions are given. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. Optimized structures of the CD defective (colored yellow) armchair (5,5) SWCNT with twelve hydrogen atoms adsorbed on the exterior wall: (a) top view, (b) side view and (c) perspective view. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 4 Selected bond lengths (in Å) total energies (Etot), HOMO and LUMO energies, energy gaps (DE), and reaction energies per hydrogen atom (Er/H) computed at the B3LYP/6-31G* level of theory for the hydrogen-chemisorbed SWCNTs. (All energies in eV except total energies (Etot) in Hartrees and reaction energies (Er) in kcal/mol). Structure (3,3)-CD+12H, (4,4)-CD+12H, (5,5)-CD+12H, (6,6)-CD+12H, (7,7)-CD+12H, (8,8)-CD+12H,
outside outside outside outside outside outside
Formula
C1–C2
C2–C3
C3–C4
C44H24 C58H28 C72H32 C86H36 C100H40 C114H44
1.576 1.575 1.574 1.573 1.572 1.572
1.590 1.573 1.569 1.565 1.563 1.563
1.555 1.555 1.552 1.551 1.550 1.550
system. The (3,3)-CD+H(1,2), outside is 89.4 kcal/mol, whereas the (3,3)-CD+12H, outside is 63.7 kcal/mol. The (8,8)-CD+H(1,2), outside is 82.1 kcal/mol, whereas the (8,8)-CD+12H, outside is 56.4 kcal/mol. In each and every (n,n) case, the Er/H for the 12H systems are consistently 26 kcal/mol weaker in magnitude and consequently less thermodynamically stable than the 2H, outside systems.
Etot 1690.74359 2226.80140 2762.83410 3298.86689 3834.89360 4370.91586
HOMO 3.54 3.61 3.50 3.54 3.59 3.63
LUMO 2.71 2.76 2.83 2.79 2.75 2.73
DE 0.84 0.85 0.68 0.76 0.84 0.90
Er/H 63.7 60.4 58.1 57.1 56.6 56.4
4. Conclusions In summary, the structural and electronic properties of hydrogenated armchair and zigzag SWCNTs with carbon ad-dimer (CD) defect have been studied theoretically. It is found that, the chemisorptions of two hydrogen atoms on the exterior sidewalls of CD defective armchair SWCNTs are thermodynamically more stable
D. Wang et al. / Journal of Molecular Structure: THEOCHEM 962 (2010) 62–67
than the pristine nanotubes with two hydrogen atoms chemisorbed. The adsorption on the CD defective armchair SWCNTs is slightly stronger than on the CD defective zigzag ones. The addition at H(1,2) positions is more favored than addition at H(1,3), H(2,4), and H(1,4) positions for both armchair and zigzag nanotubes when two hydrogen atoms are attached to the exterior sidewalls. With the increase of the number of hydrogen atoms, the HOMO–LUMO gap and reaction energy decrease. A remarkable property of CD defective SWCNTs is that the reaction energy of hydrogen chemisorption on the exterior sidewalls of SWCNTs is almost independent of the tube diameter. This is different from the results reported on pristine nanotubes. The present results might be useful for further investigations related to the chemical functionalization of CD defective nanotubes because of the high reactivity of their exterior surface. Acknowledgement This work was supported by Department of Education of Liaoning Province (Grant No. 2009A784). Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.theochem.2010.09.015. References [1] S. Iijima, Nature 354 (1991) 56. [2] M.S. Dresselhaus, G. Dresselhaus, A. Jorio, Annu. Rev. Mater. Res. 34 (2004) 247. [3] C. Liu, Y.Y. Fan, M. Liu, H.T. Cong, H.M. Cheng, M.S. Dresselhaus, Science 286 (1999) 1127. [4] J. Kong, N.R. Franklin, C.W. Zhou, M.G. Chapline, S. Peng, K.J. Cho, H.J. Dai, Science 287 (2000) 622.
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