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Addition of diazomethane to armchair single-walled carbon nanotubes and their reaction sequences: A computational study
Chemical Physics Letters 436 (2007) 218–223 www.elsevier.com/locate/cplett
Addition of diazomethane to armchair single-walled carbon nanotubes and their reaction sequences: A computational study Banchob Wanno a, A.J. Du b, Vithaya Ruangpornvisuti a
a,*
, Sean C. Smith
b,*
Supramolecular Chemistry Research Unit, Department of Chemistry, Faculty of Science, Chulalongkorn University, 10330 Bangkok, Thailand b Centre for Computational Molecular Science, Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, QLD 4072, Brisbane, Australia Received 20 December 2006; in final form 10 January 2007 Available online 20 January 2007
Abstract The sidewall additions of diazomethane to (n, n), n = 3–10 armchair single-walled carbon nanotubes (SWCNTs) on two different orientations of C–C bonds have been studied using the ONIOM(B3LYP/6-31G(d):PM3) approach. The binding energies of SWCNTs complexes with CH2N2, CH2 and their transition-state structures were computed at the B3LYP/6-31G(d) level. The effects of diameters of armchair SWCNTs on their binding energies were studied. Relative reactivities of all the SWCNTs and their complexes based on their frontier orbital energies gaps are reported. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Over the past few years, research has been focused on functionalizations of SWCNTs for enhancement their properties, especially the solubility [1,2]. Successful functionalizations of SWCNTs such as non-covalent exohedral functionalization with polymers, defect-group functionalization with carboxylic acid groups, non-covalent exohedral functionalization with molecules through p-stacking, endohedral functionalization with fullerene (C60) and side-wall (covalent) functionalization have been reported [1–5]. Additionally, SWCNT side-wall functionalizations using fluorine [6,7], diazonium salts [8], organic radicals [9], azomethine ylides [10], and nitrenes [11], have received attention. The reaction of carbenes with organic p-systems such as fullerenes and graphenes has been widely applied for the synthesis of cyclopropane derivatives [12]. The carbenes
* Corresponding authors. Fax: +66 2 254 1309 (V. Ruangpornvisuti), +61 7 334 63992 (S.C. Smith). E-mail addresses: [email protected] (V. Ruangpornvisuti), s.smith@ uq.edu.au (S.C. Smith).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.01.048
generated from chloroform or phenyl(bromodichloromethyl)mercury, a precursor for free dichlorocarbene, covalently bound with SWCNTs to form the soluble SWCNTs have been reported [13]. A lot of theoretical studies have been performed to predict their reaction mechanism and geometry structures of the direct carbene or carbene analogue addition onto the side-walls of SWCNTs. Methanofullerenes, the cyclopropane derivatives, have been synthesized by Smith et al. via 1,3-dipolar cycloaddition of diazomethane followed by thermal extrusion of nitrogen gas [14,15]. For the synthesis route, in the first step, the diazo compound adds to a C–C bond of fullerene to produce the stable pyrazoline intermediate which can be detected and isolated. The second step is the thermal extrusion of nitrogen gas from the pyrazoline intermediate with formation of methanofullerenes. The formation of methanofullerenes by addition of diazo compounds to benzene and fullerenes has been studied theoretically by Diederich and coworkers [16]. In principle, the SWCNT wall, a multiply p-bonded system, should be amenable to these reactions with diazomethane. However, experimental and theoretical studies of the side-wall addition to SWCNT of diazomethane to from the methanonanotubes product have not yet appeared to the best of our knowledge.
B. Wanno et al. / Chemical Physics Letters 436 (2007) 218–223
219
In the present work, the effect of armchair SWCNT sizes on the formation of the pyrazoline intermediate and methanonanotube product, especially the structures and adsorption energies has been investigated. The systematic reaction mechanism of diazomethane addition into sidewall armchair SWCNTs to form the methanonanotube has also been theoretically predicted.
any symmetry constraints. All transition states were characterized by a single imaginary frequency. The vibration frequencies computations were performed at 298.15 K and the standard pressure. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy gaps have also been determined. All calculations were performed with the GAUSSIAN 03 program [22].
2. Computational details
3. Results and discussion
Ten-layered (n, n) armchair SWCNTs, n = 3–10 were applied for all tube models. The hydrogen atoms are used to saturate the carbon atoms with dangling bonds at the two ends. For the variation of theoretical methods on adsorption properties, geometry optimizations of two cycloaddition adducts of side-wall (5, 5) armchair SWCNT (C100H20 model), pyrazoline intermediate (SWCNT/ CH2N2) and methanonanotube product (SWCNT/CH2) were performed using three different methods namely the semiempirical PM3 [17], the two-layered ONIOM(B3LYP/6-31G(d):PM3) [18,19] and the B3LYP/6-31G(d) methods [20,21]. The ball atoms of a pyrene (C16) model cluster and those belonging to diazomethane molecule were treated at the higher B3LYP/6-31G(d) level, and the remaining SWCNT atoms were treated with the PM3 method. Based on the two-layered ONIOM approach, a pyrene molecule shown as ball atoms was selected to be the high level layer and orientations of its C1–C2 bond are defined as Type I, perpendicular and Type II, alongside with the SWCNTs tube-length as shown in Fig. 1 which the (5, 5) armchair C100H20 SWCNT is presented as a representative model. The (n, n) SWCNTs, n = 3–10 and the (n, n) SWCNTs, n = 3, 5 and 7 were chosen for the adsorption energy and the systematic reaction mechanism studies, respectively. All of the structure of reactants, transition states, intermediates and products were located by the two-layer ONIOM(B3LYP/6-31G(d):PM3) model achieved without
3.1. The optimized structures at various methods The structure optimizations of (5, 5) armchair SWCNT and its complexes with CH2N2 and CH2 and transitionstate structures were carried out at the PM3, ONIOM(B3LYP/6-31G(d):PM3) and B3LYP/6-31G(d) levels of theory in order to examine the reliability of the ONIOM(B3LYP/6-31G(d):PM3) approach. All the structure optimizations of various diameters of (n, n), n = 3–10 armchair SWCNTs, their complexes with CH2N2 and CH2 and transition-state structures were carried out at the ONIOM(B3LYP/6-31G(d):PM3) level. The selected bond distances of the PM3, ONIOM(B3LYP/6-31G(d):PM3) and B3LYP/ 6-31G(d)-optimized structures for (5, 5) armchair SWCNT system are shown in Table 1, for which the atoms are defined in Fig. 1. Geometrical data optimized at the ONIOM(B3LYP/631G(d):PM3) and B3LYP/6-31G(d) levels not much different. The ONIOM(B3LYP/6-31G(d):PM3) approach was regularly employed in all the structure optimizations. The high-layer ONIOM(B3LYP/6-31G(d):PM3)-optimized structures for transition states TS1 and TS2 involved in the diazomethane addition to Type I and II, C1–C2 bonds of the side-wall for the (a) (3, 3), (b) (5, 5) and (c) (7, 7) armchair SWCNTs are shown in Fig. 2. The transition states TS1 and TS2 of these three SWCNTs are representative of those for the (n, n), n = 3–10 armchair SWCNTs. Fig. 2 reveals the effects of the nanotube curvature on the adsorbed
Fig. 1. Based on the two-layered ONIOM approach, a pyrene molecule shown as ball atoms was selected to be the high level layer and orientations of its C1–C2 bond are defined as (a) perpendicular (Type I) and (b) alongside (Type II) with the SWCNTs tube-length.
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B. Wanno et al. / Chemical Physics Letters 436 (2007) 218–223
Table 1 ˚ ) for the (5, 5) SWCNT complexes with CH2N2 and CH2 at two different C1–C2 binding sites of Types I and II, optimized at Selected bond distances (in A the B3LYP/6-31G(d), ONIOM(B3LYP/6-31G(d):PM3) (in parenthesis) and PM3 [in bracket] levels of theory Complexes
C1–C2
C1–C3
C2–N1
C3–N2
N1–N2
Type I SWCNT/CH2N2 SWCNT/CH2
1.638 (1.641) [1.615] 2.217 (2.226) [2.238]
1.586 (1.579) [1.567] 1.495 (1.497) [1.494]
1.593 (1.570) [1.536] 1.495 (1.497) [1.494]
1.464 (1.465) [1.482] –
1.221 (1.223) [1.215] –
Type IIb SWCNT/CH2N2 SWCNT/CH2
1.568 (1.580) [1.584] 1.564 (1.572) [1.544]
1.564 (1.563) [1.558] 1.516 (1.514) [1.508]
1.560 (1.559) [1.530] 1.516 (1.514) [1.508]
1.478 (1.478) [1.486] –
1.231 (1.231) [1.218] –
a
a b
Orientation of C1–C2 binding site is defined as the perpendicular direction with the tube length as shown in Fig. 1. Orientation of C1–C2 binding site is defined as alongside direction with the tube length as shown in Fig. 1.
complex structures and their hydrogen bond distances. The C1–C2 bond distances for the ONIOM(B3LYP/6-31G(d): PM3)-optimized structures of the complexes with H2N2 and CH2with (n, n), n = 3–10 armchair SWCNTs are listed in Table 2. The Type I, C1–C2 bond distances for the H2N2 adsorption on the large SWCNT diameters such as (9, 9) and (10, 10) SWCNTs are gradually decreased and expected to convert at a certain value. Nevertheless, the Type II, C1–C2 bond distances on the complex systems of CH2 adsorbed on the (8, 8) and (9, 9) SWCNTs are lar˚ . This phenomenon gely decreased from 2.194 to 1.717 A describes formation of the C–C bond which caused by the reduction of SWCNT strain. 3.2. Binding energies of adsorptions, energy profiles and reaction mechanism The plots against diameters of SWCNTs of the B3LYP/ 6-31G(d)//ONIOM(B3LYP/6-31G(d):PM3) binding ener-
gies for the addition of CH2N2 and CH2 on the C1–C2 bonds Types I and II are shown in Fig. 3. Based on the various diameters of (n, n), n = 3–10 armchair SWCNTs, their SWCNT/CH2 complexes are obviously more stable than the corresponding SWCNT/CH2N2 complexes by 47 to 69 kcal/mol for the C1–C2 bond Type I and 21–31 kcal/ mol for Type II. The adsorption reaction becomes progressively more favorable thermodynamically as the diameter of the SWCNT decreases. Energy profiles based on the B3LYP/6-31G(d)// ONIOM(B3LYP/6-31G(d):PM3) computations for the side-wall addition of diazomethane and mechanistic sequences for (a) Type I and (b) Type II of (3, 3), (5, 5) and (7, 7) armchair SWCNTs are shown in Fig. 4. It is apparent that the complexes and transition states for of the (3, 3) SWCNT system are the most stable species – considerably more so than those of the larger diameter SWCNTs. This effect is most pronounced for the Type I reaction.
Fig. 2. The two transition states (TS1 and TS2) shown as the high-layered ONIOM(B3LYP/6-31G(d):PM3)-optimized structures for the diazomethane addition on C1–C2 bonds, Types I and II of side-wall (a) (3, 3), (b) for (5, 5) and (c) (7, 7) armchair SWCNTs.
B. Wanno et al. / Chemical Physics Letters 436 (2007) 218–223
221
Table 2 ˚ ) for the ONIOM(B3LYP/6-31G(d):PM3)-optimized structures of various sizes of SWCNTs as two different complexes The C1–C2 bond distances (in A and on two different Types of C1–C2 bond’s orientations Binding site/complexes
SWCNTs (3, 3)
(4, 4)
(5, 5)
(6, 6)
(7, 7)
(8, 8)
(9, 9)
(10, 10)
Type I SWCNT/CH2N2 SWCNT/CH2
1.671 2.262
1.664 2.241
1.641 2.226
1.628 2.214
1.619 2.203
1.612 2.194
1.607 1.717
1.602 1.690
Type II SWCNT/CH2N2 SWCNT/CH2
1.553 1.561
1.581 1.568
1.580 1.572
1.578 1.573
1.577 1.572
1.575 1.571
1.575 1.570
1.574 1.536
Fig. 3. Plots against diameters of SWCNTs of the B3LYP/6-31G(d)//ONIOM(B3LYP/6-31G(d):PM3) binding energies for the addition of CH2N2 (m) and CH2 (j) on the C1–C2 bonds (a) Type I and (b) Type II of armchair (n, n) SWCNTs, n = 3–10.
3.3. Reactivities against diameter of SWCNTs The orbital energies ELUMO and EHOMO and frontier molecular orbital energy gaps, EHOMO–LUMO of all SWCNTs systems based on the ONIOM(B3LYP/631G(d):PM3)-optimized structures are listed in Table 3 and the orbital energy plots of all SWCNTs and their complexes SWCNT/CH2N2 and SWCNT/CH2 are shown in Fig. 5. The EHOMO–LUMO of the isolated SWCNTs and their complexes SWCNT/CH2N2 and SWCNT/CH2 for the adsorption Type II and only the isolated SWCNT for the Type I are the exponential growth functions. For the large diameter SWCNTs of both Types I and II, the
approach to a stable value of the DEHOMO–LUMO is expected. Based on the general correlation between DEHOMO–LUMO and reactivity [23], the relative reactivities for the absorption Type II of the isolated SWCNTs and their complexes SWCNT/CH2N2 and SWCNT/CH2 are in the decreasing order as their SWCNT diameters are increased. It is apparent that there are some anomalous effects in the progressions of Fig. 5 for the Type I adsorptions of the (3, 3) SWCNT/CH2N2 system and the (9, 9) and (10, 10) SWCNT/CH2 systems, for reasons that are not yet clear. However, the general trends are sufficiently clear given the qualitative nature of this band-gap/reactivity correlation.
Fig. 4. Energy profiles based on the B3LYP/6-31G(d)//ONIOM(B3LYP/6-31G(d):PM3) computations for the side-wall addition of diazomethane and mechanistic sequences for (a) Type I and (b) Type II of (3, 3), (5, 5) and (7, 7) armchair SWCNTs.
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Table 3 The ELUMO and EHOMO and energy gaps, DEHOMO–LUMO of the ONIOM(B3LYP/6-31G(d):PM3)-optimized structures of SWCNTs on two different binding sites Species
ELUMO a SWCNT
EHOMO a SWCNT/ CH2N2
SWCNT/ CH2
SWCNT
DEHOMO–LUMO a SWCNT/ CH2N2
SWCNT/ CH2
SWCNT
SWCNT/ CH2N2
SWCNT/ CH2
Type I CN33t CN44t CN55t CN66t CN77t CN88t CN99t CN1010t
2.99 2.75 2.64 2.56 2.53 2.50 2.48 2.48
2.88 2.99 2.88 2.80 2.75 2.75 2.72 2.69
2.91 2.67 2.56 2.50 2.48 2.45 2.53 2.53
3.76 4.00 4.22 4.35 4.44 4.49 4.54 4.57
4.00 3.89 4.08 4.19 4.30 4.35 4.38 4.41
3.78 4.05 4.22 4.35 4.44 4.49 4.38 4.41
0.76 1.25 1.58 1.80 1.91 1.99 2.07 2.10
1.12 0.90 1.20 1.39 1.55 1.61 1.66 1.71
0.87 1.39 1.66 1.85 1.96 2.04 1.85 1.88
Type II CN33p CN44p CN55p CN66p CN77p CN88p CN99p CN1010p
2.94 2.69 2.61 2.53 2.50 2.48 2.48 2.48
2.80 2.61 2.50 2.48 2.45 2.45 2.45 2.45
2.69 2.50 2.45 2.39 2.39 2.39 2.39 2.39
3.78 4.05 4.25 4.38 4.46 4.52 4.57 4.60
4.08 4.33 4.44 4.52 4.57 4.60 4.63 4.63
3.95 4.16 4.33 4.44 4.52 4.54 4.60 4.60
0.84 1.36 1.63 1.85 1.96 2.04 2.10 2.12
1.28 1.71 1.93 2.04 2.12 2.15 2.18 2.18
1.25 1.66 1.88 2.04 2.12 2.15 2.20 2.20
a
In eV.
Fig. 5. Plots against SWCNTs diameters of orbital energy gaps (above) and orbital energies LUMOs and HOMOs (below) based on the C1–C2 binding sites (a) Type I and (b) Type II. The frontier orbital energy gaps (–j–), (–m–) and (––) (above), LUMOs (h), (D) and (s) and HOMOs (j), (m) and (d) are of the isolated SWCNT, SWCNT/CH2N2 and SWCNT/CH2, respectively.
4. Conclusions The binding energies of addition of CH2N2 and CH2on the C1–C2 bonds Types I and II of (n, n), n = 3–10 armchair
SWCNTs were obtained using a two-layered B3LYP/631G(d)//ONIOM(B3LYP/6-31G(d):PM3) level of theory. Based on the various diameters of (n, n), n = 3–10 armchair SWCNTs, their SWCNT/CH2 complexes are obviously
B. Wanno et al. / Chemical Physics Letters 436 (2007) 218–223
more stable than their corresponding SWCNT/CH2N2 complexes by 47–69 kcal/mol for the C1–C2 bond Type I and 21–31 kcal/mol for Type II. The adsorption reaction becomes energetically more favorable as the diameter of the SWCNT progressively decreases. This trend also likely to hold for the kinetics of the reactions is supported by the specific reaction pathway energy profiles calculated for the (3, 3), (5, 5) and (7, 7) nanotubes, as well as the energy band gaps computed across the range of diameters. We note finally that the band gaps for these SWCNT systems are likely to be reduced further if longer nanotubes are studied, e.g., via periodic boundary methods. We expect nevertheless that the trends observed in this work as a function of nanotube diameter should be strongly confirmed. Acknowledgements The Royal Golden Jubilee (RGJ) Grant No. PHD47K0164 supported by TRF to BW is acknowledged. The facility provided by Research Affairs, Chulalongkorn University is also gratefully acknowledged. We also thank the Thailand Research Fund (TRF) and the National Nanotechnology Center (NANOTEC), NN-B-22-m10-1049-18, National Science and Technology Development Agency, Thailand for partial support of this work. This work has also been facilitated by generous grants of computer time on the Computational Molecular Science cluster facility during BW’s research visit to the Centre for Computational Molecular Science at The University of Queensland.
223
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Addition of diazomethane to armchair single-walled carbon nanotubes and their reaction sequences: A computational study Banchob Wanno a, A.J. Du b, Vithaya Ruangpornvisuti a
a,*
, Sean C. Smith
b,*
Supramolecular Chemistry Research Unit, Department of Chemistry, Faculty of Science, Chulalongkorn University, 10330 Bangkok, Thailand b Centre for Computational Molecular Science, Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, QLD 4072, Brisbane, Australia Received 20 December 2006; in final form 10 January 2007 Available online 20 January 2007
Abstract The sidewall additions of diazomethane to (n, n), n = 3–10 armchair single-walled carbon nanotubes (SWCNTs) on two different orientations of C–C bonds have been studied using the ONIOM(B3LYP/6-31G(d):PM3) approach. The binding energies of SWCNTs complexes with CH2N2, CH2 and their transition-state structures were computed at the B3LYP/6-31G(d) level. The effects of diameters of armchair SWCNTs on their binding energies were studied. Relative reactivities of all the SWCNTs and their complexes based on their frontier orbital energies gaps are reported. Ó 2007 Elsevier B.V. All rights reserved.
1. Introduction Over the past few years, research has been focused on functionalizations of SWCNTs for enhancement their properties, especially the solubility [1,2]. Successful functionalizations of SWCNTs such as non-covalent exohedral functionalization with polymers, defect-group functionalization with carboxylic acid groups, non-covalent exohedral functionalization with molecules through p-stacking, endohedral functionalization with fullerene (C60) and side-wall (covalent) functionalization have been reported [1–5]. Additionally, SWCNT side-wall functionalizations using fluorine [6,7], diazonium salts [8], organic radicals [9], azomethine ylides [10], and nitrenes [11], have received attention. The reaction of carbenes with organic p-systems such as fullerenes and graphenes has been widely applied for the synthesis of cyclopropane derivatives [12]. The carbenes
* Corresponding authors. Fax: +66 2 254 1309 (V. Ruangpornvisuti), +61 7 334 63992 (S.C. Smith). E-mail addresses: [email protected] (V. Ruangpornvisuti), s.smith@ uq.edu.au (S.C. Smith).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.01.048
generated from chloroform or phenyl(bromodichloromethyl)mercury, a precursor for free dichlorocarbene, covalently bound with SWCNTs to form the soluble SWCNTs have been reported [13]. A lot of theoretical studies have been performed to predict their reaction mechanism and geometry structures of the direct carbene or carbene analogue addition onto the side-walls of SWCNTs. Methanofullerenes, the cyclopropane derivatives, have been synthesized by Smith et al. via 1,3-dipolar cycloaddition of diazomethane followed by thermal extrusion of nitrogen gas [14,15]. For the synthesis route, in the first step, the diazo compound adds to a C–C bond of fullerene to produce the stable pyrazoline intermediate which can be detected and isolated. The second step is the thermal extrusion of nitrogen gas from the pyrazoline intermediate with formation of methanofullerenes. The formation of methanofullerenes by addition of diazo compounds to benzene and fullerenes has been studied theoretically by Diederich and coworkers [16]. In principle, the SWCNT wall, a multiply p-bonded system, should be amenable to these reactions with diazomethane. However, experimental and theoretical studies of the side-wall addition to SWCNT of diazomethane to from the methanonanotubes product have not yet appeared to the best of our knowledge.
B. Wanno et al. / Chemical Physics Letters 436 (2007) 218–223
219
In the present work, the effect of armchair SWCNT sizes on the formation of the pyrazoline intermediate and methanonanotube product, especially the structures and adsorption energies has been investigated. The systematic reaction mechanism of diazomethane addition into sidewall armchair SWCNTs to form the methanonanotube has also been theoretically predicted.
any symmetry constraints. All transition states were characterized by a single imaginary frequency. The vibration frequencies computations were performed at 298.15 K and the standard pressure. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energy gaps have also been determined. All calculations were performed with the GAUSSIAN 03 program [22].
2. Computational details
3. Results and discussion
Ten-layered (n, n) armchair SWCNTs, n = 3–10 were applied for all tube models. The hydrogen atoms are used to saturate the carbon atoms with dangling bonds at the two ends. For the variation of theoretical methods on adsorption properties, geometry optimizations of two cycloaddition adducts of side-wall (5, 5) armchair SWCNT (C100H20 model), pyrazoline intermediate (SWCNT/ CH2N2) and methanonanotube product (SWCNT/CH2) were performed using three different methods namely the semiempirical PM3 [17], the two-layered ONIOM(B3LYP/6-31G(d):PM3) [18,19] and the B3LYP/6-31G(d) methods [20,21]. The ball atoms of a pyrene (C16) model cluster and those belonging to diazomethane molecule were treated at the higher B3LYP/6-31G(d) level, and the remaining SWCNT atoms were treated with the PM3 method. Based on the two-layered ONIOM approach, a pyrene molecule shown as ball atoms was selected to be the high level layer and orientations of its C1–C2 bond are defined as Type I, perpendicular and Type II, alongside with the SWCNTs tube-length as shown in Fig. 1 which the (5, 5) armchair C100H20 SWCNT is presented as a representative model. The (n, n) SWCNTs, n = 3–10 and the (n, n) SWCNTs, n = 3, 5 and 7 were chosen for the adsorption energy and the systematic reaction mechanism studies, respectively. All of the structure of reactants, transition states, intermediates and products were located by the two-layer ONIOM(B3LYP/6-31G(d):PM3) model achieved without
3.1. The optimized structures at various methods The structure optimizations of (5, 5) armchair SWCNT and its complexes with CH2N2 and CH2 and transitionstate structures were carried out at the PM3, ONIOM(B3LYP/6-31G(d):PM3) and B3LYP/6-31G(d) levels of theory in order to examine the reliability of the ONIOM(B3LYP/6-31G(d):PM3) approach. All the structure optimizations of various diameters of (n, n), n = 3–10 armchair SWCNTs, their complexes with CH2N2 and CH2 and transition-state structures were carried out at the ONIOM(B3LYP/6-31G(d):PM3) level. The selected bond distances of the PM3, ONIOM(B3LYP/6-31G(d):PM3) and B3LYP/ 6-31G(d)-optimized structures for (5, 5) armchair SWCNT system are shown in Table 1, for which the atoms are defined in Fig. 1. Geometrical data optimized at the ONIOM(B3LYP/631G(d):PM3) and B3LYP/6-31G(d) levels not much different. The ONIOM(B3LYP/6-31G(d):PM3) approach was regularly employed in all the structure optimizations. The high-layer ONIOM(B3LYP/6-31G(d):PM3)-optimized structures for transition states TS1 and TS2 involved in the diazomethane addition to Type I and II, C1–C2 bonds of the side-wall for the (a) (3, 3), (b) (5, 5) and (c) (7, 7) armchair SWCNTs are shown in Fig. 2. The transition states TS1 and TS2 of these three SWCNTs are representative of those for the (n, n), n = 3–10 armchair SWCNTs. Fig. 2 reveals the effects of the nanotube curvature on the adsorbed
Fig. 1. Based on the two-layered ONIOM approach, a pyrene molecule shown as ball atoms was selected to be the high level layer and orientations of its C1–C2 bond are defined as (a) perpendicular (Type I) and (b) alongside (Type II) with the SWCNTs tube-length.
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Table 1 ˚ ) for the (5, 5) SWCNT complexes with CH2N2 and CH2 at two different C1–C2 binding sites of Types I and II, optimized at Selected bond distances (in A the B3LYP/6-31G(d), ONIOM(B3LYP/6-31G(d):PM3) (in parenthesis) and PM3 [in bracket] levels of theory Complexes
C1–C2
C1–C3
C2–N1
C3–N2
N1–N2
Type I SWCNT/CH2N2 SWCNT/CH2
1.638 (1.641) [1.615] 2.217 (2.226) [2.238]
1.586 (1.579) [1.567] 1.495 (1.497) [1.494]
1.593 (1.570) [1.536] 1.495 (1.497) [1.494]
1.464 (1.465) [1.482] –
1.221 (1.223) [1.215] –
Type IIb SWCNT/CH2N2 SWCNT/CH2
1.568 (1.580) [1.584] 1.564 (1.572) [1.544]
1.564 (1.563) [1.558] 1.516 (1.514) [1.508]
1.560 (1.559) [1.530] 1.516 (1.514) [1.508]
1.478 (1.478) [1.486] –
1.231 (1.231) [1.218] –
a
a b
Orientation of C1–C2 binding site is defined as the perpendicular direction with the tube length as shown in Fig. 1. Orientation of C1–C2 binding site is defined as alongside direction with the tube length as shown in Fig. 1.
complex structures and their hydrogen bond distances. The C1–C2 bond distances for the ONIOM(B3LYP/6-31G(d): PM3)-optimized structures of the complexes with H2N2 and CH2with (n, n), n = 3–10 armchair SWCNTs are listed in Table 2. The Type I, C1–C2 bond distances for the H2N2 adsorption on the large SWCNT diameters such as (9, 9) and (10, 10) SWCNTs are gradually decreased and expected to convert at a certain value. Nevertheless, the Type II, C1–C2 bond distances on the complex systems of CH2 adsorbed on the (8, 8) and (9, 9) SWCNTs are lar˚ . This phenomenon gely decreased from 2.194 to 1.717 A describes formation of the C–C bond which caused by the reduction of SWCNT strain. 3.2. Binding energies of adsorptions, energy profiles and reaction mechanism The plots against diameters of SWCNTs of the B3LYP/ 6-31G(d)//ONIOM(B3LYP/6-31G(d):PM3) binding ener-
gies for the addition of CH2N2 and CH2 on the C1–C2 bonds Types I and II are shown in Fig. 3. Based on the various diameters of (n, n), n = 3–10 armchair SWCNTs, their SWCNT/CH2 complexes are obviously more stable than the corresponding SWCNT/CH2N2 complexes by 47 to 69 kcal/mol for the C1–C2 bond Type I and 21–31 kcal/ mol for Type II. The adsorption reaction becomes progressively more favorable thermodynamically as the diameter of the SWCNT decreases. Energy profiles based on the B3LYP/6-31G(d)// ONIOM(B3LYP/6-31G(d):PM3) computations for the side-wall addition of diazomethane and mechanistic sequences for (a) Type I and (b) Type II of (3, 3), (5, 5) and (7, 7) armchair SWCNTs are shown in Fig. 4. It is apparent that the complexes and transition states for of the (3, 3) SWCNT system are the most stable species – considerably more so than those of the larger diameter SWCNTs. This effect is most pronounced for the Type I reaction.
Fig. 2. The two transition states (TS1 and TS2) shown as the high-layered ONIOM(B3LYP/6-31G(d):PM3)-optimized structures for the diazomethane addition on C1–C2 bonds, Types I and II of side-wall (a) (3, 3), (b) for (5, 5) and (c) (7, 7) armchair SWCNTs.
B. Wanno et al. / Chemical Physics Letters 436 (2007) 218–223
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Table 2 ˚ ) for the ONIOM(B3LYP/6-31G(d):PM3)-optimized structures of various sizes of SWCNTs as two different complexes The C1–C2 bond distances (in A and on two different Types of C1–C2 bond’s orientations Binding site/complexes
SWCNTs (3, 3)
(4, 4)
(5, 5)
(6, 6)
(7, 7)
(8, 8)
(9, 9)
(10, 10)
Type I SWCNT/CH2N2 SWCNT/CH2
1.671 2.262
1.664 2.241
1.641 2.226
1.628 2.214
1.619 2.203
1.612 2.194
1.607 1.717
1.602 1.690
Type II SWCNT/CH2N2 SWCNT/CH2
1.553 1.561
1.581 1.568
1.580 1.572
1.578 1.573
1.577 1.572
1.575 1.571
1.575 1.570
1.574 1.536
Fig. 3. Plots against diameters of SWCNTs of the B3LYP/6-31G(d)//ONIOM(B3LYP/6-31G(d):PM3) binding energies for the addition of CH2N2 (m) and CH2 (j) on the C1–C2 bonds (a) Type I and (b) Type II of armchair (n, n) SWCNTs, n = 3–10.
3.3. Reactivities against diameter of SWCNTs The orbital energies ELUMO and EHOMO and frontier molecular orbital energy gaps, EHOMO–LUMO of all SWCNTs systems based on the ONIOM(B3LYP/631G(d):PM3)-optimized structures are listed in Table 3 and the orbital energy plots of all SWCNTs and their complexes SWCNT/CH2N2 and SWCNT/CH2 are shown in Fig. 5. The EHOMO–LUMO of the isolated SWCNTs and their complexes SWCNT/CH2N2 and SWCNT/CH2 for the adsorption Type II and only the isolated SWCNT for the Type I are the exponential growth functions. For the large diameter SWCNTs of both Types I and II, the
approach to a stable value of the DEHOMO–LUMO is expected. Based on the general correlation between DEHOMO–LUMO and reactivity [23], the relative reactivities for the absorption Type II of the isolated SWCNTs and their complexes SWCNT/CH2N2 and SWCNT/CH2 are in the decreasing order as their SWCNT diameters are increased. It is apparent that there are some anomalous effects in the progressions of Fig. 5 for the Type I adsorptions of the (3, 3) SWCNT/CH2N2 system and the (9, 9) and (10, 10) SWCNT/CH2 systems, for reasons that are not yet clear. However, the general trends are sufficiently clear given the qualitative nature of this band-gap/reactivity correlation.
Fig. 4. Energy profiles based on the B3LYP/6-31G(d)//ONIOM(B3LYP/6-31G(d):PM3) computations for the side-wall addition of diazomethane and mechanistic sequences for (a) Type I and (b) Type II of (3, 3), (5, 5) and (7, 7) armchair SWCNTs.
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Table 3 The ELUMO and EHOMO and energy gaps, DEHOMO–LUMO of the ONIOM(B3LYP/6-31G(d):PM3)-optimized structures of SWCNTs on two different binding sites Species
ELUMO a SWCNT
EHOMO a SWCNT/ CH2N2
SWCNT/ CH2
SWCNT
DEHOMO–LUMO a SWCNT/ CH2N2
SWCNT/ CH2
SWCNT
SWCNT/ CH2N2
SWCNT/ CH2
Type I CN33t CN44t CN55t CN66t CN77t CN88t CN99t CN1010t
2.99 2.75 2.64 2.56 2.53 2.50 2.48 2.48
2.88 2.99 2.88 2.80 2.75 2.75 2.72 2.69
2.91 2.67 2.56 2.50 2.48 2.45 2.53 2.53
3.76 4.00 4.22 4.35 4.44 4.49 4.54 4.57
4.00 3.89 4.08 4.19 4.30 4.35 4.38 4.41
3.78 4.05 4.22 4.35 4.44 4.49 4.38 4.41
0.76 1.25 1.58 1.80 1.91 1.99 2.07 2.10
1.12 0.90 1.20 1.39 1.55 1.61 1.66 1.71
0.87 1.39 1.66 1.85 1.96 2.04 1.85 1.88
Type II CN33p CN44p CN55p CN66p CN77p CN88p CN99p CN1010p
2.94 2.69 2.61 2.53 2.50 2.48 2.48 2.48
2.80 2.61 2.50 2.48 2.45 2.45 2.45 2.45
2.69 2.50 2.45 2.39 2.39 2.39 2.39 2.39
3.78 4.05 4.25 4.38 4.46 4.52 4.57 4.60
4.08 4.33 4.44 4.52 4.57 4.60 4.63 4.63
3.95 4.16 4.33 4.44 4.52 4.54 4.60 4.60
0.84 1.36 1.63 1.85 1.96 2.04 2.10 2.12
1.28 1.71 1.93 2.04 2.12 2.15 2.18 2.18
1.25 1.66 1.88 2.04 2.12 2.15 2.20 2.20
a
In eV.
Fig. 5. Plots against SWCNTs diameters of orbital energy gaps (above) and orbital energies LUMOs and HOMOs (below) based on the C1–C2 binding sites (a) Type I and (b) Type II. The frontier orbital energy gaps (–j–), (–m–) and (––) (above), LUMOs (h), (D) and (s) and HOMOs (j), (m) and (d) are of the isolated SWCNT, SWCNT/CH2N2 and SWCNT/CH2, respectively.
4. Conclusions The binding energies of addition of CH2N2 and CH2on the C1–C2 bonds Types I and II of (n, n), n = 3–10 armchair
SWCNTs were obtained using a two-layered B3LYP/631G(d)//ONIOM(B3LYP/6-31G(d):PM3) level of theory. Based on the various diameters of (n, n), n = 3–10 armchair SWCNTs, their SWCNT/CH2 complexes are obviously
B. Wanno et al. / Chemical Physics Letters 436 (2007) 218–223
more stable than their corresponding SWCNT/CH2N2 complexes by 47–69 kcal/mol for the C1–C2 bond Type I and 21–31 kcal/mol for Type II. The adsorption reaction becomes energetically more favorable as the diameter of the SWCNT progressively decreases. This trend also likely to hold for the kinetics of the reactions is supported by the specific reaction pathway energy profiles calculated for the (3, 3), (5, 5) and (7, 7) nanotubes, as well as the energy band gaps computed across the range of diameters. We note finally that the band gaps for these SWCNT systems are likely to be reduced further if longer nanotubes are studied, e.g., via periodic boundary methods. We expect nevertheless that the trends observed in this work as a function of nanotube diameter should be strongly confirmed. Acknowledgements The Royal Golden Jubilee (RGJ) Grant No. PHD47K0164 supported by TRF to BW is acknowledged. The facility provided by Research Affairs, Chulalongkorn University is also gratefully acknowledged. We also thank the Thailand Research Fund (TRF) and the National Nanotechnology Center (NANOTEC), NN-B-22-m10-1049-18, National Science and Technology Development Agency, Thailand for partial support of this work. This work has also been facilitated by generous grants of computer time on the Computational Molecular Science cluster facility during BW’s research visit to the Centre for Computational Molecular Science at The University of Queensland.
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