The isomerization mechanism of X , ASWCNT (X ¼ CH2 and SiH2)

Chong Zhang, Ruifang Li, Zhenfeng Shang, Jianrong Li, Yumei Xing,Yinming Pan, Zunsheng Cai, Xuezhuang Zhao*

Department of Chemistry, Nankai University, Weijin Road, Tianjin 300071, China

Received 6 February 2004; accepted 4 May 2004

Abstract

Based on AM1 calculations, we found that the isomerization among the four isomers of (5,5) CH2 , ASWCNT (herein, ‘ , ’ denotes that

the connection of :CH2 group with ASWCNT needs two s bonds) includes three basic parts, that is, (i) S-open ! TS1 ! S-closed, (ii)

S-closed ! TS2 ! V-closed, and (iii) V-closed ! TS3 ! V-open isomer. Combining two or three of the basic parts we further deduce the

isomerization mechanisms between any other two of the four isomers of (5,5) CH2 , ASWCNT. An analogous system, (5,5) SiH2 ,

ASWCNT, was also investigated using the same method, and gives only two isomers, i.e. S-closed and V-open ones. The isomerization

between them can be expressed as S-closed ! TS2 ! V-open isomer. Thermodynamic and kinetic analyses suggest that, in normal

conditions, the S-open and S-closed isomers of (5,5) CH2 , ASWCNT should be mixed together when the dihydrocarbene adds on to the

sloppy bond and the translation from S-closed to V-closed is very difficult, while the predominant isomer would be V-open when the vertical

bond is being attacked by dihydrocarbene. In addition, the calculation based on the same method predicts that the S-closed and V-closed

isomers of (5,5) SiH2 , ASWCNT may be isolated in room temperature.

q 2004 Elsevier B.V. All rights reserved.

Keywords: Armchair single-walled carbon nanotubes (ASWCNTs); Dihydrocarbene; Silylene; Isomerization

1. Introduction

Since their seminal discovery by Iijima [1], the single-

walled carbon nanotubes (SWCNTs) appear to hold great

promise of being practical solution [2] to many problems

such as sorption of toxic substances [3], storage of hydrogen

[4,5], template-mediated growth of crystals [6], conductors,

semi-conductors, super-conductors [7], and so on. Bearing a

structural resemblance to graphite, however, they also

display quite high chemical stability and insolubility, which

limit their flexibility for further applications. So chemical

modifications of SWCNTs, especially the sidewall functio-

nalization is of critical importance, because the appropriate

modification of SWCNTs would improve their solubility,

processibility and chemical reactivity effectively, ultimately

leading to new property profiles [8,9]. There are many

examples of sidewall functionalization of SWCNTs

obtained so far, including fluorination at elevated tempera-

ture [10], noncovalent attachment of a bifunctional

molecule (1-pyrenebutaboic acid, succinimidyl ester) [11],

electrochemical reduction of aryl diazonium salts [12],

covalent attachment of nitrenes [13]. Recently, more and

more attention was paid to the investigations of direct

[2 þ 1] cycloaddition [14,15] of carbene and silylene [16]

on the SWCNTs sidewalls. Research suggested that these

cyclic derivatives would be subject to a great deal of ring-

opening reactions in synthetic organic chemistry, and

various organic functional groups can be further introduced

onto the sidewalls of SWCNTs subsequently, resulting in

many novel applications [17,18].

Till date, there were sporadic reports regarding the

addition of carbene [19–22] and silylene [15] onto the

sidewalls of SWCNTs. For example, Haddon et al. [19–21]

found that the covalent bond by carbene addition onto the

wall of the soluble SWCNTs can change their band structure

and mechanical properties. Li et al. [22] discussed the

structure and properties of dichlorocarbene adduct on the

sidewall of ASWCNTs and characterized their infrared

properties theoretically. Lu et al. [16] suggested that

silylene might be an appropriate candidate to be used

for the functionalization and purification of SWCNTs.

0166-1280/$ - see front matter q 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2004.05.025

Journal of Molecular Structure (Theochem) 681 (2004) 225–230

www.elsevier.com/locate/theochem

* Corresponding author. Tel.: þ86-22-2350-5244; fax: þ86-22-2350-

2458.

E-mail address: zhaoxzh@nankai.edu.cn (X. Zhao).

However, the study of cycloaddition and isomerization

mechanisms of dihydrocarbenes adding onto the sidewall of

SWCNTs has not been reported so far. Therefore, in this

paper, taking advantage of armchair (5,5) tube (its sidewall

is more reactive due to its high curvature/smaller diameter

than those with low curvature/larger ones, resulting in the

facility of addition of (5,5) tube with other agents such as

OsO4 [23]), we select dihydrocarbene and silylene as

candidates to systematically investigate their direct cycload-

dition onto the sidewall of SWCNT, especially the

isomerization mechanisms. Herein we report the results.

2. Computational methods

The typical length of SWCNTs is about 1–50 mm [24]. It

is impossible to simulate the whole ASWCNTs to study

their structure and properties for their gigantic length.

Fortunately, it is suggested that [22] studying the properties

of the middle part of a relatively short tube could show the

properties of infinitely long nanotube, and the AM1 method

in GAUSSIAN 94 package [25] is preferred to other semi-

empirical methods for studying of fullerence or single-

walled carbon nanotube derivatives [26]. Therefore, in this

paper, a fragment of SWCNT (5,5) that consists of totally 70

atoms is selected and calculated using AM1 method, and the

dangling bonds at its ends are saturated by hydrogen atoms,

giving a C70H20 tube as shown in Fig. 1. It should be noted

that, in Fig. 1, there are only two types of inequivalent

neighboring C–C pair sites, i.e. the 1,2 pair site and the 2,3

pair site [15] in the middle part of C70H20 tube. Herein, we

call them sloppy bond (S) and vertical bond (V),

respectively, for convenience. Thus, the dihydrocarbene

(:CH2) and silylene (:SiH2) can either be adsorbed on the

sloppy bond (S) or the vertical bond (V), resulting in

different isomers.

3. Results and discussion

3.1. Isomerization of (5,5) CH2 , ASWCNT

Based on AM1 calculations, we found that the cycload-

dition of dihydrocarbene group (:CH2) onto the sidewall of

(5,5) ASWCNT produces four CH2 , ASWCNT isomers,

i.e. the sloppy-closed (S-closed), sloppy-open (S-open),

vertical-closed (V-closed), and vertical-open (V-open) ones,

corresponding to the distance of final substrate C–C bond

(S or V bonds) that can be considered either closed or open

(Fig. 2). Their geometrical parameters are expressed in

Table 1.

From Table 1, we can see that the substrate C–C bond

length in S-closed and V-closed structures are 1.56 and

1.63 A, respectively. This suggests that each of the two

closed isomers has an additional three-membered ring on

the sidewall, in which the substrate C–C bonds are retained,

but severely elongated because of rehybridization from sp2

to sp3 induced by the dihydrocarbene cycloaddition

reaction. Tanner et al. [18] suggested that such closed

isomers with a three-membered ring might be subjected to

nucleophilic ring-opening accompanied by the attachment

of other organic functional groups as other [2 þ 1]

cycloadducts, such as the aziridino-SWCNTs. So, the

formation of S-closed and V-closed isomers paves a new

way to expand the chemical modification on the sidewall of

SWCNTs, which eventually leads to many new

applications.

In the case of S-open and V-open isomers of (5,5)

CH2 , ASWCNT, their substrate C–C bond lengths are

2.24 and 2.20 A, respectively, suggesting totally broken

probably due to the attack by dihydrocarbene of the

sidewall. Simultaneously, this also shows that the formation

of the isomers with open substrate C–C bond damages the

skeleton of pristine SWCNT more severely than those

with closed ones. The broken substrate C–C bond could

effectively release the high strain of ASWCNTs with small

Fig. 1. The numbering of the atoms in the reaction site of the (5,5) tube

fragment; V and S represent the sloppy bond and vertical bond,

respectively.

Fig. 2. The predicted profile charts of all the isomers of (5,5) X ,

ASWCNT (X ¼ CH2, Y ¼ SiH2).

C. Zhang et al. / Journal of Molecular Structure (Theochem) 681 (2004) 225–230226

diameters due to high curvature of their sidewall, which is

similar to their analogue of methanofullerenes [27,28].

In the investigation of the isomerization mechanism of

(5,5) CH2 , ASWCNT species, three transition states, TS1,

TS2 and TS3 were observed on the reaction pathway based

on AM1 calculations (see Fig. 2, their geometrical

parameters are listed in Table 1). Herein, TS1 refers to the

transition states from the S-open to S-closed isomer, TS2

from the S-closed to V-closed isomer, and TS3 from

V-closed to V-open isomer. Calculations following the

intrinsic reaction coordinate (IRC) for TS1, TS2 and TS3

have shown a monotonic decrease in energy and the

formation of the suggested products and reactants in each

transition, with no distinct intermediates or second tran-

sition structures being found (see Fig. 3), which confirmed

our calculation is correct.

The heat of formation (HF) and activation energies ðEaÞ

of all the isomers and transition states of (5,5) CH2 ,

ASWCNT at the AM1 level are listed in Table 2, and the

energy profile for the isomerization in Fig. 4. From Fig. 4,

we can see that the isomerization among all the (5,5)

CH2 , ASWCNT species includes three basic parts: (i)

S-open ! TS1 ! S-closed, (ii) S-closed ! TS2 ! V-

closed and (iii) V-closed ! TS3 ! V-open. Furthermore,

combining two or three basic parts we can deduce that the

rearrangement of any other paired-isomers includes two or

three transition states. For example, combining (i) and (ii),

the S-open isomer translating into V-open one may follow

the route: S-open ! TS1 ! S-closed ! TS2 ! V-closed,

with two transition states passing through. Thus, the study of

(i), (ii) and (iii) is enough for us to understand the nature of

the isomerization of all the paired-isomers in (5,5) CH2 ,

ASWCNT species.

The part (i) is the rearrangement of S-open and S-closed

isomers of (5,5) CH2 , ASWCNT, in which the C1–C2

bond in TS1 is shortened by 0.352 A from the original bond

length of 2.243 A in S-open but elongated by 0.335 A in the

S-closed isomer, and the w (C1–CH2–C2) in TS1 is

reduced by 19.78 from the original 99.18 in S-open isomer

but increased by 18.38 in S-closed one (see Table 1).

However, the CH2–C1 (or CH2–C2) bond lengths in the

three species (S-open, TS1 and S-closed) ranging from

0.039 to 0.025 A are nearly unchangeable. Thus, it is clear

that the translation from S-open to S-closed isomer may be a

stepwise closing process between the separated C1 and C2

atoms in the S-open isomer, eventually forming a single

C1–C2 sloppy bond. In addition, from Table 2 and Fig. 4

we can find that the isomerization from the S-open to

S-closed isomer must climb up energy barrier height ðEaÞ by

40.64 kJ/mol or a nearly equal reverse barrier ½EaðrÞ� of

38.98 kJ/mol, whereas the isomerization heat ðDHrÞ of this

step is only 1.02 kJ/mol. This shows that the translation

between the S-open and S-closed isomers could easily be

Table 1

The critical AM1 calculated geometrical parameters of (5,5) CH2 , ASWCNT isomers and the isomerization transition state

Bond length R (A) Bond angle w (8)

C1–C2 C2–C3 CH2–C1 CH2–C2 CH2–C3 C1–CH2–C2 C2–CH2–C3 CH2–C2–C1 CH2–C2–C3

S-open 2.243 1.387 1.475 1.473 2.550 99.1 126.1

TS1 1.891 1.426 1.482 1.481 2.639 79.4 129.4

S-closed 1.556 1.473 1.507 1.508 2.695 61.1 58.9 129.4

TS2 1.505 1.502 2.324 1.486 2.403 102.0 107.1

V-closed 1.458 1.627 2.548 1.504 1.504 65.4 118.6 57.3

TS3 1.444 1.750 2.535 1.495 1.496 71.6 119.2

V-open 1.410 2.200 2.488 1.493 1.493 94.9 118.0

ASWCNT 1.434 1.401

Fig. 3. The AM1 calculated intrinsic reaction coordinates for the

rearrangement among the isomers of (5,5) CH2 , ASWCNT.

Table 2

The AM1 calculated heats of formation (HF), relative heat of formation

(RHF) of all the isomers and transition states of (5,5) CH2 , ASWCNT,

together with activation energy ðEaÞ; reverse activation energy EaðrÞ; heats

of reaction ðDHrÞ and reverse heats of reaction ðDHrðrÞÞ for their

isomerization (kJ/mol)

HF RHF Ea EaðrÞ DHr DHrðrÞ

S-open 2417.98 95.82 21.02

TS1 2458.63 136.46 40.64 238.98

S-closed 2419.00 96.84 1.02 58.65

TS2 2616.95 294.79 215.95 2256.60

V-closed 2360.35 38.19 258.65 38.19

TS3 2362.20 40.04 2.85 240.04

V-open 2322.16 0 238.19

C. Zhang et al. / Journal of Molecular Structure (Theochem) 681 (2004) 225–230 227

carried out both thermodynamically and kinetically, and the

two isomers should co-exist in normal conditions.

In (ii), there is one more transition state (TS2, see Fig. 2)

existing in the pathway of the translation from the S-closed

to V-closed isomer as predicted by the AM1method. From

Table 1, we can see that the bond angles CH2–C2–C1 and

CH2–C2–C3 are 102.0 and 107.18, respectively, suggesting

that CH2–C2 bond in TS2 is nearly erective above the (5,5)

ASWCNT skeleton and the CH2 group is only connected to

C2 atom. Meanwhile, the C1–C2 and C2–C3 bond lengths

(with an average value of 1.504 A) in TS2 are both slightly

shorter than the typical single C–C bond (1.56 A in ethane).

This may suggest such a transition mechanism: in order to

translate into V-closed isomer, the S-closed one must first

elongate its C1–CH2 bond, then the CH2 group begins to

migrate away from the sloppy bond and erect itself, and fall

onto the vertical bond, resulting in the S-closed isomer

finally. The activation energies of the forward reaction and

reverse reaction (from S-closed to V-closed and V-closed to

S-closed) are 215.95 and 256.60 kJ/mol, respectively (see

Table 2), which indicate that the transition is very difficult in

normal conditions in (ii).

In (iii), it is expected that the third transition state (TS3,

see Fig. 3) connecting the V-closed and V-open isomers has

a broken substrate C2–C3 bond (1.750 A) based on our

calculations, which is longer by 0.123 A than the corre-

sponding one in V-closed isomer and shorter by 0.550 A

than that in V-open isomer. Meanwhile, the bond

angle C2 –CH2 – C3 of TS3 (71.68) is also between

the corresponding ones of V-closed (65.48) and the

V-open isomers (94.98). This demonstrates that the third

step may be a substrate C2–C3 bond broken process from

V-closed to V-open isomer. At the same time, the energy

barrier ðEaÞ of isomerization from the V-closed to V-open

isomer is only 2.85 kJ/mol and the exothermicity is

38.19 kJ/mol, while the activation energy of the reverse

isomerization ½EaðrÞ� is 40.04 kJ/mol and the endothermi-

city is 38.19 kJ/mol (see Table 2). Therefore, the V-closed

isomer is easy to translate into the V-open one in normal

conditions, and the V-open isomer should be the predomi-

nant form when dihydrocarbene attacks the vertical bond on

the sidewall of (5,5) ASWCNT directly.

In summary, it is reasonable for us to assert that the

isomerization of any two of the four isomers of (5,5)

CH2 , ASWCNT can occur either from any one of parts (i),

(ii) and (iii), or the combination of two or three of them. In

addition, from thermodynamical and kinetical analyses, we

conclude that the V-open isomer is the most stable and

the S-closed is the most unstable one among the four

CH2 , ASWCNT isomers, as can be seen in Fig. 4.

3.2. Isomerization of (5,5) SiH2 , ASWCNT

Different from the cycloaddition of dihydrocarbene

group (:CH2), the cycloaddition of silylene (:SiH2) onto

the sidewall of (5,5) ASWCNT only produces the S-closed

and V-closed isomers (Fig. 2) based on the same method.

No S-open and V-open isomers found probably attribute to

the larger atomic diameter of silicon and weaker nucleo-

philicity of silylene group, which maybe prevents the

formation of the hypothetical S-open and V-open species,

and simultaneously decreases the deformation of (5,5)

ASWCNT skeleton. The main geometrical parameters are

collected in Table 3.

As shown in Table 3, we can find that the substrate C–C

bond lengths of S-closed and V-closed isomers of (5,5)

SiH2 , ASWCNT are 1.539 and 1.579 A, respectively.

They are both longer than that of the pristine ASWCNT

but shorter by 0.017 and 0.048 A than that of the CH2 ,

ASWCNT species. Whereas, the SiH2–C bonds in S-closed

or V-closed isomers are all longer by about 0.3 A than the

CH2–C bonds in CH2 , ASWCNT species. This demon-

strates that, compared with dihydrocarbene, the cycloaddi-

tion by silylene (:SiH2) onto the sidewall not only affects

Fig. 4. The AM1 calculated energy profile for the rearrangement among the

isomers of (5,5) CH2 , ASWCNT.

Table 3

The critical AM1 calculated geometrical parameters of (5,5) SiH2 , ASWCNT isomers and the isomerization transition state

Bond lengths R (A) Bond angles w (8)

C1–C2 C2–C3 SiH2–C1 SiH2–C2 SiH2–C3 C1–SiH2–C2 C2–SiH2–C3 SiH2–C2–C1 SiH2–C2–C3

S-closed 1.539 1.437 1.864 1.868 3.053 48.7 65.5 131.7

TS4 1.489 1.487 2.521 1.851 2.639 97.4 103.9

V-closed 1.465 1.579 2.851 1.857 1.857 50.3 117.8 64.9

ASWCNT 1.434 1.401

C. Zhang et al. / Journal of Molecular Structure (Theochem) 681 (2004) 225–230228

the structure of pristine (5,5) ASWCNT, but also leads to

weaker interaction with its sidewall.

The calculation results suggest that there is only one

transition state (TS4, see Fig. 2) between the S-closed and

V-closed isomers. Their geometrical parameters are listed in

Table 3 and the heat of formation of the S-closed, TS4 and

V-closed, along with their isomerization activation energy

in Table 4. IRC calculations verify that TS4 really lies on

the pathway of the interconversion of S-closed and V-closed

isomers with no other stationary points between them being

observed (Fig. 5). The energy profile of the rearrangement is

shown in Fig. 6. Different from the rearrangement of

CH2 , ASWCNT, the isomerization of SiH2 , ASWCNT

at the AM1 level is much more simple based on our

calculations, which can be expressed briefly as: S-closed !

TS4 ! V-closed.

In TS4, the bond angles w (SiH2–C2–C1) and w (SiH2–

C2–C3) are 97.4 and 103.98 (see Table 3), respectively. The

SiH2–C2 bond in TS4 is also nearly erective on the sidewall

of (5,5) ASWCNT (shown in Fig. 2), which is similar to the

CH2–C2 bond in the TS2 in (5,5) CH2 , ASWCNT. This

demonstrates that the rearrangement from S-closed to

V-closed isomer may be a migration process of silylene

group (:SiH2) from the sloppy to vertical bond. In this

process, the SiH2 –C1 bond in S-closed isomer first

elongates, and simultaneously the silylene group (:SiH2)

approaches the C2 atom, absorbing 108.66 kJ/mol until TS4

is formed (see Table 4 and Fig. 6). Then the silylene group

(:SiH2) in TS4 continues to migrate towards the vertical

bond, resulting in the final product, i.e. the V-closed isomer.

This is an exothermic process, giving out 11.07 kJ/mol. In

the reverse reaction, we find that the activation barrier for

the conversion of the V-closed to S-closed isomer is

120.27 kJ/mol and endothermic by 11.07 kJ/mol. Thus, we

can predict that the S-closed and V-closed isomers of (5,5)

SiH2 , ASWCNT are all stable species and may be isolated

from each other if they were synthesized someday.

4. Conclusions

The whole isomerization process of all the (5,5) CH2 ,

ASWCNT species includes three basic parts: (i) is the

stepwise closeness between the separated substrate carbon

atoms of S-open isomer, resulting in S-closed one; (ii) is the

migration of dihydrocarbene (:CH2) from the sloppy bond

of S-closed isomer to vertical bond, forming the V-closed

isomer, but it is very difficult for the very higher activation

energy (both Ea and 2Ea); (iii) is the broken process of

vertical bond of V-closed isomer, with the formation of

product, i.e. V-open one finally. Both thermodynamic and

kinetic analyses suggest that the most and least stable

isomers of CH2 , ASWCNT species are V-open and

S-closed isomers, respectively.

The cycloaddition of silylene (:SiH2) onto the sidewall of

(5,5) ASWCNT can produce only two SiH2 , ASWCNT

isomers, i.e. S-closed and V-closed. In the rearrangement

process from the S-closed to V-closed isomer, the silylene

(:SiH2) migrates from the sloppy bond in S-closed to

vertical bond in V-closed isomer, which is similar to that of

basic part (ii) in the rearrangement of CH2 , ASWCNT

species described above, and the two isomers are predicted

to be separated from each other in normal conditions at the

AM1 level.

Acknowledgements

This work was supported by National Nature Science

Foundation of China (No. 20073002).

Table 4

The AM1 calculated heat of formation (HF), relative heat of formation

(RHF) of isomers and transition state of (5,5) SiH2 , ASWCNT, together

with activation energy ðEaÞ; reverse activation energy EaðrÞ; heat of reaction

ðDHr) and reverse heat of reaction ðDHrðrÞÞ for their isomerization (kJ/mol)

HF RHF Ea EaðrÞ DHr DHrðrÞ

S-closed 2388.97 11.07 108.66 11.07

TS4 2498.17 120.27

V-closed 2377.90 0 2120.27 211.07

Fig. 5. The AM1 calculated intrinsic reaction coordinate for the

isomerization between the S-closed and V-closed isomers of (5,5) SiH2 ,

ASWCNT.

Fig. 6. The AM1 calculated energy profile for the isomerization between the

S-closed and V-closed isomers of (5,5) SiH2 , ASWCNT.

C. Zhang et al. / Journal of Molecular Structure (Theochem) 681 (2004) 225–230 229

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