The nitrene cycloaddition on the sidewall of armchair

single-walled carbon nanotubes

Chong Zhang a,b,c,*, Rui fang Li b, Yunxiao Liang b, Zhenfeng Shang b, Guichang Wang b,

Yumei Xing b, Yinming Pan b, Zunsheng Cai b, Xuezhuang Zhao b, Chengbu Liu b

a Institute of Theoretical Chemistry, Shandong University, Jinan 250100, People’s Republic of Chinab Department of Chemistry, Nankai University, Tianjin 300071, People’s Republic of China

c Department of Chemistry and Technology, Liaocheng University, Liaocheng 252059, People’s Republic of China

Received 14 August 2005; received in revised form 10 December 2005; accepted 12 December 2005

Abstract

The calculations based on AM1 and PM3 methods suggest that the cycloaddition between the nitrene (HN:) group and (5,5) armchair single-

walled carbon nanotube (ASWCNT) produces four isomers, and their thermodynamic stability can be described as follows, V-open OV-closed O

S-open OS-closed. The kinetic analysis, however, suggests that the predominant forms are S-open and V-open in the mixture of HN!ASWCNT

isomers. The cycloaddition reactivity of nitrene on ASWCNTs is predicted to decrease with the diameter enlarging for both thermodynamic and

kinetic reasons. When the diameter of ASWCNT increases gradually, the percentage of its S-closed and V-closed isomers becomes greater in the

mixtures, and thus the breaking of C–C bond is predicted to be more difficult when being attacked by the HN: group accordingly. In addition, all

the calculations in this paper demonstrate that the AM1 and PM3 methods give similar results when investigating the properties of HN!ASWCNT isomers.

q 2006 Published by Elsevier B.V.

Keywords: Armchair single-walled carbon nanotubes (ASWCNTs); Nitrene (HN:); Cycloaddition reactivity; Semi-empirical calculations (AM1 and PM3)

1. Introduction

Since, the discovery of carbon nanotubes by Ijima in 1993

[1], a lot of efforts have been made focusing on their chemical

modifications [2–5], especially on their sidewall functionaliza-

tions by, for example, fluorination at elevated temperature [6],

electrochemical reduction of aryl diazonium salts [7], and

noncovalent attachment of a bifunctional molecule [8]

(1-pyrenebutaboic acid, succinimidyl ester). In addition,

researchers also found that some biradical groups, such as

dichlorocarbene and nitrene, could effectively modify the

sidewall of carbon nanotubes through covalent attachments.

For example, in 1998, R.C. Haddon discovered that the

dichlorocarbene covalently bonds to the sidewall of soluble

single-walled carbon nanotubes and changes their band

structure obviously [9]. Subsequently, the possible

0166-1280/$ - see front matter q 2006 Published by Elsevier B.V.

doi:10.1016/j.theochem.2005.12.017

* Corresponding author. Address: Institute of Theoretical Chemistry,

Shandong University, Jinan 250100, People’s Republic of China. Tel.: C86

531 83 65745; fax: C86 531 85 64464.

E-mail address: zhangchong@sdu.edu.cn (C. Zhang).

dichlorocarbene cycloaddition isomers of ASWCNTs and the

isomerization mechanism of X!ASWCNT (XZCH2 and

SiH2) [10] were further predicted theoretically. In 2001,

Holzinger and co-workers synthesized a series of imino!SWCNT derivatives [NR!SWCNTs (RZ –H, –CH3, –COO–

Ethyl, –COO-tert-Butyl)] by direct cycloaddition of nitrene

onto the sidewall of SWCNTs [11], which are proved to be

very encouraging in the chemical modification field of carbon

nanotubes because Xie [12] and Dai et al. [13] have discovered

that the cycloadducts would be subject to a great deal of ring-

opening reactions [1,12]. Recently, Zdenek Slanian et al.

reported a computational study on both the thermodynamic

enthalpy changes and kinetic activation barriers for oxygen

addition to six selected bonds in some narrow nanotubes [14].

These papers take the very lead in exploring the cycloaddition

chemistry of single-walled carbon nanotubes with biradical

groups. However, until now the possible structure and mutual-

translation of these nitrene cycloadducts have not been

revealed yet. At the same time, since it is suggested that the

reactivity of carbon nanotubes is largely influenced by their

surface curvatures, further exploration of the nitrene cyclo-

addition changing with their diameters should surely enrich the

cycloaddition chemistry of single-walled carbon nanotubes.

Journal of Molecular Structure: THEOCHEM 764 (2006) 33–40

www.elsevier.com/locate/theochem

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 764 (2006) 33–4034

Thus, the purpose of the present work is twofold: (i) to explore

the structures, stability, especially possible mutual-rearrange-

ment mechanism of the nitrene (the simplest nitrene, HN:, is

selected as a model in this paper) cycloadducts of (5,5)

ASWCNT, (ii) to predict the dependence of the nitrene

cycloaddition reactivity and the possible isomer distribution

on the diameter of (n,n) ASWCNTs (nZ3, 4, 5, 6).

2. Computational methods

Full geometry optimizations are performed without any

symmetry constraints in cartesian coordinates using AM1 type

semi-empirical calculation method (suitable for systems

containing carbon and/or heteroatoms [15]). In addition,

since Zdenek Slanian et al. [14] have successfully predicted

the stability and structural parameters of oxygen cycloadducts

of SWCNTs using PM3 method recently, the PM3 method is

also used in this paper simultaneously for comparison.

Vibrational analysis indicates that all the optimized structures

have no imaginary frequency or only one imaginary frequency,

suggesting true minimum or transition state accordingly. All

calculations are carried out with GAUSSIAN 98 programs [16].

Both the experimental and theoretical investigations

confirm that the carbon nanotubes have either open or capped

ends. It is suggested that the chemical reactivity of the tip is

more active than to the sidewall in carbon nanotubes [14].

However, since the typical length of a single-walled carbon

nanotube is 1–50 mm, one can reasonably predict that the most

chemical modifications maybe mainly occur on their sidewalls.

Thus, a piece of (5,5) ASWCNT sidewall represented by a

C80H20 fragment is taken as a model in this paper (see Fig. 1),

in middle of which there are two kinds of inequivalent CaC

bonds (denoted as skew and vertical ones, respectively). Thus,

the HN: group could cycloadd either on the skew or on the

vertical bond, resulting in different isomers. In addition, in

order to eliminate the possible deviations caused by the

tube length as much as possible, a series of (n,n) ASWCNTs

(nZ3,4,5,6) models utilized in this paper all have same length

(i.e. eight layers carbon atoms along the tube axis as shown

in Fig. 1).

Fig. 1. The (5,5) ASWCNT sidewall model of C80H20 utilized in this paper, in

which ‘V’ (vertical bond) and ‘S’ (skew bond) represent the bonds vertical and

skew to the tube axis, respectively.

3. Results and discussion

3.1. Nitrene cycloaddition with (5,5) ASWCNT

3.1.1. Geometries and thermodynamic stability

of (5,5) HN!ASWCNT isomers

The nitrene (HN:) cycloaddition onto the sidewall of (5,5)

ASWCNT model utilized in this paper produces four isomers

(HN!ASWCNT) based on AM1 and PM3 levels, denoting as

vertical-closed (V-closed), vertical-open (V-open), skew-

closed (S-closed) and skew-open (S-open), respectively (see

Fig. 2). This is consistent with the cycloadducts of ASWCNT

of dihydrocarbene [10] and dichlorocarbene [17]. Their critical

bond lengths and bond angles based on the two semi-empirical

methods are shown in Table 1.

It can be seen from Table 1 that the difference of

AM1geometrical parameter to PM3 one for all the (5,5)

HN!ASWCNT isomers and transition states is very small. In

fact, the difference between the AM1 data and PM3 data are

only K0.05 to 0.042 A for bond lengths and K2.9 to 3.88 for

bond angles. This suggests that the two methods obtain similar

geometrical parameters and are both suitable in calculating the

geometries of the HN: cycloadducts of ASWCNTs. At the

same time, the energy sequence of these isomers and transition

state also keeps the same order based on the AM1 and PM3

methods too, though the AM1 energies for them are below

352.0 to 360.9 kJ/mol compared with those of PM3 method.

This demonstrates that the AM1 method can obtain similar

results with PM3 when investigating the relative stability of

cycloaddition isomers of carbon nanotubes. Thus, if not

especially specified, only the AM1 geometrical parameters

and energies are discussed below.

For the S-closed and V-closed isomers of (5,5)

HN!ASWCNT, their AM1 substrate C–C bond lengths are

1.557 (C2–C3) and 1.601 A (C1–C2), respectively, being

longer by 0.014 and 0.194 A than the corresponding C–C bond

lengths in pure (5,5) ASWCNT. This infers that the substrate

C–C bonds of S-closed and V-closed are still retained, but are

severely elongated because of the rehybridization of carbon

NH

NH

NH

NH

(V-closed) (V-open)

(S-open)(S-closed)

orientation of the tube axis

12

3

1

1

12

2

2

3

3

3

NH

1 2

3

NH1 2

3

(TS5S)

(TS5V

)

NH

12

3

(TSS-V

)

Fig. 2. The geometries of the isomers and transition states of (5,5) HN!ASWCNT; the C atom labels are the same as those shown in Fig. 1.

Table 1

The AM1 and PM3 obtained bond lengths (A), bond angles (8), energies (E, kJ/mol), and relative energies (DE, kJ/mol) of the isomers and transitions states (TS) of

the (5,5) HN!ASWCNT; the data in parenthesis refer to the PM3 geometrical difference compared with those AM1 one

Isomer/TS Methods HN:C

ASWCN

S-open TS5S S-closed TSS-V V-closed TS5V V-open

E AM1 3160.9 2831.1 2911.9 2893.0 3061.8 2784.0 2787.0 2722.1

PM3 2744.0 2472.5 2554.5 2532.1 2689.9 2426.5 2434.0 2370.1

DE AM1 0.0 K329.8 K249.0 K267.9 K99.1 K376.9 K373.9 K438.8

PM3 0.0 K271.5 K189.5 K182.6 K54.0 K317.5 K310.0 K373.8

C1–C2 AM1 1.407a 1.406 1.439 1.484 1.522 1.601 1.734 2.184

PM3 (K0.05) (K0.013) (K0.005) (K0.001) (K0.026) (K0.028) (0.024) (0.017)

C2–C3 AM1 1.443a 2.208 1.774 1.557 1.523 1.472 1.459 1.434

PM3 (0.00) (0.018) (0.009) (K0.012) (K0.016) (0.001) (K0.005) (K0.007)

N–C2 AM1 1.420 1.441 1.464 1.431 1.463 1.452 1.443

PM3 (0.012) (0.024) (0.028) (0.042) (0.028) (0.023) 1.461

C1NC2 AM1 66.3 73.3 98.3

PM3 (K2.6) (0.1) (K0.6)

C2NC3 AM1 102.3 76.0 64.3

PM3 (K0.6) (K1.0) (K1.9)

NC2C1 AM1 124.2 126.7 130.1 106.6 56.8

PM3 (K0.1) (0.1) (K0.9) (3.8) (1.4)

NC2C3 AM1 57.8 114.7 117.2 117.7 116.4

PM3 (1.0) (K2.9) (K0.7) (K0.3) (K0.4)

a Refer to the corresponding C–C bond length of pure ASWCNT.

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 764 (2006) 33–40 35

atoms from sp2 to sp3 induced by HN: attacking, and thus the

S-closed and V-closed isomers each has a additional

cyclopropane-like three-membered ring with two newly

formed HN–C bonds. Similar to other cycloadducts with

three-membered rings such as aziridino!SWCNTs [18], these

two closed-bonded isomers might be subject to further

chemical manipulations, such as ring opening accompanied

by the attachment of other chemical functional groups [19],

which may lead to new applications eventually in the future.

For S-open and V-open isomers of (5,5) HN!ASWCNT,

one can find from Table 1 that their AM1 substrate C–C bond

lengths are as long as 2.208 (C2–C3) and 2.184 A (C1–C2),

respectively, being broken obviously. This suggests that the

two open-bonded isomers each has a seven-membered

annulenene on sidewall, which is predicted to effectively

release the strain of ASWCNT. The result is very similar to the

cycloaddition of dichlorocarbene with ASWCNTs [17] or

fullerenes such as C60 [20], whose [5,6] or [6,6] bond can be

also remained or open when being attacked by nitrene. This

suggests that, despite of their totally different shapes, the

fullerene and SWCNT have similar chemical reactivity, which

may be derived from the similar surface curvature they share.

The energies (E) and relative energies (DE) of S-closed,

S-open, V-closed and V-open at AM1 and PM3 levels are listed

in Table 1. The data in bracket refer to the PM3 energy

difference with AM1 method. Herein, DE is defined as the

energy difference between the HN!ASWCNT isomers and its

reactants (ASWCNT plus HN: group). From Table 1, one can

see that the AM1 calculated DE of S-closed, S-open, V-closed

and V-open are K267.9, K329.8, K376.9 and K438.8 kJ/

mol, respectively. This indicates that the cycloaddition

between the HN: and (5,5) ASWCNT is highly exothermic,

and thermodynamic stability of the resulted isomers can be

described as follows, V-openOV-closedOS-open O S-closed.

The PM3 energy data also show the same trend. These results

are also similar to the cycloaddition between the dihydrocar-

bene and (5,5) ASWCNT [17], in which the vertical bond are

predicted to be more reactive thermodynamically than the skew

bond.

3.1.2. The transformation mechanism between

(5,5) HN!ASWCNT isomers

Since the HN: cycloaddition onto the skew and vertical

bonds of (5,5) ASWCNT produces two skew-bonded (S-closed

and S-open) and two vertical-bonded isomers (V-closed and

V-open) based on AM1 and PM3 methods, the transformation

between any two of the four isomers could be divided into three

types based on our chemical intuition. The first type is the

transformation between two skew-bonded isomers, i.e. the

S-closed and S-open. The second type is the transformation

between two vertical-bonded isomers, i.e. V-closed and

V-open. The third type is the transformations between one

skew-bonded and one vertical-bonded isomers, including

the isomerization between S-closed and V-closed, the

isomerization between S-closed and V-open, the isomerization

between S-open and V-closed, and the isomerization between

the S-open and V-open isomers. Calculation based on AM1 and

PM3 methods suggests that the transformation between two

skew-bonded isomers (S-closed and S-open) in the first type

has only one transition state (TS5S, Fig. 2); the transformation

between two vertical-bonded isomers (V-closed and V-open)

in the second style also has one transition state (TS5V, Fig. 2);

However, the third style is much more complex because in

which only the transformation between S-closed and V-closed

has one transition state (TSS–V, Fig. 2), others all have two or

three transition states. This can be seen more directly from their

respective AM1 transformation potential surfaces shown in

Fig. 3a–c, respectively; the data in parenthesis refer to

2700

2750

2800

2850

2900

2950

3000

3050

3100

V-open

V-closed

TS5v

TSs-v

Ene

rgie

s (k

J/m

ol)

S-open

S-closed

TS5S

80.8(82.0)

18.9(22.4)

168.8(157.8)

277.8(263.4)

3.0(7.5)

64.9(63.9)

(a) (b) (c)

(A)

Fig. 3. The AM1 and PM3 (shown in parenthesis) calculated profiles of

potential surface showing the isomerizations of (5,5) HN!ASWCNT

(a) S-open and S-closed (b) S-closed and V-closed (c) V-closed and V-open.

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 764 (2006) 33–4036

the corresponding energy values based on PM3 level. The

calculations following the intrinsic reaction coordinate (IRC)

for the above three transition states (TS5S, TS5V, and TSS–V)

show a monotonic decrease in energy and result in the

suggested products and reactants. No distinct intermediates or

second transition structures are found, suggesting that they are

all the true first-order saddle points (see Fig. 4a–c; the PM3

results are omitted in Fig. 4). The AM1geometrical parameters

of TS5S, TS5V and TSS–V based on the two semi-empirical

methods are listed in Table 1; the data in parenthesis in Table 1

are those PM3 geometrical parameter differences (very small

as mentioned above) compared with corresponding AM1 ones.

–2.5 –2.0 –1.5 –1.0 –0.5 0.0 0.5 1.0 1.52840

2850

2860

2870

2880

2890

2900

2910

2920

Ene

rgie

s(kJ

/mol

)

s/aum1/2bohr

S-open

S-closed

TS5S(a)

(b

–0.5 0.0 0.52720

2730

2740

2750

2760

2770

2780

2790

V-closed

Ene

rgie

s(kJ

/mol

)

s/aum

TS5V(c)

Fig. 4. The AM1 obtained intrinsic reaction coordinates for the isomerization betwe

V-open.

Thus, only the AM1 geometrical data are discussed from now

on in this paper for convenience.

3.1.2.1. The isomerization mechanism between S-open and

S-closed isomers. From Table 1, one can see that the substrate

C2–C3 bond (skew bond) of TS5S is 1.774 A, which is shorter

than that of S-open (2.208 A) but longer than that of S-closed

(1.557 A); the bond angle C2–N–C3 of TS5S is 76.08, which is

smaller than that of S-open (102.38) but larger than that of

S-closed (64.38). This suggests that the transformation from

S-open to S-closed is in fact a gradual shortening process

between the substrate C2 and C3 atoms, in which the separated

C2 and C3 atoms in S-open isomer gradually come closer until

forming a connecting C2–C3 bond in S-closed isomer. As can

be seen from Fig. 3a, in order to translate into S-closed isomer,

the S-open isomer must climb up activation energy by 80.8

(82.0 for PM3) kJ/mol; while in the opposite way, the

activation energy is only 18.9 (22.4 for PM3) kJ/mol. This

demonstrates that the S-closed is less stable than the S-open

isomer kinetically, and therefore the former can translate into

the latter much easier through breaking its skew C2–C3 bond.

3.1.2.2. Isomerization mechanism between S-closed and

V-closed isomers. From Table 1, the AM1 bond angle values

of NC2C1 in S-closed, TSS–V, and V-closed are 130.1, 106.6,

56.88, respectively, diminishing gradually. This suggests that in

this process the HN: group gradually migrates to C1 atom. At

the same time, their respective bond angle values of NC2C3 are

–8 –6 –4 –2 0 2 4 6 8 102750

2800

2850

2900

2950

3000

3050

3100 TSS-V

V-closed

S-closed

Ene

rgie

s(kJ

/mol

)

s/aum1/2bohr

)

1.0 1.5 2.0 2.5

V-open

1/2bohr

en (a) S-open and S-closed (b) S-closed and V-closed isomers (c) V-closed and

Tab

le2

Th

eA

M1

and

PM

3ca

lcu

late

dd

iam

eter

inth

ece

nte

r(D

C)

and

atth

een

ds

(DE)

for

(n,n

)A

SW

CN

Ts

(nZ

3,4

,5,6

);DD

mea

ns

the

PM

3ca

lcu

late

dd

iam

eter

dif

fere

nce

wit

hA

M1

calc

ula

ted

on

e;(D

EKD

C)

den

ote

sth

e

dia

met

erel

ong

atio

nfr

om

the

cen

ter

par

tto

the

end

par

to

fth

etu

be;

(DEKD

C)/

nd

eno

tes

the

val

ue

of

(DEKD

C)

div

ided

by

the

nu

mb

ero

fC

–C

bo

nds

con

tain

edin

the

tub

eci

rcu

mfe

ren

ce

(3,3

)/U

nit

:A(4

,4)

/Un

it:

A

DC

DE

DEKD

C(D

EK

DC

)/n

DC

DE

DEKD

C(D

EKD

C)/n

AM

14

.11

04

.28

10

.17

10

.05

85

.487

5.6

91

0.2

04

0.0

52

PM

34

.10

34

.27

60

.17

30

.05

85

.476

5.6

97

0.2

21

0.0

56

DD

K0

.00

7K

0.0

05

K0

.011

0.0

06

(5,5

)/u

nit

:A

(6,6

)/u

nit

:A

DC

DE

DEKD

C(D

EK

DC

)/n

DC

DE

DEKD

C(D

EKD

C)/n

AM

16

.77

66

.999

0.2

23

0.0

44

8.1

47

8.4

20

0.2

73

0.0

46

PM

36

.76

07

.003

0.2

43

0.0

48

8.1

31

8.3

89

0.2

58

0.0

44

DD

K0

.01

60

.004

K0

.016

0.0

04

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 764 (2006) 33–40 37

57.8, 114.7, 117.28, respectively, increasing gradually. This

suggests that the isomerization from S-closed to V-closed (or

from V-closed to S-closed) is a migration process of HN: group

from the skew to vertical bond (or vertical to skew bond). The

IRC analysis of TSS–V (Fig. 4b) also confirms this conclusion,

in which the resulting isomers are S-closed and V-closed. In

this process, as shown in Fig. 3b, the isomerization activation

energy from S-closed to V-closed is 168.8 (157.8 for PM3) kJ/

mol; the reverse one is 277.8 (263.4 for PM3) kJ/mol.

Considering that the translation from S-closed to S-open

isomer needs only activation energy of 18.9 (22.4 for PM3) kJ/

mol as shown in Fig. 3a, we reasonably expect that the S-closed

isomer very easier translate into S-open than into V-closed

isomer.

3.1.2.3. Isomerization mechanism between the V-closed and

V-open isomers. From Table 1, based on AM1 level, the

substrate bond length C1–C2 and bond angle C1–N–C2 of

TS5V are 1.734 A and 73.38, respectively, both larger than

those of V-closed (1.601 A and 66.38) but smaller than those of

V-open isomers (2.184 A and 98.38), respectively. This

suggests that the translation from V-closed to V-open isomer

is a gradual broken process of vertical C1–C2 bond. As can be

seen from Fig. 3c, the activation energy of the forward reaction

is 3.0 (7.5 for PM3) kJ/mol, whereas the reverse one is as high

as 64.9 (63.9 for PM3) kJ/mol. Combing the fact that the

energy barrier from V-closed to S-closed is 277.8 (263.4 for

PM3) kJ/mol as shown in Fig. 3b, we can conclude that the

V-closed is nearly impossible to translate into S-closed isomer

for kinetic reasons, and thus the V-open is the predominant

form when the HN: attacking the vertical bond of (5,5)

ASWCNT.

3.2. The nitrene cycloaddition with ASWCNTs with different

diameter

3.2.1. The difference between the diameter at the tube ends and

in the center for (n,n) ASWCNTs (nZ3,4,5,6)

As mentioned above, in order to further explore the

dependence of nitrene cycloaddition reactivity on different

diameters of ASWCNT, a series of (n,n) ASWCNT

(nZ3,4,5,6) fragments with same length (i.e. 8 layers carbon

atoms along the tube axis as shown in Fig. 1) are taken as

models in this paper. Since all these models are open, it must be

very interesting firstly to study the difference between the

optimized diameter at the tube ends and in the center.

The results based on AM1 and PM3 are listed in Table 2. In

Table 2, the DC and DE denote the diameter in the center and at

the tube ends, respectively; DD means the PM3 calculated

diameter difference with AM1 calculated one; (DEKDC)

denotes the diameter elongation from the center part to

the end part of the tube; (DEKDC)/n denotes the value of

(DEKDC) divided by the number of C–C bonds contained in its

circumference (since each circumference contains n C–C

bonds for (n,n) ASWCNT), which roughly represents the

average contribution each C–C bond in the circumference pays

to the diameter elongation.

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 764 (2006) 33–4038

First, it can be seen from Table 2 that the difference (DD)

between the AM1 diameter and PM3 diameter is K0.016 to

0.006 A, suggesting again that AM1 method would produce

similar geometrical results with PM3 method when studying

(n,n) HN!ASWCNTs (nZ3,4,5,6) isomers. Second, the

(DEKDC) values based on AM1 (PM3) level for (3,3), (4,4),

(5,5) and (6,6) ASWCNTs are 0.171 (0.173), 0.204 (0.221),

0.223 (0.243) and 0.273 (0.258) A, respectively. This

demonstrates that the diameter at tube ends is larger than the

diameter in the center, and the larger the tube diameter is, the

more obvious the difference is. The reason for this perhaps lies

in the fact that the strain at the open ends is more easily to

release than in the center, and thus would result in larger

diameter at the open ends. Third, though the (DEKDC) values

increase from (3,3) to (6,6) ASWCNT gradually, the AM1

obtained (DEKDC)/n values decrease from 0.058 (0.058 for

PM3) to 0.046 (0.044 for PM3) A accordingly. This is not

surprising since the strain of ASWCNT with larger diameter is

less than that with smaller diameter, which would make

each C–C bond at its end circumference less seriously

elongated, and thus the average contribution of each C–C

bond contained in its end circumference to the diameter

elongation, i.e. (DEKDC)/n, would decrease accordingly.

3.2.2. The HN!ASWCNT isomers with different diameter

In order to find all the possible isomers of (n,n)

HN!ASWCNTs (nZ3,4,5,6), the potential energy surface

curves (PESCs) of their substrate C–C bond elongating

processes changed from 1.4 to 2.2 A are calculated based on

AM1 and PM3 methods. Since the results obtained from the two

methods are similar, only the AM1 PESC is plotted in Fig. 5, in

which Fig. 5a is the PESC for skew C–C bond elongation and

Fig. 5b for vertical C–C bond elongation. From Fig. 5a, one can

see that there are two minima (corresponding to the substrate C–

Cz1.8 and 2.2 A, respectively) for the skew C–C bond

elongation PESCs of (3,3), (4,4), (5,5) and (6,6) HN!ASWCNTs. As shown in Fig. 5b, however, there are only one

minimum (substrate C–Cw2.2 A, broken) for the vertical C–C

bond elongation PESCs of (3,3) and (4,4) HN!ASWCNTs

though there are still two minima (substrate C–Cz1.8 and

2.2 A) for those of (5,5) and (6,6) ones. This demonstrates that

(

2820284028602880290029202940296029803000302030403060308031003120

(5, 5)

(4, 4)

(6, 6)

(3, 3)

Ene

rgie

s (k

J/m

ol)

The substrate skew C-C bond length (Angstrom)

1.4 1.6 1.8 2.0 2.2 2.4 2.6

(a)

Fig. 5. The relationship between the AM1 energies and substrate C–C distance of (a)

result is similar to that of AM1, and thus is omitted in this figure.

the attacking of HN: group to the vertical bond of ASWCNT

with larger diameter can form both V-closed and V-open

isomers, while the attacking of nitrene to that with smaller

diameter can only produce V-open one. This is coincided with

the cycloaddition result of dichlorocarbene with ASWCNTs too

[21]. The reason for this maybe lies in two facts. First, compared

with skew bond, the vertical bond has much greater strain since

it is right along the tube circumference, and thus is easier to be

broken when being attacked by nitrene in order to release greater

strain. This would lead to no formation of the V-closed isomer

for those ASWCNTs with very smaller diameter. Second, since

the vertical bond is chemically reactive than the skew bond

[6,21,22], the HN: group would prefer break the vertical bond to

the skew bond.

Through optimizing all the minima of those shown in Fig. 5

based on AM1 and PM3 methods, all the possible isomers for

(3,3), (4,4), (5,5) and (6,6) HN!ASWCNTs are found and

their energetics are listed in Table 3. In Table 3, Ea is the

isomerization activation energy from S-closed\V-closed to

S-open\V-open and Ea(r) is that in the reverse direction; DEf

(formation energies)ZE(HN!ASWCNT)KE(ASWCNT)KE(HN:); DEi(energy of isomerization)ZE(S-open\V-open)KE(S-closed\V-closed).

3.2.3. The nitrene cycloaddition reactivity of ASWCNT with

different diameter

From Table 3, the AM1 (PM3) predicted DEf of S-closed/

S-open for (3,3), (4,4), (5,5) and (6,6) HN!ASWCNTs

is K440.6(K366.8)/K411.0(K331.7), K301.0(K240.8)/K357.8(K296.3), K267.9(K211.9)/K329.8(K271.5) and

K246.0(K193.0)/K310.5(K255.9) kJ/mol, respectively,

both increasing gradually, which further verifies that the

AM1 method could obtain similar results with PM3 method

when investigating the properties of HN!ASWCNTs isomers.

This is also true for the V-closed/V-open isomer of (5,5)

and (6,6) HN!ASWCNTs, in which their AM1 (PM3)

predicted DEf are K376.9(K317.5)/K438.8(K373.9) and

K358.2(K303.8)/K400.4(K337.7) kJ/mol, respectively,

with the later being larger than the former. These data suggest

that: (1) the nitrene cycloaddition occurring on both the skew

and vertical bonds is highly exothermic, which may be caused

2700

2750

2800

2850

2900

2950

3000

3050

3100

(4, 4)

(5, 5)

(6, 6)

(3, 3)

Ene

rgie

s (k

J/m

ol)

The substrate vertical C-C bond length (Angstrom)

1.4 1.6 1.8 2.0 2.2 2.4 2.6

b)

skew bond (b) vertical bond of (n,n) HN!ASWCNT of (nZ3,4,5,6); the PM3

Table 3

The energies (E), formation energies (DEf), energies of isomerization (DEi), together with the isomerization activation energies Ea (from S-closed\V-closed to S-

open\V-open), and the reverse isomerization activation energies Ea(r) (from S-open\V-open to S-closed\V-closed) of (n,n) HN!ASWCNT (nZ3,4,5,6) predicted by

AM1 and PM3 (shown in brackets) calculations

Tubes Isomers or TS E (kJ/mol) DEf (kJ/mol) DEi (kJ/mol) Ea (kJ/mol) Ea(r) (kJ/mol) Ea(r)KEa (kJ/mol)

(3, 3) Reactantsa 3467.7(3054.2) 0.0(0.0)

S-closed 3027.1(2687.4) K440.6(K366.8)

TS3S 3068.2(2734.9) K399.5(K319.3) 41.1(47.5) 11.5(12.4) K29.6(K35.1)

S-open 3056.3(2722.5) K411.0(K331.7) 29.6(35.1)

(4,4) Reactants 3195.2(2796.1) 0.0(0.0)

S-closed 2894.2(2555.3) K301.0(K240.8)

TS4S 2918.3(2582.4) K276.9(K213.7) 24.1(27.1) 80.9(82.6) 56.8(55.5)

S-open 2837.4(2499.8) K357.8(K296.3) K56.8(K55.5)

(5,5) Reactants 3160.9(2744.0) 0.0(0.0)

S-closed 2893.0(2532.1) K267.9(K211.9)

TS5S 2911.9(2554.5) K249.0(K189.5) 18.9(22.4) 80.8(82.0) 61.9(59.6)

S-open 2831.1(2472.5) K329.8(K271.5) K61.9(K56.9)

V-closed 2784.0(2426.5) K376.9(K317.5)

TS5V 2787.0(2434.0) K373.9(K310.0) 3.0(7.5) 64.9(63.9) 61.9(56.4)

V-open 2722.1(2370.1) K438.8(K373.9) K61.9(K56.4)

(6,6) Reactants 3239.1(2791.9) 0.0(0.0)

S-closed 2993.1(2598.9) K246.0(K193.0)

TS6S 3007.2(2617.2) K231.9(K174.7) 14.1(18.3) 78.5(81.2) 64.4(62.9)

S-open 2928.6(2536.0) K310.5(K255.9) K64.4(K62.9)

V-closed 2880.9(2488.1) K358.2(K303.8)

TS6V 2889.5(2502.4) K349.6(K289.5) 8.6(14.3) 50.8(48.2) 42.2(33.9)

V-open 2838.7(2454.2) K400.4(K337.7) K42.2(K33.9)

a The ‘reactant’ herein refers to the ‘HN:CASWCNT’.

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 764 (2006) 33–40 39

by the strong electronphilic ability of HN: group when it reacts

with the ethene-like CaC bond in ASWCNT; (2) the

ASWCNT with smaller diameter is easier to react with HN:

group than that with larger diameter, which again confirms the

fact that the tube with smaller diameter has higher chemical

reactivity due to its higher curvature compared with that with

larger diameter [23].

In addition, these data also suggest that releasing a HN:

group from the (n,n) HN!ASWCNT isomer (i.e. the negative

value of formation energy DEf) needs much more energy than

their isomerization activation energy. Let us take (5,5) HN!ASWCNT as an example. Based on AM1 method, the releasing

energy of HN: group from its four isomers is 267.9–

438.8 kJ/mol, while the largest isomerization activation energy

(from S-open to S-closed) is only 80.8 kJ/mol. The latter is

smaller by over 187.1 kJ/mol than the former. This trend is also

true for (3,3), (4,4) and (6,6) HN!ASWCNT isomers. That is

to say, it is mainly the kinetic reason (isomerization activation

energy), not the thermodynamic reason (negative value of

formation energy), that determines the stability of the isomer.

The PM3 energetics also obtains the same result. This further

verifies the conclusion reported in Ref. [14], which proposes

that the stability of oxygen addition isomers may be explained

by kinetic rather than thermodynamic control.

3.2.4. The isomerizations for HN!ASWCNT with different

diameter

Since the isomerizations between two skew-bonded isomers

(S-closed and S-open) and isomerization between two vertical-

bonded (V-closed and V-open) isomers are much easier than

the isomerization between the S-closed and V-closed isomer

for kinetic reasons as mentioned above, only the former two

types are studied in this paper. Herein, the transition states

connecting the S-closed and S-open isomers for (3,3), (4,4),

(5,5) and (6,6) HN!ASWCNTs are named as TS3S, TS4S,

TS5S, TS6S, respectively; the transition states connecting

V-closed and V-open isomers for (5,5) and (6,6) HN!ASWCNTs are named as TS5V, TS6V, respectively.

From Table 3, one can see that the AM1 (PM3) energies of

isomerization (DEi) from S-closed to S-open isomers for (n,n)

HN!ASWCNT (nZ3,4,5,6) are 29.6(35.1), K56.8(K55.5),

K61.9(K56.9) and K64.4(K62.9) kJ/mol, respectively, while

the differences between their Ea(r) and Ea are K29.6(K35.1),

56.8(55.5), 61.9(59.6) and 64.4(62.9) kJ/mol, respectively. The

AM1 and PM3 obtain similar results. This demonstrates that the

percentages of S-open isomers should become less and less in

the HN!ASWCNT mixtures when their diameter increase

gradually. At the same time, the AM1 (PM3) energies of

isomerization (DEi) from V-closed to V-open isomers of (5,5)

and (6,6) HN!ASWCNTs are K64.4(K62.9) and

K42.2(K33.9) kJ/mol; meanwhile the difference between

their Ea(r) and Ea are 61.9(56.4) and 42.2(33.9) kJ/mol,

respectively, also suggesting that the percentage of V-open

isomer with larger diameter should be less than that with smaller

diameter. Thus, we can reasonably predict that both the vertical

and skew bonds of ASWCNTs should become more and more

difficult to be broken by HN: group when their diameter

enlarging gradually and thus the closed-bonded isomers (S-

closed and V-closed) should be the predominant forms in the

HN!ASWCNT mixtures with larger diameter accordingly.

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 764 (2006) 33–4040

4. Conclusions

It is predicted from AM1 and PM3 calculations that the

skew and vertical bonds of (5,5) ASWCNT can be both

remained and broken when being attacked by a HN: group. The

thermodynamic stability of the resulted four isomers can be

described as follows, V-open O V-closed O S-open OS-closed. AM1 (PM3) kinetic analysis suggest that the

isomerization from S-closed to V-closed isomer needs 168.8

(157.8) kJ/mol in the forward direction and 277.8 (263.4)

kJ/mol in the reverse direction. However, the isomerization

from S-closed to S-open isomer and the isomerization from

V-closed to V-open isomer only need 18.9 (22.4) and 3.0 (7.5)

kJ/mol activation energies, respectively. This suggests that the

S-closed and V-closed are very easily translated to S-open and

V-open isomers, respectively, and thus the V-open and S-open

should be the most stable forms in the mixture of (5,5) HN!ASWCNT isomers from kinetic viewpoints. The cycloaddition

of HN: onto the (3,3) and (4,4) ASWCNTs gives birth to

S-closed, S-open, and V-open isomers; while that onto the (5,5)

and (6,6) ASWCNTs produces S-closed, S-open, V-closed and

V-open isomers. More interestingly, both the kinetic and

thermodynamic analysis suggest that the percentage of

S-closed and V-closed isomers would become larger when

the diameter of their host ASWCNT enlarges, and so both its

vertical and skew bonds become more difficult to be broken

when being attacked by HN: group accordingly. In addition, all

the calculations verify that the AM1 method produces similar

results with PM3 method. Thus, both of them would be suitable

semi-empirical methods in investigating the geometrical and

energetical properties of HN!ASWCNT isomers.

Acknowledgments

This work was supported by the National Natural Science

Foundation of China (20133020, 20373033), 973 Program

(2004CB719102), and the China Youth National Nature

Science Foundation (No. 20303010).

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