theoretical explorations on bn-doped armchair single-walled carbon nanotubes

Theoretical explorations on BN-doped armchair

single-walled carbon nanotubes

Chong Zhang a,b,c,*, Ruifang Li b, Dongju Zhang a, Zhenfeng Shang b, Guichang Wang b,

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

a Institute of Theoretical Chemistry, Shandong University, Shan da Road, Jinan, Shandong 250100, Chinab Department of Chemistry, Nankai University, Tianjin 300071, China

c Department of Chemistry and Technology, Liaocheng University, Liaocheng 252059, China

Received 6 August 2005; received in revised form 27 November 2005; accepted 5 December 2005

Abstract

The geometries and stabilities of mono-BN doped (5,5) armchair single-walled carbon nanotube (ASWCNT) isomers for a smaller C50H20

model are first investigated by both AM1 and HF/4-31G methods. The calculations suggest that both the two methods obtain similar results,

demonstrating that the AM1 method is reliable in calculating the properties of BN-doped ASWCNT isomers. Then, the equilibrium structures and

relative stabilities of the mono-, di-, and tri-BN doped isomers for a larger (5,5) ASWCNT model (C110H20) are further studied based on AM1

level. For mono-BN doped ASWCNT, the thermodynamic stabilities of its isomers in general decrease with the separation between two

heteroatoms, and the isomer with two neighbored B and N atoms is the most stable one. For di- or tri-BN doped ASWCNT isomers, the N–N and

B–B bonds should be avoided and the isomer with a B–N–B–N or B–N–B–N–B–N chain in same hexagon is the most stable one. The BN-doping

generally enhances the redox and electron excitation properties of BN-doped ASWCNT isomers compared with their host tube, and their

stabilities increase with their diameter enlargement on the whole.

q 2006 Published by Elsevier B.V.

Keywords: Armchair single-walled carbon nanotubes (ASWCNTs); BN doping; Redox and excitation energies; Geometries

1. Introduction

Soon after the discovery of carbon nanotubes by Ijima [1] in

1991, the B-doped, N-doped and BN-doped carbon nanotubes

(CNTs) have also been synthesized by a carbon nanotube

substitution reaction in which carbon atoms of starting CNTs

are substituted partially or totally by boron and/or nitrogen

atoms by reaction with B2O3 under Ar or N2 atmosphere [2].

Compared with un-doped carbon nanotubes, it is expected that

the BN-doped nanotubes have many novel electronic,

mechanic, conductive and optical properties, and thus possess

potential applications in many fields, such as nanosized

photonic [3] and electronic [4–6] devices, superhard materials

[7,8], electron field emitters [9], sensitive sensors [10]. Among

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

doi:10.1016/j.theochem.2005.12.002

* Corresponding author. Address: Institute of Theoretical Chemistry,

Shandong University, Shan da Road, Jinan, Shandong 250100, China. Tel.:

C86 531 8365745; fax: C86 531 8564464.

E-mail address: [email protected] (C. Zhang).

these findings, the most intriguing one perhaps is the hybrid

BN-doped CNTs with equal-numbered B and N atoms because

of their structural similarities and isoelectronic relationship

with their parent carbon molecules, which have been

investigated recently by several groups for their interesting

electrochemistry properties. For example, Quinonero et al.

have carried out theoretical investigations on boron and

nitrogen-doped zigzag single-walled carbon nanotubes to

explore the capability of the nanotubes to incorporate LiC

ion in its interior, and found that the BN-doped nanotubes have

higher interaction energies with lithium cation than the pure

nanotubes [11]. Zhou et al. have investigated the lithium

adsorption properties in nitrogen-doped and boron-doped

nanotubes through first-principle calculations concluding that

a boron-doped nanotube decreases the Li-adsorption energies

and, on the contrary, a nitrogen-doped nanotube increases the

Li-adsorption energies [12,13]. Thus, in this paper, the

thorough exploration of the BN distributions, geometries,

stabilities and other properties of the BN-doped CNTs,

especially for those with different diameters, should be an

interesting work for realizing these potential applications in the

future.

Journal of Molecular Structure: THEOCHEM 765 (2006) 1–11

www.elsevier.com/locate/theochem

http://www.elsevier.com/locate/theochem

Fig. 1. The side-view of (5,5) armchair single-walled carbon nanotubes models (A) C110H20 (B) C50H20.

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 765 (2006) 1–112

On the other hand, since Li [14] and Lu [15] et al. suggested

that the armchair single-walled carbon nanotubes (ASWCNTs)

are more thermodynamically stable than the zigzag and spiral

ones, we herein, carry out systematic investigations theoreti-

cally on the equal-numbered B and N atoms substituted

ASWCNTs with different diameters. The structural patterns,

atomic arrangements, as well as oxidative and reductive

properties of BN-doped ASWCNTs will be predicted

theoretically. Thus, the stepwise BN substituting effects of

carbon nanotubes can be primarily revealed based on our

calculations.

2. Computational methods

Figs. 1a and 2 represent the side-view and expanded part of

(5,5) ASWCNT (diameter w6.7 A) model utilized in this

paper, respectively, with each end saturated by 10 H atoms,

thus giving a C110H20 model. It is expected that the middle part

of a reasonably short carbon nanotube can reflect the properties

of a long carbon nanotube to some degree [14], so we select a

C70 cluster in its middle (see the numbered part in Fig. 1a) as

the BN substituting area in this paper.

Because of the limitation of our computation resource, the

direct ab initial calculations for the BN-doped (5,5) C110H20

ASWCNT model is impossible. Therefore, the isomers of a

smaller (5,5) BN-doped C50H20 ASWCT fragment (Fig. 1b,

Fig. 2. The expanded chart of (5,5) armchair sing

their carbon atom labels are also as those in Fig. 2) are first

studied by HF/4-31G method to validate the reliability of the

AM1 method. Then the geometries, stabilities and other

properties of (5,5) BN-doped ASWCNT isomers for C110H20

model are further investigated based on AM1 method. The

harmonic vibrational frequencies are also done at the same

time to ensure true minima.

In order to study the BN-doped ASWCNTs with different

diameters, we also apply the most energetically stable BN

distribution patterns of (5,5) ASWCNT model to the (3,3),

(4,4) and (6,6) ones with the same length in this paper (all of

them have 11 layers of carbon atoms along the tube axis as the

C110H20 model).

All these calculations are carried out with GAUSSIAN 98

programme package [16].

3. Results and discussion

3.1. The comparative AM1 and ab initio study for BN-doped

ASWCNTs

3.1.1. The AM1 and ab initial energetics of BN-doped

ASWCNTs for C50H20 model

Since the limitations of semiempirical calculations are

widely known and, consequently, the reliability of the AM1 in

studying BN-doped ASWCNTs must be first validated in this

le-walled carbon nanotubes model (C110H20).

Table 1

The AM1 and HF/4-31G calculated DE (relative energy, kcal/mol) of (5,5) mono-BN doped ASWCNT isomers (C50H20 model, the notation m-n denotes that the B

atom substitutes a C atom at mth position and a N atom at nth position)

Isomers AM1 HF/4-31G Isomers AM1 HF/4-31G Isomers AM1 HF/4-31G

11-1 0.0 0.0 26-11 30.7 47.2 27-11 40.8 59.3

1-11 4.6 3.5 11-26 30.7 47.2 11-25 40.8 59.3

1-10 13.7 18.7 19-1 29.5 47.3 17-1 40.5 60.6

10-1 13.7 18.7 1-20 29.9 47.9 3-1 42.0 61.2

22-11 12.2 20.6 23-11 32.8 50.0 1-3 40.6 61.3

11-22 12.2 20.6 11-29 32.8 50.0 15-1 43.7 62.5

24-11 22.0 34.2 1-13 35.3 50.3 18-1 42.5 63.1

11-24 22.0 34.2 29-11 32.1 50.9 1-17 46.7 63.2

2-1 25.3 36.7 11-23 32.1 50.9 1-15 48.2 65.3

1-2 25.3 36.7 1-19 35.6 51.5 16-1 44.7 65.4

30-11 24.3 38.7 11-28 39.3 56.0 1-18 47.9 66.1

11-30 24.3 38.7 28-11 39.3 56.6 1-16 49.8 67.1

21-11 19.5 38.9 4-1 41.8 57.7 8-1 48.8 68.5

11-21 19.5 38.9 1-4 41.8 57.7 1-8 48.9 68.5

12-1 22.0 41.8 14-1 37.1 58.0 6-1 51.9 70.7

1-12 26.3 44.8 25-11 41.4 58.6 1-6 51.9 70.7

20-1 24.7 45.2 11-27 41.4 58.6 1-5 51.3 71.5

13-1 31.4 47.1 1-14 42.7 59.0 5-1 52.0 72.0

C. Zhang et al. / Journal of Molecular Structure: THEOCHEM 765 (2006) 1–11 3

paper. For this purpose, the mono-BN doped isomers for a

smaller ASWCNT model (C50H20 fragment as shown in

Fig. 1b), which only contains 1, 2, 2 0, 3 and 3 0 layers (see

Fig. 2) of carbon atoms with 10 H atom at each end, are

optimized using AM1 and HF/6-31G depending on our

computational facilities. Since this C50H20 model is relatively

short, we can only consider the mono-BN substitutions on

those carbon atoms of 1, 2 and 2 0 layers around the tube

circumference (see Fig. 2). Considering the high symmetry

(D5h) of C50H20 model, total of 27 isomers m–n are produced if

the B and N atoms substitute the mth and nth position C atoms,

respectively (mZ1 and 11, nZ2–30 except 11). In addition,

Table 2

The AM1 and HF/4-31G calculated critical bond lengths (A) and bond angles (8) of

doped C50H20 model

Isomers Methods Bond lengths Bond angles

B1C10 N2C3 C11B1C21 C

1-2 AM1 1.518 1.426 118.76 1

HF/4-31G 1.535 1.430 118.02 1

B1C10 N3C2 C11B1C21 C

1-3 AM1 1.522 1.408 120.32 1

HF/4-31G 1.544 1.428 118.32 1

B1C10 N4C5 C11B1C21 C

1-4 AM1 1.524 1.424 121.08 1

HF/4-31G 1.546 1.425 120.21 1

B1C10 N5C4 C11B1C21 C

1-5 AM1 1.524 1.419 120.70 1

HF/4-31G 1.551 1.430 119.50 1

B1C10 N6C7 C11B1C21 C

1-6 AM1 1.524 1.426 120.72 1

HF/4-31G 1.552 1.434 119.62 1

B1C10 N8C9 C11B1C21 C

1-8 AM1 1.519 1.423 120.88 1

HF/4-31G 1.546 1.435 119.77 1

B1N10 –a C11B1C21 N

1-10 AM1 1.505 121.87 1

HF/4-31G 1.505 120.57 1

a Indicating that the convergence is not met utilizing UHF calculation for this iso

exchanging the position of the two heteroatoms in each isomer

would get another 27 isomers. Thus, total of 54 isomers are

obtained for this mono-BN doped C50H20 model, whose AM1

and HF/4-31G energies are shown in Table 1. Among these 54

isomers, only the geometrical parameters of those isomers with

two heteroatoms on the middle circumference (1-2, 1-3, 1-4, 1-

5, 1-6, 1-8 and 1-10) of C50H20 are listed in Table 2, together

with their diameters are shown in Fig. 3.

From Table 1, first, both the AM1 and HF/4-31G methods

suggest that the most stable isomer is 11-1 and the least stable

one is 5-1, respectively. Second, the stability sequence of these

isomers is the same on the whole for both methods. Thus, it

those isomers with two heteroatoms on same circumference for (5,5) mono-BN

10B1C11 C10B1C21 C12N2C22 C3N2C12 C3 N2C22

17.17 117.17 120.64 115.43 115.43

18.20 118.20 120.83 116.51 116.51

10B1C11 C10B1C21 C13B3C23 C2N3C13 C2N3C23

16.64 116.64 119.53 118.59 118.59

17.42 117.42 118.95 119.65 119.65

10B1C11 C10B1C21 C14N4C24 C5N4C14 C5N4C24

13.48 116.48 119.33 116.00 116.00

17.18 117.18 119.09 117.76 116.76

10B1C11 C10B1C21 C15N5C25 C4N5C15 C4N5C25

16.47 116.47 120.45 117.38 117.38

16.85 116.85 120.19 118.36 118.36

10B1C11 C10B1C21 C16N6C26 C7N6C16 C7N6C26

16.49 116.49 120.26 116.76 116.76

16.94 116.94 119.93 117.88 117.88

10B1C11 C10B1C21 C18N8C28 C9N8C18 C9N8C28

16.43 116.43 120.27 117.65 117.65

16.63 116.63 119.91 118.71 118.71

10B1C11 N10B1C21 C20N10C30 B1N10C20 B1N10C30

17.77 117.77 121.12 115.68 115.68

17.91 117.91 121.86 117.01 117.01

mer.

Fig. 3. The HF/4–31 (A) and AM1 (in parenthesis, A) optimized diameters of 1-2, 1-3, 1-4, 1-5, 1-6, 1-8, 1-10 BN-doped isomers and their pristine (5,5) ASWCNT of

C50H20 model.


should be reliable to use AM1 method to study the BN-doping

energetics of the following larger BN-doped ASWCNT model

(C110H50).

3.1.2. The AM1 and ab initial geometries of BN-doped

ASWCNTs for C50H20 model

Since there are as many as 54 BN-doped isomers for the

C50H20 model, investigating the geometrical parameter of all

these isomers must be a tedious and unnecessary work. Herein,

only those isomers with two heteroatoms on the middle

circumference are selected, and they are 1-2, 1-3, 1-4, 1-5, 1-6,

1-8 and 1-10, respectively. Their AM1 and HF/4-31G

calculated geometrical parameters and diameters are listed in

Table 2 and Fig. 3, respectively. In Table 2, only those C–N

and B–N bond lengths on the middle circumference and those

bond angles related to B and N atoms are shown.

From Table 2, we can see that the differences between the

AM1 and HF/4-31G calculated geometrical parameters are

very small for these selected isomers. In fact, the most

significant calculated bond length difference by the two

methods is only 0.028 A and the bond angle difference is less

than 1.28 for most of isomers. Even the largest bond angle

deviation is only 3.78 (bond angle C10B1C11 in isomer 1-4).

These data demonstrate that the AM1 method is also reliable in

calculating the geometrical diameters.

Fig. 3 shows that the difference between the diameter

calculated by AM1 and that by HF/4-31G method is only 0.00–

0.07 A and, especially, the BN substitutions make the diameter

of the host ASWCNT change more or less, making the transect

of host ASWCNT displays a ellipsoid alike shape. The largest

difference between the longer and shorter diameter of the

elliptoid transect happens on isomer 1-2 (0.38 A for HF/4-31G

and 0.33 A for AM1). This conclusion is similar to the work of

Professor Antonio et al. [11], who have pointed out that the

B-doped, N-doped or BN-doped substitutions could make the

cylinder of the host zigzag single-walled carbon nanotube

distort. More importantly, these data again confirm that the

AM1 method could provide similar results as HF/4-31G

method, and is a suitable semi-empirical method for

investigating the properties of BN-doped ASWCNTs.

Table 3

The restricted (Es) and unrestricted (Et) energies based on AM1 and UHF/4-31G levels for 1,3 isomers of mono-BN doped ASWCNTs for C50H20 model; the

subscript ‘s’ in ‘Es’ or ‘t’ in ‘Et’ denotes the isomer calculated is in singlet or triplet

AM1 HF/4-31G

Es (a.u.) Et (a.u.) EtKEs (kcal/mol) Es (a.u.) Et (a.u.) EtKEs (kcal/mol)

1-12 0.6568064 0.5990375 K36.3 K1905.6077215 K1905.7799747 K108.1

1-20 0.6624147 0.6352465 K17.0 K1905.6026493 K1905.702938 K62.9

11-21 0.5765308 0.5768982 0.3 K1905.6170882 K1905.7979054 K113.5

12-1 0.6499147 0.5898362 K37.7 K1905.6123695 –a –a

21-11 0.6459194 0.5768983 K43.3 K1905.6170882 K1905.7979054 K113.5

a Indicating that the convergence is not met utilizing UHF calculation for this isomer.


3.1.3. The AM1 and ab initial unrestricted calculations

of BN-doped ASWCNTs for C50H20 model

In order to explore the 1,3 isomers of mono-BN doped

nanotubes are biradicalar structures or not, the singlet and triplet

of all the 1,3 isomers for C50H20 model are optimized further

usingAM1 andUHF/4-31Gmethods, respectively. TheUHF/4-

31G calculated results shown in Table 3 demonstrate that the 1,3

isomers in triplet are all stable by 62.9–113.5 kJ/mol than in

singlet except isomer 12-1,whose triplet is not converged by this

UHF method. However, the AM1energy differences between

the triplet and singlet for these 1,3 isomers are very different to

those based on UHF/4-31G. For example, the UHF/4-31G

energy of triplet for isomer 11-21 are stable by 113.5 kJ/mol

than that of its singlet and, on the contrary, the AM1 calculation

obtains the reverse conclusion (its singlet is stable 0.3 kJ/mol

than its triplet!). These data demonstrate that theAM1method is

not reliable for calculating the biradicalar structures of BN-

doped isomers. Thus, only the singlet of mono-, di-, and tri-BN

dopedASWCNTs are carried out in the following based onAM1

calculations.

3.2. Energetics and stabilities of BN-doped (5,5) ASWCNTs for

C110H20 model

Since, the reliability of AM1 method in investigating BN-

doped carbon nanotubes is validated compared with ab initial

method as mentioned above, the AM1 method will be utilized

from now on to further study the BN distributions, stabilities,

geometry parameters, and other properties for a larger (5,5)

ASWCNT model with 11 layers of C atoms and 10 H atoms

saturating each end (C110H20, Fig. 1a). If not especially

specified, the (5,5) ASWCNT model mentioned following just

refer to this C110H20 model.

3.2.1. Mono-BN doped (5,5) ASWCNTs

For the (5,5) ASWCNT of C110H20 model (Fig. 1a), we not

only consider the BN substitution occurring on those carbon

atoms positioned at 1, 2 and 2 0 layers around the tube

circumference, but also on those carbon atoms along the tube

axis, such as C1, C11, C21, C31, C41, C51and C61 atoms (see

Fig. 2). For the former, there are 54 isomers obtained as the

BN-doped C50H20 model as mentioned above. For the latter, 12

isomers are additionally produced, and named as 1-11, 11-1,

11-21, 21-11, 11-41, 41-11, 31-41, 41-31, 41-51, 51-41, 51-61

and 61-51, respectively. Among these isomers, if we omit six

duplicate ones, i.e. 1-11, 11-1, 11-21, 21-11, 11-41 and 41-11,

there are total of 60 isomers both around the tube

circumference and along the tube axis. Their ascending

energies calculated by AM1 method are listed in Table 4.

From Table 4, we can see that:

(i) The energy difference between m-n and n-m isomers is

very small and, in most instances, they are equal at

AM1 level. This trend is also same as that obtained by

HF/4-31G method as mentioned above for BN-doped

C50H20 ASWCNT model (see Table 1). This suggests

that the position exchange between B and N atoms in

mono-BN doped ASWCNT isomers does not influence

their thermodynamic stabilities apparently. This may be

caused by their similar electronic structure between the

m-n and n-m isomers due to their high symmetries

(D5h). For this reason, we call them equal-position

isomer in this paper.

(ii) The most stable four isomers are 1-11, 11-1, 1-10 and

10-1, respectively. The former two and latter two are

both equal-position isomers, with the energies of the

former being lower by 8.1 kcal/mol at AM1 level.

Interestingly, these four isomers are all 1,2-substitution

products, while other isomers shown in Table 4 are all

1, n-substitution (nR3) ones. This suggests that the B

and N atoms prefer to stay together and the sloppy bond

of carbon nanotubes can be easily replaced by

heteroatoms in thermodynamic limit. The reason

perhaps is that these 1,2-substitution isomers have

two neighbored heteroatoms, which makes the affluent

electrons on N atom more easily transfer to B atom than

those isomers with two disconnected heteroatoms. So,

these four 1,2-substitution isomers have the least

damaged p–p conjugation in the whole CNT systems,

which make them the most thermodynamic stable

isomers of all.

(iii) The most unstable two isomers are also one pared

equal-position isomers of 51-61 and 61-51, followed by

another pared equal-position isomers of 51-41 and

41-51, with the energy of the former higher about

5.0 kJ/mol than the latter. In addition, we can also find

from Fig. 1a that the B and N atoms in these four

isomers are all along the tube axis. These data suggest

890

895

900

905

910

915

920

925

t of

form

atio

n (K

cal/

Mol

)

Table 4

The AM1 calculated energies E and relative energiesDE (kcal/mol) of (5,5) mono-BN doped ASWCNT isomers (C110H20 model, the notation m-n denotes that the B

atom substitute a C atom at mth position and a N atom at nth position)

Isomers E DE Isomers E DE Isomers E DE

ASWCNT 875.7 K6.9

1-11 882.6 0.0 1-19 912.7 30.1 1-18 921.1 38.5

11-1 883.1 0.5 13-1 913.0 30.4 17-1 921.2 38.6

1-10 890.7 8.1 4-1 915.3 32.7 18-1 921.3 38.7

10-1 890.7 8.1 1-4 915.3 32.7 27-11 921.5 38.9

22-11 899.6 17.0 11-23 915.5 32.9 11-25 921.5 38.9

11-22 899.6 17.0 29-11 915.5 32.9 15-1 921.5 38.9

2-1 901.8 19.2 11-29 915.7 33.1 25-11 921.6 39.0

1-2 901.8 19.2 23-11 915.7 33.1 11-27 921.6 39.0

21-11 903.7 21.1 1-3 915.8 33.2 31-41 921.8 39.2

11-21 903.7 21.1 3-1 916.4 33.8 41-31 921.8 39.2

1-12 904.1 21.5 11-26 918.4 35.8 1-6 922.6 40.0

12-1 905.0 22.4 26-11 918.4 35.8 6-1 922.6 40.0

1-20 907.6 25.0 1-14 918.7 36.1 1-5 922.9 40.3

20-1 908.2 25.6 14-1 919.3 36.7 1-16 922.9 40.3

30-11 909.2 26.6 11-28 919.5 36.9 5-1 923.2 40.6

11-30 909.2 26.6 28-11 919.5 36.9 16-1 923.3 40.7

24-11 912.1 29.5 8-1 920.9 38.3 41-51 923.4 40.8

11-24 912.1 29.5 1-8 920.9 38.3 51-41 923.6 41.0

19-1 912.4 29.8 1-15 921.1 38.5 51-61 928.6 46.0

1-13 912.5 29.9 1-17 921.1 38.5 61-51 928.6 46.0


that the B and N atoms are more preferential to

substitute the C atoms around the circumference than

those along the tube axis. This may be explained by the

fact that the p–p conjugated interaction between the C

atoms along the tube axis is larger than that around the

tube circumference due to the intrinsic curvatures of

ASWCNTs, and thus the C atoms around the tube

circumference are more active to be substituted by B

and N atoms than those along the tube axis.

(iv) Except the four most stable isomers as mentioned

above, other isomers all have two separated heteroa-

toms by one or more C atoms. Herein, we plot their

energies against the number of intervening C atoms

(Fig. 4), which approximately represents the distance

between the B and N atoms. It can be seen from Fig. 4

that the separation between the two heteroatoms

gradually increases the energy of corresponding isomer

in general. As the number of intervening C atoms is

equal to or more than 5, the energy increment becomes

less and less. This suggests that the separation of B and

N atoms decreases thermodynamic stability of the

isomer. This can be explained by the fact that the

electron transfer from N to B atom should become

difficult for the larger distance separating the two

heteroatoms, leading to less conjugation of whole

ASWCNT system accordingly.

0 2 4 6 8 10

880

885Hea

Number of C atoms seperating heteroatoms

Fig. 4. Dependence of the AM1 calculated energies of mono-BN doped (5,5)

ASWCNT on the number of carbon atoms separating the heteroatoms.

3.2.2. Di-BN doped (5,5) ASWCNTs

From the above discussions, we can reasonably propose that

the di-BN doped ASWCNT should be built by another stepwise

substitution of C2 unit based on the most stable mono-BN

doped isomer (1-11). Hence, there are total of 66 isomers

obtained if we only consider the further BN substitution

occurring on one C2 unit contained in the 1, 2, 2 0, 3 and 3 0

layers (Fig. 2) of isomer 1-11. Their AM1 energies according

to increasing sequence are listed in Table 5.

From Table 5, we can see that:

(i) The most thermodynamically stable isomer is 1-11-22-

21 (this notion represents that the C atoms at 1, 11, 22

and 21 positions are substituted by B, N, B, N atoms,

respectively, and other denotations express the same

meaning), followed by 1-11-12-2, 1-11-20-10, 1-11-40-

31, 1-11-30-10 and 1-11-12-32 in turn. It is very

interesting to notice that each of the former four

isomers has a B–N–B–N chain in same hexagon, and

each of the latter two has a B–N–B–N chain but in

Table 5

The AM1 calculated relative energiesDE (kcal/mol) of di-BN doped (5,5) ASWCNT isomers (herein, the notation m-n-p-q denotes that two B atoms substitute two C

atoms in mth and pth positions, and two N atoms substitute two C atoms in nth and qth positions, respectively)

Isomers DE Isomers DE Isomers DE Isomers DE Isomers DE

ASWCNT 8.0

1-11-22-21 0.0 1-11-23-24 20.2 1-11-14-13 23.4 1-11-30-50 27.2 1-11-50-30 32.7

1-11-12-2 1.5 1-11-39-38 20.2 1-11-33-32 23.8 1-11-9-8 29.3 1-11-38-18 33.5

1-11-20-10 4.6 1-11-20-19 20.4 1-11-19-9 23.8 1-11-18-38 29.6 1-11-43-23 33.7

1-11-40-31 4.6 1-11-32-33 20.4 1-11-13-3 24.7 1-11-40-20 29.6 1-11-42-22 34.1

1-11-30-10 5.6 1-11-38-39 20.7 1-11-21-22 24.7 1-11-3-2 29.9 1-11-8-28 35.1

1-11-12-32 11.5 1-11-48-49 20.9 1-11-13-14 25.2 1-11-28-48 30.2 1-11-20-40 35.2

1-11-50-41 16.9 1-11-49-48 20.9 1-11-10-20 25.3 1-11-39-19 30.5 1-11-21-41 36.0

1-11-30-29 17.4 1-11-29-30 20.9 1-11-29-9 25.4 1-11-8-9 30.8 1-11-40-31 47.5

1-11-41-50 17.9 1-11-9-29 21.1 1-11-23-3 25.7 1-11-22-2 30.9 1-11-2-12 48.2

1-11-41-21 18.1 1-11-3-23 21.1 1-11-22-42 26.1 1-11-23-43 31.9 1-11-32-12 62.8

1-11-43-42 18.7 1-11-42-43 21.4 1-11-2-3 26.5 1-11-19-39 31.9

1-11-3-13 19.5 1-11-8-28 22.9 1-11-2-22 26.9 1-11-13-33 32.0

1-11-9-19 19.5 1-11-28-8 23.0 1-11-10-30 27.1 1-11-29-49 32.4

1-11-24-23 19.8 1-11-19-20 23.3 1-11-33-13 27.1 1-11-49-29 32.5

B

N

N

B

1

2

3 4

5

B

N

B

N

1

2

3 4

5

A B

Fig. 5. Part of (5,5) ASWCNT sidewall with a B–N–B–N chain in one hexagon

(A), or in different hexagons (B).


different hexagons. This suggests that the isomer with a

B–N–B–N chain in same hexagon is energetically

preferable. Through further investigation, we find that

the B–N–B–N chain in same hexagon causes the

neighboring hexagons (such as hexagons of 1, 2, 3, 4

and 5 shown in Fig. 5A) each has six p electrons,

resulting in a perfect p system. While the B–N–B–N

chain in different hexagons makes neighboring hexa-

gons has either five or seven p electrons each (such as

hexagon of 2, 4 or 5 shown in Fig. 4B), resulting in

imperfect p system. So the isomer with a B–N–B–N

chain in the same hexagon is more energetically

preferable.

(ii) The most unstable isomer is 1-11-32-12, in which there

is a B–N–N–B chain in different hexagons. The next

two most unstable isomers are 1-11-2-12 and 1-11-40-

31 in turn, and each of them also has a B–N–N–B chain

but in same hexagon. This further verifies that the

substitution of heteroatoms in same hexagon makes the

isomer energetically preferable than in different

hexagon. More importantly, the fact indicates that the

direct connection between two N atoms makes the host

ASWCNT energetically most unstable, which is

coincided with the BN substitution of fullerenes

[17,19]. This may be caused by the stronger repulsion

between the lone-pair electrons in two neighbored N

atoms.

(iii) Since the B–N–B–N or B–N–N–B chain makes the

isomer most stable or unstable as mentioned above,

exploring what role the N–B–B–N chain plays on the

thermodynamic stability of BN doped ASWCNT

isomers must be very interesting. So we select all the

isomers with an N–B–B–N chain from Table 5, which

includes 1-11-21-22, 1-11-10-20, 1-11-10-30, 1-11-21-

41 isomers. As expected, the former two isomers with

an N–B–B–N chain in same hexagon are thermo-

dynamically stable than the latter two in different

hexagons. However, these isomers are not necessary

stable or unstable than those isomers with two BN units

separated by one or more than one C atoms. This

suggests that the N–B–B–N chain and the number of

intervening carbon atoms between the two discon-

nected BN units are two competing factors in

dominating the thermodynamic stabilities of the BN-

doped ASWCNT isomers.

3.2.3. Tri-BN doped (5,5) ASWCNTs

Based on the above discussions, the most stable isomer of

tri-BN doped (5,5) ASWCNT should have a B–N–B–N–B–N

ring in the same hexagon, denoting as 1-11-21-22-2-12 in this

paper. The BN distribution patterns of the most stable mono-,

di-, and tri-BN doped (5,5) ASWCNT isomers can be seen

more directly in Fig. 6.

3.3. The BN-doped ASWCNTs with different diameters

Since the carbon nanotubes can be regarded as a cylinder

structure rolled by a sheet of graphite, the BN distribution in

H

H

H H

H H

H H

H H

H H

H H

N

H

B

B

H

H H

N

N

B

H

H

H

H

H H

H H

H

H

H

H

H H

HH

B

H

H

H

H

N

NB

H

H

H

H

H

H

H

H

H

H

H

HH

HH

H H

H

H

H

N

B

H

H

mono-BN doped (5, 5) ASWCNT tri-BN doped (5, 5) ASWCNT di-BN doped (5, 5) ASWCNT

Fig. 6. The BN substitutions of the most stable mono-, di- and tri-BN doped (5,5) ASWCNT isomers.


the most stable isomer of ASWCNTs with different diameter

should be similar, i.e. one B and one N atoms prefer to stay

together and substitute a C2 unit of a sloppy bond in middle of

tube; two BN units form a B–N–B–N chain in one hexagon;

and three BN units form a B–N–B–N–B–N ring. Based on this

consideration, the above mono-, di- and tri-doped BN

distributions for the most stable isomers are further applied

to a series of (n, n) ASWCNTs (nZ3, 4, 5, 6) models with same

length (all have 11 carbon layers along the tube axis as C110H20

model). Therefore, the most stable isomer of the BN-doped

ASWCNTs with different diameter can be also obtained.

Table 6

The stabilization energies (E#, unit: kcal/mol) of the most stable isomers for the

mono-, di- and tri-BN doped (n, n) ASWCNTs (nZ3, 4, 5, 6) and their

3.3.1. Stabilization energy E#

For sake of comparison, a stabilization energy E# [17] is

presented herein to interpret the relative stabilities of the most

stable isomers of mono-, di- and tri-BN doped (n, n)

ASWCNTs (nZ3, 4, 5, 6) according to the gas-phase reaction

nCCmXZCnXm, and can be calculated by E#(CnXm)ZHf(CnXm)KnHf(C)KmHf(X). It is obvious that the more

negative the E# the greater the stability. The AM1 calculated

E# of the most stable isomers of BN-doped (n, n) ASWCNTs is

summarized in Table 6. The data suggest that the ASWCNTs

cannot be stabilized by BN-doping, and the stabilities decrease

with increasing number of the BN units. In addition, the BN-

doped carbon nanotube with larger diameter is more

thermodynamically stable than that with smaller diameter,

which can be explained by the fact that the p–p conjugation of

the former is stronger than that of the latter due to its smaller

sidewall curvature.

corresponding pure ASWCNTs based on AM1 level

(3,3)

ASWCNT

(4,4)

ASWCNT

(5,5)

ASWCNT

(6,6)

ASWCNT

Undoped K13,732.3 K18,750.1 K23,684.3 K28,579.2

Mono-BN doped K13,622.9 K18,631.9 K23,562.6 K28,455.7

Di-BN doped K13,531.6 K18,533.8 K23,462.7 K28,352.4

Tri-BN doped K13,445.7 K18,448.7 K23,376.0 K28,266.9

3.3.2. Ionization potentials (IP), electron affinities (EA) and

LUMO–HOMO gaps (Eg)

Before investigations of ionization potentials (IP), electron

affinities (EA) and LUMO–HOMO energy gaps (Eg) for BN-

doped ASWCNT with different diameters, it is necessary to

study the IP, EA and Eg of BN-doped ASWCNT with certain

diameter first to primarily explore their redox properties on

different heteroatom distributions. Herein, we only consider

one-pared BN substitution on the sidewall of (5,5) ASWCNT

C110H20 model, and the dependence of IP, EA and Eg on the

energies of all its isomers based on AM1 level are shown in

Fig. 7.

It can be seen from Fig. 7 that the BN substitution perturbs

both HOMO and LUMO obviously. The mono-BN doped (5,5)

ASWCNT isomers have somewhat smaller ionization poten-

tials (KEHOMO, IP) and bigger electron affinities (KELUMO,

EA) compared with the host ASWCNTs, confirming that the

BN-doping could make the ASWCNT not only lose electron

more easily but also add electron more easily. In another word,

the BN-doping could enhance the redox characteristic of

carbon nanotubes, which is similar to the results of mono-BN

doped fullerenes [18]. In addition, the LUMO–HOMO energy

gaps (Eg) of mono-BN doped (5,5) ASWCNTs, which are

associated with the electronic excitation properties, are also

somewhat smaller than that of the host (5,5) ASWCNT, and

there is a general trend that Eg decrease with energies

increasing. This suggests that BN-doping could obviously

enhance the excitation ability of host carbon nanotube,

resulting in lower thermodynamic stability. More importantly,

it can be seen from Fig. 7A and B that the most stable isomer of

mono-BN substituted ASWCN basically has the lowest redox

870 880 890 900 910 920 930

60

80

100

120

140

160

(5, 5) ASWCNTIP

/EA

(K

cal/m

ol)

heats of formation (Kcal/mol)

A B

IP EA

870 880 890 900 910 920 93085

90

95

100

105

110

Eg

(5, 5) ASWCNT

LU

MO

-HO

MO

gap

(K

cal/m

ol)

heats of formation (Kcal/mol)

Fig. 7. Dependence of ionization potentials (IP), electron affinities (EA) and LUMO–HOMO gaps (Eg) on the energies of momo-BN doped (5,5) ASWCNTs.


and electron excitation ability of all. So, in this paper, only the

ionization potentials (IP), electron affinities (EA) and LUMO–

HOMO gaps (Eg) of the most stable BN-doped ASWCNT

isomers with different diameter are studied and the results are

summarized in Table 7.

From Table 7, one can see that the IP increases, EA

decreases, and Eg increases with BN unit increasing from 1 to

3. This suggests that the redox and excitation stabilities

generally diminish by gradually BN-doping. It is also expected

from Table 7 that the BN-doped carbon nanotubes with larger

diameters usually have smaller IP, larger EA and smaller

LUMO–HOMO gaps, which is same as that of the undoped

carbon nanotubes. This demonstrates that the redox and

electron excitation properties of BN-substituted ASWCNTs

with larger diameter are more active than those with smaller

diameter.

3.3.3. Geometric structures of BN-doped carbon nanotubes

Similar to the BN-doped C50H20 model as mentioned above,

the AM1 results also suggest that the BN substitution changes

the cylindrical shape of the host ASWCNT and makes its cross

section containing heteroatoms like a slightly distorted ellipse.

However, since the diameter change for C110H20 model is not

as apparently as that for C50H20 model, only the geometric

parameter around the heteroatoms for the former model are

discussed further. In this section, the most stable mono-, di-,

and tri-BN substituted (5,5) ASWCNTs are first investigated to

reveal the gradual BN substituting effects on geometries, and

then the BN-doped ASWCNTs (nZ3, 4, 5, 6) are further

Table 7

The ionization potentials (IP), electron affinities (EA) and the LUMO–HOMO gaps

calculated at AM1 level

(3,3) ASWCNT (4,4) ASWCNT

IP EA Eg IP EA Eg

Undoped 169.5 59.2 110.4 170.7 57.0 113

Mono-BN doped 173.3 54.9 118.4 170.8 55.3 115

Di-BN doped 176.1 54.1 122.0 173.5 54.0 119

Tri-BN doped 175.7 52.9 122.8 175.1 52.3 122

studied in order to explore the geometrical changes on different

tube diameters.

Fig. 8 summarizes the AM1 calculated bond lengths and

atomic charges of the most stable mono-, di- and tri-BN doped

(5,5) ASWCNT isomers and their host carbon nanotube for the

region where heteroatoms substitute carbon atoms. For the

most stable mono-BN doped (5,5) ASWCNT isomer, the B–N

bond length is 1.463 A, while the corresponding C–C bond

length in pristine ASWCNT is 1.419 A. For the most stable di-

BN doped (5,5) ASWCNT isomer, the B–N, N–B and B–N

bond lengths are 1.461, 1.470 and 1.496 A, respectively, while

the corresponding C–C bond lengths in pristine ASWCNT are

1.416, 1.419 and 1.419 A, respectively. For the most stable tri-

BN doped (5,5) ASWCNT isomer, the B–N bond lengths are

between 1.473 and 1.482 A, while the corresponding C–C bond

lengths are between 1.416 and 1.419 A. This suggests that the

B–N bond lengths are all longer than the corresponding C–C

bond in the pristine ASWCNT, which again confirm that the

ASWCNT can not be stabilized by BN-doping, and the more

number of C2 units substituted by BN units, the more unstable

the host ASWCNT is. This result is coincided with the BN-

substituted fullerenes, such as C60-2x-(BN)x [19] and C70-2x-

(BN)x [17] (xZ1, 2, 3). Meanwhile, it can be seen from Fig. 8

that the Mulliken charges mainly distribute in the vicinity

around the heteroatoms, and the B and N atoms possess

positive and negative charges, respectively. This is caused by

the fact that the electronegativity of nitrogen is bigger than that

of the boron, and thus the N atom attracts electron from the B

atom.

(Eg) of the most stable isomers of BN-doped (n, n) ASWCNT (nZ3, 4, 5, 6)

(5,5) ASWCNT (6,6) ASWCNT

IP EA Eg IP EA Eg

.6 164.4 62.5 101.9 160.4 66.1 94.3

.5 165.9 61.7 104.2 161.7 65.5 96.2

.5 167.7 60.1 107.6 162.4 63.8 98.5

.9 167.9 58.6 109.4 163.4 62.6 100.8

1.419

1.419

1.416

1.419

1.419

1.416

1.442 1.442

1.426 1.426

1.441

1.41

1.442

1.419

1.442

1.419

1.442

1.4061.426

1.441

1.4421.442

1.4261.406

1.442

1.419

1.442

1.41

1.442

1.4191320

3340

2330

310

32

5251

31

4350

1211

21

42

2221

41

6261

(5, 5) SWCNT

1320

3340

2330

310

32

5251

31

4350

12

2

11

1

42

22

41

21

6261

B

N

1.463

1.512

1.39

1.444

1.4161.407

1.414

1.437 1.431

1.448

1.439

1.440

1.421 1.421

1.4461.408

1.444

1.4281.440

1.414

1.435

1.4021.410

1.450

1.407

1.5281.418

1.454

1.413

0.23

-0.20

-0.13

0.03

0.10

-0.05

-0.03

0.04

-0.11

0.03

-0.04

0.01 0.01

-0.03

0.06

-0.07

0.13

-0.05

0.00

0.01

-0.02

0.03

-0.04

0.03

(5, 5) SWCNT-(BN)1

1.442

1320

3340

2330

310

32

5251

31

4350

12

2

11

1

42

22

41

21

6261

1.496

1.470

1.416

1.461

B

N

N B 1.521

1.404

1.435

1.522

1.3991.417

1.448

1.444

1.410

1.415

1.450

1.413

1.536

1.408

1.4491.415

1.441

1.439

1.429

1.443

1.402

1.435

1.418

1.436

1.454

0.31

-0.25 0.16

-0.18

0.27-0.26

0.14

-0.06 0.02

-0.130.04

-0.03

0.06

-0.06

0.04-0.08

0.01-0.06

0.12-0.06

0.05

-0.04

-0.08

(5, 5) SWCNT-(BN)2

1.408

30 23

50

20

43

13

10 3

40 33

42

62

41

61

22

21

21

31 32

1211

5251

B

N

N B

B

N

1.481

1.481

1.482

1.473

1.4731.482

1.411

1.447

1.4461.417

1.529

1.395

1.452

1.4331.412

1.5291.411

1.447

1.446

1.417

1.395

1.452

1.433

1.414

1.451

1.4101.54

1.410

1.4511.41

0.30

-0.28

-0.28 0.32

-0.30

0.32

-0.06 0.03

-0.15 0.05

-0.07

0.16

-0.07

0.05-0.15

0.03-0.06

0.15 -0.08

0.05

-0.15

0.05

-0.08 0.15

(5, 5) SWCNT-(BN)3

Fig. 8. AM1 calculated bond lengths (A) and atomic charges (e) of the most stable isomers of mono-, di- and tri-BN doped (5,5) ASWCNT.


In order to investigate how the BN substitution affects the

structures of ASWCNTs with different diameter, the most

stable isomers of mono-, di- and tri-BN doped (3,3), (4,4), (5,5)

and (6,6) ASWCNTs are optimized by AM1 method, and the

critical bond lengths and atomic charges are collected in

Table 8 (the numbered label of B, N or C atoms are same as

those in Fig. 8). It can be seen from Table 8 that the BN bond

lengths in the most stable isomers of mono-BN doped (3,3),

(4,4), (5,5) and (6,6) ASWCNTs are 1.488, 1.469, 1.463 and

1.460 A, respectively, gradually decreasing with diameter

enlarging. This is also true for those most stable isomers of

di- and tri-BN doped (n, n) ASWCNTs (nZ3, 4, 5, 6). These

data suggest that the BN-doped ASWCNT isomers with larger

diameter are stable than those with smaller diameter. This is

consistent with the generally accepted rule about a carbon

nanotube, i.e. the tube with larger diameter has larger stability

than the tube with smaller diameter caused by its smaller

curvature.

Additionally, it can be seen from Table 8 that the charge

difference (De(B–N)) between B and N atoms becomes smaller

with diameter increasing. For example, the charge differences

between B and N atoms in mono-BN doped (3,3), (4,4), (5,5)

and (6,6) ASWCNTs are 0.54, 0.47, 0.43 and 0.42e,

respectively, decreasing in turn, while that in flat (BN)1C4H6

is only 0.16e. This can be explained by the fact that the

ASWCNT with larger diameter has larger p–p conjugation

than that with smaller diameter due to its lower surface

curvature, and part of the negative charge on N can easily

return to B atom through the big p bond covering the whole

system.

4. Conclusions

The isomers of BN-doped (5,5) ASWCNT for C50H20

model are studied at AM1 and HF/4-31G levels, resulting in

very similar equilibrium structures and relative stabilities.

This result suggests that the AM1 method is accurate

enough to investigate the properties of BN-doped carbon

nanotubes, which provides an attractable opportunity for

investigating the properties of a much larger BN-doped

Table 8

The critical bond lengths (A) and atomic charges (e) of the most stable isomers of mono-, di- and tri-BN doped ASWCNTs with different diameters calculated by

AM1 method

ASWCNTs C1–C11 C11–C12 C12–C2 C2–C22 C22–C21 C21–C1 C1 C11 C12 C2 C22 C21 De(B–N)/

ave

Undoped (3,3) 1.420 1.427 1.420 1.420 1.427 1.420 0.00 0.00 0.00 0.00 0.00 0.00

(4,4) 1.419 1.419 1.419 1.419 1.419 1.419 0.00 0.00 0.00 0.00 0.00 0.00

(5,5) 1.419 1.416 1.419 1.419 1.416 1.419 0.00 0.00 .0.00 0.00 0.00 0.00

(6,6) 1.418 1.415 1.418 1.418 1.415 1.418 0.00 0.00 0.00 0.00 0.00 0.00

C6H6 1.395 1.395 1.395 1.395 1.395 1.395 0.00 0.00 0.00 0.00 0.00 0.00

B1–N11 N11–C12 C12–C2 C2–C22 C22–C21 C21–B1 B1 N11 C12 C2 C22 C21

Mono-BN

doped

(3,3) 1.488 1.442 1.406 1.459 1.395 1.535 0.31 K0.23 0.12 K0.08 0.04 K0.13 0.54

(4,4) 1.469 1.417 1.412 1.449 1.391 1.520 0.26 K0.21 0.13 K0.08 0.06 K0.13 0.47

(5,5) 1.463 1.407 1.416 1.444 1.390 1.512 0.23 K0.20 0.13 K0.07 0.06 K0.13 0.43

(6,6) 1.460 1.402 1.418 1.441 1.390 1.508 0.22 K0.20 0.13 K0.07 0.06 K0.10 0.42

(BN)1C4H6 1.429 1.376 1.377 1.425 1.366 1.509 0.09 K0.07 0.12 K0.07 0.05 K0.12 0.16

B1–N11 N11–C12 C12–C2 C2–B22 B22–N21 N21–B1 B1 N11 C12 C2 B22 N21

Di-BN

doped

(3,3) 1.526 1.446 1.398 1.535 1.489 1.487 0.35 K0.23 0.13 K0.19 0.31 K0.27 0.58

(4,4) 1.505 1.425 1.402 1.525 1.470 1.476 0.33 K0.25 0.15 K0.19 0.29 K0.27 0.57

(5,5) 1.496 1.416 1.404 1.521 1.461 1.470 0.31 K0.25 0.16 K0.18 0.27 K0.26 0.55

(6,6) 1.491 1.412 1.405 1.519 1.456 1.467 0.31 K0.25 0.16 K0.18 0.26 K0.26 0.54

(BN)2C2H6 1.446 1.384 1.366 1.522 1.425 1.442 0.18 K0.13 0.15 K0.18 0.13 K0.15 0.25

B1–N11 N11–B12 B12–N2 N2–B22 B22–N21 N21–B1 B1 N11 B12 N2 B22 N21

Tri-BN

doped

(3,3) 1.498 1.501 1.496 1.496 1.501 1.498 0.33 K0.29 0.34 K0.30 0.34 K0.29 0.63

(4,4) 1.487 1.489 1.478 1.478 1.489 1.487 0.31 K0.28 0.32 K0.30 0.32 K0.28 0.60

(5,5) 1.481 1.482 1.473 1.473 1.482 1.481 0.30 K0.28 0.32 K0.30 0.32 K0.28 0.59

(6,6) 1.477 1.477 1.470 1.470 1.477 1.477 0.29 K0.28 0.31 K0.29 0.31 K0.28 0.58

(BN)3H6 1.445 1.445 1.445 1.445 1.445 1.445 0.18 K0.18 0.18 K0.18 0.18 K0.18 0.36


carbon nanotube model. Based on this conclusion, a series

BN-doped (n, n) (nZ3, 4, 5, 6) ASWCNTs with 11 layers

of carbon atoms along the tube axis, especially the (5,5)

one, are further studied by AM1 method. The result

demonstrates that the BN-substituted ASWCNT is generally

less stable than the host ASWCNT. For mono-BN doped

(5,5) ASWCNT, The LUMO–HOMO splitting and energies

suggest that the direct BN connection pattern is the most

thermodynamically stable one. For the di-BN doped (5,5)

ASWCNT, the N–N and B–B bonds should be avoid and

the maximum number of B–N bonds is preferable, resulting

in the most stable isomer with a B–N–B–N chain in same

hexagon. The redox and excitation properties of (5,5)

ASWCNT isomers can be usually enhanced by BN

substitutions. The geometrical parameters, atomic charges

and LUMO–HOMO gaps all suggest that the stabilities of

BN-doped ASWCNT isomers increase with their diameters

enlargement.

Acknowledgements

This work is supported by China Youth National Nature

Science Foundation (No. 20303010) and Shandong Province

Nature Science Foundation (Y2002B02).

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