The nitrene cycloaddition on the sidewall of armchair single-walled carbon nanotubes
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Transcript of The nitrene cycloaddition on the sidewall of armchair single-walled carbon nanotubes
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: [email protected] (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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