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Electronic structures of hydrogen functionalized carbon nanotube: Density functional theory (DFT) study
Accepted Manuscript Electronic Structures of Hydrogen Functionalized Carbon Nanotube: Density Functional Theory (DFT) Study Hiroto Tachikawa, Tetsuji Iyama, Hiroshi Kawabata PII:
S1293-2558(16)30044-9
DOI:
10.1016/j.solidstatesciences.2016.03.004
Reference:
SSSCIE 5297
To appear in:
Solid State Sciences
Received Date: 7 January 2016 Revised Date:
29 February 2016
Accepted Date: 8 March 2016
Please cite this article as: H. Tachikawa, T. Iyama, H. Kawabata, Electronic Structures of Hydrogen Functionalized Carbon Nanotube: Density Functional Theory (DFT) Study, Solid State Sciences (2016), doi: 10.1016/j.solidstatesciences.2016.03.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Title:
Electronic Structures of Hydrogen Functionalized Carbon Nanotube:
Density Functional Theory (DFT) Study
Hiroto Tachikawa*, Tetsuji Iyama, Hiroshi Kawabata
Division of Applied Chemistry
Hokkaido University
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Graduate School of Engineering
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Authors:
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Sapporo 060-8628, Japan
Manuscript submitted to :
Solid State Sciences
Section of the journal :
Regular Paper
Correspondence and Proof to :
Dr. Hiroto TACHIKAWA*
Division of Applied Chemistry
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Graduate School of Engineering Hokkaido University Sapporo 060-8628, JAPAN [email protected]
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Contents :
+81 11706-7897
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Fax.
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Figure captions
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2016_2_29 Revised Electronic Structures of Hydrogen Functionalized Carbon Nanotube: Density
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Functional Theory (DFT) Study Hiroto Tachikawa*, Tetsuji IYAMA, Hiroshi Kawabata
Electronic
structures
and
formation
mechanism
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ABSTRACT:
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Division of Applied Chemistry, Graduate School of Engineering Hokkaido University, Sapporo 060-8628, JAPAN
of
hydrogen
functionalized carbon nanotube (CNT) have been investigated by means of density functional theory (DFT) method. The mechanism of hydrogen addition reaction to the CNT surface was also investigated. Pure and boron-nitrogen (BN) substituted CNT
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(denoted by CNT and BN-CNT, respectively) were examined as the carbon nanotubes. It was found that the additions of hydrogen atom to B (boron atom) and C (carbon atom) sites of BN-CNT proceed without activation barrier, whereas the hydrogenation
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of N (nitrogen atom) site needs the activation energy. The electronic states of hydrogen
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functionalized CNT and BN-CNT were discussed on the basis of theoretical results.
Keywords: CNT; spin density; hyperfine coupling constant; potential energy curve
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1. Introduction Surface-functionalized fullerene, graphene, and carbon nanotube (CNT) are known as a high-performance molecular device. For example, porphyrin functionalized
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graphene is one of the most useful hybrid materials with large nonlinear optical properties [1-7]. The interaction between carbon materials and radical has recently
markedly changed by the radical addition [8-17].
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attracted considerable interest because the electronic properties of carbon materials are
The hydrogen atom is the simplest radical and behaves frequently as a dopant in
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carbon materials, and the electronic states of the materials are drastically changed by only one hydrogen atom. It is known that the electronic states of CNT are turned by the addition of hydrogen atom. [18] These carbon materials are known as the hydrogen functionalized carbon materials.
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Kim et al. investigated experimentally the hydrogen doped CNT. They found that the electronic structures of a CNT are modified by hydrogen functionalization. The hydrogen addition expanded the band gap of CNT. [19] Fujimoto and Saito [20]
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investigated theoretically the electronic states of hydrogen adsorbed on the nitrogen (N)-doped CNT using density functional theory (DFT) calculations and determined the
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favorable hydrogen adsorption site on N-doped CNT. They found that the hydrogen atom is preferentially added to the nitrogen atom of CNT. Ebrahimi and Rafii-Tabar [21] investigated the influence of hydrogen functionalization on mechanical properties of graphene and CNT. They found that the effects of hydrogen atom on elastic properties are considerable. CNT has been examined as a hydrogen storage material. Using molecular dynamics method, Ozturk et al. investigated a welded random CNT network structures with a hydrogen atom and observed that the CNT networks could
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uptake 8.85 wt.% hydrogen at 77 K [22]. The interaction of CNT with hydrogen molecule (H2) was investigated as well as the hydrogen atom. Ohno and co-workers invesitgated theoretically the electronic structure of CNTs after the hydrogenation
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(H2-CNT) [23-25].The binding and activation energies were determined. Terakura and co-workers were calculated the B and N atomic substitutions in the graphenes [26-28]. Thus, the functionalization of CNTs by hydrogen is of great importance for a
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development of nanotube-based electronics devices. However, the effects of one hydrogen atom addition to the electronic states of CNT are still unclear. Especially,
around the hydrogen atom is limited.
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information on the reaction mechanism of hydrogen addition to CNT and spin density
In the present study, the interaction of one hydrogen atom with the pure, nitrogenand boron-doped CNT’s were investigated by means of DFT method to elucidate the
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binding site and band gap of hydrogen doped CNT.
2. Calculation Methods
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All hybrid DFT calculations were carried out using Gaussian 09 program package [29]. The (10,0)-carbon nanotube (C156) was used in the present study. As the
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boron-nitrogen (BN) doped CNT (denoted by BN-CNT), BNC154 was examined. In BN-CNT, two carbon atoms around central region of CNT were substituted by boron and nitrogen atoms. In the hydrogen added CNT (denoted by H-CNT), one hydrogen atom was added to the carbon atom in the central region of CNT. The structures and electronic states of CNT, BN-CNT, H-CNT, and H-BN-CNT were calculated using the CAM-B3LYP method which has good ability to study the long-range interaction [30, 31] combining with the 6-31G(d) basis set. The geometries
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of all systems were fully optimized at the CAM-B3LYP/6-31G(d) level. These levels of theory gave reasonable electronic structures of graphene and fullerene systems [32-34].
one hydrogen atom addition to CNT is expressed by CNT + H →
H-CNT.
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Using the optimized geometries, the binding energies were calculated. The reaction of
The binding energy of hydrogen atom to CNT (Ebind) is defined by
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–Ebind = E[H-CNT] – [E(CNT) + E(H)].
Here, E[H-CNT] means a total energy of hydrogen added CNT, and E(CNT) is that of
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free-CNT, and E(H) is that of hydrogen atom. Eight and 16 binding sites were examined in CNT and BN-CNT, respectively. The electronic states of all molecules were obtained by natural population analysis (NPA) and natural bond orbital (NBO) methods at the
3. Results
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CAM-B3LYP/6-31G(d) level.
A. Structures of pure CNT and BN-CNT
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The structures of (10,0) CNT and BN-CNT were fully optimized at the CAM-B3LYP/6-31G(d) level. The structures obtained are illustrated in Fig. 1. The
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carbon atoms in CNT can be classified to two regions: cylinder and tip regions. The average C-C bond lengths in cylinder and tip regions were 1.429 and 1.425 Å, respectively. The diameter and tube length of CNT was 8.090 and 14.53 Å, respectively. The hydrogen atom addition in the cylinder region was only considered in the present study. In BN-CNT, the B-N bond length was calculated to be 1.471 Å. The average C-C distances around the B-N site in the cylinder region was calculated to be 1.430 Å, which
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is close to that of CNT (1.429 Å). The average C-C bond length in the tip region was 1.425 Å. The diameter and tube length of CNT was 8.173 and 14.53 Å, respectively, indicating that the geometrical parameters of BN-CNT were close to those of CNT.
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The NPA atomic charges on the B and N atoms were +0.756 and -0.520, respectively, indicating that the boron atom has a positive charge, and the nitrogen atom has a negative charge, indicating that the B-N site is polarized as B(+)-N(-). The atomic
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charge of carbon atoms neighboring the B atom was -0.348 (C1) and that of N atom is +0.264 (C4). These results indicate that the BN-doped CNT is locally polarized around
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the B-N site.
B. Hydrogen atom binding to CNT and BN-CNT
The binding energies of the hydrogen atom (H) to CNT and BN-CNT were
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calculated at the CAM-B3LYP/6-31G(d) level. Eight and 16 atoms in CNT and BN-CNT were examined as the positions of H-binding sites. The sites such as 0’, 0, 1, 2-14 correspond to those in Fig. 1. The binding energies are given in Fig. 2. The binding
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energies were calculated in the range 32.2-35.3 kcal/mol in CNT, indicating that the binding energy is almost constant in CNT. In contrast, the energies on BN-CNT were
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widely distributed in the range 10.4 - 43.4 kcal/mol. The binding energy in N atom was calculated to be 10.4 kcal/mol. This energy is significantly smaller than the others (33.7-43.4 kcal/mol). The result suggests that the H atom binds weakly to N-atom than those of B and C atoms, and that the hydrogen atom in N-site can be easily dissociated in comparison with the B and C sites. This reason will be discussed in the later section. The largest binding energies were found at sites 1 and 4 (43.4 and 43.3 kcal/mol, respectively). These sites (1 and 4) are located in the neighbored carbon atoms of
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heteroatoms (N and B). The other important point is that the hydrogen addition proceeds as an exothermic reaction.
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MO energy level
The energy levels of molecular orbital (MO) and spatial distribution of MO are given in Fig. 3. The energies of HOMO (Highest occupied molecular orbital) and
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LUMO (Lowest unoccupied molecular orbital) of CNT were calculated to be -5.95 and -2.59 eV, respectively. In case of BN-CNT, the HOMO and LUMO's energies were
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-5.91 and -2.64 eV, respectively. The energy differences were 3.36 eV in CNT and 3.27 eV in BN-CNT, indicating that the band gap of BN-CNT is close to that of pure CNT. The shapes of MOs were also close to each other.
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NPA atomic charges
NPA atomic charges around the H-binding sites are given in Fig. 4. The atomic charges on B and N in BN-CNT (A) were calculated to be +0.756 and -0.520,
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respectively, indicating that the B-N site is polarized as B(+)-N(-). The large dipole moment was formed in the BN site. When the hydrogen atom is added to the B atom of
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H-BN-CNT (B), the charges in the B and N atoms were +0.284 and -0.429, respectively. The value of dipole moment was diminished by the hydrogen addition to the B atom. On the other hand, the addition of hydrogen atom to N atom leads to the enhancement of dipole moment, the charges on B and N were +0.742 and -0.636, respectively. Also, the positive charge of hydrogen atom was enhanced from zero to +0.475 after the addition to the N atom. Thus, the electronic states of H-BN-CNT are strongly dependent on the binding site of hydrogen atom.
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The binding of hydrogen atom to the pure CNT was examined. The result was given in Fig.4(D). The atomic charges on C and H were -0.299 and +0.294, respectively,
magnitude of C-H polarization was relatively small.
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indicating that a slight charge transfer takes place in the C-H binding site. However, the
For comparison, the binding energies of hydrogen molecule (H2) were calculated in the same manner. The additions of H2 to the CNT and BN-CNT were endothermic
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C. Potential energy curves for hydrogen atom addition
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process (32.4 kcal/mol for H2 on CNT, and 43.0 kcal/mol for BN-CNT).
In previous section, the binding nature in the N site is different from the other binding sites (B and C). To elucidate the specific feature on the hydrogen atom in the N site, potential energy curves for the hydrogen addition to N, B and C sites were
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calculated, and the results are given in Fig. 5. It was found that both potential energy curves for B and C sites show simple attractive shapes. On the other hand, the shape of curve for the hydrogen addition to the N-site was composed of repulsive type, and the
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potential barrier existed at r(X-H)=1.610 Å. The barrier height was calculated to be 6.6 kcal/mol. The potential minima for the N, B, and C sites were located at r(X-H)=1.030,
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1.220, and 1.110 Å, respectively, and the energies of the minima were -26.5, -52.2, and -59.2 kcal/mol, respectively. NPA atomic charges on C, B, and N atoms were plotted as a function of hydrogen
addition coordinate, r(X-H) distance, in Fig. 6. Fig 6(A) shows the case of H-addition to carbon atom of CNT. At longer separation (r(X-H)=5.000 Å), the charges on H, C0, C0’ were 0.00, 0.002, and 0.012, respectively, where C0 and C0’ represent the hydrogen added-carbon atom and its neighbor carbon atom, respectively. The charges were
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changed to +0.294 (H), -0.298 (C0), and 0.036 (C0’) at the binding state (r(X-H)=1.108 Å). Fig. 6(B) shows the results for H-addition to B atom of BN-CNT. The charges on H,
0.027, -0.435, and +0.285 at r(X-H)=1.222 Å, respectively.
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N, and B atoms were calculated to be 0.000, -0.496, and 0.762 at r(X-H)=5.000 Å and
The profile of atomic charges in the H-addition to the N atom of BN-CNT was significantly different from those of B and C sites. The atomic charges on H, N, and B
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were 0.000, -0.532, and +0.791 at r(N-H)=5.000 Å. At the binding state, r(N-H)=1.030 Å, the atomic charges were +0.475 (H), -0.635 (N), and B (+0.754). This result suggests
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that the electronic state of the hydrogen atom is drastic changed before and after the addition to the N atom: the electron transfer takes place from the hydrogen to N atoms by the addition. On the other hand, the electron transfer did not occur in the B and C
D. Spin density
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site.
The special distributions of spin density of H-BN-CNT are illustrated in Fig. 7. At
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longer separation (r(N-H)=3.500 Å), the unpaired electron was localized on the hydrogen atom. At the transition state (TS), the unpaired electron penetrates into the
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BN-CNT. In product state (PD), the spin density was widely distributed around H-BN-CNT.
The hyperfine coupling constants of hydrogen atom (hfcc’s) were calculated at the at the CAM-B3LYP/6-311G(d,p)//CAM-B3LYP/6-31G(d) level of theory. The values are given in Table 2. The hfcc of free hydrogen atom was calculated to be 467.0 G. At the initial stage of the hydrogen atom addition (r(N-H)=3.500 Å), the hfcc was 466.8 G, which is slightly smaller, but is still close to that of free hydrogen atom. At the transition
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state (TS), the value of hfcc becomes smaller (340.2 G) than that of free hydrogen atom. The value of hfcc was significantly smaller (37.5 G) at the binding state (PD state), indicating that the unpaired electron is fully transferred from the hydrogen atom to the
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BN-CNT at the binding state. However, the spin density on the hydrogen atom was not zero. The results suggest that the detection of hfcc of hydrogen atom is possible by using electron spin resonance (ESR) technique.
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Table 3 shows the calculated hffc's of hydrogen atom (H) added to BN-CNT. The values are strongly dependent on the binding site. The hydrogen atom on the B site gave
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the larger hfcc (51.6 G). On the other hand, H atom on the nitrogen atom showed a small value (7.5 G). The hffc's on the carbon atoms neighbor of N and B atoms were 26.0 and 29.0 G, respectively. These results suggest that the binding site of hydrogen
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atom can be distinguished by the value of hfcc.
E. Benchmark test calculations of binding energy In the present calculations, the CAM-B3LYP/6-31G(d) method was used for all
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calculations. To check this level of theory, the binding energies of hydrogen atom were calculated at six methods. The results are given in Table 4, together with the values
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obtained from the CAM-B3LYP/6-31G(d) calculation. The binding energies on CNT, N and B atoms of BN-CNT were 32.2, 10.4, and 36.2 kcal/mol, respectively. The other methods gave the similar energies. This result indicates that the CAM-B3LYP/6-31G(d) calculation used in the present study gives the reasonable binding energy of hydrogen atom to the CNT and BN-CNT.
4. Discussion
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In the present study, the electronic states of hydrogen added carbon nanotube (CNT) and BN doped CNT (BN-CNT) were investigated by means of DFT calculations. The hydrogen atom was weakly bound to the N atom of BN-CNT, whereas the strong
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addition takes place in the B and C atom sites. In the hydrogen atom in the N site, the charge transfer from H to N atoms occurs after the H-addition. The activation barrier was found in the H addition to the N atom.
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A schematic illustration of potential energy curves for the H-addition to the N atom of BN-CNT is given in Fig. 8. At longer separation, the ground state is composed of
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neutral states of BN-CNT and H atom, expressed by CNT + H. The first excited state is composed of the charge transfer state, H+ + (CNT)-. The potential barrier was found at the middle region of H-approach (r(N-H)=1.600-2.000 Å). The barrier is caused by the avoided crossing between ground and first excited states. The potential curve near the
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potential barrier shows the attractive shape. At the binding state, the electronic state of H-(BN-CNT) was schematically expressed by (H)+-(BN-CNT)-. In case of H-addition to the B and C sites, the electron transfer does not occur, so that the potential energy curve
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is always attractive in the shape. Thus, the H-addition to the N site shows significantly
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specific feature.
Acknowledgments
The author (HT) acknowledges partial support from JSPS KAKENHI Grant Number 15K05371 and MEXT KAKENHI Grant Number 25108004.
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Values were calculated at the CAM-B3LYP/6-31G(d) level.
CNT
BN-CNT
R(B-H)
BN-CNT
R(N-H)
Distance / Å
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Parameter
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Carbon nanotube
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Table 1. Bond distances of hydrogen atom (H) from CNT and BN-CNT surfaces (in Å).
BN-CNT
1.107
1.222 1.030 1.106
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Table 2. Calculated hyperfine coupling constant of hydrogen atom (H) interacting with BN-CNT. The values were calculated at the CAM-B3LYP/6-311G(d,p)//CAM-B3LYP/
state
hfcc / gauss
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6-31G(d) level.
H atom in vacuo
467.0
RC (r(N-H)=3.50 Å)
466.8
TS(r(N-H)=1.61 Å)
340.2
PD(r(N-H)=1.03 Å)
37.5
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Table 3. Calculated hyperfine coupling constant of hydrogen atom (H) added to BN-CNT. The values were calculated at the CAM-B3LYP/6-311G(d,p)//CAM-B3LYP/
hfcc / gauss
N
7.5
B
51.6
C(N)
26.0
C(B)
29.0
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Binding state
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6-31G(d) level.
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Table 4. Binding energies of hydrogen atom to CNT and BN-CNT (Ebind in kcal mol-1) calculated at several levels of theory. The CAM-B3LYP/6-31G(d) optimized structure was used in all energy calculations. Ebind / kcal mol-1
Method
C156-H
BNC154-H (on N)
BN C154-H (on B)
32.2
10.4
36.2
B3LYP/6-311G(d,p)
31.3
11.6
33.3
CAM-B3LYP/6-311G(d,p)
32.7
13.2
34.6
M062X/6-31G(d)
27.7
9.2
31.6
M062X/6-311G(d,p)
29.2
12.5
30.8
PBE1PBE/6-311G(d,p)
31.0
11.6
31.7
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CAM-B3LYP/6-31G(d)
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Figure Captions
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Figure 1. Optimized structures of carbon nanotube (CNT) (upper) and BN doped CNT (BN-CNT) (lower) calculated at the B3LYP/6-31G(d) level. Figure 2. Binding energies of hydrogen atom to CNT and BN-CNT.
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Figure 3. Orbital energy diagram of CNT and BN-CNT calculated at the CAMB3LYP/6-31G(d) level.
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Figure 4. NPA atomic charges around the hydrogen binding site of CNT and BN-CNT. The values were calculated at the CAM-B3LYP/6-31G(d) level. Figure 5. Potential energy curves for the hydrogen atom addition to BN-CNT. The values were plotted as a function of r(X-H), where X=B, N, and C atoms. The energies were calculated at the restricted open shell CAM-B3LYP/6-31G(d) level.
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Figure 6. NPA atomic charges on H, C0, and C0’ in H-CNT and H, B, and N in H-BN-CNT. The values were plotted as a function of r(X-H), where X=B, N, and C atoms.
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Figure 7. Spatial distribution of spin densities on the H-(BN-CNT) system calculated at the B3LYP/6-31G(d) level.
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Figure 8. Schematic illustration of the reaction model of hydrogen atom addition to the nitrogen site of BN-CNT.
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Figure 8.
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Research highlights
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> Hydrogen atom can bind to the carbon and boron atoms of BN-CNT without activation barrier. > The activation barrier was found in the approaching of hydrogen atom to the nitrogen
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atom of BN-CNT. > Charge transfer process is important in the hydrogen addition to the N site of BN-CNT.
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Graphical Abstract
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Research highlights
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> Hydrogen atom can bind to the carbon and boron atoms of BN-CNT without activation barrier. > The activation barrier was found in the approaching of hydrogen atom to the nitrogen
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atom of BN-CNT. > Charge transfer process is important in the hydrogen addition to the N site of BN-CNT.
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S1293-2558(16)30044-9
DOI:
10.1016/j.solidstatesciences.2016.03.004
Reference:
SSSCIE 5297
To appear in:
Solid State Sciences
Received Date: 7 January 2016 Revised Date:
29 February 2016
Accepted Date: 8 March 2016
Please cite this article as: H. Tachikawa, T. Iyama, H. Kawabata, Electronic Structures of Hydrogen Functionalized Carbon Nanotube: Density Functional Theory (DFT) Study, Solid State Sciences (2016), doi: 10.1016/j.solidstatesciences.2016.03.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Title:
Electronic Structures of Hydrogen Functionalized Carbon Nanotube:
Density Functional Theory (DFT) Study
Hiroto Tachikawa*, Tetsuji Iyama, Hiroshi Kawabata
Division of Applied Chemistry
Hokkaido University
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Graduate School of Engineering
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Authors:
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Sapporo 060-8628, Japan
Manuscript submitted to :
Solid State Sciences
Section of the journal :
Regular Paper
Correspondence and Proof to :
Dr. Hiroto TACHIKAWA*
Division of Applied Chemistry
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Graduate School of Engineering Hokkaido University Sapporo 060-8628, JAPAN [email protected]
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Contents :
+81 11706-7897
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Fax.
Text
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Pages
Figure captions
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2016_2_29 Revised Electronic Structures of Hydrogen Functionalized Carbon Nanotube: Density
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Functional Theory (DFT) Study Hiroto Tachikawa*, Tetsuji IYAMA, Hiroshi Kawabata
Electronic
structures
and
formation
mechanism
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ABSTRACT:
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Division of Applied Chemistry, Graduate School of Engineering Hokkaido University, Sapporo 060-8628, JAPAN
of
hydrogen
functionalized carbon nanotube (CNT) have been investigated by means of density functional theory (DFT) method. The mechanism of hydrogen addition reaction to the CNT surface was also investigated. Pure and boron-nitrogen (BN) substituted CNT
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(denoted by CNT and BN-CNT, respectively) were examined as the carbon nanotubes. It was found that the additions of hydrogen atom to B (boron atom) and C (carbon atom) sites of BN-CNT proceed without activation barrier, whereas the hydrogenation
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of N (nitrogen atom) site needs the activation energy. The electronic states of hydrogen
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functionalized CNT and BN-CNT were discussed on the basis of theoretical results.
Keywords: CNT; spin density; hyperfine coupling constant; potential energy curve
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1. Introduction Surface-functionalized fullerene, graphene, and carbon nanotube (CNT) are known as a high-performance molecular device. For example, porphyrin functionalized
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graphene is one of the most useful hybrid materials with large nonlinear optical properties [1-7]. The interaction between carbon materials and radical has recently
markedly changed by the radical addition [8-17].
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attracted considerable interest because the electronic properties of carbon materials are
The hydrogen atom is the simplest radical and behaves frequently as a dopant in
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carbon materials, and the electronic states of the materials are drastically changed by only one hydrogen atom. It is known that the electronic states of CNT are turned by the addition of hydrogen atom. [18] These carbon materials are known as the hydrogen functionalized carbon materials.
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Kim et al. investigated experimentally the hydrogen doped CNT. They found that the electronic structures of a CNT are modified by hydrogen functionalization. The hydrogen addition expanded the band gap of CNT. [19] Fujimoto and Saito [20]
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investigated theoretically the electronic states of hydrogen adsorbed on the nitrogen (N)-doped CNT using density functional theory (DFT) calculations and determined the
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favorable hydrogen adsorption site on N-doped CNT. They found that the hydrogen atom is preferentially added to the nitrogen atom of CNT. Ebrahimi and Rafii-Tabar [21] investigated the influence of hydrogen functionalization on mechanical properties of graphene and CNT. They found that the effects of hydrogen atom on elastic properties are considerable. CNT has been examined as a hydrogen storage material. Using molecular dynamics method, Ozturk et al. investigated a welded random CNT network structures with a hydrogen atom and observed that the CNT networks could
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uptake 8.85 wt.% hydrogen at 77 K [22]. The interaction of CNT with hydrogen molecule (H2) was investigated as well as the hydrogen atom. Ohno and co-workers invesitgated theoretically the electronic structure of CNTs after the hydrogenation
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(H2-CNT) [23-25].The binding and activation energies were determined. Terakura and co-workers were calculated the B and N atomic substitutions in the graphenes [26-28]. Thus, the functionalization of CNTs by hydrogen is of great importance for a
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development of nanotube-based electronics devices. However, the effects of one hydrogen atom addition to the electronic states of CNT are still unclear. Especially,
around the hydrogen atom is limited.
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information on the reaction mechanism of hydrogen addition to CNT and spin density
In the present study, the interaction of one hydrogen atom with the pure, nitrogenand boron-doped CNT’s were investigated by means of DFT method to elucidate the
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binding site and band gap of hydrogen doped CNT.
2. Calculation Methods
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All hybrid DFT calculations were carried out using Gaussian 09 program package [29]. The (10,0)-carbon nanotube (C156) was used in the present study. As the
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boron-nitrogen (BN) doped CNT (denoted by BN-CNT), BNC154 was examined. In BN-CNT, two carbon atoms around central region of CNT were substituted by boron and nitrogen atoms. In the hydrogen added CNT (denoted by H-CNT), one hydrogen atom was added to the carbon atom in the central region of CNT. The structures and electronic states of CNT, BN-CNT, H-CNT, and H-BN-CNT were calculated using the CAM-B3LYP method which has good ability to study the long-range interaction [30, 31] combining with the 6-31G(d) basis set. The geometries
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of all systems were fully optimized at the CAM-B3LYP/6-31G(d) level. These levels of theory gave reasonable electronic structures of graphene and fullerene systems [32-34].
one hydrogen atom addition to CNT is expressed by CNT + H →
H-CNT.
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Using the optimized geometries, the binding energies were calculated. The reaction of
The binding energy of hydrogen atom to CNT (Ebind) is defined by
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–Ebind = E[H-CNT] – [E(CNT) + E(H)].
Here, E[H-CNT] means a total energy of hydrogen added CNT, and E(CNT) is that of
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free-CNT, and E(H) is that of hydrogen atom. Eight and 16 binding sites were examined in CNT and BN-CNT, respectively. The electronic states of all molecules were obtained by natural population analysis (NPA) and natural bond orbital (NBO) methods at the
3. Results
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CAM-B3LYP/6-31G(d) level.
A. Structures of pure CNT and BN-CNT
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The structures of (10,0) CNT and BN-CNT were fully optimized at the CAM-B3LYP/6-31G(d) level. The structures obtained are illustrated in Fig. 1. The
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carbon atoms in CNT can be classified to two regions: cylinder and tip regions. The average C-C bond lengths in cylinder and tip regions were 1.429 and 1.425 Å, respectively. The diameter and tube length of CNT was 8.090 and 14.53 Å, respectively. The hydrogen atom addition in the cylinder region was only considered in the present study. In BN-CNT, the B-N bond length was calculated to be 1.471 Å. The average C-C distances around the B-N site in the cylinder region was calculated to be 1.430 Å, which
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is close to that of CNT (1.429 Å). The average C-C bond length in the tip region was 1.425 Å. The diameter and tube length of CNT was 8.173 and 14.53 Å, respectively, indicating that the geometrical parameters of BN-CNT were close to those of CNT.
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The NPA atomic charges on the B and N atoms were +0.756 and -0.520, respectively, indicating that the boron atom has a positive charge, and the nitrogen atom has a negative charge, indicating that the B-N site is polarized as B(+)-N(-). The atomic
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charge of carbon atoms neighboring the B atom was -0.348 (C1) and that of N atom is +0.264 (C4). These results indicate that the BN-doped CNT is locally polarized around
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the B-N site.
B. Hydrogen atom binding to CNT and BN-CNT
The binding energies of the hydrogen atom (H) to CNT and BN-CNT were
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calculated at the CAM-B3LYP/6-31G(d) level. Eight and 16 atoms in CNT and BN-CNT were examined as the positions of H-binding sites. The sites such as 0’, 0, 1, 2-14 correspond to those in Fig. 1. The binding energies are given in Fig. 2. The binding
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energies were calculated in the range 32.2-35.3 kcal/mol in CNT, indicating that the binding energy is almost constant in CNT. In contrast, the energies on BN-CNT were
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widely distributed in the range 10.4 - 43.4 kcal/mol. The binding energy in N atom was calculated to be 10.4 kcal/mol. This energy is significantly smaller than the others (33.7-43.4 kcal/mol). The result suggests that the H atom binds weakly to N-atom than those of B and C atoms, and that the hydrogen atom in N-site can be easily dissociated in comparison with the B and C sites. This reason will be discussed in the later section. The largest binding energies were found at sites 1 and 4 (43.4 and 43.3 kcal/mol, respectively). These sites (1 and 4) are located in the neighbored carbon atoms of
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heteroatoms (N and B). The other important point is that the hydrogen addition proceeds as an exothermic reaction.
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MO energy level
The energy levels of molecular orbital (MO) and spatial distribution of MO are given in Fig. 3. The energies of HOMO (Highest occupied molecular orbital) and
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LUMO (Lowest unoccupied molecular orbital) of CNT were calculated to be -5.95 and -2.59 eV, respectively. In case of BN-CNT, the HOMO and LUMO's energies were
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-5.91 and -2.64 eV, respectively. The energy differences were 3.36 eV in CNT and 3.27 eV in BN-CNT, indicating that the band gap of BN-CNT is close to that of pure CNT. The shapes of MOs were also close to each other.
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NPA atomic charges
NPA atomic charges around the H-binding sites are given in Fig. 4. The atomic charges on B and N in BN-CNT (A) were calculated to be +0.756 and -0.520,
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respectively, indicating that the B-N site is polarized as B(+)-N(-). The large dipole moment was formed in the BN site. When the hydrogen atom is added to the B atom of
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H-BN-CNT (B), the charges in the B and N atoms were +0.284 and -0.429, respectively. The value of dipole moment was diminished by the hydrogen addition to the B atom. On the other hand, the addition of hydrogen atom to N atom leads to the enhancement of dipole moment, the charges on B and N were +0.742 and -0.636, respectively. Also, the positive charge of hydrogen atom was enhanced from zero to +0.475 after the addition to the N atom. Thus, the electronic states of H-BN-CNT are strongly dependent on the binding site of hydrogen atom.
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The binding of hydrogen atom to the pure CNT was examined. The result was given in Fig.4(D). The atomic charges on C and H were -0.299 and +0.294, respectively,
magnitude of C-H polarization was relatively small.
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indicating that a slight charge transfer takes place in the C-H binding site. However, the
For comparison, the binding energies of hydrogen molecule (H2) were calculated in the same manner. The additions of H2 to the CNT and BN-CNT were endothermic
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C. Potential energy curves for hydrogen atom addition
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process (32.4 kcal/mol for H2 on CNT, and 43.0 kcal/mol for BN-CNT).
In previous section, the binding nature in the N site is different from the other binding sites (B and C). To elucidate the specific feature on the hydrogen atom in the N site, potential energy curves for the hydrogen addition to N, B and C sites were
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calculated, and the results are given in Fig. 5. It was found that both potential energy curves for B and C sites show simple attractive shapes. On the other hand, the shape of curve for the hydrogen addition to the N-site was composed of repulsive type, and the
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potential barrier existed at r(X-H)=1.610 Å. The barrier height was calculated to be 6.6 kcal/mol. The potential minima for the N, B, and C sites were located at r(X-H)=1.030,
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1.220, and 1.110 Å, respectively, and the energies of the minima were -26.5, -52.2, and -59.2 kcal/mol, respectively. NPA atomic charges on C, B, and N atoms were plotted as a function of hydrogen
addition coordinate, r(X-H) distance, in Fig. 6. Fig 6(A) shows the case of H-addition to carbon atom of CNT. At longer separation (r(X-H)=5.000 Å), the charges on H, C0, C0’ were 0.00, 0.002, and 0.012, respectively, where C0 and C0’ represent the hydrogen added-carbon atom and its neighbor carbon atom, respectively. The charges were
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changed to +0.294 (H), -0.298 (C0), and 0.036 (C0’) at the binding state (r(X-H)=1.108 Å). Fig. 6(B) shows the results for H-addition to B atom of BN-CNT. The charges on H,
0.027, -0.435, and +0.285 at r(X-H)=1.222 Å, respectively.
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N, and B atoms were calculated to be 0.000, -0.496, and 0.762 at r(X-H)=5.000 Å and
The profile of atomic charges in the H-addition to the N atom of BN-CNT was significantly different from those of B and C sites. The atomic charges on H, N, and B
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were 0.000, -0.532, and +0.791 at r(N-H)=5.000 Å. At the binding state, r(N-H)=1.030 Å, the atomic charges were +0.475 (H), -0.635 (N), and B (+0.754). This result suggests
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that the electronic state of the hydrogen atom is drastic changed before and after the addition to the N atom: the electron transfer takes place from the hydrogen to N atoms by the addition. On the other hand, the electron transfer did not occur in the B and C
D. Spin density
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site.
The special distributions of spin density of H-BN-CNT are illustrated in Fig. 7. At
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longer separation (r(N-H)=3.500 Å), the unpaired electron was localized on the hydrogen atom. At the transition state (TS), the unpaired electron penetrates into the
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BN-CNT. In product state (PD), the spin density was widely distributed around H-BN-CNT.
The hyperfine coupling constants of hydrogen atom (hfcc’s) were calculated at the at the CAM-B3LYP/6-311G(d,p)//CAM-B3LYP/6-31G(d) level of theory. The values are given in Table 2. The hfcc of free hydrogen atom was calculated to be 467.0 G. At the initial stage of the hydrogen atom addition (r(N-H)=3.500 Å), the hfcc was 466.8 G, which is slightly smaller, but is still close to that of free hydrogen atom. At the transition
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state (TS), the value of hfcc becomes smaller (340.2 G) than that of free hydrogen atom. The value of hfcc was significantly smaller (37.5 G) at the binding state (PD state), indicating that the unpaired electron is fully transferred from the hydrogen atom to the
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BN-CNT at the binding state. However, the spin density on the hydrogen atom was not zero. The results suggest that the detection of hfcc of hydrogen atom is possible by using electron spin resonance (ESR) technique.
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Table 3 shows the calculated hffc's of hydrogen atom (H) added to BN-CNT. The values are strongly dependent on the binding site. The hydrogen atom on the B site gave
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the larger hfcc (51.6 G). On the other hand, H atom on the nitrogen atom showed a small value (7.5 G). The hffc's on the carbon atoms neighbor of N and B atoms were 26.0 and 29.0 G, respectively. These results suggest that the binding site of hydrogen
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atom can be distinguished by the value of hfcc.
E. Benchmark test calculations of binding energy In the present calculations, the CAM-B3LYP/6-31G(d) method was used for all
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calculations. To check this level of theory, the binding energies of hydrogen atom were calculated at six methods. The results are given in Table 4, together with the values
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obtained from the CAM-B3LYP/6-31G(d) calculation. The binding energies on CNT, N and B atoms of BN-CNT were 32.2, 10.4, and 36.2 kcal/mol, respectively. The other methods gave the similar energies. This result indicates that the CAM-B3LYP/6-31G(d) calculation used in the present study gives the reasonable binding energy of hydrogen atom to the CNT and BN-CNT.
4. Discussion
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In the present study, the electronic states of hydrogen added carbon nanotube (CNT) and BN doped CNT (BN-CNT) were investigated by means of DFT calculations. The hydrogen atom was weakly bound to the N atom of BN-CNT, whereas the strong
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addition takes place in the B and C atom sites. In the hydrogen atom in the N site, the charge transfer from H to N atoms occurs after the H-addition. The activation barrier was found in the H addition to the N atom.
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A schematic illustration of potential energy curves for the H-addition to the N atom of BN-CNT is given in Fig. 8. At longer separation, the ground state is composed of
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neutral states of BN-CNT and H atom, expressed by CNT + H. The first excited state is composed of the charge transfer state, H+ + (CNT)-. The potential barrier was found at the middle region of H-approach (r(N-H)=1.600-2.000 Å). The barrier is caused by the avoided crossing between ground and first excited states. The potential curve near the
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potential barrier shows the attractive shape. At the binding state, the electronic state of H-(BN-CNT) was schematically expressed by (H)+-(BN-CNT)-. In case of H-addition to the B and C sites, the electron transfer does not occur, so that the potential energy curve
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is always attractive in the shape. Thus, the H-addition to the N site shows significantly
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Acknowledgments
The author (HT) acknowledges partial support from JSPS KAKENHI Grant Number 15K05371 and MEXT KAKENHI Grant Number 25108004.
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Values were calculated at the CAM-B3LYP/6-31G(d) level.
CNT
BN-CNT
R(B-H)
BN-CNT
R(N-H)
Distance / Å
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Table 1. Bond distances of hydrogen atom (H) from CNT and BN-CNT surfaces (in Å).
BN-CNT
1.107
1.222 1.030 1.106
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Table 2. Calculated hyperfine coupling constant of hydrogen atom (H) interacting with BN-CNT. The values were calculated at the CAM-B3LYP/6-311G(d,p)//CAM-B3LYP/
state
hfcc / gauss
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H atom in vacuo
467.0
RC (r(N-H)=3.50 Å)
466.8
TS(r(N-H)=1.61 Å)
340.2
PD(r(N-H)=1.03 Å)
37.5
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Table 3. Calculated hyperfine coupling constant of hydrogen atom (H) added to BN-CNT. The values were calculated at the CAM-B3LYP/6-311G(d,p)//CAM-B3LYP/
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N
7.5
B
51.6
C(N)
26.0
C(B)
29.0
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Table 4. Binding energies of hydrogen atom to CNT and BN-CNT (Ebind in kcal mol-1) calculated at several levels of theory. The CAM-B3LYP/6-31G(d) optimized structure was used in all energy calculations. Ebind / kcal mol-1
Method
C156-H
BNC154-H (on N)
BN C154-H (on B)
32.2
10.4
36.2
B3LYP/6-311G(d,p)
31.3
11.6
33.3
CAM-B3LYP/6-311G(d,p)
32.7
13.2
34.6
M062X/6-31G(d)
27.7
9.2
31.6
M062X/6-311G(d,p)
29.2
12.5
30.8
PBE1PBE/6-311G(d,p)
31.0
11.6
31.7
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Figure Captions
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Figure 1. Optimized structures of carbon nanotube (CNT) (upper) and BN doped CNT (BN-CNT) (lower) calculated at the B3LYP/6-31G(d) level. Figure 2. Binding energies of hydrogen atom to CNT and BN-CNT.
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Figure 3. Orbital energy diagram of CNT and BN-CNT calculated at the CAMB3LYP/6-31G(d) level.
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Figure 4. NPA atomic charges around the hydrogen binding site of CNT and BN-CNT. The values were calculated at the CAM-B3LYP/6-31G(d) level. Figure 5. Potential energy curves for the hydrogen atom addition to BN-CNT. The values were plotted as a function of r(X-H), where X=B, N, and C atoms. The energies were calculated at the restricted open shell CAM-B3LYP/6-31G(d) level.
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Figure 6. NPA atomic charges on H, C0, and C0’ in H-CNT and H, B, and N in H-BN-CNT. The values were plotted as a function of r(X-H), where X=B, N, and C atoms.
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Figure 7. Spatial distribution of spin densities on the H-(BN-CNT) system calculated at the B3LYP/6-31G(d) level.
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Figure 8. Schematic illustration of the reaction model of hydrogen atom addition to the nitrogen site of BN-CNT.
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Figure 4.
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Figure 5.
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Figure 6.
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Figure 7.
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Figure 8.
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Research highlights
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> Hydrogen atom can bind to the carbon and boron atoms of BN-CNT without activation barrier. > The activation barrier was found in the approaching of hydrogen atom to the nitrogen
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atom of BN-CNT. > Charge transfer process is important in the hydrogen addition to the N site of BN-CNT.
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Graphical Abstract
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Research highlights
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> Hydrogen atom can bind to the carbon and boron atoms of BN-CNT without activation barrier. > The activation barrier was found in the approaching of hydrogen atom to the nitrogen
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atom of BN-CNT. > Charge transfer process is important in the hydrogen addition to the N site of BN-CNT.
0