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C: Energy Conversion and Storage; Energy and Charge Transport

Mechanism of Hydrogen Storage in the Graphene Nanoflake-Lithium-H System 2

Hiroto Tachikawa, and Tetsuji Iyama J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b01152 • Publication Date (Web): 27 Mar 2019 Downloaded from http://pubs.acs.org on March 27, 2019

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The Journal of Physical Chemistry

Mechanism of Hydrogen Storage in the Graphene Nanoflake-Lithium-H2 System Hiroto TACHIKAWA* and Tetsuji IYAMA Division of Applied Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, JAPAN Abstract: Carbon materials, such as graphene nanoflakes, carbon nanotubes, and fullerene, can be used for hydrogen storage. Alkali doping of these materials generally increases their H2-storage density. In this study, the interaction of hydrogen molecules with Li-doped graphene nanoflakes was systematically investigated using density functional theory (DFT). A large polycyclic aromatic hydrocarbon composed of 37 benzene rings (referred to as GR) was used as a model of a graphene nanoflake, and GR-Li-(H2)n and GR-Li+-(H2)n (n = 0–13) clusters were used as hydrogen storage systems. The first and second coordination shells of H2 around GR-Li were saturated at n = 3 and 7, respectively. The binding energy of H2 to GR-Li decreased with increasing n, reaching a limiting value at n = 10. For GR-Li+-(H2)n, similar results were obtained and the Li atom on GR was shown to be activated by electron transfer from Li to GR. The diffusion barrier of Li+ on GR decreased upon addition of H2 to Li+ from 6.35 kcal/mol (n = 0) to 3.62 kcal/mol (n = 4). The mechanism of H2 addition is discussed herein based on the calculated results.

Corresponding Author: Hiroto Tachikawa, [email protected]

1 ACS Paragon Plus Environment

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1. Introduction Molecular hydrogen (H2) is the ultimate clean energy source with high abundance in the form of water.1-3 The thermal efficiency of H2 combustion is three times higher than that of gasoline (143 vs. 44 MJ/kg).4 However, the volume efficiency of H2 is significantly lower than that of gasoline (0.0108 vs. 34.8 MJ/kg) and hydrogen has a wide explosion limit concentration range (4–75%) in air.5 Therefore, technology for the high-density storage and safe transportation of hydrogen must be developed quickly to shift to a hydrogen-energy-based society.1-3,6-8 Hydrogen storage remains a significant challenge for the hydrogen economy because of the lack of effective high-capacity H2 carriers.9,10 Because of their large surface area, carbon nanostructures, such as carbon nanotubes (CNTs) and graphene nanoflakes, have been extensively investigated as potential hydrogen storage media.11-16 Dillon et al.12 showed that single-walled CNTs can absorb approximately 5–10 wt% H2 at 133 K. However, CNTs are not suitable for hydrogen storage at room temperature because of their weak interactions with H2.17,18 Recently, it was demonstrated that alkali doping increases the hydrogen storage ability of carbon materials.19-26 Chen et al. experimentally demonstrated that lithiumdoped CNTs can absorb approximately 14 wt% hydrogen at room temperature.19 This value is greater than those obtained in metal hydride and cryoadsorption systems. Hydrogen stored in the lithium-doped CNTs can be released at higher temperatures and the sorption-desorption cycle can be repeated with negligible decreases in sorption capacity. The high hydrogen-uptake capacity of these systems originates from the catalytic effect of the alkali metal. To understand the structures and binding energies of these carbon material-H2


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systems, theoretical calculations have been performed by several groups.27-32 The first original work regarding the carbon material-Li-H2 system was reported by Kolmann et al. in 2008.33 The authors utilized benzene (Bz) as a model for carbon materials (graphene nanoflakes) and density functional theory (DFT) calculations were applied to the Bz-Li-H2 system. The binding energy was calculated to be 4.7 kcal/mol at the CCSD(T)/MP2 level. More recently, D’Arcy et al. investigated the Bz-Li-(H2)n system (n = 1, 2) using quantum Monte Carlo simulations34,35 and obtained binding energies of 4.5 kcal/mol (n = 1) and 3.2 kcal/mol (n = 2). Zhu et al. calculated the binding energy using a larger aromatic hydrocarbon GR(14) composed of 14 benzene rings. The binding energy of the Li atom to GR(14) was determined to be 14.8 kcal/mol (n = 1).21 Although theoretical approaches have been reported by several groups, a simple benzene molecule and GR(14) were used as models of graphene or graphene nanoflakes. These molecules are much smaller than real graphene nanoflakes and the number of H2 molecules in the previous calculations were limited (n = 1–5). In addition, the mechanism of lithium activation remains unclear because of the lack of systematic studies using efficient-sized graphene nanoflakes and a wide range of H2 molecules. To understand the mechanism of lithium activation in graphene nanoflakes, the interactions of hydrogen molecules with lithium-doped graphene nanoflakes were investigated using DFT. The large graphene nanoflake was composed of 37 benzene rings, as this size is similar to that of the real carbon material. The change in the electronic states of H2 and graphene nanoflakes caused by Li doping was examined in detail.



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2. Computational Methods 2.1. Binding of Li+/Li to the graphene nanoflake A graphene nanoflake composed of 37 benzene rings was used in this study and is hereafter referred to as GR. DFT calculations were performed using a Coulombattenuating exchange-correlation energy functional (CAM-B3LYP)36 with a 6311G(d,p) basis set,37 which are expressed as CAM-B3LYP/6-311G(d,p). First, the structure of GR was optimized and the lithium atom or ion was placed in the central region of the GR. The structures of GR-Li and GR-Li+ were optimized, where all GR-Li+/Li atoms were fully optimized. The binding energy of the lithium atom to GR is defined as follows: ― 𝐸𝑏𝑖𝑛𝑑 = 𝐸(𝐺𝑅 ― 𝐿𝑖) ―[𝐸(𝐿𝑖) +𝐸(𝐺𝑅)]

(1)

where E(X) is the total energy of X. If Ebind(Li) is positive, the lithium atom binds exothermally to GR.

2.2. Binding of H2 to GR-Li. In the GR-Li-hydrogen systems, expressed as GR-Li-(H2)n, 1–13 hydrogen molecules (n = 1–13) were added to GR-Li+ or GR-Li, while all atoms in GR-Li-(H2)n were fully optimized without straining the structure. The binding energy of the nH2 molecules to GR-Li was calculated as follows: ― 𝐸𝑏𝑖𝑛𝑑(𝑛,𝐻2) = [𝐸(𝐺𝑅 ― 𝐿𝑖 ― (𝐻2)𝑛) +𝑛𝐸(𝐻2) ―𝐸(𝐺𝑅 ― 𝐿𝑖)]/𝑛

(2)

If Ebind(H2) is positive, the addition of the hydrogen molecule to GR-Li proceeds and the addition reaction, H2 + GR-Li → H2-GR-Li, is exothermic. The atomic charges were calculated using natural bond population analysis (NPA).38 All calculations were performed using the Gaussian 09 software package.39 In 4 ACS Paragon Plus Environment

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previous studies,40-44 we investigated the interaction between graphene and various molecules using DFT at the same level of theory. A similar technique was applied to the GR-Li-(H2)n system in this study.

2.3. Effects of basis set, functional, and graphene nanoflake size To check the influence of several factors on the relevant electronic states and binding energies, a graphene nanoflake composed of 7, 14, and 19 benzene rings, denoted as GR(7), GR(14), and GR(19), respectively, and the 6-31G(d) basis set were examined. The PW96PW96 and APFD functionals were also examined to check the functional dependence. It should be noted that the effects of basis set, functionals, and graphene nanoflake size on the electronic states and binding energies were negligible in this system, as discussed in Sections 3F and 3I. 3. Results 3.1. Structures of the Li doped-graphene nanoflake The optimized structures of GR-Li and GR-Li+ are shown in Figures 1 and S1 (see, supporting information, SI), respectively. Both Li and Li+ were bound to the hexagonal site of the GR surface. The heights of Li and Li+ from the graphene surface were calculated to be 1.736 and 1.771 Å, respectively. The binding distance of Li was slightly shorter than that of Li+, and the mechanism underlying this phenomenon is discussed in Section 3C. The binding energies of Li and Li+ were 17.1 and 52.8 kcal/mol, respectively, indicating that Li+ bonding is three times stronger than that of Li. These results are in good agreement with previous calculations of the coronene-Li (or Li+) system.45



The NPA atomic charges on Li and Li+ were +0.93 and +0.94, respectively, and the net charge of Li is very similar to that of Li+. This suggests that significant electron transfer occurs from Li to GR after binding (0.93e).

3.2. Binding structures of the hydrogen molecules to GR-Li.

The binding structures of the H2 molecules to GR-Li are shown in Figure 2. The geometries of the GR-Li-(H2)n systems (n = 1–13) were fully optimized at the CAMB3LYP/6-311G(d,p) level. For n = 1, the distances of H1 and H1’ in (H2)1 from Li were calculated to be R1 = 2.027 Å (H1) and R1’ = 2.027 Å (H1’). The positions of both H1 and H1’ atoms relative to Li were equivalent, suggesting that the H2 molecule binds to the Li atom with a side-on structure. For n = 2, the distances of R1, R1’, R2, and R2’ were 2.081, 2.082, 2.081, and 2.082 Å, respectively, indicating that the binding structure is side-on, similar to that of the n = 1 case. The addition of a second hydrogen molecule, (H2)2, affects the bond distance of (H2)1, where it is slightly elongated by the addition of the second H2 (2.08 vs. 2.03 Å). For n = 3, the binding structure remained side-on. The R1, R2, and R3 distances were 2.198, 2.212, and 2.221 Å, respectively, indicating that the three hydrogen molecules are nearly equivalent. The distance of H2 from Li gradually elongated after the hydrogen molecule addition (2.03–2.22 Å), although the distance increase is small. For n = 4, the R1, R2, R3, and R4 distances were 2.161, 2.161, 2.165, and 4.080 Å, respectively. The additional hydrogen molecule (i.e., the fourth hydrogen molecule, (H2)4) cannot bind directly to Li, and instead was weakly bound to the hydrogen molecules already binding to Li. Hydrogen molecules (H2)5 and (H2)6 are also bound to H2 in the inner shell. The seventh and eleventh hydrogen molecules, (H2)7 and (H2)11,


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were located further from the Li atom. The binding structures of H2 to GR-Li+ (ion) were calculated in the same manner and the optimized structures are shown in Figure S2. Similar binding structures were obtained for Li+ where the H2 molecules bind to GR-Li+ in the side-on orientation in the inner shell. Stick diagram To understand the bonding structures in more detail, the distances of the hydrogen atoms in H2 from the Li atom, R(Li-H), are represented in the form of a stick diagram in Figure 3. For n = 1, the R(Li-H) distances are both 2.027 Å (doubly degenerate). Until n = 3, all hydrogen atoms were located similar distances away from Li. In contrast, the distance of the fourth H2 in n = 4 was much further away from Li (4.080 Å) compared to those of n = 1–3 (2.20 Å), indicating that the first coordination shell is saturated by three hydrogen molecules (n = 3). Thus, the fourth hydrogen molecule, (H2)4, binds to GR-Li-(H2)1-3 as a ligand in the second coordination shell. From the distance distributions of n = 7 and 8, it is clear that the second coordination shell is saturated at n = 7, with the third coordination shell beginning at n = 8. The data for n = 1–13 are provided in Figure S3 in the SI and the stick diagrams of GR-Li+-(H2)n (n = 1–13) are shown in Figure S4. NPA charge The NPA atomic charge of Li and NPA total atomic charges of the six carbon atoms in the hexagonal site of GR (denoted as 6C, Figure 1) are plotted as a function of n in Figure 4. For n = 0, the NPA atomic charge of Li was +0.929, which decreased linearly to n = 3, where it plateaued at +0.633. The NPA charge of 6C increased linearly to n = 3, where it plateaued (-0.352) and became saturated at n >3. The constant values



of NPA for n = 3–12 originate from the completion of the first solvation shell at n = 3. The effects of the second and third coordination shells on NPA charges were negligible due to the large separation of H2 from Li. The changes in the NPA charges of Li+ were very similar to those of Li.

3.3. Height of Li from the GR surface

The height of Li from the GR surface (h) is plotted in Figure 5 as a function of the number of H2 molecules (n). The height of Li was calculated to be h = 1.735 Å without hydrogen molecules (n = 0). After H2 addition, h was drastically elongated up to n = 3: 1.744 Å (n = 1), 1.787 Å (n = 2), and 1.831 Å (n = 3), saturating from n = 4 onwards, 1.836 Å (n = 4) and 1.846 Å (n = 13), because the first coordination shell is saturated at n = 3. The effects of the second and third coordination shells on the height of Li are negligible. The height of Li+ from the GR surface (h) is also plotted in Figure 5. The trends observed for Li were similar for Li+ where the height saturates after n = 3. However, the height of Li+ was systematically larger than that of the Li atom: h = 1.735 Å (GR-Li) and h = 1.771 Å (GR-Li+) at n = 0, and h = 1.846 Å (GR-Li) and h = 1.893 Å (GR-Li+) at n = 3. For the GR-Li system, electrons are transferred from Li to GR, to form an electronic state of Li(+0.929)-GR(-0.929). A significant attractive interaction (positivenegative) is generated in GR-Li and the height of Li (h) decreases. In contrast, the electronic state in GR-Li+ is Li(+0.937)-GR(+0.063), indicating that a weak repulsive interaction occurs, resulting in increased separation in the GR-Li+ system.

3.4. Binding energy of H2 to GR-Li


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The binding energy of hydrogen to GR-Li (per H2 molecule) is plotted in Figure 6 as a function of n. The binding energy of the first addition of H2 to GR-Li was calculated to be 3.83 kcal/mol (n = 1), which gradually decreased as a function of n. The binding energy of n = 3 and 7 were 2.85 and 1.43 kcal/mol, respectively, and the energy became almost saturated at n = 12–13. These trends strongly indicate that GR-Li can be used as a H2 storage material. The GR-Li system can store H2 up to the second coordination shell (n = 7), if the threshold of binding energy is assumed to be 1.4 kcal/mol. Similar features were observed in the GR-Li+-(H2)n system. To elucidate the effect of GR on the binding energy between Li and H2, the binding energy of H2 to bare Li was calculated without GR and the results are plotted in Figure 6 (open squares). The binding energy can be defined as -Ebind(n) = [E(Li-(H2)n)-(E(Li) + nE(H2)] / n, and the calculated energies were 1.35 kcal/mol (n = 4), 0.82 kcal/mol (n = 7), and 0.50 kcal/mol (n = 12). The binding energies of Li-(H2)n without GR were significantly lower than those of GR-Li-(H2)n, suggesting that GR activates the lithium via electron capture, and the lithium atom behaves as a lithium ion on the GR surface. This electron transfer activates the Li atom on the GR.

3.5. Calculation of binding energies in the benzene-lithium-H2 system In this study, all calculations were performed at the CAM-B3LYP/6-311G(d,p) level. To check the suitability of this theory level, the binding energies of H2 to the GRLi systems were calculated at several levels and the results are listed in Table 1. A benzene molecule was used as a graphene nanoflake model, as in a variety of previous studies.33-35 The binding energies calculated at the MP2 level ranged from 4.64 to 5.18 kcal/mol, while that



obtained at the cam-B3LYP/6-311G(d,p) level was 4.78 kcal/mol. This value is in excellent agreement with those of the MP2 level and a previously reported value (4.7 kcal/mol).33 Therefore, the level of theory used in the calculation is adequate for discussion of the electronic states of the GR-Li-H2 systems.

3.6. Effects of the graphene nanoflake size The influence of graphene size was investigated using GR(7), GR(14), and GR(19), and the obtained binding energies were compared with those of GR(37), as shown in Figure 7. The binding energies of n = 1 in GR(7), GR(14), GR(19), and GR(37) were 4.4, 4.3, 4.2, and 4.2 kcal/mol, respectively. At n = 6, the respective values were 1.8, 1.7, 1.7, and 1.7 kcal/mol, indicating that the effect of size is negligible in this system.

3.7. Coexistence effects of lithium ions In real systems, it is possible that multiple lithium ions could be located on the graphene surface. To examine possible coexistence effects of Li+ on the binding energies, two lithium ions located on the graphene sheet were examined using a model system composed of (H2)n on (Li+)2-GR(19) (n = 0–5). The optimized structures of n = 4 are given in Figure 8 as a representative example. At n = 4, three structural forms are possible: n = 4(A,B) = 4(4, 0), n = 4(3,2), and n = 4(2,2), where (A, B) indicate the numbers of H2 molecules on the lithium ions (Li)A and (Li)B, respectively. The binding energies of H2 were 2.60, 3.67, and 4.02 kcal/mol for n = 4(4,0), n = 4(3,1), and n = 4(2,2), respectively. The H2 molecules prefer the separate addition to Li+ ions on two lithium added surfaces. All results for n = 1–5 are provided in Table 2. In all cases, H2 prefers to disperse and adsorb onto separated Li+ ions rather than concentrate in a single


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location. This is because the binding energy of H2 to Li-GR is largest for the first H2 addition (n = 1) and decreases with increasing number of H2 molecules (n).

3.8. Effects of the hydrogen molecules on the diffusion barrier of Li+ The lithium ion can diffuse on the graphene surface under thermal activation and the diffusion energy must overcome an activation barrier. The effects of H2 on the diffusion barrier of Li+ on the GR surface were examined. The structures of GR(19)-Li+(H2)n (n = 0–4) in the binding state and transition state (TS) were optimized at the CAM-

B3LYP/6-311G(d,p) level. The optimized structures for n = 3 are illustrated in Figure 9 as a representative example. In the n = 3 binding state (reactant), Li+ was located in the hexagonal site of the benzene ring (position A), while the height of Li+ from the surface was 1.883 Å. The mean intermolecular distance of H2 from Li+ was 2.192 Å. In the TS, Li+ was located at the central position of the C-C bond of GR and the height of Li+ was 2.144 Å. The mean intermolecular distance of H2 from Li+ was 2.082 Å in the TS, which was significantly shorter than that of binding state (2.192 Å). Thus, the Li+ ion in the TS is strongly bound by H2 molecules. The diffusion barriers for n = 0–4 (activation barriers) are listed in Table 3 and imaginary frequencies were obtained for all cases (n = 0–4). The normal mode of imaginary frequency corresponds to the translational mode of Li+(H2)n between the benzene rings (A to B positions). The activation barriers for n = 0, 1, 2, 3, and 4 were calculated to be 6.35, 6.35, 4.95, 3.73, 3.62 kcal/mol, respectively, indicating that the barrier height decreases with increasing numbers of hydrogen molecules (n) and became saturated at n = 3–4. The saturation of the first coordination shell at n = 3 resulted in decreased activation energies.



The binding energies of (H2)n to Li+ were calculated for the binding state and TS, and the differences in solvation energies (denoted as Ebind) are listed in Table 3. The results suggest that the binding energies in the TS are larger than those in the binding state. Especially, the binding energy in the TS was largest at n = 3, and the overall trend showed decreasing activation energy with increasing n up to n = 3.

3.9. Effects of the basis set and functionals The effects of the basis set and functionals in DFT on the binding energy and electronic states were examined, and the corresponding results are shown in Figures S5S7. The binding energies calculated using CAM-B3LYP/6-31G(d) were in good agreement with those obtained using 6-311G(d,p), indicating that the basis set dependence was negligible in this system. The binding energies were also calculated at the PW91PW91 and APFD/6-311G(d,p) levels to determine the effects of the functionals. Similar decay curves for the binding energy were obtained using this basis set, although these functionals resulted in slightly larger binding energies. 4. Discussion 4.1. Comparison with previous studies Recently, several theoretical calculation studies regarding hydrogen storage with carbon materials studies have been performed to elucidate the details of binding in the systems. Table 4 shows the calculated binding energies of H2 to several types of carbon. In 2014, Seenithurai et al. investigated the binding energies of H2 to a Li dopedgraphene surface (3×3 periodic super cell) using DFT, yielding binding energies of 8.5 kcal/mol (n = 1) and 6.9 kcal/mol (n = 5).32 Hydrogen molecules on graphene


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nanoflakes have been investigated by several groups.33-35 Kolmann et al. investigated the electronic states of H2 on a graphene nanoflake using ab initio calculations.33 A benzene molecule-Li+ complex was used as the model system, and the binding energy was determined to be 4.7 kcal/mol (n = 1). Zhu et al. investigated the H2 structure interacting with Li on a slightly larger graphene nanoflake, GR(14), composed of 14 benzene rings and reported a binding energy of 3.9 kcal/mol (n = 1).21 In this study, the electronic states of H2 on GR-Li (or GR-Li+) were systematically investigated using a large graphene nanoflake composed of 37 benzene rings, GR(37). The binding energies obtained were in good agreement with the previously reported values. Furthermore, the electronic states of both Li and Li+ on GR were analyzed in detail.

4.2. Additional comments In this study, we used several approximations to calculate the interaction of H2 with Li-doped graphene nanoflakes. First, polycyclic aromatic hydrocarbons (PAHs) were used as a model of the graphene nanoflake, as they have been widely used as models of graphene and nanoflakes.45,46 Second, Li (or Li+) was placed in the central region of GR. The position of Li on GR may change the coordination structure of H2 around GRLi, especially at large coordination numbers (n > 7). Third, GR defects were completely neglected. In the future, we will investigate these issues using larger GR models. Despite the assumptions used in this study, valuable information regarding the electronic states of the hydrogen molecules, lithium, and GR were obtained and may be useful in the development of hydrogen storage materials.



5. Concluding remarks In this study, the effects of lithium atoms and ions on the binding of H2 to the GR surface were investigated by DFT. Although the binding energies of H2 to pure GR was close to zero (without Li), the doping of Li (or Li+) significantly increased the binding energies. Both Li and Li+ on GR can bind added H2 molecules with largely the same efficiency. This is because of the large amount of electron transfer from Li to GR, resulting in the net charge on Li atom changing from zero to +0.929 upon addition to GR, the same as that of Li+ on GR. The binding energies in the first and second shells were calculated, and ranged from 3.83 kcal/mol (n = 1) to 1.43 kcal/mol (n = 7). These values are significantly larger than the binding energies between H2 molecules and Li determined in vacuo (i.e., H2-- and Li--(H2)n without GR). This suggests that Li-GR is a suitable candidate for efficient hydrogen gas storage for various applications in the hydrogen economy. Electron transfer activates the Li atom on GR, allowing GR-Li to be a promising candidate for hydrogen storage.

Acknowledgments. The author (H.T.) acknowledges partial support from JSPS KAKENHI Grant Numbers 18K05021 and 17H03292. Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: The optimized structure of the GR-Li+(ion) and GR-Li+(ion)-(H2)n, stick diagrams of the interatomic distances of GR-Li(atom)-(H2)n and GR-Li+(ion)-(H2)n (n = 1–12), binding energies calculated using the PW91PW91 functional with GR(19), CAM-B3LYP functional with GR(19), and cluster size dependence on binding energy are provided in the SI.


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Table 1. Binding energies of H2 to the benzene-lithium ion (Bz-Li+, kcal/mol) calculated at several levels of theory. The geometry of Bz-Li+- H2 was optimized for each method. Method

Ebind/ kcal mol-1

Reference

cam-B3LYP/6-311G(d,p)

4.78

Present work

cam-B3LYP/6-

4.82

Present work

MP2/6-311G(d,p)

5.18

Present work

MP2/6-311++G(d,p)

5.12

Present work

MP2/6-311++G(2d2p)

4.64

Present work

MP2/6-311++G(3df,2pd)

4.93

Present work

MP4SDQ/6-311++G(d,p)

5.12

Present work

CCSD(T)/B3LYPa

4.7

311++G(d,p)

Ref. 33, CPL 2008, 467, 126-130

aGeometry

was optimized at the B3LYP/6-311+G(2df,p) level and the energy was calculated at the CCSD(T)/6-311+G(3df,2p) level.



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Table 2. Binding energies of H2 to two Li+ ions in the system, (Li+)2-GR(19) (per H2 molecule in kcal/mol) calculated at the CAM-B3LYP/6-311G(d,p) level. n 1

(A, B) (1,0)

Ebind / kcal mol-1 4.81

2

(2,0) (1,1)

4.04 4.80

3

(3,0) (2,1)

3.30 4.28

4

(4,0) (3,1) (2,2)

2.60 3.67 4.02

5

(5,0) (4,1) (3,2)

2.16


3.03 3.62

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Table 3. Diffusion (activation) barriers of Li+(H2)n (n = 0–4) on the GR(19) surface (Ea in kcal/mol) calculated at the CAM-B3LYP/6-311G(d,p) level. The term Ebind refers to the differences in binding energies in the transition state (TS) and binding state (per H2 molecule in kcal/mol). n 0 1 2 3 4

Ea / kcal mol-1

Ebind / kcal mol-1

6.35 6.35 4.95 3.73 3.62

0.0 0.01 -0.70 -0.87 -0.68



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Table 4. Binding energies of the hydrogen molecules on Li (or Li+)-doped graphene and graphene nanoflakes calculated using several methods. carbon materials

lithium

model

method

Ebind / kcal mol-1

Reference

graphene

Li

3x3 periodic

PBE

Ref. 32

nanoflake nanoflake

Li+ Li

benzene GR(14) a

CCSD(T)/MP2

8.5 (n = 1) 6.9 (n = 5) 4.7 (n = 1) 3.9 (n = 1)

nanoflake

Li

GR(37) b

CAM-B3LYP/ 6-311G(d,p)

3.83 (n = 1)

present

1.43 (n = 7) 0.89 (n = 13) 4.13 (n = 1)

present

nanoflake

Li+

GR(37) b

B3LYP/3-21G(d,p)

CAM-B3LYP/ 6-311G(d,p)

1.51 (n = 7) 0.90 (n = 13) aGraphene bGraphene

nanoflake composed of 14 benzene rings. nanoflake composed of 37 benzene rings.


Ref. 33 Ref. 21

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Figure captions Figure 1. Optimized structure of the GR-Li(atom) calculated at the CAM-B3LYP/6311G(d,p) level with a GR composed of 37 benzene rings. Figure 2. Optimized structures of GR-Li(atom)-(H2)n (n = 1, 2, 3, 4, 7, and 11). The calculations were performed at the CAM-B3LYP/6-311G(d,p) level. Figure 3. Stick diagrams of interatomic distances between the Li and hydrogen atoms of H2 in GR-Li(atom)-(H2)n (n = 1, 3, 4, 7, 8, and 11). The calculations were performed at the CAM-B3LYP/6-311G(d,p) level. Figure 4. NPA atomic charges of the Li atom and NPA total charges of six carbon atoms in the hexagonal site of GR. The calculations were performed at the CAMB3LYP/6-311G(d,p) level. Figure 5. Heights of Li and Li+ from the GR surface (in Å). Figure 6. Binding energies of H2 to GR-Li and GR-Li+ (per H2 molecule). The open squares represent the binding energies of H2 to the Li atom without GR, Li(H2)n. Figure 7. Grapehene-size dependency of binding energy of H2 to GR-Li+ (per H2 molecule). The calculations were performed at the CAM-B3LYP/6-311G(d,p) level. Figure 8. Optimized structures of (H2)n on (Li+)2-GR(19) (n = 4). The calculations were performed at the CAM-B3LYP/6-311G(d,p) level. Binding energy of H2 to (Li+)2GR(19) (Ebind in kcal/mol per H2 molecule). Figure 9. Optimized structures of GR(19)-Li+-(H2)n (n = 3) in the binding state and transition state (TS) calculated at the CAM-B3LYP/6-311G(d,p) level. Bond distances are given in Å.



Figure 1


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Figure 2.



Figure 3.


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Figure 4.



Figure 5.


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Figure 6.



Figure 7.


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Figure 8



Figure 9.


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Mechanism of Hydrogen Storage in the Graphene ... - ACS Publications

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