Reactions of Graphene Nano-Flakes in Materials Chemistry and Astrophysics

Abstract

The elucidation of the mechanism of the chemical evolution of the universe is one of the most important themes in astrophysics. Polycyclic aromatic hydrocarbons (PAHs) provide a two-dimensional reaction field in a three-dimensional interstellar space. Additionally, PAHs play an important role as a model of graphene nanoflake (GNF) in materials chemistry. In the present review, we introduce our recent theoretical studies on the reactions of PAH and GNF with several molecules (or radicals). Furthermore, a hydrogen storage mechanism for alkali-doped GNFs and the molecular design of a reversible hydrogen storage device based on GNF will be introduced. Elucidating these reactions is important in understanding the chemical evolution of the universe and gives deeper insight into materials chemistry.

1. Introduction

Understanding the mechanisms of the chemical evolution of the universe is one of the most important topics of recent research in astrophysics and astrochemistry [1,2,3] About 20% of the total carbon in the universe is widely distributed in space in the form of polycyclic aromatic hydrocarbons (PAHs) [4], although the actual distribution in space and structure of PAHs are still unclear [5]. PAH is thought to provide a two-dimensional reaction field in three-dimensional interstellar space [6,7,8]. The reaction probability of bimolecular collisions increases significantly with the adsorption of molecules to the surface of PAH. Therefore, understanding the interaction between PAH and molecules is important for understanding the chemical evolution of the universe.

On the other hand, in the field of materials science, PAH is used as a model compound of graphene nanoflake (GNF) [9,10,11,12]. GNF has a wide range of applications such as hydrogen storage and lithium-ion batteries. Other applications include solar cells, energy storage devices, bio-devices, thermal management and piezoelectric materials, antibacterial materials, and filtration materials. Thus, PAH and GNF play an important role in a wide range of fields. In this review article, we introduce our theoretical studies on the interaction between PAH (GNF) and molecules. For example, the reactions of GNF (PAH) with hydrogen atoms, methyl radicals, and organic radicals are introduced here. Chemical reactions occurring on the surface of GNF are also presented. A mechanism of hydrogen storage composed of alkali-doped GNF and the molecular design of a reversible hydrogen storage device based on GNFs are introduced. The interaction of GNFs with molecules and radicals will play an important role both in the early reactions in the chemical evolution of the universe and in materials chemistry.

2. Interaction of Hydrogen Atoms with GNF

Atomic and molecular hydrogen are most abundant in interstellar space [13] If atomic hydrogen is adsorbed onto a GNF surface, several reactions can take place with other small atoms and molecules, forming more complicated molecules. Hence, the interaction of GNFs with atomic hydrogen plays an important role in the initial reactions of chemical evolution in the universe. In the field of materials science, GNF is used as a model compound of graphene [14,15,16,17]. In this chapter, the mechanism of hydrogen addition to GNFs is introduced using the results from density functional theory (DFT) calculations.

2.1. Bonding Structure of Hydrogen Atoms to GNFs

In density functional theory (DFT) calculations of the interaction system composed of GNF and a hydrogen atom (H), H was added to the carbon atom near the center of GNF, and the geometry was optimized. The GNF and the hydrogen-added GNF are denoted as GNF(n) and H-GNF(n), respectively, where n is the number of benzene rings in the GNF. Figure 1 shows examples of the GNFs(n) (n = 19 and 37) used in the calculations. The DFT calculations were performed on GNFs consisting of 7–37 benzene rings (See Figure S1 in Supporting Information). The basis sets are 6-31G(d) and 6-311G(d,p) [18] and the functional Coulomb-attenuating method (CAM-B3LYP) [19] is used. Atomic charges and spin densities were determined by natural population analysis (NPA) and natural bond orbital (NBO) methods.

The optimized structure of H-GNF is shown in Figure 2. The planar structure around the H-bonded carbon atom (C₀) of GNF is changed to a pyramidal one after the addition of H. The distance between the added hydrogen (H) and the bonded carbon atom (C₀) is R1 = 1.114 Å. The atomic charges of C₀ and H are −0.274 and +0.245, respectively, indicating that the C-H bond is locally polarized as (C₀)^−0.274–(H)^+0.245. This suggests that the addition of H to the nonpolar GNF generates a dipole moment that facilitates the attraction of other molecules in interstellar space [20].

2.2. Potential Energy Curve

The potential energy curve (PEC) for the approach of H to the GNF surface is plotted in Figure 3A as a function of C₀-H distance (R₁). The calculations are carried out at the CAM-B3LYP/6-311G(d,p) level. All geometrical parameters except for the C₀-H distance (R₁) are optimized at each value of R₁. When H approaches the GNF surface, the first energy minimum was found at R₁ = 3.50 Å, corresponding to a van der Waals (vdW) complex composed of GNF and H. The binding energy of H to GNF is 0.2 kcal/mol. The H atom is bound by vdW force to the π-orbital of the GNF surface. Subsequently, the energy barrier corresponding to transition state (TS) is found at R₁ = 1.71 Å, where the barrier height is 6.2 kcal/mol relative to the dissociation limit (GNF + H). The energy decreases significantly after TS and reaches the lowest energy point corresponding to the bound state of H-GNF, i.e., the product state (PD). The barrier is caused by the change in the electronic state in the carbon atom (C₀) from sp² to sp³ upon the addition of hydrogen.

The PEC for the addition of a proton (H⁺) is also given for comparison. The shape of PEC for the addition of H⁺ is significantly different from that of the addition of hydrogen. The H⁺ can bind directly to the graphene surface without an activation barrier. A large quantity of exothermic energy is generated in H⁺ because of the high proton affinity of GNF.

The spatial distribution of the spin density of H-GNF is shown in Figure 3B. In the vdW state, the spin density is localized to the H atom and does not flow into the PAH side. At TS, the spin density of H is 0.794, which indicates that about 20% of the unpaired electrons dissipated into the GNF side. The spin density on GNF is 0.988 in PD, indicating that the unpaired electron of the H atom is almost completely transferred to GNF.

2.3. Activation and Binding Energies

The size dependence of the activation barrier and binding energy of GNFs is shown in Figure 4. The activation energies are calculated to be 6.6 kcal/mol (n = 7), 5.6 kcal/mol (n = 14), 6.2 kcal/mol (n = 19), 5.2 kcal/mol (n = 29), and 7.0 kcal/mol (n = 37). These results indicate that the activation energy is independent of the GNF size and is nearly constant (~5–7 kcal/mol). In contrast, the binding energy was slightly dependent on the size of GNF. The binding energies for n = 14 and 29, specifically, are higher than the other binding energies.

2.4. Behavior of Hydrogen Atoms on GNF (PAH) Surfaces

In this section, the interactions and reactions between H atom and GNF surface ere described, which were obtained by the DFT method. A schematic energy diagram of the interaction between the hydrogen atom and the GNF surface is shown in Figure 5. The H atom from interstellar space is first weakly bound to the GNF surface by vdW interaction. The binding energy is about 0.1–0.2 kcal/mol, and the H atom is located at 2.8–3.5 Å from the surface. This binding energy is large enough to stay on the GNF surface in interstellar space because the temperature is lower than 10 K in interstellar space. Hydrogen atoms can diffuse freely on the surface at 10 K. The diffusion barrier is about 0.2 kcal/mol. The H atom trapped on the surface in the vdW state is an active species and can readily react with other molecules. If H atom gains excess energy higher than the activation barrier, hydrogenated GNF (H-GNF) is formed. H-GNF is reactive species due to a radical with dipole moment.

3. Interaction of GNFs with Methyl Radicals

The methyl radical (CH₃) is the simplest organic radical observed in interstellar space and is the basis for the formation of more complex organic molecules. It was first discovered in space by Feuchtgruber et al. [21] in Sgr A* using the infrared space telescope of the European Space Agency. It was subsequently discovered by Knez et al. in NGC7538 [22]. Methyl radicals adsorbed on GNF surfaces can evolve by reacting with other atoms and molecules, as discussed by us [23].

In materials science, a methyl radical is an important intermediate generated from the catalytic reaction of alkane and its related compounds. In this chapter, the mechanism of the addition of a methyl radical to GNFs is introduced [22].

3.1. Binding Structure of Methyl Radical to GNF

The optimized binding structure of methyl radical added to GNF, CH₃-GNF, is shown in Figure 6. The C-C bond distance of the binding site was calculated to be R1 = 1.574 Å. The molecular charges of CH₃ and GNF parts are +0.084 and −0.084, respectively. Although CH₃ shows a slight electron donor property, the magnitude of the charge transfer is very small. Therefore, CH₃-GNF has no dipole moment.

3.2. Potential Energy Curve

Figure 7A shows potential energy along the intrinsic reaction coordinate (IRC) for the addition reaction of CH₃ to the GNF surface. The barrier height of TS is 14.0 kcal/mol higher in energy than the initial vdW complex. The distance of the CH₃ from GNF in TS is R1 = 2.131 Å. After TS, the energy decreases and reaches the PD of CH₃-GNF. The activation energy associated with the binding of CH₃ to GNF is 14.0 kcal/mol, which is larger than that of H-GNF (6.2 kcal/mol). The addition reaction of CH₃ is a 3.0 kcal/mol exothermic reaction.

The spatial distribution of the spin density of CH₃-GNF is shown in Figure 7B. In the vdW state, the spin density of CH₃ is 0.994, which is almost localized to the CH₃ radical. In TS, the spin density of the CH₃ part is 0.661 and that of GNF is 0.339, which means that almost 30% of the unpaired electrons flow from CH₃ to GNF. In PD, on the contrary, the spin density of GNF is 0.931, indicating that the unpaired electron of methyl radical is almost completely transferred to GNF.

3.3. Activation and Binding Energies

The addition of CH₃ to GNF needs an activation barrier. The size dependence of the activation and binding energies of GNFs is shown in Figure S2 (in Supporting Information). The activation energies for n = 4, 7, 19, and 37 are 15.1, 14.7, 13.8, and 13.4 kcal/mol, respectively, at the CAM-B3LYP/6-311G(d,p) level. These results indicate that there is almost no size dependence of the activation energy of GNFs. In contrast, the binding energy was slightly dependent on the size of the GNF, and the binding energy increased slightly with size.

3.4. Behavior of Methyl Radicals on GNF Surface

In this section, the interaction of CH₃ with the GNF surface was described. A schematic energy diagram of the interaction between CH₃ and the GNF surface is shown in Figure 8. The methyl radical from interstellar space binds weakly to the GNF surface through the vdW interaction. The binding energy is about 0.1–0.2 kcal/mol. When the methyl radical receives a quantity of kinetic energy of about 14 kcal/mol, it reacts with carbon atoms on the surface to form CH₃-GNF.

3.5. Activation Energies of Alkyl Radicals Addition to GNF

The activation energies of radical addition reaction, E(TS), reaction energies leading to PD, E(PD), and the binding energies of vdW complexes, E(vdW), are given in

Table 1. Activation energies of radical addition reaction to graphene nanoflake, E(TS), reaction energies leading to PD, E(PD), and binding energies of vdW complexes, E(vdW) (in kcal/mol). Notations are CH₃, Et, n-Pr, iso-Pr, n-Bu, sec-Bu, tert-Bu, iso-Bu mean methyl, ethyl, iso-propyl, normal-butyl, secondary butyl, tertiary-butyl radicals, respectively. Zero level of relative energy corresponds to dissociation limit (radical + GNF). The calculations were carried out at the CAM-B3LYP/6-311G(d,p) level. Halogen atoms (F and Cl) can bind to GNF without activation barrier (i.e., E(TS) = 0.0 kcal/mol).

Radical	E(TS)	E(PD)	E(vdW)
CH3	13.8	−3.6	−0.3
Et	14.7	1.1	−0.6
n-Pr	15.2	1.3	−0.2
iso-Pr	17.6	8.1	−0.8
n-Bu	15.2	1.4	−0.2
sec-Bu	18.7	9.7	−0.4
tert-Bu	22.1	16.6	−0.9
iso-Bu	20.1	9.0	−0.7
F	0.0	−29.4	--
Cl	0.0	−6.5	--

. The calculated values of methyl (CH₃), ethyl (Et), n-propyl (n-Pr), iso-propyl (iso-Pr), n-butyl (n-Bu), secondary-butyl (sec-Bu), tertiary-butyl (tert-Bu), and iso-butyl (iso-Bu) radicals are given. The activation energy of CH₃ is 13.8 kcal/mol, and the activation energy increases as the bulk of the molecule increases. The reaction energies are positive except for the CH₃ radical, indicating that the addition of alkyl radicals is endothermic. In all radicals, vdW complexes composed of GNF and radical are exothermic formed.

4. Chemical Reaction on GNF Surface

When a molecule is adsorbed onto a GNF (PAH) surface, the electronic state of the molecule will be changed by the interaction with GNF. It is expected that a reaction mechanism will be affected by interaction from the surface. The effects of GNF on the reaction mechanism are considered in this chapter. The hydrogen addition reaction to acetylene (HCCH) on the GNF surface is presented as a sample reaction to elucidate the effect of the GNF surface on the reaction mechanism. The reaction is expressed as

HCCH + H → TS → H₂CCH (radical)

(1)

The H₂CCH radical is formed by the addition of hydrogen to HCCH as a product. The transition state (TS) structure for reaction (1) in the gas phase is illustrated in Figure 9. The hydrogen atom is located at 1.996 Å from the carbon atom of HCCH, and the linear structure of HCCH is changed to a slightly bent form in TS. The activation energy of the addition reaction is 1.3 kcal/mol in vacuum. Next, the structural parameters of TS on the GNF surface are given in Figure 9 (in parenthesis). Both lengths and angles on the GNF surface are close to those in vacuum. The structure on GNF is significantly similar to that in vacuum, indicating that the GNF surface effect on the electronic states of TS is quite small.

Potential energy along the IRC is illustrated on Figure 10A. First, HCCH and the H atom are adsorbed onto GNF due to the vdW interaction (vdW(1)). In the TS structure, the distance of the H atom from the carbon atom of HCCH is 1.998 Å, which is close to the structure in vacuum. After TS, the addition of a H atom to HCCH takes place and forms a radical product (H₂CCH). This radical remains on the surface with vdW interaction (vdW(2)). The radical is then desorbed from the surface, yielding the same reaction product (H₂CCH) as in vacuum.

The relative energies at each point along IRC are summarized in

Table 2. Effects of GNF surface on energetics for hydrogen addition reaction to acetylene: H(atom) + HCCH → H₂CCH (radical). Relative energies with respect to vdW state are given in parenthesis. The calculations were carried out at the CAM-B3LYP/6-311G(d,p) level.

State	Vacuo	on GNF
RC (H + HCCH)	0.0	0.0 (1.3)
vdW(1)	--	−1.3 (0.0)
TS	1.3	0.2 (1.5)
vdW(2)	--	−48.7 (−47.4)
PD (H2CCH)	−47.6	−47.6 (−46.3)

. In vacuum, the activation and reaction energies are 1.3 kcal/mol and −47.6 kcal/mol, respectively. In the reaction on GNF, the activation energy is 1.5 kcal/mol. There is almost no energy difference between the GNF surface and the vacuum is very small. This indicates that the GNF surface largely does not change the electronic state of the adsorbed molecules, but contributes only as a reaction field.

5. Mechanism of Hydrogen Storage in the Graphene Nanoflake Doped by Alkali-Metals

GNF acts as an important reaction field in interstellar space. On the other hand, GNFs have been studied in materials chemistry as a model molecule for graphene nanoflakes. Carbon materials, such as graphene nanoflakes and fullerene, can be used for hydrogen storage. Alkali doping these materials generally increases their H₂-storage density. In this article, DFT studies on the mechanism of hydrogen storage using GNFs doped by alkali-metals are presented [24].

GNF (37) is used as a model of a graphene nanoflake (denoted GNF), and hydrogen added clusters, GNF-M-(H₂)_n and GNF-M⁺-(H₂)_n (M = Li and Na, n = 0–12), are employed as hydrogen storage systems.

First, the structure of GNF is optimized, and then alkali metal M (or M⁺) is placed in the central region of GNF. The structures of GNF-M is optimized, where all GNF-M⁺/M atoms are fully optimized. The binding energy of M to GNF is defined as follows:

$$-{\mathrm{E}}_{\mathrm{bind}}\left(\mathrm{M}\right)=\mathrm{E}\left(\mathrm{GR}-\mathrm{M}\right)-\left[\mathrm{E}\left(\mathrm{M}\right)+\mathrm{E}\left(\mathrm{GR}\right)\right]$$

(2)

where E(X) is the total energy of X. If E_bind(M) is positive, M can bind exothermally to GNF. The binding energy of H₂ to GNF-M (per one H₂ molecule) is defined as defined as follows:

$$-{\mathrm{E}}_{\mathrm{bind}}\left(\mathrm{n}\right)=\left[\mathrm{E}\left(\mathrm{GR}-\mathrm{M}-{\left({\mathrm{H}}_2\right)}_{\mathrm{n}}\right)-\left[\mathrm{E}\left(\mathrm{GR}-\mathrm{M}\right)+\mathrm{nE}\left({\mathrm{H}}_2\right)\right]\right]/\mathrm{n}$$

(3)

If E_bind(n) is positive, the H₂ molecule binds exothermally to GNF-M.

5.1. Structures of the Li Doped-Graphene Nanoflake

First, the structures of GNF-Li and GNF-Li⁺ are optimized, and the binding energies are summarized in

Table 3. Binding energies of M–GNF and M⁺–GNF (E_bind in kcal/mol, M = Li and Na), M–GNF-surface distances (h in Å), and NPA-determined atomic charges for M on GNF, calculated at the CAM-B3LYP/6-311G(d,p) level.

	Ebind	Height (h)	NPA
GNF-Li	17.1	1.736	+0.929
GNF-Li+	52.8	1.771	+0.937
GNF-Na	4.4	2.247	+0.978
GNF-Na+	37.5	2.288	+0.979

. Both Li and Li⁺ are bound to the hexagonal site of the GNF surface. The similar heights, i.e., the distance of Li (or Li⁺) from the GNF surface, are obtained (1.736 Å for Li and 1.771 Å for Li⁺). The binding energies are 17.1 kcal/mol (Li) and 52.8 kcal/mol (Li⁺). These results are in good agreement with previous calculations of the coronene-Li (or Li⁺) system [25]. The NPA atomic charges on Li and Li⁺ were +0.93 and +0.94, respectively, suggesting that the net charge of Li is very similar to that of Li⁺. This implies that significant electron transfer takes place from Li to GNF after binding (0.93 e).

5.2. Binding Structures of the Hydrogen Molecules to GNF-Li

Figure 11 shows the binding structures of the H₂ molecules to GNF-Li. In case of first H₂ addition (n = 1), both distances of hydrogen atoms from Li are equivalent with 2.027 Å, indicating that H₂ binds to Li with a side-on structure. For n = 2–3, the binding structures are side-on, similar to that of the n = 1 case.

For n = 4, the fourth hydrogen molecule cannot bind directly to Li, and instead is weakly bound to the hydrogen molecules already binding to Li. The outer hydrogen molecules (n = 5 and 6) are also bound to H₂ in the inner shell. The similar binding structures are obtained for the GNF-Li⁺ (ion)-H₂ system because the electronic state of GNF-Li⁺ (ion) is very similar to that of GNF-Li (atom).

5.3. Binding Energy of H₂ to GNF-Li

The binding energy of H₂ to GNF-Li plotted as a function of n (per H₂ molecule) are in Figure 12. The binding energy for the first addition of H₂ (n = 1) is 3.83 kcal/mol, and it decreases with increasing n. The binding energies are 2.85 (n = 3) and 1.43 kcal/mol (n = 7). The energy is almost saturated at n = 12. The large energy strongly indicates that GNF-Li can be used as a H₂ storage material. Similar features were observed in the GNF-Li⁺-(H₂)_n system.

To elucidate the effect of GNF on the binding energy, the binding energy of H₂ to bare Li was calculated without GNF and the results are plotted in Figure S3 (open squares). The calculated energies for n = 4, 7, and 12 are 1.35, 0.82, and 0.50 kcal/mol, respectively. The binding energy in Li-(H₂)_n without GNF is significantly lower than that with GNF, suggesting that GNF activates Li via electron capture. This electron transfer activates the Li atom on the GNF.

5.4. Binding Structures of H₂ to GNF-Na

Establishing an appropriate means of transportation is an important element in achieving a hydrogen energy society [27,28]. Carbon materials can safely store hydrogen [29,30] and lithium (Li)-doped graphene is a particularly effective storage material [31,32]. Unfortunately, lithium is high cost metal because it must travel long distances to be commercialized. In this regard, sodium (Na) is an inexpensive metal with chemical properties similar to those of Li [26].

The geometry optimizations of GNF-Na and GNF-Na⁺ indicate that both Na and Na⁺ bind to the hexagonal sites of GNF. The heights of Na (or Na⁺) from GNF, binding energies of Na to GNF, and NPA atomic charge of Na are given in Table 3. The heights are 2.247 Å (Na) and 2.288 Å (Na⁺), and both Na and Na⁺ are located at a similar distance from the GNF surface, although the binding energies are different from each other: 4.4 (Na) and 37.5 kcal/mol (Na⁺).

The atomic charges are +0.978 (Na) and +0.979 (Na⁺), indicating that the net charge of Na on GNF is very similar to that of Na⁺ on GNF, which suggests that significant electron transfer occurs from Na to GNF (0.98e). These features in GNF-Na are in good agreement with the GNF-Li system, as summarized in Table 3, where the atomic charges on Li and Li⁺ adsorbed on GNF are +0.929 and +0.937, respectively.

Next, the binding of H₂ to GNF-Na is examined to elucidate its hydrogen storage ability. The binding structures of H₂ to GNF-Na (n = 1–6) are illustrated in Figure 13. In n = 1, H₂ is bound to Na with a side-on structure, where the two hydrogen atoms of H₂ are equivalently bound to Na. Similar binding structures are obtained for n = 1–4. The fifth H₂ molecule binds to Na in a manner orthogonal to the surface, with a distance of 2.833 Å, which is larger than those of n = 1–4 (2.45 Å). These results indicate that the first coordination shell is saturated at n = 4. The sixth H₂ molecule interacts with a H₂ molecule in the first coordination shell and is not directly bound to Na (the distances between the sixth H₂ molecule and Na and the nearest H₂ molecule are 5.037 and 3.625 Å, respectively). Side-on coordination structures were observed in all clusters (n = 7–12).

5.5. Binding Energies of H₂ to GNF-Na

The binding energies of H₂ to GNF-Na or GNF-Na⁺ plotted as a function of n (per H₂ molecule) are in Figure 12. The binding energy for n = 1 is 2.72 kcal/mol, and it decreases with increasing n. The binding energies are 2.67 (n = 2), 2.50 (n = 3), 2.34 (n = 4), and 2.01 kcal/mol (n = 5).

In the case of a GNF-Li-H₂ system, the binding energies are 3.83 (n = 1), 3.29 (n = 2), 2.85 (n = 3), 2.20 (n = 4), and 1.83 kcal/mol (n = 5). These trend indicates that GNF-Li interacts more strongly with H₂ than GNF-Na for n = 1–3, while the interactions are comparable for both Li and Na at n = 4. GNF-Na interacts slightly more strongly with H₂ in larger systems (n = 5–12). Thus, GNF-Na appears to have a higher H₂-storage ability than GNF-Li. The GNF-Na⁺-(H₂)_n (Na⁺ ionic system) exhibits similar features (Figure 12). Since the Na–(H₂)_n binding energy is close to zero in the absence of GNF, GNF clearly enhances binding through electron transfer from Na to GNF: GNF + Na → (GNF)⁻-Na⁺.

These results strongly suggest that GNF-Na is a suitable candidate for the efficient storage of hydrogen gas for various applications in the hydrogen economy, and that sodium is an alternative to lithium for that purpose.

For comparison, the hydrogen adsorption capacity of K⁺ was examined. The binding energy of H₂ to GNF-K⁺ is plotted in Figure 12. The binding energies in GNF-K⁺ were lower than those of GNF-Li⁺ and GNF-Na⁺, suggesting that GNF-K⁺ is poor as a H₂ storage.

6. Molecular Design of Reversible Hydrogen Storage Device

In previous sections, the hydrogen storages of Li- and Na-doped GNFs were introduced. In this section, the molecular design of a reversible hydrogen storage device based on GNFs is presented. Magnesium has three valence states: neutral, mono-, and divalent, expressed as Mg, Mg⁺, and Mg²⁺. Here, the GNF-Mg system is examined as a reversible hydrogen storage device [33].

6.1. Structures of Mg-Doped GNF

First, the structures of Mg-doped GNF, GNF-Mg^m+ (m = 2, 1, and 0), were fully optimized. Figure 14A shows the structures of GNF-Mg^m+ (m = 2), and those for m = 1 and 2 are illustrated in Figures S4 and S5, respectively. Neutral and ionic species of Mg are bound to the hexagonal site of GNF. The binding energies of Mg^m+ to GNF are 0.3 kcal/mol (m = 0), 39.9 kcal/mol (m = 1), and 159.8 kcal/mol (m = 2), indicating that the binding energy is strongly dependent on the charge of Mg. The height of Mg from the GNF surface (h) is also dependent on the atomic charge of Mg: h = 4.339 Å (m = 0), 2.214 Å (m = 1), and 1.806 Å (m = 2). Mg²⁺ is shorter than Mg⁺, and a neutral Mg atom cannot bind to GNF. The atomic charges of the Mg moiety of GNF-Mg^m+ for m = 0, 1, and 3 are −0.001, +0.960, and +1.882, respectively, indicating that the electron transfer from GNF to Mg species is small in the GNF-Mg system.

6.2. Binding Structures and Energies of H₂ to GNF-Mg^m+ (m = 1 and 2)

Figures S6 and S7 show the binding structures of H₂ to GNF-Mg²⁺ (m = 2). The H₂ molecule binds to Mg²⁺ with a side-on structure. In both cases (m = 1 and 2), the first coordination shells were closed up to n = 4. The second shell consisted of one H₂ molecule (5-th H₂). Figure 14B shows the binding energy of H₂ to GNF-Mg^m+ (per H₂ molecule) plotted as a function of n. The first addition of H₂ to GNF-Mg²⁺ causes a binding energy of 13.22 kcal/mol, which gradually decreases as a function of n: the binding energies are 9.99 kcal/mol (n = 3), 6.79 kcal/mol (n = 5), and 5.03 kcal/mol (n = 7).

In contrast, the binding energies of GNF-Mg⁺-(H₂)_n (monovalent state, m = 1) are significantly lower than those for Mg²⁺: 0.31 kcal/mol (n = 1), 0.28 kcal/mol (n = 3), 0.26 kcal/mol (n = 5), and 0.24 kcal/mol (n = 7). These trends strongly indicate that GNF-Mg²⁺ can be used as a H₂ storage material, whereas the ability of GNF-Mg⁺ is quite low. Additionally, it was found that the ability for H₂ storage in GNF-Mg^m+ is changed by the charge of GNF-Mg. Adsorption–desorption is controlled by the molecular charge in the GNF-Mg^m+-(H₂)_n system (m).

6.3. Electron Capture Dynamics of GNF-Mg²⁺-H₂

In previous section, it was found that the structure of GNF-Mg-H₂ and the binding energy of H₂ to GNF-Mg are largely dependent on the atomic charge of Mg. This specific property in the Mg system is much different from the Li and Na-GNF systems. Additionally, this makes GNF-Mg-H₂ suitable for use as a H₂ storage device with reversible adsorption–desorption properties. In this section, direct ab initio molecular dynamics (AIMD) calculations [34,35,36] for the electron and hole capture processes of the GNF-Mg-H₂ system are described.

The result of the electron capture dynamics of GNF-Mg^m+-(H₂)₄ (m = 2), calculated by means of the direct AIMD method, is given in Figure 15, where snapshots of GNF-Mg⁺-(H₂)₄ are shown. The initial structure at time zero was set to the optimized geometry of GNF-Mg²⁺-(H₂)₄ and then a trajectory of GNF-Mg⁺-(H₂)₄ following the electron capture of GNF-Mg²⁺-(H₂)₄ was started without excess energy. The electron capture makes a change to the charge on Mg (Mg²⁺ to Mg⁺). The intermolecular distance between the Mg and H₂ molecules (denoted as <R>, average distance) and the height of Mg⁺ from the GNF surface (h) were drastically varied as a function of time. The H₂ molecules and Mg⁺ were located at <R> = 2.253 Å and h = 1.908 Å at time = 0 fs (vertical electron capture point), respectively. After the electron capture, the H₂ molecules gradually left the Mg⁺: <R> = 2.327 Å (51.7 fs) and 3.034 Å (85.9 fs). In the final stage of electron capture reaction (100 fs), the H₂ molecules were fully dissociated as <R> = 4.014 Å. The position of Mg⁺ was elongated to h = 2.526 Å at 100.0 fs. The reaction is expressed as follows:

GNF-Mg²⁺-(H₂)_n + e⁻ → GNF-Mg⁺-(H₂)_n (H₂ in the gas phase)

(4)

Thus, H₂ molecules were released into the gas phase after the electron capture.

6.4. Hole Capture Dynamics of GNF-Mg⁺-H₂

In contrast, the dissociated hydrogen molecules return from gas phase to GNF-Mg²⁺ after a hole capture of GNF-Mg⁺. The hole capture dynamics of GNF-Mg^m+-(H₂)₄ (m = 1) are given in Figure 16. The molecular charge of GNF-Mg is changed from GNF-Mg⁺ to GNF-Mg²⁺ by a hole capture, and the electronic state is thus drastically changed. The initial geometry of GNF-Mg²⁺-(H₂)₄ was chosen as one of the dissociation structures in the gas phase. At the vertical hole capture point (time zero), the distance between GNF-Mg and H₂ molecules was <R> = 3.704 Å (average distance), while the height of Mg⁺ from the GNF surface was h = 2.472 Å. At 40.2 fs, the distance of H₂ was shortened to be <R> = 3.636 Å, while the height of Mg²⁺ became very low (1.786 Å). Mg²⁺ collided with the GNF surface at 57.7 fs (h = 1.451 Å). The hole capture reaction took 86.6 fs become placid. The distance of H₂ and Mg from the GNF surface was <R> = 2.787 and h = 2.787 Å, respectively. These geometrical changes indicate that the H₂ molecules can be fully rebound to GNF-Mg²⁺ after hole capture, and the structure was recovered by the addition of H₂ to GNF-Mg²⁺. The reverse process is finished at ~90 fs. The reaction is expressed as follows:

GNF-Mg⁺ + (H₂)_n (gas phase) + hole → GNF-Mg²⁺–(H₂)_n (adsorption)

(5)

These results strongly indicate that the reversible adsorption–desorption reaction of H₂ is easily controlled by the charge switching of GNF-Mg.

7. Conclusions

In the present review article, the reactions of hydrogen atom and methyl radicals with graphene nanoflakes (GNFs) are first studied from a quantum-chemical point of view. The reactions of alkyl radicals with GNF are also presented. These species can react with GNFs, and radical-added GNFs are formed as products. The addition reactions need activation energies corresponding to sp²-sp³ hybridization. In contrast, the addition of a halogen atom (F and Cl) to the GNF surface proceeds without an activation barrier due to the large exothermic energy involved. The dipole moment is generated by the addition of a H atom to the GNF, and spin density is widely distributed over H-GNF, indicating that the non-reactive GNF is activated by the addition of H in interstellar space.

Second, the effects of the GNF surface on the chemical reaction are presented. The reaction associated with the addition of a hydrogen atom to acetylene was examined as a sample reaction. The GNF surface largely did not affect the electronic states of the adsorbed molecule. This indicates that the GNF surface does not much change the electronic state of the adsorbed molecules, but contributes as a two-dimensional reaction field for the reaction to proceed in three-dimensional interstellar space.

Next, the hydrogen storage mechanism of alkali doped GNFs is presented. Lithium and sodium were examined as an alkali atom and ion. In both atoms and ions, hydrogen molecules are efficiently stored in doped GNFs, indicating that the GNF-Li and GNF-Na systems can be used as hydrogen storage devices.

Lastly, the molecular design of a reversible hydrogen storage device based on GNFs was introduced. Magnesium takes three valence states: neutral, mono-, and divalent, expressed as Mg, Mg⁺, and Mg²⁺. A molecular device composed of GNF and Mg, GNF-Mg, was examined as a reversible hydrogen storage device. GNF-Mg²⁺ can efficiently store hydrogen molecules, whereas GNF-Mg⁺ releases H₂ molecules to the gas phase. Direct AIMD calculations showed that the reversible processes take place within 100 fs. These results strongly suggest that the GNF-Mg system has the potential to be used as a reversible H₂ adsorption–desorption device.

Thus, GNFs can take on a wide variety of reactivity and electronic states. In interstellar space, it provides an important reaction field for space molecules. In addition, GNFs show many characteristic properties in material chemistry. The development of new GNF materials is expected to continue in the future.