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][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][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]}[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.

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]}[14,15,16,17]. 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^[23], 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. 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. 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. 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.