Scandium Decoration of Boron Doped Porous Graphene for High-Capacity Hydrogen Storage

The hydrogen storage properties of the Scandium (Sc) atom modified Boron (B) doped porous graphene (PG) system were studied based on the density functional theory (DFT). For a single Sc atom, the most stable adsorption position on B-PG is the boron-carbon hexagon center after doping with the B atom. The corresponding adsorption energy of Sc atoms was −4.004 eV. Meanwhile, five H2 molecules could be adsorbed around a Sc atom with the average adsorption energy of −0.515 eV/H2. Analyzing the density of states (DOS) and the charge population of the system, the adsorption of H2 molecules in Sc-B/PG system is mainly attributed to an orbital interaction between H and Sc atoms. For the H2 adsorption, the Coulomb attraction between H2 molecules (negatively charged) and Sc atoms (positively charged) also played a critical role. The largest hydrogen storage capacity structure was two Sc atoms located at two sides of the boron-carbon hexagon center in the Sc-B/PG system. Notably, the theoretical hydrogen storage capacity was 9.13 wt.% with an average adsorption energy of −0.225 eV/H2. B doped PG prevents the Sc atom aggregating and improves the hydrogen storage effectively because it can increase the adsorption energy of the Sc atom and H2 molecule.


Introduction
The development of human society faces the severe challenge of environmental pollution, which is urgently needed to explore more ideal energy materials to meet the growing energy demand [1][2][3]. Hydrogen (H 2 ) is used as a promising energy carrier because of recycling, no pollution, high energy density and high calorific value [4][5][6]. Graphene is a two-dimensional material with a hexagonal honeycomb structure composed of sp2 hybrid orbits. Graphene-based materials possess large specific surface area, good adsorption kinetics, low density, high chemical stability and reversible hydrogen storage, which is a potential candidate in many areas, such as solid-state hydrogen storage, electronics and sensors [7][8][9][10][11][12][13][14]. However, due to a large surface inertness and weak binding ability to H 2 molecules, clean graphene is difficult to become a promising hydrogen storage material [15][16][17][18][19].
Recently, transition metal atoms [20,21] modified graphene has attracted researchers' attention since significantly increasing the adsorption energy of H 2 molecules. Faye et al. [22] found that Pd double-sided modified graphene could adsorb up to eight H 2 molecules using local density approximation (LDA) of Dmol3 software. The transition metal atoms Sc, Ti and V decorated on both sides of graphene could adsorb four H 2 molecules with an average adsorption energy of 0.300-0.500 eV/H 2 [23].
Yet the transition metal atom modified graphene is prone to aggregation, which reduces the adsorption site of H 2 and weakens the hydrogen storage performance of graphene. Investigations have shown that the introduction of impurity atoms or vacancies can prevent the agglomeration of Firstly, six structures of B doped PG were considered. The optimized structures and lattice parameters of 1~6 B-doped PG systems are shown in Table 1. The calculation results show that: As the number of doped B atoms increased, the formation of the doping system became larger and larger, and the energy barrier to be overcome by the doping increased, making doping difficult, which was consistent with Lu et al. [38]. Therefore, we only considered the case of doping one B atom. The optimized structure of a single B-doped PG system is shown in Table 1. The lattice constant was 7.57 Å, the B-H bond length was 1.19 Å, and the formation energy required for doping was 121.3 meV/atom. The lattice constant of 7.57 Å was significantly higher than that of clean porous graphene 7.49 Å [37], but it was consistent with the lattice constant of 7.57 Å obtained by Lu [38]. The increase in the lattice constant was due to the radius of the B atom being greater than the radius of the replaced C atom. The measured B-H bond length of 1.19 Å was completely consistent with that of Lu et al. [38]. The formation energy of the B-PG doping system was 121.30 meV/atom, which was also close to the result of 120.20 meV/atom [38], indicating that the calculation method and accuracy were feasible.
In order to study the effect of B atom doping on the performance of porous graphene, the density of states of a single B atom doped porous graphene system was calculated. The results are shown in Figure 1. It can be seen that there was an energy band passing near the Fermi surface after doping B atoms compared with the clean porous graphene density of states; the change of density of states near the Fermi surface of the doping system mainly came from the contribution of the 2p orbit of the B atom. In addition, the 2p orbit of the B atom overlapped with the porous graphene in the vicinity of the Fermi surface. We obtained the B-PG system band gap of 0.349 eV, which was much smaller than the undoped PG's band gap value of 2.399 eV. From Figure 1, in the interval of −3.0~−2.0 eV, the peak of PG shifted to the right due to the influence of the B atom 2p orbit. The doping system electrons were close to the Fermi level. This indicates that B atom doping increases the chemical activity of the PG system to some extent and can improve the hydrogen storage performance of the PG system.  [38]. The increase in the lattice constant was due to the radius of the B atom being greater than the radius of the replaced C atom. The measured B-H bond length of 1.19 Å was completely consistent with that of Lu et al. [38]. The formation energy of the B-PG doping system was 121.30 meV/atom, which was also close to the result of 120.20 meV/atom [38], indicating that the calculation method and accuracy were feasible.  [38]. The increase in the lattice constant was due to the radius of the B atom being greater than the radius of the replaced C atom. The measured B-H bond length of 1.19 Å was completely consistent with that of Lu et al. [38]. The formation energy of the B-PG doping system was 121.30 meV/atom, which was also close to the result of 120.20 meV/atom [38], indicating that the calculation method and accuracy were feasible.  [38]. The increase in the lattice constant was due to the radius of the B atom being greater than the radius of the replaced C atom. The measured B-H bond length of 1.19 Å was completely consistent with that of Lu et al. [38]. The formation energy of the B-PG doping system was 121.30 meV/atom, which was also close to the result of 120.20 meV/atom [38], indicating that the calculation method and accuracy were feasible.  [38]. The increase in the lattice constant was due to the radius of the B atom being greater than the radius of the replaced C atom. The measured B-H bond length of 1.19 Å was completely consistent with that of Lu et al. [38]. The formation energy of the B-PG doping system was 121.30 meV/atom, which was also close to the result of 120.20 meV/atom [38], indicating that the calculation method and accuracy were feasible.  [38]. The increase in the lattice constant was due to the radius of the B atom being greater than the radius of the replaced C atom. The measured B-H bond length of 1.19 Å was completely consistent with that of Lu et al. [38]. The formation energy of the B-PG doping system was 121.30 meV/atom, which was also close to the result of 120.20 meV/atom [38], indicating that the calculation method and accuracy were feasible.  [38]. The increase in the lattice constant was due to the radius of the B atom being greater than the radius of the replaced C atom. The measured B-H bond length of 1.19 Å was completely consistent with that of Lu et al. [38]. The formation energy of the B-PG doping system was 121.30 meV/atom, which was also close to the result of 120.20 meV/atom [38], indicating that the calculation method and accuracy were feasible. In order to study the effect of B atom doping on the performance of porous graphene, the density of states of a single B atom doped porous graphene system was calculated. The results are shown in Figure 1. It can be seen that there was an energy band passing near the Fermi surface after doping B atoms compared with the clean porous graphene density of states; the change of density of states near the Fermi surface of the doping system mainly came from the contribution of the 2p orbit of the B atom. In addition, the 2p orbit of the B atom overlapped with the porous graphene in the vicinity of the Fermi surface. We obtained the B-PG system band gap of 0.349 eV, which was much smaller than the undoped PG's band gap value of 2.399 eV. From Figure 1, in the interval of −3.0~−2.0 eV, the peak of PG shifted to the right due to the influence of the B atom 2p orbit. The doping system electrons were close to the Fermi level. This indicates that B atom doping increases the chemical activity of the PG system to some extent and can improve the hydrogen storage performance of the PG system.

Adsorption Structure of Single Sc Atom Modified B-PG
First, the adsorption of Sc atoms on porous graphene doped with a B atom was investigated. When only one Sc atom was modified, six different adsorption sites were considered. As shown in Table 1 on 1B/PG, adsorption sites were named 1, 2, 3, 4, 5, and 6, which represented the hole position of the C ring, C-C bridge, half C ring hole position, large hexagon hole position, C top position and B top position. Results indicated that position 1 was the most easily adsorbed position of a single Sc atom on B-PG, which was similar to the situation of the undoped-PG adsorbing Sc atom [42]. The optimized geometry is shown in Figure 2a. The Sc atom was located at the central hole of the Boron carbon six-membered ring and was slightly deviated. Simultaneously, the B-PG plane was slightly deformed, and the adsorption energy of the Sc atom on the B-PG was −4.004 eV. In our previous study, the adsorption energy of a single Sc atom on clean PG was −2.143 eV [42], which was much smaller than that of single Sc on B-PG of −4.004 eV. It can be seen that B doping can enhance the adsorption activity of the system; compared with pure porous graphene, the Sc atom was closer to the substrate and therefore had greater binding energy on the B-doped PG.

Adsorption Structure of Single Sc Atom Modified B-PG
First, the adsorption of Sc atoms on porous graphene doped with a B atom was investigated. When only one Sc atom was modified, six different adsorption sites were considered. As shown in Table 1 on 1B/PG, adsorption sites were named 1, 2, 3, 4, 5, and 6, which represented the hole position of the C ring, C-C bridge, half C ring hole position, large hexagon hole position, C top position and B top position. Results indicated that position 1 was the most easily adsorbed position of a single Sc atom on B-PG, which was similar to the situation of the undoped-PG adsorbing Sc atom [42]. The optimized geometry is shown in Figure 2a. The Sc atom was located at the central hole of the Boron carbon six-membered ring and was slightly deviated. Simultaneously, the B-PG plane was slightly deformed, and the adsorption energy of the Sc atom on the B-PG was −4.004 eV. In our previous study, the adsorption energy of a single Sc atom on clean PG was −2.143 eV [42], which was much smaller than that of single Sc on B-PG of −4.004 eV. It can be seen that B doping can enhance the adsorption activity of the system; compared with pure porous graphene, the Sc atom was closer to the substrate and therefore had greater binding energy on the B-doped PG.  Figure 3 shows the partial densities of states (PDOS) of the Sc-B/PG system and the density of states of the clean PG system. It can be seen that the 2p orbit of the B atom and the 3d orbit of the Sc atom overlaps in the interval of −2.0~−1.0 eV, indicating that there was a strong interaction between the B atom and Sc atom. The 2p orbit of the C atom overlaps with the 3d orbit of the Sc atom in the range of −3.0~−1.0 eV. In the interval of −1.0 to 0.0 eV, the peaks of the orbits of C and Sc atoms also overlap, meaning that the C and Sc atoms have an existing strong interaction. In addition, comparing the total density of states of the Sc-B/PG system with the clean PG system, we can see that the 3d orbit of the Sc atom significantly changes the properties of the clean porous graphene near the Fermi surface; the peak of the Sc-B/PG system shifts to the left; and the electrons are close to the Fermi level, the system is more stable after doping the Sc and B atom.  Figure 3 shows the partial densities of states (PDOS) of the Sc-B/PG system and the density of states of the clean PG system. It can be seen that the 2p orbit of the B atom and the 3d orbit of the Sc atom overlaps in the interval of −2.0~−1.0 eV, indicating that there was a strong interaction between the B atom and Sc atom. The 2p orbit of the C atom overlaps with the 3d orbit of the Sc atom in the range of −3.0~−1.0 eV. In the interval of −1.0 to 0.0 eV, the peaks of the orbits of C and Sc atoms also overlap, meaning that the C and Sc atoms have an existing strong interaction. In addition, comparing the total density of states of the Sc-B/PG system with the clean PG system, we can see that the 3d orbit of the Sc atom significantly changes the properties of the clean porous graphene near the Fermi surface; the peak of the Sc-B/PG system shifts to the left; and the electrons are close to the Fermi level, the system is more stable after doping the Sc and B atom.

The Adsorption of H2 on a Single Sc Atom Modified B-PG System
A single Sc-modified B-doped porous graphene system can adsorb 5 H2 molecules, and the optimized structures are given in Figure 4. Moreover, Table 2 lists the adsorption and average adsorption energy of H2, the distance between Sc atom and H2 molecules, and the distance between the Sc and C atom on the B-PG. A single H2 molecule has multiple adsorption sites on Sc-modified B-PG, including the C-C bridge position, the C-H bridge position, the C atom top position, and the Sc atom top position. It has been discovered that the most stable adsorption position of the first H2 molecule is the top position of the C atom. This H2 molecule has an adsorption energy of −0.677 eV. Meanwhile, the H-H bond was stretched to 0.868 Å. To further explore the hydrogen storage behavior of the system, H2 molecules were continuously added to the system. Table 2 indicates that H2 molecules' binding energies fluctuated with the number of adsorbed H2 molecules. The third H2 molecule adsorbed above the B-H bond and was slightly away from the hexagonal ring, so the adsorption energy decreased suddenly. However, the trend of was a complete contrast to the trend of the H2 molecule adsorption energy. That is, the smaller the distance between Sc and the B-PG substrate, the greater the adsorption energy of hydrogen, and vice versa because the addition of hydrogen affects the position of Sc, and the position of Sc in turn affects the adsorption of hydrogen. The system eventually reaches a steady state through this mutually adjusted process. As a result of the symmetry of the H2 molecular bonding configuration, all H2 molecules were symmetrically distributed on every side of the Sc atom when the fourth H2 was adsorbed. The distance from the H2 molecule to the Sc atom always increased, but when the fourth H2 molecule adsorbed, the suddenly decreased. At this time, the Sc atom was located at the center of the carbon ring doped by the B atom. Additionally, the first four H2 molecules were located on the same horizontal plane, which was parallel to the PG layer. Due to the limited space around the Sc atom and the repulsion between the adsorbed H2 molecules, the fifth H2 molecule moved to the upper layer after relaxation in Figure 4e. Therefore, the fifth H2 molecule had a H-H bond length of 0.762 Å, and it had a minimum adsorption energy of −0.187 eV, which was still bigger than −0.093 eV of the Sc-PG system without B doped [42]. The bond length of the adsorbed H2 molecule was in the range of 0.762~ 0.831 Å, and no dissociation of the H2 molecule was found. Therefore, the B doped PG decorated by Sc was more suitable for hydrogen storage at room temperature, and the practical application prospect was greater. The PG system modified by a single Sc atom can adsorb up to 5 H2 molecules due to the doping of B atom. In a single Sc-modified B-doped porous graphene system,

The Adsorption of H 2 on a Single Sc Atom Modified B-PG System
A single Sc-modified B-doped porous graphene system can adsorb 5 H 2 molecules, and the optimized structures are given in Figure 4. Moreover, Table 2 lists the adsorption and average adsorption energy of H 2 , the distance between Sc atom and H 2 molecules, and the distance between the Sc and C atom on the B-PG. A single H 2 molecule has multiple adsorption sites on Sc-modified B-PG, including the C-C bridge position, the C-H bridge position, the C atom top position, and the Sc atom top position. It has been discovered that the most stable adsorption position of the first H 2 molecule is the top position of the C atom. This H 2 molecule has an adsorption energy of −0.677 eV. Meanwhile, the H-H bond was stretched to 0.868 Å. To further explore the hydrogen storage behavior of the system, H 2 molecules were continuously added to the system. Table 2 indicates that H 2 molecules' binding energies fluctuated with the number of adsorbed H 2 molecules. The third H 2 molecule adsorbed above the B-H bond and was slightly away from the hexagonal ring, so the adsorption energy decreased suddenly. However, the trend of d Sc−C was a complete contrast to the trend of the H 2 molecule adsorption energy. That is, the smaller the distance between Sc and the B-PG substrate, the greater the adsorption energy of hydrogen, and vice versa because the addition of hydrogen affects the position of Sc, and the position of Sc in turn affects the adsorption of hydrogen. The system eventually reaches a steady state through this mutually adjusted process. As a result of the symmetry of the H 2 molecular bonding configuration, all H 2 molecules were symmetrically distributed on every side of the Sc atom when the fourth H 2 was adsorbed. The distance from the H 2 molecule to the Sc atom always increased, but when the fourth H 2 molecule adsorbed, the d Sc−H 2 suddenly decreased. At this time, the Sc atom was located at the center of the carbon ring doped by the B atom. Additionally, the first four H 2 molecules were located on the same horizontal plane, which was parallel to the PG layer. Due to the limited space around the Sc atom and the repulsion between the adsorbed H 2 molecules, the fifth H 2 molecule moved to the upper layer after relaxation in Figure 4e. Therefore, the fifth H 2 molecule had a H-H bond length of 0.762 Å, and it had a minimum adsorption energy of −0.187 eV, which was still bigger than −0.093 eV of the Sc-PG system without B doped [42]. The bond length of the adsorbed H 2 molecule was in the range of 0.762~0.831 Å, and no dissociation of the H 2 molecule was found. Therefore, the B doped PG decorated by Sc was more suitable for hydrogen storage at room temperature, and the practical application prospect was greater. The PG system modified by a single Sc atom can adsorb up to 5 H 2 molecules due to the doping of B atom. In a single Sc-modified B-doped porous graphene system, the average adsorption energy (−0.515 eV/H 2 ) and the hydrogen storage capacity (4.91 wt.%) are better than that of a Ti-PG system (−0.486 eV) [43].   Considering the interaction among the Sc atom with the adsorbed H2 molecule, we analyzed the partial densities of states (PDOS) of the H2 molecule and the Sc atom in Figure 5. It can be seen that the band broadening occurred in the H2 molecule from −11.0 to −8.0 eV. In the interval of −9.5~−7.5 eV, the 1s orbit of H2 overlapped with the 3d orbit of Sc, indicating that the 1s orbit of H2 and the 3d orbit of Sc had a existing interaction. When 1~4 H2 molecules were adsorbed on the Sc-decorated B-PG system, it could be seen that the peak of the H2 1s orbit overlapped with the peak of the Sc 3d orbit in the range of −3.0~0.0 eV, which was in accordance with the strong adsorption energy of the H2 molecules (except the fifth hydrogen).  Considering the interaction among the Sc atom with the adsorbed H 2 molecule, we analyzed the partial densities of states (PDOS) of the H 2 molecule and the Sc atom in Figure 5. It can be seen that the band broadening occurred in the H 2 molecule from −11.0 to −8.0 eV. In the interval of −9.5~−7.5 eV, the 1s orbit of H 2 overlapped with the 3d orbit of Sc, indicating that the 1s orbit of H 2 and the 3d orbit of Sc had a existing interaction. When 1~4 H 2 molecules were adsorbed on the Sc-decorated B-PG system, it could be seen that the peak of the H 2 1s orbit overlapped with the peak of the Sc 3d orbit in the range of −3.0~0.0 eV, which was in accordance with the strong adsorption energy of the H 2 molecules (except the fifth hydrogen).
To further investigate the combined effects of the B atom and Sc atom on H 2 molecule adsorption, the PDOS of one H 2 molecule adsorbed in a single Sc-modified B-PG system was analyzed (as shown in Figure 6). From 1.0 to 0.0 eV, there were overlapping peaks between B 2p orbit, Sc 3d orbit and 1s orbit of the H 2 molecule, which means that B and Sc both played a role in H 2 adsorption. In addition, it can be observed that the 2p orbit of B atoms overlapped with the 3d orbit of Sc atoms in most energy intervals, indicating that there was a strong interaction between B and Sc, which further explained why Sc had a higher binding energy in the B doping system. To further investigate the combined effects of the B atom and Sc atom on H2 molecule adsorption, the PDOS of one H2 molecule adsorbed in a single Sc-modified B-PG system was analyzed (as shown in Figure 6). From 1.0 to 0.0 eV, there were overlapping peaks between B 2p orbit, Sc 3d orbit and 1s orbit of the H2 molecule, which means that B and Sc both played a role in H2 adsorption. In addition, it can be observed that the 2p orbit of B atoms overlapped with the 3d orbit of Sc atoms in most energy intervals, indicating that there was a strong interaction between B and Sc, which further explained why Sc had a higher binding energy in the B doping system. The adsorption mechanism could be better understood by analyzing the charge density difference. Figure 7 shows the electronic charge density difference of the system after H2 molecules adsorbed. The blue and yellow isosurfaces represented the electron accumulation and electron loss regions, respectively, and the isosurface unit was 0.007 e/Å . It can be observed from Figure 7a,b that the yellow electron-depleting region was concentrated between the Sc atom and the B-PG, meaning that there was a large amount of charge transfer from the Sc atom to the B-PG. We also analyzed the Mulliken charge population before and after the adsorption of the Sc atom in the B-PG system. We found that the B atom 2p orbit and the C atom had an accumulation of electrons, while the 4s orbit of Sc lost electrons by 1.5 e. Combined with the PDOS of Sc, B and C atom in Figure 3, it was found  To further investigate the combined effects of the B atom and Sc atom on H2 molecule adsorption, the PDOS of one H2 molecule adsorbed in a single Sc-modified B-PG system was analyzed (as shown in Figure 6). From 1.0 to 0.0 eV, there were overlapping peaks between B 2p orbit, Sc 3d orbit and 1s orbit of the H2 molecule, which means that B and Sc both played a role in H2 adsorption. In addition, it can be observed that the 2p orbit of B atoms overlapped with the 3d orbit of Sc atoms in most energy intervals, indicating that there was a strong interaction between B and Sc, which further explained why Sc had a higher binding energy in the B doping system. The adsorption mechanism could be better understood by analyzing the charge density difference. Figure 7 shows the electronic charge density difference of the system after H2 molecules adsorbed. The blue and yellow isosurfaces represented the electron accumulation and electron loss regions, respectively, and the isosurface unit was 0.007 e/Å . It can be observed from Figure 7a,b that the yellow electron-depleting region was concentrated between the Sc atom and the B-PG, meaning that there was a large amount of charge transfer from the Sc atom to the B-PG. We also analyzed the Mulliken charge population before and after the adsorption of the Sc atom in the B-PG system. We found that the B atom 2p orbit and the C atom had an accumulation of electrons, while the 4s orbit of Sc lost electrons by 1.5 e. Combined with the PDOS of Sc, B and C atom in Figure 3, it was found The adsorption mechanism could be better understood by analyzing the charge density difference. Figure 7 shows the electronic charge density difference of the system after H 2 molecules adsorbed. The blue and yellow isosurfaces represented the electron accumulation and electron loss regions, respectively, and the isosurface unit was 0.007 e/A 3 . It can be observed from Figure 7a,b that the yellow electron-depleting region was concentrated between the Sc atom and the B-PG, meaning that there was a large amount of charge transfer from the Sc atom to the B-PG. We also analyzed the Mulliken charge population before and after the adsorption of the Sc atom in the B-PG system. We found that the B atom 2p orbit and the C atom had an accumulation of electrons, while the 4s orbit of Sc lost electrons by 1.5 e. Combined with the PDOS of Sc, B and C atom in Figure 3, it was found that the 4s orbit of Sc transferred some electrons to the 2p orbit of B and C, respectively. The charge population indicated that the 3d orbit of Sc obtained 0.45 e electrons, which meant that the B-PG transferred electrons to the Sc atom. On the whole, the Sc carries a positive charge, and the B-PG layer carries a negative charge. Therefore, an electric field is formed between the Sc atom and the B-PG. The adsorption energy of Sc atoms on B-PG was large due to the strong electrostatic Coulomb interaction between Sc and B-PG, and the orbital interaction between Sc, B and C atoms. Since the Sc atom has a positive charge, this will attract the negative charge in H 2 and accumulate near the metal. It can also be seen from Figure 7 that the blue electron region was concentrated between H 2 and Sc. Near the side of the Sc atom, polarization occurred in the perpendicular direction of the H 2 molecule. It has been indicated that the H 2 molecule undergoes charge redistribution due to the electrostatic field between the Sc atom and the B-PG. Combined with the Mulliken charge population of the 1Sc-B-PG system it adsorbed two H 2 molecules, the H atoms in the polarized H 2 molecule were negatively charged at −0.17 e and −0.16 e. Conversely, the Sc atom was positively charged at 1.94 e. Therefore, there was a Coulomb attraction between the H 2 molecule and the Sc atom. The C atom also had a partial charge transfer on B-PG, indicating that these C atoms also play a role on the H 2 molecule adsorption. Consequently, the adsorption of H 2 molecules in the Sc-modified B-PG system is mainly attributed to the orbital interaction between H and Sc atoms. Furthermore, the Coulomb attraction between H 2 molecules (negatively charged) and Sc atoms (positively charged) strengthen the adsorption of H 2 molecules.
is mainly attributed to the orbital interaction between H and Sc atoms. Furthermore, the Coulomb attraction between H2 molecules (negatively charged) and Sc atoms (positively charged) strengthen the adsorption of H2 molecules.
To better understand the bonding environment of all B-H bonds in this structure after adsorption, we calculated a Bond Population of B-H bond and Mulliken charge Population of B, H, and Sc atoms in B-PG, Sc-B/PG and H2 adsorbed Sc-B/PG system, where H was the H atom in the first to fifth hydrogen molecules adsorbed. As shown in Table 3, the B-H population gradually increased as the hydrogen molecules continued to adsorb. After Sc atom modification, the positive charge of B atom decreased rapidly, indicating that Sc was stable on B-PG. Thereafter, the positive charge of the B atom fluctuated with the adsorption of hydrogen. The positive charge of Sc in the hydrogen storage process had been increasing. After the first H2 molecule was adsorbed by the Sc-B/PG structure, the Sc atom was charged to 1.72 e, which is greater than that of 1.56 e in the undoped B atom system [42]. It was shown that after doping the B atom, the catalytic effect of Sc atoms in hydrogen storage was more obvious. As the hydrogen molecules continuously adsorbed, the H atom in H2 molecules started to be negatively charged and the charge amount gradually decreased. The H atom of the first H2 molecule after doping B atoms was charged −0.17 e, and its absolute value was greater than that of −0.13 e in the undoped system [42]. This indicated that doping B atom enhanced the interaction between H2, Sc atoms and PG, which was more conducive to hydrogen storage. To better understand the bonding environment of all B-H bonds in this structure after adsorption, we calculated a Bond Population of B-H bond and Mulliken charge Population of B, H, and Sc atoms in B-PG, Sc-B/PG and H 2 adsorbed Sc-B/PG system, where H was the H atom in the first to fifth hydrogen molecules adsorbed. As shown in Table 3, the B-H population gradually increased as the hydrogen molecules continued to adsorb. After Sc atom modification, the positive charge of B atom decreased rapidly, indicating that Sc was stable on B-PG. Thereafter, the positive charge of the B atom fluctuated with the adsorption of hydrogen. The positive charge of Sc in the hydrogen storage process had been increasing. After the first H 2 molecule was adsorbed by the Sc-B/PG structure, the Sc atom was charged to 1.72 e, which is greater than that of 1.56 e in the undoped B atom system [42]. It was shown that after doping the B atom, the catalytic effect of Sc atoms in hydrogen storage was more obvious. As the hydrogen molecules continuously adsorbed, the H atom in H 2 molecules started to be negatively charged and the charge amount gradually decreased. The H atom of the first H 2 molecule after doping B atoms was charged −0.17 e, and its absolute value was greater than that of −0.13 e in the undoped system [42]. This indicated that doping B atom enhanced the interaction between H 2 , Sc atoms and PG, which was more conducive to hydrogen storage. Transition metal atoms are prone to aggregation on the surface of graphene, resulting in a decrease in the free surface area of the graphene. Metal aggregation is mainly attributed to the high cohesive energy of the atoms [44][45][46]. The cohesive energy of the Sc atom is 3.900 eV [47], each Sc atom is equivalent to an H 2 adsorption site. To further increase the amount of hydrogen storage, a second Sc atom is added to the same side of the system. Figure 2b shows one of the most stable geometries for adsorbing two Sc atoms on B-PG. It can be seen that the second Sc atom tended to adsorb at the center of the other carbon ring instead of agglomeration with the first Sc atom, which was attributed to the Coulomb repulsion between the two Sc atoms (the two Sc atoms have a positive charge of 0.90 e, 0.97 e, respectively), and there was a strong interaction between the Sc atom and the B-PG. The average binding energy of the two Sc atoms on B-PG was −4.069 eV, and its absolute value was greater than the cohesive energy of the Sc atom, which was 3.900 eV. This means that the adsorption structure of the two Sc atoms on PG is more stable than that of the single Sc atom on B-PG.
The structure of two Sc atoms on both sides of B-PG was also studied to open up enough space to adsorb H 2 molecules. Each transition metal atom is an active adsorption site. The double-sided modification of B-PG by the transition metal atom can raise the hydrogen storage area. On account of Figure 2a, the second Sc atom had four adsorption sites on the opposite side of the B-PG, including two carbon ring centers, C-C bridge site, and half C ring pore sites on the opposite side. The most stable adsorption structure was obtained as shown in Figure 2c. The average binding energy of two Sc atoms was −4.085 eV, larger than that of two Sc atoms in the clean PG system. Therefore, the presence of B atoms in PG prevented the Sc atoms from aggregating. In addition, it can be seen from Figure 2a,b that the B-PG system underwent slight deformation after Sc atoms were adsorbed. However, Figure 2c did not undergo any deformation, which was related to the symmetric distribution of Sc atoms.

Hydrogen Storage of two Sc Atoms Modified B-PG
The B-PG system with two Sc atoms modified on one side can adsorb 10 H 2 molecules. The optimized geometry structure is shown in Figure 8. The average adsorption energy of the B-PG system was about −0.339 eV/H 2 with the hydrogen storage capacity (7.73 wt.%). Because the adsorption energy of two Sc atoms on B-PG was larger than their cohesion energy, the distance between them was close without bonding.  Figure 2c is a stable structure of two Sc atoms modified B-PG on both sides, and the structure after hydrogen storage is shown in Figure 9. The distance between the two Sc atoms was large enough to prevent the aggregation where double-sided modified B-PG was concerned. There was no deformation that occurred in the B doped porous graphene surface, which was different from the distortion in the single Sc modified B-PG after hydrogen storage. The first eight H2 molecules were symmetrically distributed, but the ninth to twelfth H2 molecules gradually moved away from the Sc atoms and tended to adsorb to the top of the C-H bond of adjacent carbon rings. Therefore, the average adsorption energy of H2 decreased. Two Sc double-sided modified B-PG systems can adsorb up to 12 H2 molecules with an average adsorption energy of −0.225 eV/H2. According to the standards of the U.S. Department of Energy and the International Energy Agency, the hydrogen storage capacity of ideal hydrogen storage materials should be greater than 5.50 wt.%, and the adsorption energy between H2 molecules and materials should be from 0.200 to 0.700 eV [48,49]. Therefore, the average adsorption energy of the H2 molecule was also in the range of reversible hydrogen storage. The corresponding theoretical hydrogen storage capacity is 9.13 wt.%, which is higher than the storage hydrogen content of the Sc-PG system 9.09 wt.% [42] and is greater than the amount of hydrogen storage of the Y-PG system 7.87 wt.% [36]. The interaction between the H2 molecule, the Sc atom and the B-PG system in the two Sc atoms modified the B-PG system and was similar to the single Sc atom modification B-PG system, and is not described here. By comparing Figure 4e, Figure 8 and Figure 9f, it can be seen that the single Sc atom modified B-PG and the two Sc atoms single-sided modified B-PG adsorbed H2 molecules were layered. However, there was no hydrogen stratification with two Sc double-sided decorated B-PG. Moreover, the latter two H2 molecules adsorbed above the C-H bond of another carbon six-membered ring. Therefore, the hydrogen storage spaces were larger in the Sc double-sided modification B-PG system than the Sc single-sided modification. In addition, the H2 molecules around a single Sc were parallel to the B-PG plane. When the two Sc atoms were modified on the same side, the H2 molecule changed from parallel to vertical, but they were not completely perpendicular to the B-PG surface due to the interaction. The perpendicular adsorption of H2 molecules is more likely to occur when two Sc atoms are modified at double sides, which is due to the interaction of H2 molecules on both sides of the B-PG. In summary, the two Sc located in the same boron-carbon ring position on the opposite side of B-PG is the most suitable structure for hydrogen storage, and Sc modified B-PG is a promising hydrogen storage material.  Figure 2c is a stable structure of two Sc atoms modified B-PG on both sides, and the structure after hydrogen storage is shown in Figure 9. The distance between the two Sc atoms was large enough to prevent the aggregation where double-sided modified B-PG was concerned. There was no deformation that occurred in the B doped porous graphene surface, which was different from the distortion in the single Sc modified B-PG after hydrogen storage. The first eight H 2 molecules were symmetrically distributed, but the ninth to twelfth H 2 molecules gradually moved away from the Sc atoms and tended to adsorb to the top of the C-H bond of adjacent carbon rings. Therefore, the average adsorption energy of H 2 decreased. Two Sc double-sided modified B-PG systems can adsorb up to 12 H 2 molecules with an average adsorption energy of −0.225 eV/H 2 . According to the standards of the U.S. Department of Energy and the International Energy Agency, the hydrogen storage capacity of ideal hydrogen storage materials should be greater than 5.50 wt.%, and the adsorption energy between H 2 molecules and materials should be from 0.200 to 0.700 eV [48,49]. Therefore, the average adsorption energy of the H 2 molecule was also in the range of reversible hydrogen storage. The corresponding theoretical hydrogen storage capacity is 9.13 wt.%, which is higher than the storage hydrogen content of the Sc-PG system 9.09 wt.% [42] and is greater than the amount of hydrogen storage of the Y-PG system 7.87 wt.% [36]. The interaction between the H 2 molecule, the Sc atom and the B-PG system in the two Sc atoms modified the B-PG system and was similar to the single Sc atom modification B-PG system, and is not described here. By comparing Figures 4e, 8 and 9f, it can be seen that the single Sc atom modified B-PG and the two Sc atoms single-sided modified B-PG adsorbed H 2 molecules were layered. However, there was no hydrogen stratification with two Sc double-sided decorated B-PG. Moreover, the latter two H 2 molecules adsorbed above the C-H bond of another carbon six-membered ring. Therefore, the hydrogen storage spaces were larger in the Sc double-sided modification B-PG system than the Sc single-sided modification. In addition, the H 2 molecules around a single Sc were parallel to the B-PG plane. When the two Sc atoms were modified on the same side, the H 2 molecule changed from parallel to vertical, but they were not completely perpendicular to the B-PG surface due to the interaction. The perpendicular adsorption of H 2 molecules is more likely to occur when two Sc atoms are modified at double sides, which is due to the interaction of H 2 molecules on both sides of the B-PG. In summary, the two Sc located in the same boron-carbon ring position on the opposite side of B-PG is the most suitable structure for hydrogen storage, and Sc modified B-PG is a promising hydrogen storage material.

Conclusion
We unambiguously investigated the hydrogen storage of the B atom doped Sc decorated PG. With an average adsorption energy (−0.515 eV/H2), the most stable adsorption position could adsorb five H2 molecules on the center of the boron-carbon ring for a single Sc atom system. By adding a second Sc atom to another side of the PG system, the hydrogen storage capacity effectively could be improved. When the two Sc atoms were located at both sides of the central boron-carbon hexagon, the theoretical hydrogen storage capacity could reach the maximum (~9.13 wt.%), which could . Optimized geometries of two Sc double-sided modified B-PG systems with two H2 molecules (a), four H2 molecules (b), six H2 molecules (c), eight H2 molecules (d), ten H2 molecules (e), and twelve H2 molecules (f) adsorbed.

Conclusions
We unambiguously investigated the hydrogen storage of the B atom doped Sc decorated PG. With an average adsorption energy (−0.515 eV/H 2 ), the most stable adsorption position could adsorb five H 2 molecules on the center of the boron-carbon ring for a single Sc atom system. By adding a second Sc atom to another side of the PG system, the hydrogen storage capacity effectively could be improved.
When the two Sc atoms were located at both sides of the central boron-carbon hexagon, the theoretical hydrogen storage capacity could reach the maximum (~9.13 wt.%), which could adsorb twelve H 2 molecules. At the same time, the two Sc atoms structure was the most suitable hydrogen storage for the Sc-B/PG system, possessing the average adsorption energy (−0.225 eV/H 2 ). Furthermore, the adsorption of these H 2 molecules in the Sc-modified B/PG system was also responsible for two aspects via the analysis of DOS and charge population: (i) The orbital interaction between H and Sc atoms; (ii) the Coulomb attraction between H 2 molecules (negatively charge) and Sc atoms (positively charge). The H 2 molecules were negatively charged due to polarization of the electrostatic field between Sc and B-PG. Therefore, Sc-modified B-doped porous graphene is expected to be used in the field of hydrogen storage.
Author Contributions: We would like to give great thanks to Y.C. because he designed the project. J.W. performed the calculations and prepared the manuscript, C.Z. revised the paper, L.Y. and M.Z. analyzed the data, and all authors discussed the results and commented on the manuscript.