First-principles study on methane storage properties of porous graphene modified with Mn

Porous graphene (PG) has a promising future for gas storage owing to its unique pore characteristics and large specific surface area. The adsorption properties of PG and Mn atoms decorated PG (Mn-PG) for methane (CH4) molecules have been studied based on the first-principles density functional theory. It is discovered that the optimum adsorption position of CH4 on PG is the carbon ring pore, and the adsorption energy is − 0.174 eV. The optimal position of the PG system decorated by single Mn atom is the central hole of the carbon ring, and the optimal position of the two Mn atoms is that Mn atoms are, respectively, located at different carbon ring holes on the opposite side of PG, with an average binding energy of − 4.101 eV. The modification of the Mn atom enhances the electronegativity of the PG substrate and forms a negative electrical center at the carbon ring, which facilitates the enhancement of the adsorption performance of the CH4 molecules that are positively charged with the surface. The CH4 molecule, close to Mn atom shows negative charge, and its strong electrostatic interaction with positively charged Mn atom is dominant, resulting in higher adsorption energy. The surface of CH4 molecule far away from the Mn atom is positively charged, the weak electrostatic interaction with the negatively charged PG substrate and the Van der Waals interaction between CH4 molecules are dominant, and the adsorption energy is low. The CH4 molecules are adsorbed on the PG surface through the electrostatic interaction with Mn atoms and PG substrate as well as the intermolecular force of CH4 molecules. The Mn-PG system is single-sided adsorption 6 CH4 molecules, and the average adsorption energy is − 0.345 eV. When two Mn atom modification PG, 12 CH4 molecules can be adsorbed on both sides, and the average adsorption energy is − 0.338 eV, the adsorption capacity is up to 38.43 wt.%.


Introduction
With the development of science and technology, people have been exploring the earth deeply; at the same time, it also brings various problems such as energy depletion and environmental pollution. The combustion of coal, oil, and other fossil fuels will produce CO 2 and a large number of harmful gases [1]. The main component of natural gas is methane (CH 4 ) [2]. Compared with other fossil fuels, CH 4 combustion produces less CO 2 , and the energy produced by a CH 4 molecule is 3.1 times that of a hydrogen (H 2 ) molecule. Natural gas resources are rich globally, and it is an important transition fuel to achieve low-carbon energy [3]. In addition, CH 4 is a greenhouse gas, escaping into the atmosphere will aggravate the greenhouse effect, accounting for about 20% of global warming [4]. The adsorption and storage of CH 4 gas is a hot topic in scientific research, which is an effective means to solve the greenhouse effect and low-carbon alternative energy. Therefore, it is necessary to seek a kind of efficient, safe, and large storage capacity of CH 4 storage materials. CH 4 storage materials are usually characterized by porous structures, such as zeolite [5], molecular sieves [6], activated carbon [7], covalent organic framework materials Qiuyu Zhao and Yingjie Zhao are co-first authors. (COFs) [8], metal-organic framework materials (MOFs) [9,10] are common gas storage materials. The storage capacity of CH 4 is an obvious linear relationship with the surface area of the molecular sieve and other materials, the larger the surface area, the more adsorption capacity, but the upper limit is low [11]. COFs, MOFs porous material surface area, aperture, pore volume have an important impact on the gas storage capacity of CH 4 [12]. Studies have shown a new synthetic COFs material (COP-150) at 273 K, 100-5 bar cycle pressure of CH 4 working capacity reached 0.625 g/g (294 cm 3 stp /cm 3 ), and the flexibility of the material provides fast desorption of CH 4 , and hydrophobicity and the nature of the covalently bonded framework allows the material to tolerate harsh conditions [13]. MOFs materials have also achieved much progress as one of the best materials for CH 4 storage performance. The CH 4 adsorption capacity of various MOFs can reach 236-263 cm 3 stp /cm 3 , under the circulating pressure of 298 K and 100-5 bar [14][15][16], higher pressure can increase the adsorption capacity of CH 4 to 324 cm 3 stp /cm 3 (298 K, 250 bar) [17]. However, whether the CH 4 working capacity can reach the storage target of the U.S. Department of Energy (DOE) (0.5 g/g (low pressure) and 350 cm 3 stp / cm 3 (65-5 bar) are more important in practical applications, currently CH 4 working capacity is 200-208 cm 3 stp / cm 3 at 298 K and 80-5 bar, which still does not meet the standard of the U.S. DOE [14,16,18]. Increased pressure such as Nu-1501-Al (270 K, 100-5 bar) working capacity reached 0.60 g/g (238 cm 3 stp /cm 3 ) [15], and ST-2 at 298 K, 200-5 bar working capacity is 0.567 g/g (289 cm 3 stp /cm 3 ) [17]. Although the weight storage capacity of some new materials had reached (0.5 g/g) the target, the volume capacity is still not achieved, or a large amount of storage is implemented under high-pressure conditions, the actual application still remain difficult.
Graphene is a two-dimensional material, and its unique nanostructure gives it excellent thermal conductivity [19], mechanical [20], optical [21], and electrical properties [22]. It is a strong competitor in the fields of sensors, composites, and energy storage [23], as well as a potential medium for CH 4 storage. The adsorption energy of CH 4 on graphene increases as the number of graphene layers increases, with a maximum of − 0.267 eV [24], indicating that the adsorption of CH 4 on intrinsic graphene is weak. Regulating the electronic structure of graphene through defects, doping or metal element modification can improve the adsorption performance of gas [25][26][27]. Calculations show that the adsorption energy of Ag modified graphene can reach − 0.399 eV in the presence of ambient O 2 [28], and that of Pt-modified graphene can reach − 0.485 eV [29], which is much higher than that on intrinsic graphene. Compared with intrinsic graphene, CH 4 has higher adsorption energy, more charge transfer, smaller adsorption distance, and stronger interaction on metal-modified graphene. However, owing to the small pore defects of graphene structure and limited adsorption space, the overall adsorption capacity is low.
Porous graphene is a two-dimensional structure derived from graphene. There are nanopores with adjustable size and shape on the structure, and it has a porous structure which is a common feature of energy storage materials. It has been revealed that porous graphene with different geometrical configurations will exhibit different properties of semiconductor, semi-metal, or metal [30]. The existence of defects makes it have a larger specific surface area and more active sites compared with intrinsic graphene, which creates good conditions for gas adsorption and storage [31][32][33]. Bieri et al. [34] successfully prepared a porous graphene (PG) composed of two C 6 H 3 rings through experiments, with the pore spacing of 7.400 Å. The mass of the porous graphene in the same size crystal cell is about two-thirds that of the intrinsic graphene, and it has a larger specific surface area, showing good gas adsorption performance. H 2 storage performance of PG modified with transition metal shows that H 2 is physically adsorbed on the substrate surface in molecular form. The main mechanism is coulomb interaction between H 2 and metal atoms and Van der Waals interaction between the polarization charge of H 2 and PG. The average adsorption energy is -0.2 to -0.6 eV/CH 4 , and the adsorption capacity can reach 9.09 wt.% [35,36], which is higher than the U.S. DOE technical targets for onboard hydrogen storage for light-duty vehicles [37,38], so we chose PG as the substrate to study the adsorption properties of CH 4 . The adsorption performance of CH 4 was tested by studying the graphene and graphdiyne modified by alkali metals, alkaline earth metals, and transition metals. The results showed that the adsorption energy of CH 4 was larger (− 0.861 eV, − 0.751 eV) when Mn-modified intrinsic graphene (Mn-GR) and N-doped graphdiyne (Mn-N-GDY), and the adsorption capacity was greatly improved, meanwhile, the geometric structure of the base remains stable [39,40]. The adsorption capacity of 2Mn-GR can reach 32.93 wt.%, which is far behind the storage target of U.S. DOE [39]. To improve CH 4 adsorption capacity, this paper studied the CH 4 adsorption performance of PG structure and Mn-modified PG structure (Mn-PG), hoping to provide theoretical support for the research and development of safe and efficient CH 4 storage.

Calculation methods and models
The calculation used in this study employs the CASTEP module under Material Studio 8.0 software [41], based on the first-principles pseudopotential plane-wave method considering density functional theory. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional in the generalized gradient approximation (GGA) form was selected [42], and the super-soft pseudopotential was determined to describe the interaction between electrons and ions. Because the GGA functional may underestimate the weak adsorption energy of CH 4 molecules on the PG surface, the Van der Waals correction (DFT-D method) was used in the calculation [43]. All the atoms in the calculation were completely relaxed, and the convergence criterion of structure optimization was that the force of each atom was less than 0.03 eV/Å, the energy difference was less than 1.0 × 10 -6 eV/atom, and the self-consistent field convergence threshold was 1.0 × 10 -6 eV/atom. By testing the cut-off energy and K-point sampling of the system, considering the calculation accuracy and calculation cost, the cut-off energy was selected as 400 eV, and the K-point sampling in the Brillouin zone was 5 × 5 × 1. The calculation of the porous graphene crystal cell satisfies the periodic boundary conditions, and the vacuum layer was 25 Å to avoid interlayer interaction.
The binding energy ( E b ) and average binding energy ( E b ) of the Mn atom on PG are defined as follows, respectively: where E nMn+PG and E (n−1)Mn+PG , respectively, represent the total energy of PG modified by n and (n−1)Mn atoms, E PG is the total energy of PG, and E Mn is the energy of a free Mn atom.
The continuous adsorption energy ( E ad ) and average adsorption energy ( E ad ) of the CH 4 molecule are defined as follows: where E iCH 4 +nMn+PG and E (i−1)CH 4 +nMn+PG , respectively, represent the total energy of n Mn-PG system with i and i − 1 CH 4 molecules, and E CH 4 is the energy of a free CH 4 molecule.
In the Mn-modified PG structure, the calculation formula of stored CH 4 mass fraction (CH 4 molecule adsorption capacity) is defined as follows: where m CH 4 and m nMn+PG , respectively, represent the mass of CH 4 molecules and the PG system modified by n Mn atoms.
According to the experimental results, the PG structure is formed by two C 6 H 3 rings connected, or it can be seen as formed by H atoms saturated suspension bonds after removing part of C atoms in 3 × 3 graphene supercells. The optimized geometry of the PG primitive cell is shown in Fig. 1a, and the lattice constant is 7.480 Å, which is in good agreement with the experimental value of 7.400 Å [34]. The length of C sp 2 −C sp 2 bond of carbon hexagonal ring is 1.400 Å; the length of C sp −C sp bond connecting two carbon hexagonal rings is 1.492 Å, and the length of C−H bond is 1.084 Å. The calculated direct bandgap of PG is 2.398 eV, which is consistent with 2.400 eV calculated by VASP software [44], indicating that the calculation model adopted in this paper is correct, the calculation method and calculation accuracy are reasonable, and the calculation results are reliable.

Adsorption properties of CH 4 molecules on porous graphene
In the porous graphene system, six symmetric adsorption sites as shown in Fig. 1a are considered: 1 is the carbon ring hole; 2 is the bridge between the two carbon rings; 3 is the carbon-hydrogen ring hole, and 4 is the center of the carbonhydrogen macrocycle; 5 is the C top of the carbon ring; 6 is the C-C bridge in the carbon ring. After placing CH 4 molecules in the above six initial positions for geometric structure optimization, the optimal adsorption position of CH 4 molecules on the porous graphene system was explored by calculating the adsorption energy. It is discovered that the best adsorption position of single CH 4 molecule on the porous graphene system is the top position of position 1, as shown in Fig. 2, where the adsorption energy is − 0.174 eV, and the distance between CH 4 molecule and PG substrate is 3.353 Å. This is similar to the optimal adsorption position of CH 4 in the intrinsic graphene structure, which is the central hole of carbon ring [39]. The adsorption energy of CH 4 molecule in PG system is lower, but it has more adsorption sites than that in intrinsic graphene system. Therefore, based on the research of Mn atom modified intrinsic graphene, we continue to use Mn atom modified porous graphene system, hoping to further improve the adsorption performance of PG system for CH 4 molecule.

Geometric structure of PG modified by single Mn atom
Firstly, the optimum modification position of single Mn atom on the PG system was studied, and the six initial positions as shown in Fig. 1a were also selected for optimization test. The results show that the Mn atoms at positions 5 and 6 relax to position 1 after optimization, and the Mn atoms at position 2 relax to position 3 after optimization.
The Mn atoms at position 4 cannot be adsorbed on the PG system, while the Mn atoms at positions 1 and 3 can be adsorbed stably. The PG system modified by single Mn atom has two stable structures, as shown in Fig. 1b, c. The binding energies of Mn atoms are − 4.017 eV and − 3.134 eV, respectively. In Fig. 1b, the binding energy of the Mn atom is the largest and the substrate structure is more stable, which is the optimal modification position of Mn atom in PG system (that is, the central hole of carbon ring). The distance between Mn atom and PG substrate is 1.503 Å. From Table.1, the Mulliken charge population of the PG before and after Mn-modification (C1-C6 are the six C atoms in the carbon ring where Mn atom is located on the PG substrate). As shown, after Mn atom is adsorbed on PG system, the Mn atom loses 1.11 e, the positive charge increases, the PG substrate gains electrons, the negative charge increases, and the carbon ring surrounded by C1-C6 gets more electrons, forming an evident negative charge center. An electric field is generated between the two, which causes a small part of electrons on C atoms in the PG system to transfer to the lower energy orbital of the Mn atom, resulting in Dewar effect [45]. Figure 3a,c is single Mn decorated PG electron density difference, the blue and yellow isosurface represent the gain and loss of electrons regions, respectively. As shown, most of the surrounding area of the Mn atom is yellow, indicating that the Mn atom has lost electrons, and a small part of the top is blue, indicating that the Mn atom has gained electrons. The C atoms of the base hexagon all gained electrons to form an obvious electronegative center. The larger blue area of the three C atoms (C2, C4, and C6) close to H atoms indicated that more electrons were gained, which was consistent with the Mulliken charge population analysis in Table 1. The loss of electrons from C-C and C-H bonds indicates that the covalent bond is weakened. Ionic bonds are formed between the Mn Fig. 2 Geometric structure of the optimal adsorption position of single CH 4 molecule on the PG system. a is a top view, b is a side view First-principles study on methane storage properties of porous graphene modified with Mn atom that loses electrons and the carbon hexagonal ring that gains electrons, and the electron localization function (ELF) gives consistent results. The interaction between Mn and PG can also be seen from the partial state of the density (PDOS) of the Mn-PG system shown in Fig. 4a. In the range of − 2.20 to − 0.34 eV, the 2p orbital of the C atom and the 3d orbital of the Mn atom overlap strongly. In the range of 0-0.72 eV, the s, p, and d orbitals of the Mn atom overlap with the 2p orbital of the C atom, indicating that there is a strong orbital hybridization between Mn and PG. This action makes the Mn atoms adsorb stably on the PG surface.

Geometric structure of PG modified by two Mn atoms
There are three stable structures after the optimization of the PG structure modified by two Mn atoms, as shown in Fig. 5a-c. In Fig. 5a, two Mn atoms are located on the center of two carbon rings on the same side. In Fig. 5b, the two Mn atoms are located on both sides of the same carbon ring center and are symmetrical to the PG surface. In Fig. 5c, two Mn atoms are located on the center of different carbon rings on different sides respectively, showing a centrally symmetric structure relative to the PG substrate. In the structure shown in Fig. 5b, the average binding energy of Mn atom is − 3.119 eV, and the substrate is partially deformed and the overall stability of the structure is poor. In Fig. 5a, c, the average binding energy of Mn atom is − 4.176 eV and − 4.101 eV, respectively. The substrate has no obvious deformation, and the average binding energy value of Mn atom is greater than its cohesion energy − 2.920 eV [46], so the possibility of Mn atom agglomeration is avoided. When two Mn atoms modify PG system, they can be adsorbed on the same or different sides of different carbon rings. Figure 3c, d is the electron density difference of two Mn atoms in the center of different carbon rings in the PG. As shown, the Mn atoms lose more electrons when the two Mn atoms modifications PG, and the substrate carbon ring obtains more electrons, so the ionic bonds in the Mn atom and the carbon ring are more obvious. The yellow region of the C-C bond and C-H bond becomes larger, indicating that more electrons are lost and the covalent bond is further weakened. ELF gives consistent results.

Adsorption of CH 4 on Mn-PG system
The most stable structure of the single Mn atom modified PG system is shown in Fig. 1b. CH 4 has several adsorption positions on the Mn-PG system, including Mn atom top, C-C bridge position, hydrocarbon ring hole position, and C atom top position. Studies have discovered that the most stable adsorption site of CH 4 molecules is above Mn atom near the C-H bond, as shown in Fig. 6a. At this position, the adsorption energy of the CH 4 molecule is − 0.840 eV, which is much higher than that of CH 4 molecule on unmodified  To study the interaction mechanism, Fig. 4b shows the partial density of states of the Mn-PG system when adsorbing a CH 4 molecule. As shown, there is no orbital coupling phenomenon between the 3d orbital of the Mn atom and the orbital of the CH 4 molecule, so there is a weak interaction between the two. The adsorption of the CH 4 molecule on PG belongs to physical adsorption.
To study the adsorption capacity of CH 4 in the Mn-PG system, the adsorption conditions of multiple CH 4 molecules on the Mn-PG system were further calculated. It was discovered that up to 6 CH 4 molecules could be adsorbed on one side, and the optimized structure was shown in Fig. 6 a − f. As shown, CH 4 molecules are mainly adsorbed around Mn atoms or above the carbon ring. When the fifth CH 4 molecule is adsorbed, the adsorption space of CH 4 molecules in the same plane tends to be saturated and stratification occurs. Table2 lists the continuous adsorption energy (E ad ) , and average adsorption energies ( E ad ) of the CH 4 molecule on the PG system, d Mn−PG represents the distance between the Mn atom and the PG plane, d Mn−CH 4 ,d PG−CH 4 denote the distance between the C atom of the CH 4 molecule and the Mn atom, and the distance between the C atom of the CH 4 molecule and PG plane when Mn-PG system adsorption 1-6 CH 4 molecules. As shown, the distance between the Mn atom and PG plane changes only slightly during the continuous adsorption of CH 4 molecules, which indicates that the two-dimensional structure of the Mn-PG system remains stable and does not deform or collapse with the increase of the number of CH 4 molecules adsorbed.
Table1 also lists the Mulliken charge population of CH 4 molecule, Mn-PG system, and Mn-PG system adsorb 1-6 CH 4 molecules, in which C and H1-H4 are carbon atoms and four hydrogen atoms on CH 4 molecule, respectively. After the first CH 4 molecule adsorption, Mn atoms lose 0.45 e, and a small number of electrons (0.07 e) transfer to PG substrate further enhance the negative electrical properties  molecule also shows strong polarity. After adsorption, CH 4 molecules display negatively charged and interact with positively charged the Mn atom, which enhances the adsorption performance of CH 4 molecules. As the number of CH 4 molecules increases, the adsorption energy of CH 4 molecules decreases. When the third to sixth CH 4 molecules are adsorbed, the distance between CH 4 molecules and Mn atoms is longer, the charge transfer is less, and the electrostatic interaction is weakened. However, the modification of the Mn atom enhances the overall electronegativity of PG substrate and forms the negative charge center. It makes the surface of CH 4 molecule with positive electricity on the PG surface far away from the modified atom; the adsorption can also be produced, which is mainly caused by the interaction between the positive charge on the surface of CH 4 and the PG substrate with the negative charge. The adsorption energy of the fifth CH 4 molecule is much lower than that of the other CH 4 molecules because the stratification phenomenon occurs during the adsorption of the fifth CH 4 molecule, which makes the CH 4 molecule far from the PG substrate, so the interaction is weakened. The sixth CH 4 molecule is closer to the PG surface than the fifth CH 4 molecule, which is located on the first layer of CH 4 molecule adsorption. The addition of the sixth CH 4 molecule makes the position of most of the original CH 4 molecules relax, so the adsorption energy is increased compared with the fifth CH 4 molecule. The Mn-PG system adsorbed six CH 4 molecules on one side, one more CH 4 molecule than the Mn-modified intrinsic graphene system [39], and the number of porous graphene atoms was less than that of intrinsic graphene, so the adsorption capacity of the CH 4 molecule was improved. Figure 7 shows the electron density difference of Mn-PG system adsorbing 1-3 CH 4 molecules. The blue and yellow isosurface represent the electron gain and electron loss regions, respectively. As shown, there are more electron transfer between the first and second CH 4 molecules and Mn atoms, CH 4 molecules show obvious polarity after adsorption, and CH 4 molecules have strong interaction, so the adsorption energy is larger, and the number of CH 4 molecules is promoted. The electron transfer of the third to sixth CH 4 molecules is less, which is not obvious in the same precision electron density difference, which is the same as the result of Mulliken charge population analysis. The polarity and intermolecular interaction of CH 4 molecules are weakened after adsorption. They are mainly due to the electrostatic interaction between the positive charge on the surface of CH 4 molecule and the negatively charged PG substrate.

Adsorption of CH 4 on 2Mn-PG system
When the PG system is modified by two Mn atoms, the energies of the two stable structures shown in Fig. 5a, c are nearly the same. After the adsorption test of CH 4 molecule, it is discovered that the substrate in Fig. 5a will undergo obvious bending deformation after the CH 4 molecule is adsorbed. This is because the two Mn atoms on the same Fig. 7 Top and side views of electron density difference of Mn-PG system adsorbed 1st-3rd CH 4 molecules side of the PG plane have an electrostatic interaction with the CH 4 molecule and the strong force between the Mn atom itself and carbon ring, so that the PG substrate is bent to the CH 4 molecule, destroying its two-dimensional structure. The structure in Fig. 5c remains a stable two-dimensional structure after the adsorption of CH 4 . Therefore, the structure in Fig. 5c is selected to study the adsorption performance of CH 4 molecules in the 2Mn-PG system.
In the 2Mn-PG system, 12 CH 4 molecules can be adsorbed on both sides, and 6 CH 4 molecules can be adsorbed on each side. The optimized geometric structures are shown in Fig. 8a-l. As shown, the distance between the two Mn atoms and PG remains unchanged during the continuous adsorption of CH 4 , and the two-dimensional structure of the substrate is stable. The adsorption position of CH 4 molecule is the same as that of single Mn atom. Each side of CH 4 molecule is first adsorbed near Mn atom, and the Mn atom plays an important role in the adsorption process of CH 4 molecule. The first to fourth CH 4 molecules are adsorbed on one side in the same plane. When the fifth CH 4 molecule is adsorbed, because the repulsive force between CH 4 molecules, a large number of CH 4 Fig. 8 Top and side views of the geometric configuration of the 1-12 CH 4 molecules adsorbed by 2Mn-PG system molecules cannot coexist in the same plane, so stratification occurs. At the same time, CH 4 molecules in the first layer relax, and the adsorption space reaches saturation after the adsorption of six CH 4 molecules. When CH 4 molecules adsorbed on both sides of the system are saturated, the overall structure is more symmetrical. Figure 9 shows the continuous adsorption energy E ad , the average adsorption energy E ad of CH 4 molecules in the 2Mn-PG system, and the distance d PG−CH 4 from the CH 4 molecule to the PG plane. As shown, the distance between the CH 4 molecules in the first layer on each side and the PG surface is 3-4 Å, and the adsorption energy decreases with the increase in the number of CH 4 molecules adsorption, ranging from − 0.853 eV to − 0.114 eV. The distance between the CH 4 molecules in the second layer and the PG surface is more than 5 Å, and the adsorption energy is generally lower than − 0.100 eV. This is because the distance between the CH 4 molecules in the second layer and the PG surface is far, and the interaction between the positively charged CH 4 molecules on the surface and the negatively charged PG substrate is weakened and the adsorption energy is low. When 12 CH 4 molecules were adsorbed, the average adsorption energy was − 0.338 eV, and the adsorption capacity was up to 38.43 wt.%. It is close to the CH 4 average adsorption energy of the 2Mn-GR system (− 0.402 eV) and Ag modified graphene in the presence of ambient O 2 (− 0.399 eV) [28,39]. And the CH 4 average adsorption energy is higher than two Ti atoms modified graphyne and two Ti atoms modified C 6 H 2 type PG (2Ti-PG-C 6 H 2 ) substrates (− 0.300 eV, − 0.207 eV) [47,48]. Although the adsorption capacity is reduced compared to the 2Ti-PG-C 6 H 2 system (54.7 wt.%), the average adsorption energy of 2Mn-PG system is higher. Compared with the 2Mn-GR system (32.93 wt.%), the adsorption capacity of 2Mn-PG system is increased by 5.5 wt.%, which is closer to the energy storage target proposed by the U.S. DOE. Therefore, 2Mn-PG is a more promising CH 4 storage material that balances adsorption energy and adsorption capacity.
To further verify the structural stability and eliminate the influence of edge effect, a 2 × 2 supercell was established based on the above PG structure, which contains 96 C atoms, 216 H atoms, and eight modified Mn atoms. This structure can adsorb 48 CH 4 molecules, and the optimized geometry is shown in Fig. 10 The results show that the average binding energy of the Mn atom is − 4.045 eV, which is larger than the cohesive energy and avoids the agglomeration. The average adsorption energy of CH 4 molecule is − 0.292 eV, which is less different from the calculation results of the primitive cell. It shows that the system structure is stable, and the calculation results are reasonable. There is no CH 4 molecule adsorption at the center of the supercell, which is due to the large pore size of the PG structure. The CH 4 molecule located here is far away from the negative charge center of the substrate and Mn atoms, and the interaction force is too weak for adsorption to occur. Therefore, the pore size has a great influence on the adsorption performance of CH 4 molecules. We will conduct subsequent studies on the adsorption performance of CH 4 by adjusting the pore size of the PG system. Fig. 9 The continuous adsorption energy E ad (eV) and average adsorption energy E ad (eV) of 1-12 CH 4 molecules adsorbed by the 2Mn-PG system, and the distance d PG−CH 4 (Å) between CH 4 molecules and PG substrate

Conclusion
Based on first-principles density functional theory, the adsorption properties of PG and Mn-PG systems for CH 4 molecules were studied, and the following conclusions were obtained: (1) The optimum adsorption location of CH 4 molecule on porous graphene is the carbon rings hole position, with the adsorption energy of −0.174 eV and the distance between CH 4 molecule and PG substrate is 3.353 Å.
(2) The optimal position of the PG system modified by single Mn atom is the hexagonal carbon ring hole position. When two Mn atoms modified the PG system, only the system with two Mn atoms located at different carbon rings hole sites on the opposite side can maintain structural stability when CH 4 was adsorbed, and the average binding energy is − 4.101 eV. The charge transfer between Mn atoms and PG substrate resulted in strong orbital hybridization, and the ionic bond is formed from the carbon hexagonal ring, which made it stably modified on PG surface. The modification of Mn atom enhances the electronegativity of PG substrate and generates a negative charge center at the carbon ring, which is beneficial to enhance the adsorption performance of CH 4 molecules with positive charge on the surface.
(3) Mn atom modification can improve the adsorption performance of CH 4 molecules in the PG system. The best adsorption position of single CH 4 molecule in the Mn-PG system is above Mn atom near the C-H bond, and the adsorption energy can reach − 0.840 eV, which belongs to physical adsorption. The CH 4 molecule close to the Mn atom shows negatively charged and has a strong electrostatic interaction with the positively charged Mn atom, which plays a major role in the adsorption. The adsorption energy is large, and the molecules have polarity, which reduces the intermolecular repulsion and is conducive to the increase in the adsorption number of CH 4 molecules. The surface of CH 4 molecule far away from Mn atom is positively charged, and the weak electrostatic interaction with negatively charged PG substrate is dominant in the adsorption, and the adsorption energy is low. The CH 4 molecules are adsorbed on the PG surface through the electrostatic interaction with Mn atoms and PG substrates as well as the synergistic effect of the intermolecular forces of CH 4 . (4) The Mn-PG system can adsorb 6 CH 4 molecules on one side, and the average adsorption energy is − 0.345 eV. 2Mn-PG can adsorb 12 CH 4 molecules on both sides with an average adsorption energy of − 0.338 eV and an adsorption capacity of 38.43 wt.%, which is close to the energy storage target proposed by the U.S. DOE. Therefore, PG is a kind of CH 4 storage material with good development prospects.