Investigation of Electronic and Topological Properties of Magnesium-coated Boron Fullerenes and Their Interaction with Hydrogen Molecule

INTRODUCTION
Nowadays, nanomaterials have wide applications in human life, and a more accurate knowledge of their structure helps to extend their applications, because of relationship between macroscopic and microscopic properties. Various nanostructures, which are composed of carbon, boron and nitrogen, have been widely investigated as alternative materials for hydrogen storage using experimental and computational techniques [1-13]. One method to store hydrogen is using nanomaterials such as fullerenes and metal-coated nanotubes which have higher binding energies [14-18]. Metal-coating of nanotubes increase the ability of the nanostructures to absorb hydrogen molecules [19]. Metals such as Sc and Ti, were among the first elements investigated for coating nanotubes and fullerenes [17, 18]. These metals show favorable binding interaction with hydrogen molecules in the range of 0.2 to 0.6 eV through the Kubas mechanism [20]. Dong et al. [21] demonstrated that the B40 fullerene coated by 6 Ti atoms (Ti6B40) can store up to 34 H2 molecules, corresponding to a maximum gravimetric density of 8.7 wt%. It takes 0.20-0.40 eV/H2 to add one H2 molecule, which assures reversible storage of H2 molecules under ambient conditions. Tang, C and Xue, Z [22] found that the average hydrogen adsorption energies per H2 for B40 (Sc-nH2)6 (n =1-5) are in the energy range from 0.33 to 0.58 eV. Liu et al. [23] indicated that Sc4B38 systems could effectively absorb 24H2 and have an average adsorption energy of 0.22 eV. Boron nanostructures coated with metal have been widely analyzed for hydrogen storage using density functional theory (DFT) [21, 24-29]. One of the conditions for reversible hydrogen molecule adsorption is that the adsorption energy lies between the energy of physical and chemical adsorption types (between 0.2 and 0.4 eV/H2) [30]. Szwacki et al. [31] predicted a stable nanostructure of boron fullerene family and suggested a stable boron cage of B80, in which the inclusion of metal atoms on these nanostructures often raises hydrogen storage capacity due to the strong binding energy. Zhou et al. reported the hydrogen adsorption on alkli-metal (Na, K) doped B80. They found that Na12B80 and K12B80 show fairly low adsorption energies (0.07 eV/H2 and 0.09 eV/H2), indicating that alkli-metal is unsuitable for hydrogen storage. Calcium coated nanotubes and fullerenes are appropriate coating systems for hydrogen storage [5, 26, 28, 30, 32]. Yoon et al. demonstrated that calcium atoms can be placed on each of the 32 rings in C60 and create the Ca32C60 structure that absorbs 92 hydrogen molecules [33]. A polarization mechanism for the adsorption of H2 molecules has been developed by evaluation of the radial component of the electric field related to the charge redistribution [34]. In many cases, fullerene B80 has been used as a calcium coatings substrate for binding of hydrogen molecule [35]. Since the Ca32C60 complex has been shown to achieve a high specific density, calcium-coated B80 may achieve a similar or greater specific density. In addition, the larger surface area of B80 compared to C60 may make the calcium-coated B80 complex a better material for adsorption H2 molecules. Recently it has been showed that a calcium-coated B80 fullerene, Ca12B80, is a promising material for hydrogen storage [24]. The Ca12B80 complex includes one calcium atom placed on each of the 12 pentagonal rings of B80. The average binding energy of calcium in Ca12B80, 0.12–0.40 eV/H2, is greater than the binding energy of bulk calcium metal, which highly reduces the probability of clustering in B80 and it represents a high capacity hydrogen storage material with the required properties.
Since calcium and magnesium-coated B80 fullerenes exhibit high hydrogen storage capability, in this research, different magnesium-coated boron fullerenes were selected to investigate hydrogen binding energies and molecular descriptors which can provide a lot of information to interpret and predict the properties of the entitled systems.

COMPUTATIONAL DETAILS
All calculations for Mg, H2, B80, Mg12B80, Mg20B80, Mg30B80 systems and their complexes with hydrogen molecule have been carried out by using Gaussian 09 software [36] at B3LYP/6-31G//M062X/6-31G** level of theory, which has been show as a popular level to predict binding energies of molecules [37], and vibrational harmonic frequency calculations have been done to confirm stable structures. The amount of charge transfer from magnesium atoms to boron atoms for Mg12B80, Mg20B80 and Mg30B80 when magnesium atoms are bind to boron pentagonal rings and boron hexagonal rings, respectively, has been calculated using Mulliken charge distribution. To determine the type of interaction of hydrogen molecule with B80, Mg12B80, Mg20B80 and Mg30B80, critical points have been calculated by using AIM2000 software [38]. Some molecular descriptors are obtained for the entitled systems using Dragon ver. 7 (5270/3D) software [39].

RESULTS AND DISCUSSION
Fig. 1 shows optimized structures in which Mg atoms bind to the boron atoms in boron fullerene (B80). According to the structure presented by Szwacki et al. [31], when Mg atoms bind to the boron fullerene, charge transfer takes place from Mg atoms to B atoms. Tables 1 to 3 include amount of charge transfers for Mg12B80, Mg20B80 and Mg30B80 when Mg atoms bind to boron pentagonal and boron hexagonal rings, calculated in the context of Mulliken population analysis.This charge transfers make Mg atoms to become positively-charged, that leads to interaction with boron fullerene with negative charge. 
The binding energies for boron fullerene doped with Mg is calculated by

                                    
where EMgB80, EB80 and EMg are the total energy of B80 doped with Mg, the energies of B80 molecule and separate Mg atom, respectively, and m is the number of Mg atoms. The calculated binding energies are listed in Table 4. 
Our calculated results show that the average binding energy in the Mg12B80, Mg20B80 and Mg30B80 are -0.76, -1.13 and -0.35 eV/Mg, respectively. To investigate the interaction of the hydrogen molecule with the B80 coated with Mg, a hydrogen molecule is added to this system, that displaces the absorbed Mg atoms. The electric field due to the positively charged Mg atoms increases the polarizability of the H2 molecule which leads to adsorption of H2 molecule without dissociation. 
The polarization interaction between the Mg atom and the absorbed H2 molecule results in increase in the H-H bond length, compared to a single H2 molecule, as can be seen in Table 4. Fig. 2 shows the adsorption of a H2 molecule on B80, Mg12B80 and Mg30B80 structures.
The hydrogen adsorption energy on boron fullerenes doped with magnesium is calculated by:

               
where EMgB80H2, EMgB80 and EH2 are the energy of H2 on B80 doped with magnesium, the energy of B80 doped with magnesium and the energy of H2 molecule, respectively, and n reflects the number of adsorbed H2 molecules. Total energies of the structures and adsorption energies per H2 molecule as well as H-H bond lengths in H2 molecules are given in Table 4. Entries in table 4 shows that boron fullerenes doped with magnesium atoms have more hydrogen absorption capacity than boron fullerenes. The adsorption energies for B80, Mg12B80, Mg20B80 and Mg30B80 are     -0.02, -0.22, -0.06 and -0.05 eV/H2, respectively. Mg12B80 has the highest adsorption energy, which indicates that its reactivity and hydrogen storage capability is more than B80, Mg20B80 and Mg30B80, which corresponds to the condition of the reversible hydrogen molecular absorption (between 0.2 and 0.4 eV/H2). Table 5 includes a comparison of the results of our calculations and the calculations of previous papers for the values of hydrogen absorption energy  on Metal-coated Boron nanostructures.
To determine the type of interaction of hydrogen molecule with B80, Mg12B80, Mg20B80 and Mg30B80, critical points of electron density distribution have been calculated by using AIM2000 software. The results of these calculations, such as the values of charge density, ρ(r), Laplacian of ρ, ∇2(ρ), Lagrangian Kinetic Energy, G(r), Hamiltonian Kinetic Energy, K(r), and Virial Field Function, V(r), for the hydrogen absorption bond and the corresponding atoms, have been shown in Tables 6 to 9. Our calculated results show that the ∇2(ρ) values, for the critical points between the hydrogen molecule and B80, Mg12B80, Mg20B80 and Mg30B80, are all positive and consequently of electrostatic type.
The ∇2(ρ) value for Mg12B80 is lower than that B80, Mg20B80 and Mg30B80, which is equal to 0.0006, 0.0065, 0.0028 and 0.0029, respectively. By plotting the molecular graph, we found that the critical point of H2 molecule adsorption on Mg12B80 is located between the H atom and the Mg atoms on the pentagonal boron ring, while the critical point of H2 molecule adsorption on Mg20B80 and Mg30B80 is located between the H and one of the B atoms in the hexagonal boron ring.
By using the energy of HOMO and LUMO orbitals, EH and EL, the values of ionization energy (IP), electron affinity (EA), electronegativity (χ), and hardness (ƞ) can be obtained:

IP ≈ -EH, EA ≈ -EL, ƞ = (IP - EA)/2, χ = (IP + EA)/2        (3)    
Some electronic properties of B80, B80H2, Mg12B80, Mg12B80H2, Mg20B80, Mg20B80H2, Mg30B80 and Mg30B80H2 are given in Table 10.
Table 10 shows Mg12B80 possesses the lowest value of ΔEH-L, which indicates a lower kinetic stability (higher reactivity) of this structure compared to B80, Mg20B80 and Mg30B80. When a hydrogen molecule binds to these structures, the ΔEH-L increases which indicates that the adsorption potency decreases for subsequent hydrogen molecule. Also, the hardness value (ƞ) for Mg12B80 is lower than for B80, Mg20B80 and Mg30B80 which shows that it has a lower energy gap and more reactivity. Numerical value of some molecular descriptors for B80, Mg12B80, Mg20B80 and Mg30B80 which were calculated using Dragon ver. 7 (5270/3D) has been given in Table 11.
The data show that values of MLOGP and MLOGP2 for B80, Mg12B80, Mg20B80 and Mg30B80 are the same, the values of ZM1, ZM2, DBI, BBI, TIE and Wap for Mg12B80 are higher than B80, Mg20B80 and Mg30B80. Also, the values of VvdwMG, PHI and MSD increases according to the number of atoms and the size of the structure, while values of V index, X index and Y indices decreases with respect to the number of atoms and the size of the structure. In other words, values of these descriptors depends on the size and number of atoms in the structure. Therefore, it can be concluded higher values of ZM1, ZM2, DBI, BBI, TIE and Wap, result in higher adsorption capability.

CONCLUSION
Through B3LYP/6-31G//M062X/6-31G** calculations, results showed that magnesium doping of boron fullerenes rises the hydrogen storage capacity. Mg atoms binds to the boron fullerenes due to the charge transfer from Mg to B atoms. This charge transfer creates an electric field around Mg atoms with a positive charge when hydrogen molecules approach the system, the hydrogen molecules become polarized, and they are adsorbed to these boron fullerenes doped with Mg atoms. Analysis of critical points shows that the Laplacian of ρ, ∇2(ρ), for the critical points between the hydrogen molecule and B80, Mg12B80, Mg20B80 and Mg30B80, is a positive value, reveling an electrostatic interaction. Our results show that Mg12B80 possesses the lowest ΔEH-L and the highest adsorption energy, which indicates higher reactivity of this structure compared to B80, Mg20B80 and Mg30B80. Also, the hardness value (ƞ) for Mg12B80 is lower than those of B80, Mg20B80 and Mg30B80, that shows a lower energy gap and more reactivity. Numerical values of some molecular descriptors show that for Mg12B80, values of ZM1, ZM2, DBI, BBI, TIE and Wap are all higher than other structures, that results higher adsorption capacity.

CONFLICT OF INTEREST
The authors declare that there is no conflict of interests regarding the publication of this manuscript.