DFT study of Hydrogen storage capacity on Hf doped graphene

We explored the molecular hydrogen storage capacity of complex system with Hafnium doped graphene (Gr-Hf) using the Density Functional Theory (DFT) method. We efficiently adsorbed molecular six hydrogens on the Hf doped graphene surface. The quantum chemically calculated adsorption energy is found negatively in the range of - 344.433 Ry to -333.836 Ry this implies as increasing the adsorbed hydrogen molecule on hafnium doped graphene (Gr-Hf) sheet the adsorption energy decreases continuously. The binding energy of after adsorbing second hydrogen molecule too much larger than the next adsorbed H2 molecules i.e., the binding energy per hydrogen molecule highly decreases when we increase adsorbed atom (2.197 Ry in 2H2 to 1.048 Ry in 3H2) then small decreases for next adsorbed H2 molecules. The extracted binding energy found in the range 2.197 Ry to 2.120 Ry, fermi energy found minimum for 1H2 shows the minimum electron occupancy at the different energy levels. The fermi energy increases accordingly, the electron occupancy also increases and evaluates higher electron occupancy with fermi energy 2.850 eV for 6H2 and density of states (DOS) confirm the weak interaction between σ bonding electrons of H2 molecule with Hf doped graphene complex system. The proposed system opens a new insight for hydrogen storage-based devices.


1.
Introduction There is an abrupt decrease in the reserves of fossil fuel which causes environmental pollution.It's our prime responsibility to find a suitable alternative of sustainable renewable energy resources.We know that hydrogen is abundantly available in the molecular form on the Earth [1][2].However, hydrogen has specific characteristics due to which it makes it complicated to store in large quantities and lack a specified amount of space.Since, last few years scientists across the globe have investigated that binding ability between hydrogen molecules (H2) and pristine nanomaterials is weak [2][3][4][5][6].Graphene is a twodimensional (2D) honeycomb crystal structure with vast applicability in optical, magnetic, electrical and electronic properties [7][8].Acik M et al investigated the optical, magnetic, electrical, and electronic properties of graphene.Sun Y reported Al doped with Hf molecule can generate adsorption energy hundred times greater than intrinsic graphene [9][10].Ao Z M found average adsorption energy -0.193 eV/H2 [11], increases while increasing adsorption of H2 molecule as calculated in the range -0.31, -0.28, -0.21 eV/H2 [12], the adsorption energy found in the negative range with Sb monolayer decorated on different atoms [13].Lone B. reported Boron doped Mg decorated graphene on hydrogen molecule.The binding energy evaluated in the range -0.566 to -0.689 eV/H2 [14][15].Whereas, the increase in Titanium doped graphene [16] between -0.534 to -0.626 eV/H2.In our previous findings the s and d orbitals of H2 molecule and Cs atom at -0.2eV overlaps of main peaks represent strong hybridization and binding of s and d orbitals of H2 and Cs atom [17].Increasing the binding energy correspondingly decreases the binding distance [18].However, adsorption energy of molecular hydrogen on Mo doped graphene complex system explored in the range -0.534 eV/H2 to -0.624 eV/H2 [19].The bio-molecular system studied with adsorption of thymine with graphene evaluated the adsorption energy -6.01 kJ/mol [20].The cytosine adsorbing on SWNT shows the binding energy -0.38 eV [24] with good agreement 1291 (2023) 012016 IOP Publishing doi:10.1088/1757-899X/1291/1/012016 2 to charge transfer [25].Furthermore, in the present study, we calculated the structural and electronic properties of Hf doped graphene with up to 6H2 molecules by adsorption phenomenon.These results indicate that the hydrogen storage capacity is extensively improved by doping of Hf atom.

Computational details
We considered the model [26] by performing Density Functional Theory (DFT) [27] calculations using Quantum ESPRESSO (QE) package [28][29] to study the adsorption of H2 molecules on Hf doped graphene sheet.For valence electron interaction pseudopotential used.The modelled and optimized structure visualized with Xcrysden visualization code [30].The general gradient approximation (GGA) used to system and the approximation Perdew, Burke and Ernzerhof (PBE) applied [31].For selfconsistent calculation for the wave function the kinetic energy cut off (ecutwfe) 20 Ry and charge density cut off (ecutrho) 200 Ry are used (1 Ry = 10 -4 Ry) to perform calculation.The k-points used 4 × 4 × 4 Monk-horst Pack.The described kinetic energy cut off around ten times of charge density cut off.The mesh k-points 12 × 12 × 12 were used to fermi energy in non-self-consistent calculation.[32].The separately degauss and ecutwfc optimized in self-consistent and non-self-consistent calculations.The degauss value taken is 0.01.Number of bands 50 were used to carry non-self-consistent calculation.
The modelled graphene sheet 3 × 3 supercell containing 18 carbon atoms.The adsorption energy (Ead) of Hf doped graphene (Gr-Hf) and pristine (Gr) calculated using following expression Ead-Hf = EHf/Gr -EHf -EGr (1) Where EHf/Gr is calculated total energy of the complex Hf doped graphene sheet, Ehf energy of isolated Hf atom, EGr energy of pristine graphene sheet The average binding energy of Hf atoms in pristine graphene is calculated using expression Where the EnHfGr, EGr, nEGr are the total energy of Hf doped graphene with n atoms, pristine graphene (PGr) and pristine graphene with n atoms respectively.The optimized molecular geometries of pristine graphene and complex system Hf doped Graphene (GrHf) sheet and Hafnium (side view and top view) shown in figure 1 (a) and figure 1 (b) respectively.The pristine graphene (PGr) containing 18 carbon atoms having electronic configuration 1s 2 2s 2 2p 2 , the doping atom (Hafnium) which have outermost electronic configuration is 5d 2 6s 2 .When a carbon atom was replaced by single Hf atom in graphene sheet the change in the bond length is observed.After optimization of the considered complex system the bond length of Hf-C, C-C is found 2.6927 Å and 1.4249 Å respectively.

Structural Analysis
3

Adsorption of Hf doped on graphene surface
We performed a complex system of hafnium doped graphene (Hf-Gr) sheet and decorated six hydrogen molecules (H2) successively.Figure 2. shows optimized geometries of Hafnium doped graphene with adsorbed hydrogen molecules (a-f) top view and figure 3 shows side view of same.

Mechanism of possible adsorption sites of H2 molecule on GrHf
Table 1 shows the estimated adsorption energy binding energy (B.E.), binding energy per H2 molecule (B.E./H2) and fermi energy (Ef) of graphene hafnium doped adsorbed hydrogen molecules (1H2 -6H2).As increasing the adsorbed hydrogen molecule on hafnium doped graphene (Gr-Hf) sheet the adsorption energy decreases continuously from -333.836 to -344.433.As comparing another theoretical result [33].Experimentally, the gravimetric capacity of hydrogen storage is found to be 4% [34].The average energy is calculated when Hf is doping -408.8 eV with ZrCo alloy.While after doping Hf and Ti atoms the cohesive energy found -7.518 eV/atom and -7.531 eV/atom for Zr7Co8Ti and Zr7Co8Hf respectively [35].The binding energy of after adsorbing second hydrogen molecule too much large than the next adsorbed H2 molecules i.e., the binding energy per hydrogen molecule highly decreases when we increase adsorbed atom (2.197 Ry in 2H2 to 1.048 Ry in 3H2) then small decreases for next adsorbed H2 molecules.The evaluated fermi energy increases with same difference as while adsorbed H2 molecules increases, fermi energy found minimum for 1H2 shows the minimum electron occupancy at the different energy levels.The fermi energy increases accordingly, the electron occupancy also increases and evaluated higher electron occupancy with fermi energy 2.850 eV for 6H2.

Density of States of complex system
The density of states (DOS) for (3 × 3) hafnium doped graphene (Gr-Hf) indicated in figure 4. The studied system revels that the change in surface area due to increasing the adsorbed hydrogen molecule (H2).In the DOS plots vertical dotted line represents fermi-level set at zero which shows the variation in DOS.We analysed the density of states (DOS) considering hafnium doped graphene with decorating hydrogen molecules (1H2-6H2).The gaps between DOS plots depicts the electrical conductivity of Hfdoped Graphene.

Conclusion
We theoretically performed a hafnium doped graphene complex system using the density functional theory method.The adsorbed hydrogen molecule on graphene doped with the Hf atom gradually increases the hydrogen molecule storage capacity effectively.We adsorbed hydrogen molecules (1H2-6H2) on the surface of the considered complex model.Investigated results show hydrogen molecules exhibit weak interaction with pristine graphene.Furthermore, the hydrogen molecule chemically adsorbs on the Hf-doped graphene with adsorption energy in the range of -344.433Ry to -333.836Ry.The evaluated binding energy found in the range 2.197 Ry to 2.120 Ry.The Fermi energy is observed in the range 2.357 eV to 2.827 eV.The density of states (DOS) confirms the weak interaction between σ bonding electrons of H2 molecule with the Hf doped graphene complex system.The proposed system opens a new insight for hydrogen storage-based devices.

Acknowledgement
We

Note:
The authors declare no competing financial interest.

Table 1 .
Physical parameters of complex system GrHf sheet adsorbed adsorption energy (Eads), binding energy and binding energy per H2 molecule, of H2 molecule adsorbed on Hf doped graphene, Fermi energy (in eV)

Table 2 .
optimized bond lengths of Hafnium Doped Graphene (Hf/Gr) sheet for one to six adsorbed H2 molecules per Hf atom acknowledge the Department of Science and Technology and University Grants Commission, New Delhi, India, for providing supercomputing facilities through grants No.SR/FT/LS/020/2009(OYS 2009), Grant No.33-16-2007(SR) respectively.We Acknowledge departmental personnel from, Nanomaterials Research Laboratory.The simulation work was conducted in High Performance Computing at Nanomaterials Research Laboratory, Department of Physics, Vinayakrao Patil Mahavidyalaya, Vaijapur, Maharashtra, India.