Potential of Silicon and Carbon Nanocages (C38, F-C38, Cl-C38, Si38, F-Si38, Cl-Si38) as Anode Materials in Li-ion Battery and Mg-ion Battery

The ability and capacity of silicon and carbon nanocages (C38, F-C38, Cl-C38, Si38, F-Si38, Cl-Si38) as anodes of batteries are investigated to suggest the new nano-compounds as basic material of electrodes of batteries with suitable performance. The electrochemical parameters of C and Si nanocages as anodes of batteries are examined and compared by using of the computational models. The halogen (F and Cl) atoms are linked to Si38 and C38 as anodes in batteries to improve their capacity by theoretical models. The interaction energies of nanostructures with F and Cl atoms, interaction energies of nanostructures with Li and Mg and interaction energies of F-nanostructures and Cl-nanostructures with Li+ and Mg+2 ions are calculated by theoretical models. Finally, the F-Si38 and Cl-Si38 nanocages are suggested as suitable effective nano structures to utilize as electrodes in batteries.


Introduction
In recent years, the metal ions interactions with various types of nanoparticles as basic material of electrodes in metal-ion batteries are investigated by computational methods [1][2][3].In previous works the ability and capacity of various nanoparticles as basic materials of electrodes of batteries are examined by computational methods [4][5][6].
In recent years the various types of nanostructures, nanomaterials and nanoparticles have been used as anode and cathodes in metal ion batteries [7][8][9].Results of previous studies shown that the suitable nanostructures when have been used and anodes and cathodes of batteries [10][11][12] have improved their efficiency and performances significantly [13][14][15].Some types of batteries have low cell voltage, high cost and low capacity and in recent studies the researchers have attempted to propose the new materials with low price as anodes and cathodes of batteries in order to increase the capacity of batteries [13][14][15].In recent years, the utilization of metal-ion batteries with anodes, which are made of earth-abundant metals, have been of vast interest [14][15][16].Magnesium metal is abundant in earth and according to this reason the Magnesium can be promising metal to use in anodes and cathode of batteries [16][17][18].
In previous works [16][17][18][19] the C and Si nanostructures and nanocages have been synthesized by various experimental models and methods.The formation heat of various C and Si anocages (10 to 60 C and Si atoms) demonstrated that the thermal stability of nanocages including the 38 atoms have the highest stability than other nanocages [20][21][22].
In this study, the silicon nanocage (Si 38 ) and carbon nanocage (C 38 ) are used as anodes in batteries to find their electrochemical properties for improving the efficiency of batteries by theoretical models.The F and Cl atoms are linked to Si 38 and C 38 as anodes in batteries to improve their capacity by theoretical models.

Computational Details
In this study, structures of nanostructures and their complexes are optimized by PW91PW91/6-311 + G (2d, 2p) and M06-2X/cc-pVQZ in GAMESS [23].The electrochemical parameters of nanostructures in Mg-ion batteries and Li-ion batteries are examined by theoretical models in GAMESS software [24].The effects of solvent on these electrochemical parameters are simulated in water as polar solvent by COSMO model and theoretical models in GAMESS software [25].
In this study, we calculated the cohesive energy values halogens by PW91PW91/6-311 + G (2d, 2p) and M06-2X/ cc-pVQZ models in order to demonstrate the optimized structures of carbon and silicon nanocages and their complexes with metal ions and halogens are stable structures from thermodynamic view point [25][26][27].We calculated the frequencies of all optimized structures and their complexes (carbon and silicon nanocages and their complexes with metal ions and halogens) in temperatures 298 K by PW91PW91/6-311 + G (2d, 2p) and M06-2X/cc-pVQZ models to confirm that these optimized structures are real structures and to confirm that the thermal stability of structures and their complexes (carbon and silicon nanocages and their complexes with metal ions and halogens) [25][26][27].
The interaction energies of nanostructures with F and Cl atoms, interaction energies of nanostructures with Li and Mg and interaction energies of F-nanostructures and Cl-nanostructures with Li + and Mg +2 ions are calculated by theoretical models in GAMESS software [28].
In this work the Tight (an optimization with Opt = Tight) model is used for structure relaxing of nanocages and their complexes with metal ions and halogens, Tight is used as option tightens the cutoffs on forces and step size that are used to determine convergence [23][24][25][26][27][28].The MaxStep = 30 is considered as sets the maximum size for an optimization step to 0.01 N Bohr or radians and the cutoff energy is 44 Atomic Rydberg units for structure optimization of nanocages and their complexes with metal ions and halogens [23][24][25][26][27][28].
In this study we calculated the basis set superposition error (BSSE) values with the counterpoise method for interactions of halogens (F and Cl atoms) with nanocages in order to overestimate the binding and interaction energy values and results are reported in Table 1 [29,30].We calculated the basis set superposition error (BSSE) values with the counterpoise method for interactions of metal ions (Li + and Mg +2 ) with nanocages and results are reported in Table 1 [29,30].

The Structural Properties of C and Si Nanocages
In recent years, the metal ions interactions with various types of nanoparticles as basic material of electrodes in metal-ion batteries are investigated by computational methods [31][32][33][34].In previous works the ability and capacity of various nanoparticles as basic materials of electrodes of batteries are examined by computational methods [35][36][37][38].
The interaction energy values of nanocages with halogens (F and Cl atoms) are reported in Table 1 as following: In this study we calculated the basis set superposition error (BSSE) values with the counterpoise method for interactions of halogens (F and Cl atoms) with nanocages in order to overestimate the binding and interaction energy values and results are reported in Table 1 [29,30].
The cohesive energy (E cohesive ) of nanocages in Fig. 1 are calculated as following: Results shown that calculated E adsorption are negative and so the halogen adsorption on C and Si nanocages are exothermic reaction.The main reason for these results is that orbitals of p of F atom and orbitals of d of Cl atom have significant and important interactions with p orbitals of C atom and d orbitals of Si atom.
In recent years the various types of nanostructures, nanomaterials and nanoparticles have been used as anode and cathodes in metal ion batteries [39][40][41][42][43][44].Results of previous studies shown that the suitable nanostructures when have been used and anodes and cathodes of batteries have improved their efficiency and performances significantly [45][46][47][48][49].
In this section we calculated the interaction energies of O, O 2 , OH and H 2 O species with C and Si nanocages and we reported obtained data in Table 1.The interaction energies (1)  The interaction energies of nanostructures with F and Cl atoms, interaction energies of nanostructures with Li and Mg and interaction energies of F-nanostructures and Clnanostructures with Li + and Mg +2 ions are calculated by theoretical models in GAMESS software [68][69][70].

The C and Si Nanocages as Anodes in Battery
In this section, the silicon nanocage (Si 38 ) and carbon nanocage (C 38 ) are used as anodes in batteries to find their electrochemical properties for improving the efficiency of batteries by theoretical models.The halogen (F and Cl) atoms are The interaction energy values of metal ions with nanocages are calculated as following: We calculated the basis set superposition error (BSSE) values with the counterpoise method for interactions of metal ions (Li + and Mg +2 ) with nanocages and results are reported in Table 1 [29,30].
Results shown that the linked halogens to nanocages have higher E interaction than C 38 and Si 38 nanocages.The (5) The capacities and abilities of nanocages in water are higher than gas phase and the main reason for obtained results is that interactions of orbitals of p of F atom with p orbitals of C atoms and interactions of orbitals of d of Cl atom with d orbitals of Si atom in water as solvent phase are higher than corresponding values in gas phase.The main reason for these results is that orbitals of p of F atom and orbitals of d of Cl atom have significant and important interactions with s orbitals of Li and Li + ion and p orbitals of Mg and Mg +2 ion.Finally, the F-Si 38 and Cl-Si 38 nanocages are suggested as suitable effective nano structures to utilize as electrodes in batteries.

Conclusion
The silicon and carbon nanocages (C 38 , F-C 38 , Cl-C 38 , Si 38 , F-Si 38 , Cl-Si 38 ) are used as anodes in batteries to find their electrochemical properties for improving the efficiency of batteries by theoretical models.The electrochemical parameters of C and Si nanocages as anodes of batteries are examined and compared by using of the computational models.The cohesive energy (E cohesive ) of C and Si nanocages and their halogen linked derivatives are negative and so the used C and Si nanocages are stable structures from thermodynamic viewpoints.The main reason for these results is that orbitals of p of F atom and orbitals of d of Cl atom have significant and important interactions with p orbitals of C atom and d orbitals of Si atom.The cell voltage and theoretical capacity (V cell and C theory ) of Mg batteries with linked halogen are higher than Li batteries.The main reason for these results is that orbitals of p of F atom and orbitals of d of Cl atom have significant and important interactions with s orbitals of Li and Li + ion and p orbitals of Mg and Mg +2 ion.Finally, the F-Si 38 and Cl-Si 38 nanocages are suggested as suitable effective nano structures to utilize as electrodes in batteries.
) and carbon nanocage (C 38 ) are used as anodes in batteries to find their electrochemical properties for improving the efficiency of batteries by theoretical models.The F and Cl atoms are linked to Si 38 and C 38 as anodes in batteries to improve their capacity by theoretical models [60-64].The F-C 38 and F-Si 38 nanocages have higher E adsorption than Cl-C 38 and Cl-Si 38 .The main reason for obtained results is that orbitals of p of F atom and p orbitals of C atoms have same energy level and also orbitals of d of Cl atom and d orbitals of Si atoms have same energy level, theoretically.Therefore, interactions of orbitals of p of F atom with p orbitals of C atoms and interactions of orbitals of d of Cl atom with d orbitals of Si atom are significantly [65-67].

38 Fig. 1
Fig. 1 Structures of nanocages and their interactions with Li + and Mg 2+ ions in outer positions

( 6 )
E ion−interaction = E nanocage−Li + − (E nanocage + E Li + ) + E BSSE main reason for these results is that orbitals of p of F atom and orbitals of d of Cl atom have significant and important interactions with s orbitals of Li and Li + ion and p orbitals of Mg and Mg +2 ion.In the Mg-ion and Li-ion batteries the overall reaction is as following: Metal ion + nanocage-Metal → Metal + nanocage-Metal ion + ∆G.The Si nanocage have higher capacities and abilities than C nanocages and halogen linked to silicon nanocages have the highest capacities and abilities.

Table 1
Calculated interaction energies (eV) and cell voltage (V) of nanocages as anodes in batteries of O, O 2 , OH and H 2 O species with C and Si nanocages are lower values than I and Mg ions, significantly [50-54].Therefore, it can be concluded the adsorption of O, O 2 , OH and H 2 O species on surfaces of C and Si nanocages are physically [55-59].In this section, the silicon nanocage (Si 38