Possibility of C 38 and Si 19 Ge 19 Nanocages in Anode of Metal Ion Batteries : Computational Examination

In this study, the potential of C38 and Si19Ge19 as anode electrodes of Li-ion, Na-ion and K-ion batteries via density functional theory was investigated. Obtained results showed that Si19Ge19 as anode electrode in metal-ion batteries has higher potential than C38 ca 0.18 V. Calculated results illustrated that K-ion battery has higher cell voltage and higher performance than Li-ion and Na-ion batteries ca 0.15 and 0.31 V, respectively. Results showed that halogen adoption increased the cell voltage of studied metal-ion batteries ca 1.5–2.2 V. Results show that, Vcell values of studied metal-ion batteries in water are higher than gas phase ca 0.46 V. Finally it can be concluded that F-doped Si18Ge19 as anode electrode in K-ion battery has the highest performance and it can be proposed as novel metal-ion batteries with high performance.


Introduction
A rechargeable battery is a kind of electronic battery that has many electro-chemical various cells and it can be recharged several times.The cost of buying the rechargeable cells are higher than disposable cells, though rechargeable cells have lower destructive effects on environment.][3][4][5][6] In lithium-ion battery (LIB) there are two processes; in charging process the lithium ions transferred from the positive to negative electrode and in discharge process the motion of lithium ions is the reverse of charge process.9][20][21][22][23] The graphite due to low cost, cyclic durability, high energy stability has been used for anode electrode.6][47][48][49][50][51][52] Due to positive effects of hydrogenation, adoption and functionalization of nanostructures on potentials of metal-ion batteries, many works have been done on usage of nanostructures as anode electrodes in metal-ion batteries. 52

Computational Details
In this study, the geometries of C 38 and Si 19 Ge 19 were optimized via GAMESS software via DFT/ M06-2X theory and 6-311+G (2d, 2p) basis set.The adsorption of C 38 and Si 19 Ge 19 with halogen atoms (X = F, Cl, Br) were investigated and geometries of X-C 38 and X-Si 19 Ge 19 complexes were optimized at mentioned level of computational.
][64] In this study, the energies of the basis set superposition error (E BSSE ) for studied interactions between nanostructures and metals were calculated by using of counterpoise correction method and obtained results showed that E BSSE values are ca 0.05 Kcal/mol.][67] In the cathode and anode of LIBs, NIBs and KIBs with hypothetical nanostructure anode it can be expressed the anode reaction is (M/nanostructure ↔ M + + e − ) and cathode reaction is (M + + e − ↔ M).The complete reaction for the LIBs, NIBs and KIBs can be defined via (M + + M/nanostructure ↔ M + /nanostructure + M + ΔG cel1 ).[70]

1. C 38 and Si 19 Ge 19 as Anode in Metal-ion Batteries
Peyghan et al. 71 investigated the viability of using a BN nanotube for detection of para-chloroaniline molecule by means of density functional theory calculations.Their results showed that the molecule prefers to be adsorbed on the intrinsic BN nanotube from its N atom, releasing energy of 0.65 eV without significant effect on the electrical conductivity of the tube.Their results showed that Sidoped tube detected its presence because of the drastic increase of the electrical conductivity of the tube.Peyghan et al. 72 investigated the adsorption of two anions (F and Cl) and two cations (Li and Na) on the surface of aluminum nitride nanotubes (AlNNTs) by density functional theory.Their results showed that adsorption of anions may facilitate the electron emission from the AlNNT surface by reducing the work function due to the charge transfer occurs from the anions to the tube.
Hosseini et al. 73 investigated the performance of B 12 N 12 , and its structurally manipulated forms as anode materials for Li-ion batteries (LIBs) by means of density functional theory calculations.Their results shown that encapsulating a fluoride inside the B 12 N 12 significantly increased the electrochemical cell voltage (V cell ) of B 12 N 12 .
Najafi et al. 74 examined the applications of B 30 N 30 , B 36 N 36 , BNNT (8, 0) and BNNT (10, 0) as anode materials for lithium-ion batteries by density functional theory.Their results shown that V cell of BNNT (8, 0) and BNNT (10, 0) were higher than B 30 N 30 and B 36 N 36 .Their results shown that F functionalization of studied BN-nanostructures improved the potential of anode materials of lithium-ion batteries.
Nejati et al. 75 investigated the potential of B 12 N 12 nanocages as anode in Na-ion batteries by density func-tional theory.Their results shown that encapsulation of different halides (X = F − , Cl − , Br − ) into BN nanocage increased the cell voltage.
Hosseinian et al. 76 investigated the potential of BN nanosheets in anode of Na-ion batteries by means of density functional theory.Their results shown that replacing three N atoms of the hexagonal ring with larger P atoms increased the performance of the BN nanosheet as an anode of a Na-ion battery but the replacement of B by Al decreased its performance.
Ruiz et al. 77 proven that DFT/M06-2X method can describe the structure and energetics of hybrid inorganic-organic systems with high accuracy.Their results showed that calculated energy error bar values for hybrid inorganic-organic systems correspond to typical experimental error estimates.Their results showed that DFT/ M06-2X method has the most accurate results for the binding distance and adsorption energy.
Zhao et al. 78 compared the accuracy and energy error bar of M06-2X functional with 12 other functionals and Hartree Fock theory for 403 energetic data in 29 diverse databases.They recommend M06-2X functional for calculate the thermochemistry, noncovalent interactions and electronic excitation energies to valence and Rydberg states.They suggested the M06-2X functional with high accurate for application in organometallic and inorganometallic chemistry and for noncovalent interactions.
Mahmood et al. 79 examined the performance of 26 combinations of DFT functionals and basis sets were evaluated for the calculation of the activation energy of methylation reactions of nitronates.Their results showed that DFT method and M06-2X functional provided the most accurate results.
Wheeler et al. 80 calculated the enthalpies for bond-forming reactions by using of six DFT functionals and reaction enthalpies were decomposed into contributions from changes in bonding and other intramolecular effects via the hierarchy of homodesmotic reactions.Their results showed that M06-2X has most accurate performance for studied reactions and M06-2X is one of the more accurate functionals for the underlying bond transformations.
Hohenstein et al. 81 showed that M06-2X provide significant improvements over traditional density functionals for the noncovalent interactions.Their results showed that M06-2X correction greatly increases the accuracy of calculations without increasing the computational cost in any significant way.][79][80][81] In this section the potential of C 38 and Si 19 Ge 19 as anodes in LIB, NIB and KIB via DFT method was investigated and novel metal-ion batteries with higher performance were identified.The structures of complexes of C 38 Finally, it can be concluded: (1) the Si 19 Ge 19 as anode in metal-ion batteries has higher potential than C 38 ca 0.18 V (2) the KIB has higher V cell and higher performance than NIB and KIB ca 0.15 and 0.31 V, respectively.

2. Halogen Adoption of C 38 and Si 19 Ge 19
Hosseini et al. 73 calculated the G cell and V cell values of B 12 N 12 and F-B 12 N 12 as anode electrodes of Li-ion battery.Their results shown that encapsulating a fluoride inside the BN nanocage can be considered as suitable strategy to improvement the performance of BN nanocage as anode electrode of Li-ion batteries.
Nejati et al. 75 calculated the G cell and V cell values of B 12 N 12 as anode electrode of Na-ion battery.Their results shown that the G cell values of F-B 12 N 12 , Cl-B 12 N 12 and Br-B 12 N 12 were -85.3, -87.9 and -90.5 kcal/mol, respectively.
In this section the effects of F, Cl and Br adoption on performance of C 38  In this section the potential of F-, Cl-and Br-doped C 37 and Si 18 Ge 19 as anodes in LIB, NIB and KIB via DFT The calculated G ad values of complexes of metals with halogen-C 37 and halogen-Si 18 Ge 19 were presented in table 2. Results show that, all calculated G ad values were negatives and so the studied adsorption were possible from thermodynamic view point.Results show that G ad value of K-halogen-C 37 are higher than G ad values of Li-halogen-C 37 and Na-halogen-C 37 .Also G ad value of K-halogen-Si 18 Ge 19 are higher than G ad values of Na-halogen-Si 18 Ge 19 and K-halogen-Si 18 Ge 19 .Results display that G ad values of Li, Na and K on halogen-Si 18 Ge 19 are higher than G ad values on halogen-C 37 .
Results show that G ad values of F-Si 18 Ge 19 and F-C 37 are higher than G ad values of Cl or Br-Si 18 Ge 19 and Cl or Br-C 37 .The G ad values of complexes of metals with halogen-C 37 and halogen-Si 18 Ge 19 were decreased as following: M-Br-C 37 < M-Cl-C 37 < M-F-C 37 < M-Br-Si 18 Ge 19 < M-Cl-Si 18 Ge 19 < M-F-Si 18 Ge 19.So it can be concluded that K-F-Si 18 Ge 19 and Li-Br-C 38 have the highest and the lowest G ad absolute values, respectively.
The calculated E HOMO , E LUMO and E HLG values in eV of complexes of Li, Na and K with halogen-C 37 and halogen-Si 18 Ge 19 were reported in table 3. Results show that, E HOMO value of K-halogen-C 37 are lower than E HOMO values of Li-halogen-C 37 and Na-halogen-C 37 .Also E HOMO value of K-helogen-Si 18 Ge 19 are lower than E HOMO values of Li-halogen-Si 18 Ge 19 and Na-halogen-Si 18 Ge 19 .Results display that E HOMO values of Li, Na and K on halogen-Si 18 Ge 19 are lower than E HOMO values of halogen-C 37 .
Results show that, E HLG value of K-halogen-C 37 are lower than E HLG values of Li-halogen-C 37 and Na-halogen-C 37 .Also E HLG value of K-halogen-Si 18 Ge 19 are lower than E HLG values of Li-halogen-Si 18 Ge 19 and Na-halogen-Si 18 Ge 19 .Results show that, the E HLG values of studied complexes were decreased as following: Li-halogen-C 37 < Na-halogen-C 37 < K-halogen-C 37 < Li-halogen-Si 18 Ge 19 < Na-halogen-Si 18 Ge 19 < K-halogen-Si 18 Ge 19.So it can be concluded that K-F-Si 18 Ge 19 and Li-Br-C 37 have the lowest and the highest E HLG values, respectively.
The calculated V cell of complexes of Li, Na and K with halogen-C 37 and halogen-Si 18 Ge 19 were reported in table 2. Results show that, V cell value of K-halogen-C 37 are higher than V cell values of Li-halogen-C 37 and Na-halogen-C 37 .Also V cell value of K-halogen-Si 18 Ge 19 are higher than V cell values of Li-halogen-Si 18 Ge 19 and Na-halogen-Si 18 Ge 19 .Results display that V cell values of Li, Na and K on halogen-Si 18 Ge 19 are higher than V cell values on halogen-C 37 .Results show that, the V cell values of studied structures were decreased as following: Li-halogen-C 37 < Na-halogen-C 37 < K-halogen-C 37 < Li-halogen-Si 18 Ge 19 < Na-halogen-Si 18 Ge 19 < K-halogen-Si 18 Ge 19.So it can be concluded that K-F-Si 18 Ge 19 and Li-Br-C 37 have the highest and the lowest V cell values, respectively.Finally, it can be concluded: (1) the halogen adoption of nanostructures increased the V cell of studied metal-ion batteries ca 1.5-2.2V; (2) the F-doped metal-ion batteries have higher V cell than Cl-and Br-doped metal-ion batteries 0.3 and 0.6 V, respectively; (3) K-F-Si 18 Ge 19 can be proposed as novel metal-ion batteries with highest performance.

Solvent Effects on Potential of Studied Metal-ion Batteries
7][58][59][60][61] The calculated V cell values of metal-ion batteries with C 38 , Si 19 Ge 19 , and their halogen-doped nanostructures as anode electrodes were presented in table 3.
Results show that, V cell value of K-C 38 is higher than V cell values of Li-C 38 and Na-C 38 in water.Results display that V cell values of Li, Na and K on Si 19 Ge 19 are higher than V cell values on C 38 in water.Results show that in water, V cell value of K-halogen-C 37 are higher than V cell values of Li-halogen-C 37 and Na-halogen-C 37 .Also V cell value of K-halogen-Si 18 Ge 19 are higher than V cell values of Li-halogen-Si 18 Ge 19 and Na-halogen-Si 18 Ge 19 in water.Results display that V cell values of Li, Na and K on halogen-Si 18 Ge 19 are higher than V cell values on halogen-C 37 in water.Results show that, V cell values of studied metal-ion batteries in water are higher than gas phase ca 0.46 V.

Conclusion
In this study, the potential of C 38 and Si 19 Ge 19 as anode electrode of Li-ion, Na-ion and K-ion batteries via density functional theory was investigated.Also the effects of halogen adoption of C 38 and Si 19 Ge 19 on ability of metal-ion battery were examined.Obtained results in preset paper are: (1)  the Si 19 Ge 19 as anode in metal-ion batteries has higher potential than C 38 ca 0.18 V; (2) the KIB has higher V cell and higher performance than NIB and KIB ca 0.15 and 0.31 V, respectively; (3) the halogen adoption increased the V cell of studied metal-ion batteries ca 1.5-2.2V; (4) the F-doped metal-ion batteries have higher V cell and higher performance than Cl-and Br-doped metal-ion batteries; (5) K-F-Si 18 Ge 19 can be proposed as novel metal-ion batteries with high performance; (6) Results show that, V cell values of studied metal-ion batteries in water are higher than gas phase ca 0.46 V.

Acknowledgment
Thanks for all teachers.

- 55 Bie
et al.: Possibility of C 38 and Si 19 Ge 19 Nanocages in Anode ... In this study, in first step; the potential of C 38 and Si 19 Ge 19 nanocages as anode electrode in Li-ion battery via density functional theory was investigated.In second step; the C 38 and Si 19 Ge 19 nanocages doped with halogen atoms and effects of these adoptions on ability of Li-ion battery were examined.In third step; the potential of sodium-ion battery (NIB) and potassium-ion battery (KIB) were compared with Li-ion battery.In fourth step; the effects of halogen adoption on potential of studied NIBs and KIBs were investigated.In fifth step; novel metal-ion battery with high performance to use in industry will be proposed.The main questions have been answered in this work are: (1) How much dose cell voltages of LIBs C 38 and Si 19 Ge 19 as anode electrodes?(2) Can NIBs and KIBs be suitable batteries with high performance?(3) Can halogen adoption increase the cell voltage of LIBs? (4) Which metal-ion batteries have high performance?

Table 1 .
76ssibility of C 38 and Si 19 Ge 19 Nanocages in Anode ... and Si 19 Ge 19 with Li, Na and K were presented in figure 1.The bond lengths in Å of Li, Na and K with C 38 and Si 19 Ge 19 were reported in table 1.The calculated values of the Gibes free energy (G ad ) in kcal/mol of adsorbed metals and metal ions on surfaces of C 38 and Si 19 Ge 19 were presented in table 2. Results show that, all calculated G ad values were negatives and so the studied adsorption were possible from thermodynamic view point.Results show that G ad value of K-C 38 is higher than G ad values of Li-C 38 and Na-C 38 .Also G ad value of K-Si 19 Ge 19 is higher than G ad values of Na-Si 19 Ge 19 and K-Si 19 Ge 19 .Results show that G ad values of Li, Na and K on Si 19 Ge 19 are higher than G ad values on C 38 .Results show that, G ad values of metal ions on C 38 and Si 19 Ge 19 are higher than G ad values of metal on C 38 and Si 19 Ge 19 and the G ad values for studied metal and metal ions have same trends.The G ad values of metal-nanostructure complexes were decreased as following: Li-C 38 < Na-C 38 < Li-Si 19 Ge 19 < K-C 38 < Na-Si 19 Ge 19 < K-Si 19 Ge 19 and for metal ion-nanostructure complexes were decreased as following: Li + -C 38 < Na + -C 38 < Li + -Si 19 Ge 19 < K + -C 38 < Na + -Si 19 Ge 19 < K + -Si 19 Ge 19 .So it can be concluded that K or K + -Si 19 Ge 19 and Li or Li + -C 38 have the highest and the lowest G ad absolute values, respectively.The calculated E HOMO , E LUMO and E HLG values in eV of complexes of Li, Na and K with C 38 and Si 19 Ge 19 were reported in table 3. Results show that, E HOMO value of K-C 38 is lower than E HOMO values of Li-C 38 and Na-C 38 .Also E HOMO value of K-Si 19 Ge 19 is lower than E HOMO values of Li-Si 19 Ge 19 and Na-Si 19 Ge 19 .Results display that E HOMO values of Li, Na and K on Si 19 Ge 19 are lower than E HOMO values on C 38 .Results in table 3 show that, E HLG value of K-C 38 is lower than E HLG values of Li-C 38 and Na-C 38 .Also E HLG value of K-Si 19 Ge 19 is lower than E HLG values of Li-Si 19 Ge 19 and Na-Si 19 Ge 19 .Results show that, the E HLG values of studied metal-nanostructures were decreased as following: Li-C 38 > Na-C 38 > K-C 38 > Li-Si 19 Ge 19 > Na-Si 19 Ge 19 > K-Si 19 Ge 19.So it can be concluded that K-Si 19 Ge 19 and Li-C 38 have the lowest and the highest E HLG values, respectively.Hosseini et al. 73 investigated the E HLG values of B 12 N 12 and H 12 B 12 N 12 via B3LYP functional and 6-31G (d) basis set and their results shown that E HLG values of B 12 N 12 and H 12 B 12 N 12 were 6.84 and 2.51 eV, respectively.Also they calculated the E HLG values of complexes of B 12 N 12 and H 12 B 12 N 12 with Li atom and their results shown that the E HLG values of Li-B 12 N 12 and Li-H 12 B 12 N 12 were 6.10 and 2.38 eV, respectively.Nejati et al.75calculated the E HLG value of B 12 N 12 cage via B3LYP functional and 6-31G (d) basis set in GAMESS software and their results shown that E HLG values of B 12 N 12 and Na-B 12 N 12 were 6.84 and 1.59 eV, respectively.The E HLG values of complexes of F-B 12 N 12 , Cl-Calculated G ad (kcal/mol) and bond length (Å) values of studied complexes.12N12andBr-B 12 N 12 with Na atom and their results shown that the E HLG values of Na-F-B 12 N 12 , Na-Cl-B 12 N 12 and Na-Br-B 12 N 12 were 1.67, 1.65 and 2.01 eV, respectively.Hosseinian et al.76calculated the E HLG values of BNnanosheets via B3LYP functional and 6-31G (d) basis set and their results shown that E HLG values of BN-nanosheet, Al-BN-nanosheet and P-BN-nanosheet were 5.88, 4.98 and 5.38 eV, respectively.Also they calculated the E HLG values of complexes of nanosheets with Na atom and their results shown that the E HLG values of Na-BN-nanosheet, Na-Al-BN-nanosheet and Na-P-BN-nanosheet were 1.64, 2.09 and 1.17 eV, respectively.The calculated V cell in V of complexes of Li, Na and K with C 38 and Si 19 Ge 19 were reported in table 2. Results show that, V cell value of K-C 38 is higher than V cell values of Li-C 38 and Na-C 38 .Also V cell value of K-Si 19 Ge 19 is higher than V cell values of Li-Si 19 Ge 19 and Na-Si 19 Ge 19 .Results display that V cell values of Li, Na and K on Si 19 Ge 19 are higher than V cell values on C 38 .Results show that, the V cell values of studied complexes were decreased as following: Li-C 38 < Na-C 38 < K-C 38 < Li-Si 19 Ge 19 < Na-Si 19 Ge 19 < K-Si 19 Ge 19.So it can be concluded that K-Si 19 Ge 19 and Li-C 38 have the highest and the lowest V cell values, respectively.
Bie et al.: B and Si 19 Ge 19 as anodes of metal-ion batteries via DFT method were investigated.The calculated G ad values of F-, Cl-and Br-doped C 38 and Si 19 Ge 19 were presented in table 1. Results show that, all calculated G ad values were negatives and so the adoption of C 38 and Si 19 Ge 19 with F, Cl and Br were possible from thermodynamic view point.Results show that G ad value of F-C 37 is higher than G ad values of Cl-C 37 and Br-C 37 .Also G ad value of F-Si 19 Ge 19 is higher than G ad values of Cl-Si 18 Ge 19 and Br-Si 18 Ge 19 .Results show that, adoption of C 38 and Si 19 Ge 19 with F atom are possible processes from thermodynamic view point and F-C 37 and F-Si 18 Ge 19 can be suitable candidates as anodes of metal-ion batteries.

Table 2 .
Calculated G ad (kcal/mol) and V cell (V) values of studied complexes.

-Si 18 Ge 19
was investigated.The structures of complexes of halogen-C 37 and halogen-Si 18 Ge 19 with Li, Na and K were presented in figure1.The bond lengths of Li, Na and K with halogen-C 37 and halogen-Si 18 Ge 19 and also bond lengths of halogen atoms with bordering C or Ge atoms were reported in table 1.

Table 3 .
Calculated E HOMO , E LUMO and E HLG (eV) values of studied complexes.

Table 3 .
Calculated V cell (V) values of studied complexes in water.