Catalytic effect of TMCmHm compounds on the reaction rate of " Hydrazin - Oxygen "fuel cell "TM = Cr, Sc, Ti, V and m= 4 or 5" A DFT Study

Platinum and similar metals are suitable catalysts in response to fuel cells, however, because of being costly, their use is limited. So in this study, the catalytic eciency of some organometallic compounds with the general formula TMCmHm on the reaction rate of "Hydrazine- Oxygen "fuel cell was studied via density Functional Theory (DFT). To perform the respect calculations, the PW91 method and 6-31 G(d) basis set were used. Bonds’ length of O=O and N-N increased in response to their adsorption onto TMC m H m and theoretical study of N 2 H 4 -O 2 fuel cell the partial transfer of negative charge from organometallic compounds to their π * orbitals. Bond length of O=O increased by 24% due to its adsorption on ScC 5 H 5 and N-N on ScC 5 H 5 increased by 11%. The optimal structure of each studied organometallic compound was plotted by performing natural bond orbital calculations (NBO). The energy of the highest occupied molecular orbital (EHOMO) and the lowest unoccupied molecular orbital (ELUMO) were calculated. Besides, , the gap energies (Eg), chemical hardness ((cid:0)), chemical potential (µ), and electrophilicity (ω) were calculated in each case. Then, the optimal structure of O2/TMCmHm and N2H4/ TMCmHm pairs was plotted; the adsorption energy of O2 and N2H4 on each of TMCmHm was evaluated. The kinetic adsorption of O2 and N2H4 on the Sc C5H5 compound was investigated by the 6-31 G * method. The potential energy of O2/TMCmHm and N2H4/ TMCmHm pairs in the initial and nal position and the transient state were estimated, and the respect kinetic parameters were calculated.


Introduction
Fuel cells play an essential role in supplying green energy by converting chemical energy into highe ciency electrical energy (nearly 90%) [1,2]. Today, fuel cells are used in various elds such as electrical energy,production hybrid cars, spacecraft, military submarines, power plants, etc. [3,4] The main problem in the practical application of fuel cells is the slowness of the anode and cathode half-reactions in them as well as the high economic costs of using platinum as a catalyst [5]. Since the introduction of fuel cells, many studies have been done to increase the reaction rate in them using various catalysts [6][7][8][9][10][11][12] . To enhance the rate of the cathode and anode half-reactions in fuel cells, pure platinum and other expensive metals in pure or composite forms have been used extensively [13,14]. Nevertheless, the use of these metals is limited due to their high cost [14]. In this regard, the use of organometallic compounds containing Transition Metals as low-cost catalysts has been considered by some researchers in the eld of computational chemistry and has offered valuable results (15)(16)(17)(18)(19).
Organometallic compounds are very diverse and have many uses. There is at least one carbon-metal bond in each organometallic compound [20]. This bond may be ionic, covalent, or coordinate covalent. In some organometallic compounds, there is no direct bond between carbon and metal, but ligands with dative carbon structures share electron pairs with metal ions to occupy valance layer orbitals of the transition metal, where the intended organic metal compount reaches its stable electronic structure [21,22 ] . The ns, np, and, nd transition metal valance layer orbitals are involved in the intended organometallic compound, with the metal appearing as both an electron donor and an electron acceptor.
In this way, the rule of 18 electrons is established for the transition metal valance layer with the organometallic compound achieving signi cant stability. Metallocenes are an important class of organometallic compounds containing transition metals. Their general formula is M (C 5 H 5 ) 2 (M is a transition metalion). Ferrocene (Fe (C 5 H 5 ) 2 ) is the head of the metallocene group. Most metallocenes have high thermal stability. The melting and boiling points of ferrocene are 174 and 249 0 C, respectively [23][24][25][26].
Metallocenes have many applications. They are used as inexpensive catalysts in many industrial and functional reactions. In addition, they have been used on a large scale in pharmaceutical treatments, in reducing the viscosity of industrial oils, in the preparation of semiconductors, in the petrochemical industry as well as oil and gasoline re ning, etc. [27]. Metallocenes are somewhat unstable against thermodynamic oxidation, though this instability is compensated by their remarkable kinetic stability under normal conditions. As a result, under normal conditions, they can be safely used as cheap and effective catalysts in various reactions, especially in fuel cells [28][29][30][31]. metallocenes are also relatively stable in the presence of oxygen (under normal conditions). Thus, they can be used as catalysts in the cathodic reduction of O 2 in fuel cells. Much experimental and theoretical research has been done to nd inexpensive and e cient catalysts. Recently, signi cant computational studies based on (DFT) have been performed to activate oxygen in the cathode via various catalysts [32,33].
In this study the catalytic role of each of the studied organometallic compounds in the activation of O 2 in the cathode and N 2 H 4 anode of "N 2 H 4 -O 2 " fuel cell was studied by the DFT method. For this purpose, the intended structures were optimized for which density of state (DOS) diagrams were drawn. The energy of the highest occupied molecular orbital (E HOMO ) and the energy of the lowest unoccupied molecular orbital (E LOMO ) were also calculated. Gap energy (E g ), chemical hardness ( ), and chemical potential were calculated for each organometallic compound. Using the optimal energy of the structures used, the adsorption energy (E ad ) of each of the "adsorbent-adsorbate" systems was also calculated on which the necessary analyses were performed. The results revealed that the organometallics of transition metals used have an effective catalytic role in enhancing the reactivity of O 2 in the cathode and N 2 H 4 in the anode of "N 2 H 4 -O 2 ",fuel cell with the catalytic role of Sc C 5 H 5 being more pronounced than that of other organometallics used.

Computational Details
Calculations were performed by DFT method at PW91 level and base series 6-31 (d). The optimal structure of each TMC m H m was plotted by NBO calculations. Density of State diagrams (DOS) were plotted by Guassum software for optimized structures. Using the above diagrams, the energy of the highest occupied molecular orbital (E HOMO ) and the energy of the lowest unoccupied molecular orbital (E LUMO ) were calculated for each of the organic metal compounds used. Using these energies, the gap energy (E g ) was estimated for each organic metal compound. .In addition, the chemical hardness ( ), chemical potential (µ) and electrophilicity (ω) were calculated for each of them.Afterward, the optimal structure of each R / OM pair was plotted and its energy was evaluated in the same way as earlier (R is O2 or N 2 H 4 and OM delivers a studied organometallic). The adsorption energy (E ad ) for each "adsorbentadsorbate " (R / OM) pair was calculated from Equation (5). The bond elongation of O = O and N-N in response to their adsorption on TMC m H m were estimated; it was found that their elongation compared to the pre-adsorption state was 24% and 11%, respectively. The increase in the bond lengths is due to the transfer of some negative electric charge from the organometallic compound to their π * orbitals. From the calculations performed, it was found that the TM atom in the studied organometallics has gained some negative electric charge. Next, to evaluate the adsorption kinetics of O2 and N 2 H 4 on to the ScC 5 H 5 compound ,the 6-31G * and the PW91 methods were msed and the change of potential energy of each pair of O 2 /ScC 5 H 5 and N 2 H 4 /ScC 5 H 5 systems in terms of reaction coordinate (bond length of O=O or N-N in N 2 H 4 were evaluated and the respect plots were drawn. The theoretical calculation showed that for every pair (O 2 /ScC 5 H 5 or N 2 H 4 /ScC 5 H 5 ) exit only one transition state(TS). Using the above calculations, the potential energy of the initial state and the nal state of the "adsorbent-adsorbate" system and as well as the transition state in each case were estimated, through which it was possible to estimate the activation energies and the change in the potential energy of the adsorption process. NBO calculations brought about the estimation of the negative electric charge on the TM atom in TMC m H m . In addition, the amount of charge transfer from them to O2 and N 2 H 4 adsorbed on them was also estimated.

Results And Discussion
The optimal structure of each of the studied TMC m H m was drawn after its optimization of each organometallic compound such as TMC 4 H 4 or TMC 5 H 5 (Fig. 1 become signi cantly elongated and unstable, and their chemical a nity for participation in the cathode and anode half-reactions in oxygen-hydrazine fuel cell will be increased, respectively and the most important result would be an increase in the reaction rate of the cell in question. The amount of negative electric charge accumulated on the TM atom lied in the range of 0.489 to 0.835au in TMC 4 H 4s and in the range of 0.485 to 0.879au in TMC 5 H 5 (Table 1) (au stands for the basic unit of electric charge, the charge of an electron). Thus, Sc has gained the most negative charge in TMC 5 H 5 and can therefore emit more negative charge to the O2 and N 2 H 4 adsorbed on it, and increasing their chemical a nity for participation in the half-reaction of cathode and anode of the "oxygenhydrazine" cell, respectively. This ability is lower in other studied organometallics.
The diagram of the density of state was plotted for each of the optimized structures upon these diagram,the estimation of E HOMO and E LUMO were done for each structure. Fig. 2 (Table 1). , µ, and ω were calculated according to Equations 2 to 4 in each case as reported in Table 1 As can be seen from the data in Table 1, ScC 5 H 5 has the lowest E g (0.24eV). Thus, it can be concluded that the chemical a nity of ScC 5 H 5 for participating in the intended processes would be higher than that of the other studied organometallics and lower in Vc 5 H 5 than in the others. Looking at Table 1, it can be seen that the chemical hardness of ScC 5 H 5 is smaller than that of the others.
As chemical hardness is a measure of a molecule's resistance to breakage, as well as a measure of its chemical a nity for chemical reactions, ScC 5 H 5 is more capable of destabilizing the O 2 and N 2 H 4 adsorbed on it. As a suitable and effective catalyst, it can be well used in the structure of anode and cathode of "oxygen-hydrazine" fuel cell to boost the rate of these half-reactions.
Considering the values collected in Table 1 Figure 4 and according to Equation (5) where the results are reported in Table 2. In the table, the negative electric charge transferred from TM in TMC m H m to adsorbed O 2 and the O=O bond length in the adsorbed state ((r (O 2 )) have also been listed. As can be seen, the negative charge emitted to O 2 is higher in the O2 / ScC 5 H 5 pair as an "adsorbent-adsorbate" system, which in turn causes a further increase them O=O bond length. The calculated O 2 adsorption energy on the ScC 5 H 5 in turn is higher than the other adsorption energies (see Table 2). In conclusion, the ScC 5 H 5 has a more pronounced catalytic role in the activation of O 2 to participate in the reduction half-reaction in oxygen-hydrazine fuel cell. Nevertheless, other organometallics used have also a relatively good catalytic role. The adsorption of N 2 H 4 molecule on TMC m H m was also evaluated according to the same method as adsorption of O 2 on them, the intended structures were optimized and the optimal structures were drawn ( Fig. 4), with the repeated necessary calculations (Table 3). Here, some negative electric charge from TMs in TMC m H m is also sent to the N-N bond in N 2 H 4 and makes it unstable. This instability causes the N 2 H 4 to participate more rapidly in the anodic oxidation of the "oxygen-hydrazine" cell. Here again, ScC 5 H 5 has a more pronounced catalytic role in increasing the reactivity of N 2 H 4 in the anode of "oxygen-hydrazine" cell .

The adsorption energy of N 2 H 4 on to each TMC m H m was calculated according to Equation (5) by
considering the optimal structure of each pair of N 2 H 4 / TM -C m H m (Table 3). Here, the N 2 H 4 adsorption energy on ScC 5 H 5 is also more negative than the other adsorption energies, which is a good indication of the more pronounced catalytic e ciency of ScC 5 H 5 compared to the other organometallics evaluated in this study.
The comparison of the charge magnited transfer from TMC m H m to N-N is as follows:  ) while only one transition state was observed in each case. The potential energy of the "adsorbent-adsorbate" in the initial and nal state and the potential energy of the transition state were estimated. Based on them, it was possible to estimate the activation energies of the forward and reverse processes and the change in the intended potential energy in each case. The results of the calculations and the estimated parameters are shown in Figs. 5 and 6. Accordingly, each of the studied adsorptions would has a better advancement in the forward direction than in the reverse direction, where performing the studied adsorption processes is associated with a reduction in the potential energy.

Conclusion
The results of this study revealed that the gap energy, chemical hardness, and chemical potential of the studied organometallic compound are different and as such their resistance to breakage and their chemical activity plus reactivity will also be different. participation in the structure of the cathode and anode of "oxygen-hydrazine" fuel cell, the rate of cell reaction will be signi cantly increased. In addition, the catalytic properties of ScC 5 H 5 are more dominant than those of the others, and the mentioned compounds can be considered as a cheap and completely effective catalysts in the "oxygen-hydrazine" cell reaction. The adsorption kinetics of each of O 2 and N 2 H 4 on ScC 5 H were theoretically and computationally studied with only one transition state observed for each of them. The results of calculations revealed that the activation energy of the adsorption process in the forward direction in each case was smaller than in the reverse direction, suggesting that the adsorption processes.Kinetically in a better situation in the forward direction than the reverse. It was also found that the adsorption process in each case was accompanied with a reduction in potential energy, which is considered energetically appropriate.
Declarations Figure 1 The optimized structure of each organometallic compound such as TM -CmHm, (TM = Cr, Sc , Ti, V ) and (m = 4or5) with the bond length TM-C in each case listed on each structure.  The optimized structures of "adsorbent-adsorbate" systems (N2H4/TM -CmHm ). Other required bond lengths are also inserted on each structure in the gure (TM = Cr, Sc , Ti, V) and (m = 4or5).

Figure 5
Diagram of potential energy change of O2 / ScC5H system in terms of bond length O=O. The forward and reverse activation energies and the potential energy change and the other required kinetic parameters are given in the diagram.