Iron and Nickel -ligand bonding in metallocene: Differentiation between bond Stability and reactivity

The electronic structure and geometry optimization of ferrocene and nickelocene molecules are calculated using DFT/B3LYP with the basis set of 6-31G (d).The Eigen values, Eigen vector and population analysis of the molecules show that thefirst 13 molecular orbitals in ferrocene and 14 in nickelocene have contribution from 2pzorbitals of carbon of (C5H5) – and 4s, 4pand 3dorbitals of iron andnickel respectively. We found that the extent of involvement of metal orbitals in thetwo cases is different. In ferrocene the maximum involvement out of 4sand 4porbital is in the order 4pz > 4py > 4s > 4pxand out of 3d orbitals the order of involvement is 3dyz >3dxz >3d2z> 3dx2−y2 > 3dxy. The involvement of corresponding orbital innickelocene with respect to the 4sand 4porbitals is in the order of 4py> 4px> 4s> 4pz and in 3d orbitals the order is 3dyz >3dx2-y2 >3dxy >3dxz >3dz2molecules. The total involvement of 3d, 4s and 4porbitals of metal and 2pz orbitals of the ten carbon atomsof both ligands of (C5H5) −in ferrocene and nickelocene respectively are 42.2528 and 38.3776 hence we can conclude that ferrocene is more stable than nickelocene. Similar results are found from calculation of parameters like dipole moment, HOMO-LUMO gap and Mullikan charge distribution. The population analysis shows that only 2pz orbitals of carbon of (C5H5) −and 3d orbitals of metal provide electrons to MOs of ferrocene and nickelocene.


INTRODUCTION
In the last decade, there has been a phenomenal advancement in theoretical inorganic chemistry [1,2], much faster computers are available and commercial programs incorporating the latest methods have become widely available and are capable of providing more information about molecular orbitals (MOs), with a sample input of chemical formula. The focus of attention has been on computational transition-metal chemistry [3,4]. This is largely due to the successful employment of gradient corrected density functional theory in calculating molecules, particularly of the heavier atoms [5][6][7][8] and in the use of small-core relativistic effective core potential [9][10][11] which set the stage for calculation of geometries, bond energies, and chemical reaction and other important properties of transition metal compounds with impressive accuracy [8,12]. Application of density functional calculation to organometallic [13,14] and transition metal compounds is growing [15]. density functional parameters such as eigenvectors, eigenvalues and population analysis are well calculated with this method.
In this paper present the calculations ofeigenvectors, Eigen values and population analysis offerrocene and nickelocene in order tostudy the extent of contribution of 3d, 4sand 4p orbital in the formation of MOs. The significant of Ferrocene and nickelocene are contribute of atomic orbitals in the formation of molecular orbital, chemical stability, mediator, asymmetric catalysis and more reactive material such as Ferrocene and Nickelocene as the commercially important for production of various metallocene, polymers and co-polymers. Such a quantitative study will provide correct information about the involvement of 3d, 4s and 4p orbital of Iron and nickel in bonding will help to resolve the controversy raised by other workers [16][17][18][19][20]. MATERIALS AND METHODS In computational chemistry tools the DFT offers the fundamentals for interpreting multiple chemical concepts used in different branches of chemistry. In modern computational chemistry, quantum chemical calculations are typically performed with in a finite set of basic functions. When molecular calculations are performed, it is common to use a basis sets composed of a finite number of atomic orbitals, centered at each atomic nucleus with in the molecule, for example linear combination of atomic orbitals. The methods most commonly used for this research are DFT/B3LYP a combination of Beck's three-parameter exchange functional and Lee-Yang-Parr correlation functional with 6-31G (d) basis set. These methods are found in Gaussian 03W program. B3LYP is a DFT method with hybrid functional that provides qualitative results at a lower cost than abinitio methods with a comparable accuracy [21]. By using these methods we have optimized the energy, eigenvalues, eigenvector , population analysis, HOMO-LUMO energy gap, hardness, softness, electronegativity, visualize the HOMO and LUMO orbitals' of ferrocene and nickelocene molecules. The coefficients in linear combination for each molecular orbital being found by solution of the Roothaanequation. A widely used method to analyze SCF wave function is population analysis, introduced by Mullikan population methods [22] III.
RESULT AND DISCUSSION This research is aimed to study the electronic structure and optimized geometry of ferrocene and nickelocene molecules. Geometry optimization is used to find minima on the potential energy surface representing equilibrium structure and used to obtain structure for a single-point quantum mechanical calculation, which provides a large set of structural and electronic properties. The electronic structure and geometry of ferrocene and nickelocene molecules are found through DFT/B3LYP with a basis set of 6-31G (d) calculations. The optimized structures of these two compounds are shown in Fig 1, A and B respectively for ferrocene and nickelocene. The significant computed parameters are available in Tables 1 and 2 including the bond lengths, bond angles and dihedral angles of these two compounds. The optimized bond length of C-C double and single bonds in ferrocene rings fall in the range 1.36-1.83˚A, andnickelocene1.392-1.98 ˚A at DFT/ B3LYP, levelsthrough 6-31G (d) basis set. There are two types of C-C bonds involved in these species. These are C-C single bonds and C-C double bonds of ferrocene andnickeloceneand according to its bond length are in the order of C=C <C-C. From Tables 1and 2 we observe a slight difference in the bond lengths, bond angles and dihedral angles throughout the molecules of ferrocene and nickelocene. This indicates that the aromatic iron atom in ferrocene and nickel atom in nickelocene are relatively stable metabolically.  Table 1.due to the effect of the partial charge distribution of iron atom in ferrocene molecule, the bond connectivity of Fe-(C5H5)2 of the two ligands are asymmetrical. The iron atom in ferrocene is bonded withC12 atom with bond lengthof 1.954 (˚A) in one side of the ligand and C4with bond length of 1.856(˚A) and with C2atom of bond length 1.856 (˚A) on the opposite side. The Fe-C bond length on the two sides of the ligand have small variations due to the double bond ofC2−C4 which possess more energy to attract iron atom to-wards itself than the single bond on the other side,henceFe−C2 and Fe−C4 bonds measure shorter distance than the bond inFe−C12.In the ferrocene molecule the iron atom is located between the two ligands but inclined by -67.604 o from the plane of the cyclopentadienyl and the two ligands are almost parallel but with a slide of one from the other by a center of mass separation of 1.67˚A. As shown in Figure 2, B and Table 2. The bond connectivity of Ni-(C5H5)2of the two ligands are asymmetrical. The nickel atom in nickelocene is bonded withC12 atom of bondlength 1.976 (˚A) only from one side of the ligand. This is due to the weak ligand fields of nickelocene having high spin arrangement with two delectrons and low spin arrangement with six delectrons of nickel atom which resulted in more reactivity of nickelocene molecule with respect to the other two molecules. In the nickelocene molecule the nickel atom is located between the two ligands but inclined by -67.377 o as measured from the plane of the cyclopentadienyl and the two ligands are almost parallel but with a slide of one fromthe other by a center of mass separation of only 0.22˚A. Generally comparing the bond length and bond angles between metal atom and carbon in ferrocene and nickelocene molecules the former molecule possesses higher bond angles and the later molecule possesses larger bond length. The large the bond length the less stability but more reactivity, hence nickelocene is more reactive and less stable than the ferrocene. In the calculations of Mullikan charge distributions of ferrocene and nickelocene molecules, given in Figure   Energies of molecular orbitals are called Eigen values. The main focus has been on themolecular structure and the properties that will be evaluated can be used to determinethe molecular reactivity as well as the molecular stability. The HOMO (Highest OccupiedMolecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital) are very importantaspects to consider for these types of observations. This is because the HOMO and LUMOare the most likely locations where reaction will occur. The reaction is likely to occur therebecause the electrons in the HOMO have the highest energy and therefore the electronsare most willing to react. The LUMO is likely the location for a bond to occur as wellbecause any invading electrons for another molecules will fill in to the LUMO, that iswhy comparing the energies of these orbitals create an idea of how reactive a molecule is important parametric properties of the molecules at the DFT/B3LYP levels in 6-31G (d) basis set has been calculated and are given in Table  3 Table www.ijaers.com Page | 10 less reactive and more stable than nickelocene molecule. The most stable MO energy of ferrocene and nickelocene are respectively -254.0054, and -295.6703 -eV. In general the HOMO and LUMO energy gap reveals the chemical activity of the molecules. LUMO as an electron acceptor represents the ability to obtain an electron (i.e. the electron affinity) and HOMO as an electron donor represents the ability to donate an electron from its orbital (i.e. the Ionization Potential). The less values in the HOMO-LUMO energy gap explains eventually charge transfer interaction taking place within themolecules. Hard molecules have largeHOMO-LUMO energy gaps and soft molecule have small HOMO-LUMO energy gaps. So soft molecules (molecules with small energy gap) are favorable for easy reactions. This description also supports for ferrocene andnickelocene molecule, ferrocene is harder than nickelocene. In Table 3, the HOMO-LUMO gap, as a characteristic of reactivity, shows ferrocene has lower chemical reactivity comparing to nickelocenemolecule. Absolute hardness and softness are important properties to measure the molecular stability and reactivity. Itis apparent that the chemical hardness fundamentally signifies the resistance towards thedeformation or polarization of the electron cloud of the atoms, ions or molecules undersmall perturbation of chemical reaction. A hard molecule has a large energy gap and asoft molecule has a small energy gap. So for more energetically stable and less reactiveferrocene molecule, the HOMO-LUMO energy gap and hardness, ηis larger comparing tonickelocene molecules. The dipole moments and Mullikan charge ranges as displayed in Table 3, Nickelocene would have more charge than the ferrocenemolecule. This is due to higher dipole moment and lower HOMO-LUMO energy gap indicated that the molecule is better reactive. This indicates that nickeloceneis more polar so that it will react with polar solvents like water.Since the separation between mass centers of the two ligands is small. The higher the dipole moment, the more polar a molecule is. This could mean that the receptor is more likely toaccept polar molecules into its active site. The receptor's active sites may serve as home to atoms that have very high electron affinities that attract the negatively charged end of a polar molecule 2pzof 1C to 10C, χ41toχ49for4s, 4px, 4py, 4pz, 3dx 2 −y 2 , 3d 2 z, 3dxy, 3dxz, 3dyzof 11M andχ50to χ59for 1s of 12H to21H respectively, where M = Fe and Ni, for ferrocene and nickelocene, respectively. The 2s, 2pxand 2pyorbitals of each carbon atom of (C5H5)are involved in the formation of σbond between C-C and C-H. The orbitals involved in σ bond hence shall remain out of discussion. The 2pzorbitals of ten carbons and nine orbitals of iron or nickel i.e. in total nineteen orbitals are relevant to our discussion in respect of bonding between iron or nickel orbitals and 2pzorbital of (C5H5) − . These atomic orbitalsareχ4, χ8, χ12, χ16, χ20, χ24, χ28, χ32, χ36andχ40of carbon and χ41to χ49of iron and nickel. The coefficients of these orbitals are the eigenvector values of χ [21].They express the forms of MOs i.e. the extent of involvement of χin the formation of Φ.In order to examine the contribution of various atomic orbitals in the formation of molecular orbitals. The Eigen vector analysis has been made and studied and data are given tables 1 to 11 respectively. The coefficients of these orbital are the Eigen vector values of, χ which have been evaluated by density functional method using Gaussian-03 software.They express the form of molecular orbital that is the extent of involvement ofχin theformation of Φ. The calculated Eigen vector values of atomic orbitals of Feand Ni inthe formation of molecular orbitals in ferroceneandnickelocene in Table 4, 5, 8, and 9 respectively and the calculated Eigen vector values of 2pzorbital of carbon are given in Table 6, 7, 10 and 11. Out of the 59 molecular orbitals of ferrocene molecule only 22 molecular orbitals shallbe discussed as described in Table 4 for Iron orbital and Table 6 for Carbon orbital. In ferrocene the first 13 molecular orbitals Φ18,Φ20,Φ22,Φ23−Φ31 and Φ35are formed byonly two atomic orbitals, 3d orbital of iron and2pzorbital (C5H5) − . These orbitals are the most stable molecular orbital and have their energies in the range -2.03849 to -0.54008eV. The next nine molecular orbital Φ36−Φ37, Φ40−Φ41, Φ43, Φ50−Φ51, Φ54−Φ55haveformed from contribution of vacant 4s, 4px, 4pyand 4pzorbital of the iron and 2pzorbital of carbon. These MOs are comparatively less stable and have their energies between -0.53616and -0.107076 eV. To examine the extent of involvement of 3d, 4s and 4porbital in thef ormation of molecular orbitals the values of coefficient of each orbital have been added as shown in Table 5. -   The summation of contributions of iron orbitals are placed in Table 5 and the total contribution from each atomic orbital is shown in Figure 5. It is clearly indicated that 4pzorbital has the maximum involvement out of 4sand 4porbitals, and 3dyz orbital has the maximum involvement out of the 3dorbital. The exact order of availability of atomicorbital of Fe in ferrocene for contributions of atomic orbitals for the formation of molecular orbital is given below; 4pz >4py >4s > 4px And 3dyz>3dx 2 −y 2 >3d 2 z>3dxz >3dxyEq (1) Sum of contributions of atomic orbitals of iron in the formation of molecular orbitals of ferrocene is shown in Table 5, in here the sum of contributions of 3dxyorbital in the formation of molecular orbitals is least out of the 3dorbitals and 4pxorbital in the formation of molecular orbitals is least out of 4s and 4p orbitals. Hence 3dxyand 4pxare comparatively free for complex formations. The exact order of availability of atomic orbital of Fe in ferrocene for complex formation is given below; 4px >4s >4py >4pzx and 3dxy>3dxz >3d 2 z>3dx 2 −y 2 >3dyz Eq (2)

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[      Table 7 and Figure 6 show the summation values where the total contributions from each atomic orbital of carbon clearly indicates that eigenvector value of 2pz orbital of 16Chas the maximum involvement out of the ten carbon atoms in both (C5H5) − ligands. The sequences from the series are as below: Eq (3) Sum of contributions of atomic orbitals of carbon (2pz) in the formation of molecular orbitals of ferrocene is shown in Table 7 and Figure 6 where the 10C contributions in the formation of molecular orbitals are least out of the ten carbon atoms. Hence 10C is comparatively free for complex formation. The sequence from the series is shown below: Eq (4) Out of 59 molecular orbital Eigen values of nickelocene we shall discuss only 25 of them described in Table 8, for nickel orbitals and Table 10 for carbon orbitals. The first 14 MOsare Φ15−Φ16, Φ18−Φ20, Φ21 and Φ23−Φ30, areformed by various 3d and 2pz orbitals of (C5H5) −. These orbitals with energies in the range of -9.9338 to -0.64271eV are the most stable molecular orbital between nickel and2pzorbital of (C5H5) −. The next eleven MOs i.e.Φ36−Φ40, Φ42−Φ43, Φ50, Φ53, Φ54andΦ59are formed by interaction of 4s, 4px, 4pyand 4pz orbital of metal and 2pz orbital of carbon of (C5H5)−. These MOs with energies in the range -0.56142 to -0.10622 eV are comparatively less stable. To examine the extent of involvement of 3d, 4s, 4pand 2pz orbitals in the formation of molecular orbitals the values of coefficient of each orbital are tabulated in Table 9. -

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[Vol-4, Issue-7, July-2017] https: //dx.doi.org/10.22161/ijaers.4.7.2  ISSN: 2349-6495(P) | 2456-1908(O) www.ijaers.com Table.9: Sum of contributions and reactivity of atomic orbital's of nickel in the formation of molecular orbitals of nickelocene.   Table 9 and plotted in Fig. 7 show the total contributions from each atomic orbital. It is clearly indicated that 4pyorbital has the maximum involvement out of 4sand 4porbital and 3dyzorbital has the maximum involvement out of 3dorbitals. The sequence from the two series is given below: 4py > 4px > 4s > 4pz and 3dyz > 3dx 2 −y 2 > 3dxy > 3dxz > 3d 2 z. Eq (5) Sum of contributions of atomic orbitals of nickel in the formation of molecular orbitals of nickelocene is shown in Table 9 and Figure 7 that the sum of contributions of 3d 2 zorbital in the formation of molecular orbitals is least out of the 3dorbitals and 4pzorbital is least out of 4sand 4porbitals. Hence 3d 2 zand 4pz are comparatively free for complex formations. The exact order of availability of atomic orbitals of Ni in nickelocene for complex formation is given below; 4pz >4s>4px>4py and 3dyz >3dxz>3dxy>3dx 2 −y 2 >3dyz Eq (6)

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[      Table 11 and Figure 8 clearly indicates that contribution of 2pz orbital of 8C has the maximum involvement out of the ten carbon atoms in (C5H5) − The sequence from the series are given below: 8C >10C >16C >4C >14C >6C >11C >1C >12C >2C. Eq (7) Sum of contributions of atomic orbitals of carbon (2pz) in the formation of molecular orbitals of nickelocene is shown in Table 11 and Figure 8 where the sum of contribution of 2C of 2pzorbital's in the formation of molecular orbital's are least out of the ten carbon atoms. Hence 2C are comparatively free for complex formations. The exact order of availability of carbon atom for complex formation is given below: 2C >12C >1C >11C >6C >14C >4C >16C >10C >8C. Eq (8) The total involvement in relation to the bonding between metal orbital derived from coefficient values are 22.6107 in ferrocene, and 22.8486 in nickelocene hence nickeloceneis more stable than ferrocene. The total involvement in relation to the bonding between 2pz orbital of the ten carbon atoms of both ligands of (C5H5) − 19.889 and 15.529 in ferrocene and nickelocene respectively, hence ferrocene is more stable than nickelocene. The total involvement of 3d, 4s and 4p orbitals of metal and 2pzorbitals of the ten carbon atoms of both ligands of (C5H5) − in ferrocene and nickelocene respectively are 42.2528, and 38.3776 hence we can conclude that ferrocene is more stable than nickelocene.

Population analysis
The contribution of electrons in each occupied MO is calculated by using the population analysis method introduced by Mullikan [24, 25, and 26]. This method apportions the electrons ofn-electron molecule in to net population nrin the basis function χ(r). Let there be ni electrons in the MO Φi (ni= 0, 1, 2) and let nri symbolize the contribution of electrons inthe MO Φito the net population inχrwe have: nri =nic 2 ri Eq (9) Where, criis the coefficient of atomic orbital for the i th MO r =1-29 in ferrocene andr=1-30 in nickelocene. Eq(9) has been solved for, 58 electrons of 29 molecular orbitals in ferrocene and 60 electrons of 30molecular orbitals in nickelocene. Each MOs has two electrons inferrocene and nickelocene but (the 30 th MOs of nickelocene has only oneelectron). The coefficient of atomic orbitalcriis treated as Eigen vector value [24, 25, and 26].Values less than 0.1 have negligible contributions and are omitted in the calculations. Only 3dorbitals of metal and 2pzorbitals of carbon are considered in the calculation. The summation value of population analysis of these orbitals is shown in Table 12 of ferrocene, and 13 of nickelocene. It is indicated that in MOs 1-17 of ferrocene, in MOs 1-14 of nickelocene only 2s, 2pyand 2px electrons of carbon have contributions in the formation of molecular orbital of ferrocene andnickelocene hence are out of discussion. The summation value of population analysis of these orbitals to contribute electrons in the formation of molecular orbital is shown Tables 12 and 13 the result of the population analysis shows that only 2pzorbitals of carbon of (C5H5) − and 3dorbitalsof metal provide electrons to MOs of ferrocene, and nickelocene.  Sum of summation value of population analysis, (nri) of occupied molecular orbital of ferrocene is, 10.3302. Sum of Summation value of population analysis, (nri) of occupied molecular orbital of nickelocene is, 10.0609

IV. CONCLUSION
We studied the electronic structure and geometry optimization of ferrocene and nickelocene molecules using DFT/B3LYP with the basis set of 6-31G (d) calculations. We found that orbitals corresponding to the Eigen values (energy ranges -2.03849 to -0.54008eV in ferrocene and -9.90743 to -0.64271 eV in nickelocene) formed between 3d orbitals and 2pz orbitals are the most stable molecular orbitals. The less stable orbitals are in the energy ranges of -0.53616 to -0.10707 eV in ferrocene and in -0.56142 to -0.10622 eV nickelocene. Eigenvectors of ferrocene and nickelocene show that the first 13 MOs in ferrocene 14 MOs nickelocene are formed by various 3d orbitals of metal and 2pz orbital of carbon of (C5H5) − and the most stable MOs. The next 9 MOs in ferrocene and 11 MOs of nickelocene are formed by the interaction of 4s and 4p orbitals of metal and2pz orbital of carbon of (C5H5) − and these MOs are comparatively less stable orbitals. Out of the 3d orbitals of ferrocene and nickelocene molecules the 3dyz orbitals have maximum involvement in the formation of molecular orbitals, whereas the4pz orbital out of 4s and 4p orbital of iron and 4pyorbital out of 4s and 4p orbital of nickel show maximum involvement, in the order of 4pz >4py >4s >4px and 3dyz >3dx 2 −y 2 >3dz 2 >3dxz in ferrocene, and 4py >4px >4s >4pz and3dyz >3dx 2 −y 2 >3dxy>3dxz >3dz 2 in nickelocene.. The total involvement in relation to the bonding between metal orbital derived from coefficient values are 22 ferrocene and 22.8486 in nickelocene hence nickelocene is more stable than ferrocene. The total involvement in relation to the bonding between 2pzorbital of the ten carbon atoms of both ligands of (C5H5) − 19.889, and 15.529 in ferrocene and nickelocene respectively, hence ferrocene is more stable than nickelocene. As a summary, the total involvement of 3d,4s and 4p orbitals of metal and 2pz orbitals of the ten carbon atoms of both ligands of (C5H5) − in ferrocene and nickelocene respectively are 42.2528 and 38.3776 hence we can conclude that ferrocene is more stable than nickelocene. This is in support of the results shown in terms of the parameters like dipole moment, HOMO-LUMO gap, Ionization potential etc discussed in the above. The population analysis shows that only 2pz orbitals of carbon of (C5H5)and 3d orbitals of metal provide electrons to MOs of ferrocene and nickelocene.We recommend to simulate bigger molecules using higher basis sets and to study more properties of the molecules. Larger basis sets provide approximations more accurately by imposing fewer restrictions on the interaction of electrons in space.

ACKNOWLEDGMENT
The author acknowledges Dr. Hagos Woldeghebriel for his advising, ideas, guidance, enjoyable discussion and unforgettable support throughout my study.