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Comparative Study of Molecular Orbitals of Cobaltocene and Nickelocene Based on Molecular Mechanics

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Comparative Study of Molecular Orbitals of Cobaltocene and Nickelocene Based on Molecular Mechanics Available online a t www.scholarsresearchlibrary.com Scholars Research Library Archives of Applied Science Research, 2011, 3 (2):297-310 (http://scholarsresearchlibrary.com/archive.html) ISSN 0975-508X CODEN (USA) AASRC9 Comparative Study of Molecular Orbitals of Cobaltocene and Nickelocene Based on Molecular Mechanics Gayasuddin Khan Department of Physics, K. S. Saket Post Graduate College, Ayodhya, Faizabad, U.P. INDIA _____________________________________________________________________________ ABSTRACT Magnitude of contribution of AOs and contribution of electron in each occupied molecular orbital of cobaltocene and nickelocene based on eigenvalues, eigenvectors and population analysis have been studied. The 3D structure of both cobaltocene and nickelocene were drawn on workspace software associated with CAChe and their geometries were optimized with DFT method. The evaluation of eigenvalues, eigenvector and other parameters were done by using molecular mechanics with EHT option. The study has concluded that the first eight MOs in cobaltocene and nickelocene have contribution from 2p z orbitals of carbon of C5H5¯ and 3d orbitals of metal. The total involvement in respect of bonding between C 5H5¯ and the metal orbitals as derived from coefficient value is 22.346 in cobaltocene and 23.5716 in nickelocene. The population analysis shows that only 2p z orbitals of carbon of C 5H5¯ and 3d orbitals of metal provide electrons to MOs of cobaltocene and nickelocene. Keywords: Cobaltocene, Nickelocene, atomic orbital, molecular orbital, eigenvector, eigenvalue and population analysis. _____________________________________________________________________________ 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 [5-8] and in the use of small-core relativistic effective core potential [9-11] 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 molecular mechanics to organometallic [13, 14] and transition metal compounds is growing [15]. Molecular orbital parameters such as eigenvectors, eigenvalues and overlap matrix are well calculated with this method. In this paper I present the calculations of eigenvectors, eigenvalues and population analysis of cobaltocene and nickelocene, in order to 297 Scholars Research Library Gayasuddin Khan Arch. Appl. Sci. Res., 2011, 3 (2):297-310 ______________________________________________________________________________ study the extent of contribution of 3d, 4s and 4p orbital in the formation of MOs. Such a quantitative study will provide correct information about the involvement of 4p orbital of cobalt and nickel in bonding will help to resolve the controversy raised by other workers [16-20]. MATERIALS AND METHODS The study materials of this paper are cobaltocene and nickelocene. The 3D structure of both cobaltocene and nickelocene (Figure 1 and 2) were drawn on workspace software associated with CAChe and their geometries were optimized with DFT method. The evaluation of eigenvalues, eigenvector and other parameters were done by using molecular mechanics with EHT option. The method adopted for various calculations is based on following principles. The molecular orbitals are formed by the linear combination of basis functions. Most molecular quantum-mechanical methods (such as- SCF, CI etc.) begin the calculation with the choice of a basis functions χr, which are used to express the MOs φi as φi = Σi cri χr (c = coefficient of χ, r is the number of atomic orbital, i = molecular orbital number). The use of an adequate basis set is an essential requirement for the calculation. The basis functions are usually taken as AOs. Each AO can be represented as a linear combination of one or more Slater-type orbitals (STOs) [15, 23, 24]. Each molecular orbital φi is expressed as φi = Σi cri χr, where, the χr’ s are the STO basis functions. Here we use the STO–6G basis set (which is contracted Gaussian) [25-28] for the SCF calculation. The coefficients in linear combination for each molecular orbital being found by solution of the Roothaan equation [29]. By the above calculation, the values of orbital energies (eigenvalues) and eigenvectors (coefficients) have been calculated. A widely used method to analyze SCF wave function is population analysis, introduced by Mulliken [30, 31]. He proposed a method that apportions the electrons of an n-electron molecule into net population n r in the basis functions χr and overlap populations n r–s for all possible pairs of basis functions. With the help of these values, magnitude of contribution of atomic orbital (AO) and population analysis i.e., contribution of electron have been made. Figure 1: Structure of Cobaltocene 298 Scholars Research Library Gayasuddin Khan Arch. Appl. Sci. Res., 2011, 3 (2):297-310 ______________________________________________________________________________ Figure 2: Structure of Nickelocene. RESULTS AND DISCUSSION The MOs of cobaltocene and nickelocene are formed by linear combination of fifty AOs of two C5H5¯ units and nine orbital of cobalt or nickel. The fifty-nine AOs (χ1 to χ59 ) on LCAO approximation for fifty-nine MOs (φ1 to φ59 ). These AOs are χ1 to χ40 for 2s, 2p x, 2p y, 2p z of 1C 2 2 2 to 10C; χ41 to χ49 for 4s, 4p x, 4p y, 4p z, 3dx -y , 3dz , 3dxy, 3dxz, 3dyz of 11M; and χ50 to χ59 for 1s for 12H to 21H, respectively. Where, M = Co and Ni for cobaltocene and nickelocene, respectively. The 2s and 2p x, 2p y orbitals of each carbon atom of C 5H5¯ units are involved in the formation of σ bond between C-C and C-H. The orbitals involved in σ bond are not of our interest, hence shall remain out of discussion. The 2p z orbitals of ten carbons [32] and nine orbitals of cobalt or nickel i.e. in total nineteen orbitals are relevant to our discussion in respect of bonding between cobalt or nickel orbital and 2p z orbital of C 5H5¯ . These atomic orbitals are χ4, χ8, χ12 , χ16 , χ20 , χ24 , χ28 , χ32 , χ36 and χ40 of carbon and χ41-49 of cobalt or nickel. The coefficients [23, 33] of these orbitals are the eigenvector values of χ . They express the forms of molecular orbital i.e. the extent of involvement of χ in the formation of φ. We know that there are fifty-nine MOs, φ1 to φ59 for both cobaltocene (Scheme-1) and nickelocene (Scheme-2). The eigenvalues of MOs of cobaltocene are -1.1027, -1.0916, -0.9068, - 0.9022, -0.8721, -0.8670, -0.6877, -0.6820, -0.6797, -0.6779, -0.6064, -0.6014, -0.5610, -0.5479, -0.5443, -0.5355, -0.5234, -0.5171, -0.5110, -0.5093, -0.5079, -0.5073, -0.4935, -0.4798, - 0.4753, -0.4716, -0.4627, -0.4495, -0.4374, -0.3906, -0.3583, -0.2812, -0.2718, -0.2345, -0.2311, -0.0875, -0.0530, 0.0158, 0.0917, 0.0954, 0.1197, 0.2197, 0.2847, 0.2875, 0.2982, 0.3228, 0.3621, 0.4308, 0.4363, 0.4550, 0.5015, 0.7381, 0.7600, 1.0022, 1.0718, 2.0412, 2.0771, 2.2583 and 2.2719, respectively. Where as the eigenvalues of MOs of nickelocene are -1.1902, -1.0928, -0.9118, -0.9043, -0.8786, -0.8681, -0.6920, -0.6901, -0.6799, -0.6792, -0.6101, -0.6043, - 0.5547, 0.5477, -0.5462, -0.5287, -0.5260, 0.5212, -0.5163, -0.5139, -0.5124, -0.5095, -0.5021, - 0.5005, -0.4801, -0.4753, -0.4718, -0.4471, -0.4405, -0.3764, -0.3307, -0.2742, -0.2460, -0.2322, -0.2296, 0.0713, 0.0922, 0.1114, 0.1387, 0.1596, 0.1715, 0.1913, 0.2601, 0.2791, 0.2802, 0.4072, 0.4080, 0.4305, 0.4311, 0.5372, 0.7424, 0.8078, 0.9106, 1.1110, 1.9357, 2.0230, 2.2459, 2.2539 and 4.2942, respectively. 299 Scholars Research Library Gayasuddin Khan Arch. Appl. Sci. Res., 2011, 3 (2):297-310 ______________________________________________________________________________ MO-1 MO-2 MO-3 MO-4 MO-5 MO-6 MO-7 MO-8 MO-9 MO-10 MO-11 MO-12 MO-13 MO-14 MO-15 MO-16 MO-17 MO-18 MO-19 MO-20 MO-21 MO-22 MO-23 MO-24 MO-25 MO-26 MO-27 MO-28 MO-29 MO-30 MO-31 MO-32 MO-33 MO-34 MO-35 MO-36 MO-37 MO-38 MO-39 MO-40 300 Scholars Research Library Gayasuddin Khan Arch. Appl. Sci. Res., 2011, 3 (2):297-310 ______________________________________________________________________________ MO-41 MO-42 MO-43 MO-44 MO-45 MO-46 MO-47 MO-48 MO-49 MO-50 MO-51 MO-52 MO-53 MO-54 MO-55 MO-56 Scheme-1: Structure of Molecular orbitals of Cobaltocene MO-57 MO-58 MO-59 301 Scholars Research Library Gayasuddin Khan Arch. Appl. Sci. Res., 2011, 3 (2):297-310 ______________________________________________________________________________ MO-1 MO-2 MO-3 MO-4 MO-5 MO-6 MO-7 MO-8 MO-9 MO-10 MO-11 MO-12 MO-13 MO-14 MO-15 MO-16 MO-17 MO-18 MO-19 MO-20 MO-21 MO-22 MO-23 MO-24 MO-25 MO-26 MO-27 MO-28 MO-29 MO-30 MO-31 MO-32 MO-33 MO-34 MO-35 MO-36 MO-37 MO-38 MO-39 MO-40 302 Scholars Research Library Gayasuddin Khan Arch.
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