## Polarizability Study of Fullerene Nano- g Structures C_{20} to C_{300} by Using Monopole-Dipole ^{s} Interactions Theorem

**Avat Arman Taherpour**^{1}* and Nosratollah Mahdizadeh^{1,2}

^{1}* and Nosratollah Mahdizadeh

^{1,2}

^{1}Chemistry Department, Faculty of Science, Islamic Azad University, Iran

^{2}Chemistry Department, Payame-Noor Universit, Islamabad-Ghar, Iran

**Submission:** September 23, 2017; **Published:** September 25, 2017

***Corresponding author: ** Avat Arman Taherpour Chemistry Department, Faculty of Science, Islamic Azad University, P.O. Box 38135-567, Arak, Iran; Email: [email protected]

**How to cite this article: **Avat A T, Nosratollah M. Polarizability Study of Fullerene Nano-Structures C20 to C300 by Using Monopole-Dipole Interactions Theorem. Organic & Medicinal Chem IJ. 2017; 4(1): 555626. DOI: 10.19080/OMCIJ.2017.04.555626.

**Abstract**

Since the discovery of fullerenes (Cn), one of the main classes of carbon compounds, the unusual structures and physiochemical properties of these molecules have been discovered, and many potential applications and physicochemical properties have been introduced. Up to now, various empty carbon fullerenes with different numbers "n,” such as *C20* through *C300* (like C60, C70, C76, C82,..., C300) have been obtained. The linear uniform field electric dipole polarizability tensors of 46 fullerenes in the range C20 through C240 were calculated by the Atom MonopoleDipole Interaction (AMDI) theory, using the monopole and dipole polarizabilities of the carbon atom found previously to fit polarizability tensors of aromatic hydrocarbons. The structures are taken to be those predicted by molecular dynamics energy optimization. The isotropic mean polarizabilities calculated for *C60* and *C70* are comparable to experimental data from solid film studies and to quantum mechanical calculations. Topological indices are digital values that are assigned based on chemical composition. These values are purported to correlate chemical structures with various chemical and physical properties. They have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study were extended the calculation of the parameters concern to atom monopole-dipole moment such as Ellipsoid (αl to α3 and α), *AMDI* (Atom monopole-dipole interaction theory; αl to α3 and ā) and semi-axes a,b,c of a thin ellipsoidal shell of uniform thickness (in Å, ABC al to α3) by QSAR for C20 through C300 .

**Keywords: **Fullerenes; Polarizability; Amdi Theory; Ellipsoid; Semi-Axes Thin Ellipsoidal Shell

**Abbreviations: **AMDI: Atom Monopole Dipole Interaction; FC: Ferrocene; TI: Topological Indices; Atom Monopole Dipole Interaction (AMDI); TI: Topological Indices; MLR: Modeling; MLR: Modeling Both Linear

**Introduction**

The electrochemical properties of the fullerene C60 have been studied since the early 1990s, when these materials became available in macroscopic quantities (for a review see [1]). [1-3] in 1990, have shown that C60 is electrochemically reducible in the CH_{2}Cl_{2} medium to C60- and C60^{2-}. In 1992, have cathodically reduced both C60 in six reversible one-electron steps for -0.97 vs. Fc/Fc+ (FC=Ferrocene). This fact, along with the absence of anodic electrochemistry of fullerenes, matches the electronic structure of fullerenes: the LUMO of C60 can accept up to six electrons to form C606-, but the position of the HOMO does not allow for hole-doping under the usual electrochemical conditions. In 1991, Bard et al. [4-8] first reported on irreversible electrochemical and structural reorganization of solid fullerenes in acetonitrile medium. Dunsch et al. [5] have upgraded the experimental conditions by investigating highly organized C60 films on HOPG in aqueous medium. The reduction of such films manifested itself by re-structuring into conductive nanoclusters of ~10^{2} nm in diameter [5-9].

The linear uniform field electric dipole polarizability tensors of 46 fullerenes in the range *C20* through *C240* are calculated by the Olson Sundberg Atom Monopole-Dipole Interaction (AMDI) theory, using the monopole and dipole polarizabilities of the carbon atom found previously to fit polarizability tensors of aromatic hydrocarbons. The structures are taken to be those predicted by Zhang and co-workers by molecular dynamics energy optimization. The isotropic mean polarizabilities calculated for *C60* and *C70* are comparable to experimental data from solid film studies and to quantum mechanical calculations. Polarizability tensors are also calculated for conducting ellipsoidal shells which have the same moment of inertia tensor as the corresponding fullerenes. These are substantially smaller than the AMDI polarizabilities for the smaller fullerenes, but the two calculations tend to converge for the larger molecules. [7-15]

Graph theory has been found to be a useful tool in assessing the *QSAR* (Quantitative Structure Activity Relationship) and *QSPR* (Quantitative Structure Property Relationship). Numerous studies in the above areas have also used what are called Topological Indices (TI). It is important to use effective mathematical methods to make good correlations between several data properties of chemicals. Numerous studies have been performed related to the above mentioned fields by using the so-called Topological Indices (TI). The numbers of carbon atoms at the structures of the fullerenes were utilized here [7-15].

In this study were extended the calculation of the parameters concern to atom monopole-dipole moment such as *Ellipsoid* (α1 to α3 and ā), AMDI (Atom monopole-dipole interaction theory; al to α3 and ā) and semi-axes a,b,c of a thin ellipsoidal shell of uniform thickness (in Å, ABC α1 to α3) by QSAR for C20 through C300 .

**Graphs And Mathematical Method**

All graphing operations were performed using the *Microsoft Office Excel 2003* program. The numbers of carbon atoms at the structures of the fullerenes *Cn* were utilized to make the relationship and calculate the *Ellipsoid, AMDI* and thin ellipsoidal shell of uniform thickness. For Modeling, Both Linear (MLR) and nonlinear (ANN) models were used in this study.

**Discussion**

The polarizabilities of the ellipoids are simply correlated with their geometry, as can be seen from the fact that the principal polarizabilities are approximately proportional to the lengths of the corresponding axes. To some extent this holds for the AMDI model as well, but for the smaller members of the series there are cases where the principal polarizabilities are not in the same ratio as the axes. His is apparently because the atom dipole contribution, which is not simply related to the axis lengths, is relatively larger for the smaller members. A further measure of the correspondence between the molecules and the ellipsoids is found in the comparison of the principal polarizability axes found by the AMDI theory with the principal geometric axes of the ellipsoids. Where the three semi-axes are distinct, the axes directions are the same to within a few tenths of a degree. The numbers of carbon atoms at the structures of the fullerenes *Cn* were utilized and extended the calculation of the parameters concern to atom monopole-dipole moment such as *Ellipsoid* (α1to α3 and ā), *AMDI* (Atom monopole-dipole interaction theory;α1 to α3 and ā) and semi-axes a,b,c of a thin ellipsoidal shell ofuniform thickness (in Å, ABC al to α3) by QSAR for C20 through C300.

**References**

- RE Haufler, J Conceicao, LPF Chibante, Y Chai, NE Byrne, et al. (l990) Efficient production of C60 (buckminsterfullerene), C60H36, and the solvated buckide ion. J Phys Chem 94(24): 8634-86360.
- Q Xie, E Perez-Codero L (l992) Echegoyen Electrochemical detection of C606- and C706-: Enhanced stability of fullerides in solution. J Am Chem Soc 114(10): 3978-3980.
- C Jehoulet, YO Obeng, YT Kim, F Zhou, Aj Bard, et al. (l992) Electrochemistry and Langmuir Trough Studies of C
_{60}and C_{70}Films. J Am Chem Soc 114: 4237. - P Janda, T Krieg, L Dunsch (l998) Nanostructuring of Highly Ordered C
_{60}Films by Charge Transfer. Adv Mater 10(17): 1434-1438. - A Touzik, H Hermann, P Janda, L Dunsch, K Wetzig, et al. (2002) Nanostructuring of potassium fulleride layers. Europhys Lett 60: 411417.
- T Suzuki, K Kikuchi, F Oguri, Y Nakao, S Suzuki, et al. (l996) Electrochemical properties of fullerenolanthanides. Tetrahedron 52(14): 4973-4982.
- AA Taherpour (2007) Structural Relationship Between Degree of Unsaturation with Polarizability of (5,5) Armchair Single-Wall Carbon Nanotubes. Fullerenes, Nanotubes and Carbon Nanostructures 15: 279-289.
- AA Taherpour (2007) Quantitative Structural Relationship Study of Cis-Unsaturated Thiocrown Ethers and Their Supramolecular [X-UT-Y] [C
_{60}] and [X-UT-Y][La@C_{82}] Complexes. Fullerenes, Nanotubes and Carbon Nanostructures 15: 405-415. - YP Du, YZ Liang, BY Li, CJ Xu (2002) J Chem Inf Cmput Sci 42: ll28- 1138.
- M Randic (l975) Characterization of molecular branching. J Am Chem Soc 97(23): 6609-6615.
- SD Bolboaca, L Jantschi (2007) How Good Can the Characteristic Polynomial Be for Correlations? Int J Mol Sci 8: 335-345.
- Z Slanina, F Uhlik, SL Lee, E Osawa (2001) geometrical and thermodynamic approaches to the relative stabilities of fullerene isomers (340). Match Commun Math Comput Chem 44: 335-348.
- A. A. Taherpour (2008) Quantitative Relationship Study of Mechanical Structure Properties of Empty Fullerenes. Fullerenes, Nanotubes, and Carbon Nanostructures 16: 196-205.
- AA Taherpour, F Shafiei (2005) The structural relationship between Randi?? indices, adjacency matrixes, distance matrixes and maximum wave length of linear simple conjugated polyene compounds. J Mol Struct THEOCHEM 726: 183-188.
- AA Taherpour (2009) Structural Relationship Between Degree of Unsaturation with Fermi Energy, Chemical Hardness, and The HOMO- LUMO Gap of (5,5) Armchair Single-Walled Carbon Nanotubes. Fullerenes, Nanotubes and Carbon Nanostructures. 17(1): 26-37.