Proceedings - Interdisciplinary Center for Nanotoxicity

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92 Conference on Current Trends in Computational Chemistry 2009 The ellipticities of the C‐C bonds in cylindrical bonds including single bond (ethane) and triple bond (acetylene) is equal to zero at BCP, and in benzene and ethylene are 0.18 and 0.30, respectively. The ellipticity has the property of determining the presence of a π‐like component to the density, even in situations where the bond order is less than unity. Comparing the ε values in Table 1, denotes the N‐N bonds are single and double bonds alternately. A bond order n within the context of QTAIM can be defined by successfully fitting the following expression, A and B being constants: [23,24] n = exp [ A( ρb − B) ] (1) For defining the new bond orders, the accepted value of N‐N bond orders in N2H4, trans‐ N2H2 and N2 molecules at B3LYP/aug‐cc‐pVDZ level have been used for obtaining the constants A, B in equation 1 by fitting procedures. In this case, A and B are obtained 3.0485 and 0.2824 respectively. The calculated bond orders based on equation 1 have been gathered in Table 2. Equation 1 is a bridge between old concept of bond order and electron density value at BCP. For providing more evidences of the generality of the QTAIM bonding and structure schemes, all the vibration normal modes of each isomer have been analyzed carefully. The assigned values of frequencies for each pair of nuclei are also gathered in the last column of Table 2. These values are found to have excellent correlation with other bond indices (QTAIM bond orders, 2 internuclear distances, ρ b and ∇ ρb ). All presented data supported the general trend i.e. stronger frequencies are characterized by the greater bond orders and ρ b values and shorter inter nuclear distances. Therefore Table 2, the same as ε in Table 1, shows N‐N bonds are single and double bonds alternatively. Then N20 ring cluster doesn't have resonance structures. Table 2. Inter molecular distances, Mulliken‐Lowdin bond order, bond order based QTAIM and normal modes at B3LYP/aug‐cc‐pVDZ. Molecule N20‐ring (D5) N‐N nuclear distance 1.246 1.459 Mulliken‐Lowdin bond order 1.04 0.53 QTAIM bond order (n) 1.84 1.05 Normal mode (cm ‐1 ) 1525,1562,1606 887 We have done these researches on N4, N6 and N8 ring clusters too. The results show that N‐N bond orders in N6 ring cluster are equal and therefore this compound has resonance structures. The results from molecular charge density analysis derived from QTAIM and vibrational normal modes computations were compared. It was demonstrated that the mathematical properties of molecular graph derived from charge density analysis were in good correlation with that of the vibrational normal modes derived from ab initio computations. But the conventional methods of deducing bond like Valance Bond (VB) theory and Mulliken‐Lowdin bond order analysis were found to be incapable for describing the structure and bond for studying of resonance and anti‐resonance in these nitrogen clusters. References 1. P. Saxe, H.F. Schaefer, III. J. Am. Chem. Soc. 105 (1983) 1760. 2. R. Engelke, J. Phys. Chem. 93 (1989) 5722. 3. R. Engelke, J. Phys. Chem. 96 (1992) 10789. 4. R. J. Bartlett (2004) Available on line at http://www.qtp.ufl.edu/~bartlett/index.html
Conference on Current Trends in Computational Chemistry 2009 5. L.R. Smith, J. Chem. Ed. 7 (1978) 569. 6. J. March, Advanced Organic Chemistry, Wiley, New York, 1985. 7. E.T. Seidl, H.F. Schaefer III, J. Chem. Phys. 88 (1988) 7043. 8. K.S. Kim, H.S. Kim, J.H. Jang, H.F. Schaefer III, J. Am. Chem. Soc. 111 (1989) 7746. 9. M.M. Francl, J.P. Chesick, J. Phys. Chem. 94 (1990) 526. 10. K.M. Dumm, K. Morokuma, J. Chem. Phys. 102 (1995) 4904. 11. M.T. Nguyen, J. Phys. Chem. 94 (1990) 6924. 12. R. Engelke, J. Phys. Chem. 94 (1990) 6925. 13. G. Trinquier, J.P. Malrieu, J.L. Daudey, Chem. Phys. Lett. 80 (1981) 552. 14. M.L. Leininger, CD. Sherrill, H.F. Schaefer III, J. Phys. Chem. 99 (1995) 2324. 15. L. Gaglirdi, S. Evangelisti, B. Roos, P. Widmark, J. Mol. Struct. (Theochem) 428 (1998) 1. 16. A.A. Bliznyuk, M. Shen, H.F. Schaefer III, Chem. Phys. Lett. 198 (1992) 249. 17. T.K. Ha, O. Suleimenov and M.T. Nguyen, Chem. Phys. Lett. 315 (1999) 327. 18. A.D. Becke, J. Chem. Phys. 98 (1993) 5648. 19. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B37 (1988) 785. 20. Spartan '08, Version 1.0.0, B.J. Deppmeier, A.J. Driessen, T.S. Hehre, W.J. Hehre, J.A. Johnson, P.E. Klunzinger, J.M. Leonard, I.N. Pham, W.J. Pietro, Jianguo Yu, Wavefunction, Inc., Irvine, CA 2008 21. M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.H. Jensen, S. Koseki, N. Matsunaga, K.A.Nguyen, S.J. Su, T.L. Windus together with M. Dupuis, J.A. Montgomery, J. Comput. Chem. 14 (1993) 1347. 22. F. Biegler‐K ِ◌nig, J. Sch ِ◌nbohm, D. Bayles, AIM2000 ‐ A Program to Analyze and Visualize Atoms in Molecules, J. Comp. Chem. 22 (2001) 545. 23. R.F.W. Bader. Atoms in Molecules, A Quantum Theory; International Series of Monographs in Chemistry; Oxford University Press: Oxford, vol. 22, 1990. 24. P.L.A. Popelier, Atoms in Molecules: An Introduction, Prentice Hall, UMIST, 2000. 25. R.G. Gillespie, P.L.A. Popelier, Chemical Bonding and Molecular Geometry, New York, Oxford, 2001. 93
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Organizing Committee Shonda Allen-H
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