An application of geometrical isometries in non-planar molecules

Document Type: Research Paper

Authors

University of Kashan

Abstract

In this paper we introduce a novel methodology to transmit the
origin to the center of a polygon in a molecule structure such that the
special axis be perpendicular to the plane containing the polygon. The
mathematical calculation are described completely and the algorithm
will be showed as a computer program.

Keywords


1. W. E. Barth, R. G. Lawton, Dibenzo[ghi,mno]fluoranthene, J. Am. Chem. Soc. 88
(1966) 380–381.
2. F. Cataldo, A. Graovac, O. Ori, The Mathematics and Topology of Fullerenes, Springer, Verlag, Berlin, 2011.
3. Z. Chen, C. S. Wannere, C. Corminboeuf, R. Puchta, P. V. R. Schleyer, Nucleusindependent chemical shifts (NICS) as an aromaticity criterion, Chemical Reviews-Columbus 105 (2005) 3842–3888.
4. H. Fallah Bagher Shaidaei, C. S. Wannere, C. Corminboeuf, R. Puchta, P. V. R. Schleyer, Which NICS aromaticity index for planar rings is best?, Organic Letters 8 (2006) 863–866.
5. R. Millman and G. Parker, Elements of Differential Geometry, Prentice-Hall, 1977.
6. B. O'Neill, Elementary Differential Geometry, 2nd ed. Academic Press, 1997.
7. A. Reisi−Vanani, A. A. Rezaei, Evaluation of the aromaticity of non-planar and bowl-shaped molecules by NICS criterion, J. Mol. Graph. Model. 61 (2015) 85–88.

8. A. A. Rezaei, Polygonal tiling of some surfaces containing fullerene molecules, Iranian J. Math. Chem. 5 (2) (2014) 2 99–105.
9. A. A. Rezaei, Tiling fullerene surface with heptagon and octagon, Fullerenes, Nanotubes, Carbon Nanostructures 23 (12) (2015) 1033–1036.
10. H. Sakurai, T. Daiko, T. Hirao, A synthesis of sumanene, a fullerene fragment, Science 301 (2003) 1878–1878.