Document Type: Research Paper


Faculty of Science, Department of Mathematics, Qom University, Qom, Iran


In this paper, we introduce the concept of dynamical distance on a nuclear con guration space. We partition the nuclear conguration space into disjoint classes. This classifi cation coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish di erent molecular structures.


[1] V. I. Arnold, Ordinary Differential Equations, MIT Press 1973.

[2] R. F. W. Bader, Y. Tal, S. G. Anderson, T. T. Nguyen-Dang, Theory of Molecular Structure and its Change, Isr. J. Chem. 19 (1980), 8-29.

[3] R. F. W. Bader, T. T. Nguyen-Dang, Y. Tal, S. G. Anderson, A topological theory of molecular structure, Rep. Prog. Phys. 44 (1981), 893.

[4] R. F. W. Bader, S. G. Anderson, A. J. Duke, Quantum topology of molecular charge distributions. I, J. Am. Chem. Soc. 101 (1979), 1389.

[5] R. F. W. Bader, T. T. Nguyen-Dang, Y. Tal, Quantum topology of molecular charge distributions. II. Molecular structure and its change, J. Chem. Phys. 70 (1979), 4316.

[6] R. F. W. Bader, P. J. MacDougall, C. D. H. Lau, Bonded and nonbonded charge concentrations and their relation to molecular geometry and reactivity, J. Am. Chem. Soc. 106 (1984), 1594-1605.

[7] R. F. W. Bader, R. J. Gillespie, P. J. MacDougall, A physical basis for the VSEPR model of molecular geometry, J. Am. Chem. Soc. 110 (1988), 7329-7336.

[8] R. F. W. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, Oxford, UK 1990.

[9] H.W. Broer, F. Dumortier, S .J. van Strien, F. Takens, Structures in Dynamics Studies in Mathematical Physics, vol. 2, Elsevier Science Publishing Company, North-Holland 1991.

[10] K. Collard, G. G. Hall, Orthogonal trajectories of the electron density, Int. J. Quantum Chem. 12 (1977), 623-637.

[11] S. H. Friedberg, A. J. Insel, L. E. Spence, Linear Algebra, 3th Edition, Prentice Hall 2003.

[12] M. W. Hirsch, S. Smale, R. L. Devaney, Di erential Equations, Dynamical Systems, and An Introduction to Chaos, Elsevier Academic Press 2004.

[13] T. A. Keith, R. F. W. Bader, Y. Aray, Structural homeomorphism between the electron density and the virial fi eld, Int. J. Quantum chem. 57 (1996), 183-198.

[14] H. J. Korsch, H. J. Jodi, Chaos; a program collection for the PC, Springer-Verlag 1998.

[15] P. G. Mezey, Catchment region partitioning of energy hypersurfaces, I, Theor. Chim. Acta. 58 (1981), 309-330.

[16] P. G. Mezey, Potential Energy Hyper-surfaces, Elsevier, Amsterdom 1987.

[17] P. Nasertayoob, Sh. Shahbazian, The topological analysis of electronic charge densities: A reassessment of foundations, Journal of Molecular Structure (THEOCHEM) 896 (2008), 53-58.

[18] T. T. Nguyen-Dang, R. F. W. Bader, A theory of molecular structure, Physica A. 114 (1982), 68.

[19] J. Palis, S. Smale, Proc. Symp. Pure Math. Am. Math. Soc. 14 (1970), 223.

[20] P. L. A Popelier, On the full topology of the Laplacian of the electron density, Coord. Chem. Rev. 197 (2000), 169-189.

[21] T. Poston, I. Stewart, Catastrophe Theory and its Applications, Pitman, London 1978.

[22] M. Rahimi, P. Nasertayoob, Dynamical information content of the molecular structures: A quantum theory of atoms in molecules (QTAIM) approach, MATCH Commun. Math. Comput. Chem. 67 (2012), 109-126.

[23] C. Robinson, Dynamical Systems, Stability, Symbolic Dynamics and Chaos, CRC press 1994.

[24] Y. Tal, R. F. W. Bader, T. T. Nguyen-Dang, S. G. Anderson, Quantum topology. IV. Relation between the topological and energetic stabilities of molecular structures, J. Chem. Phys. 74 (1981), 51-62.

[25] Y. Tal, R. F. Bader, J. Erkku, Structural homeomorphism between the electronic charge density and the nuclear potential of a molecular system, Phys. Rev. A. 21 (1980), 1-11.

[26] R. Thom, Structural stability and Morphogenesis, W. A. Benjamin, Reading, Massachusett 1975.