Molecular topological definition

Tsirelson, V.G., Zou, P.F. and Bader, R.F.W. (1995) Topological definition of crystal structure determination of the bonded interactions in solid molecular chlorine, Ada Cryst., A51, 143-153. 

This unique labeling problem 14) originally required the definition of multiple equilibrium positions and redundant atom labelling schemes... resulting in a tedious over-definition of the molecular topology 14). 

Topological Definition of Atoms, Bonds, and Structure.—The definitions of an isolated atom, of an atom in a molecule, of a chemical bond, and of molecular structure derive from the properties of critical points of the charge density. 

Because of the dominant topological property exhibited by a molecular charge distribution—that it exhibits local maxima at the positions of the nuclei—the imposition of the quantum boundary condition of zero flux leads directly to the topological definition of an atom. Indeed, the interatomic... 

Gatti, C., Saunders, V.R. and Roetti, G. (1994) Crystal field effects on the topological properties of the electron density in molecular crystals the case of urea, /. Chem. Phys., 101, 10686-10696. Tsirelson, V.G., Zou, P.F. and Bader, R.F.W. (1995) Topological definition of crystal structure determination of the bonded interactions in solid molecular chlorine. Cryst., A51, 143-153. Platts, J.A. and Howard, S.T. (1996) Periodic Hartree-Fock calculations on crystalline HCN,/. Chem. Phys., 105,4668-4674,... 

For a working definition of molecular structure, we have adopted the one given by Eliel The structure of a molecule is completely defined by the number and kind of atoms and the linkages between them . We have applied the term molecular topography to the three-dimensional arrangement of the atoms in a particular conformation the term configuration is also used. The term molecular topology refers to the set of atoms and connections within the molecular skeleton, that is, the molecular structure as defined by Eliel. 

Attractive van der Waals forces between porphyrins and Ceo are definitely appreciable, when both moieties are linked to each other, rather than just mixed. Importantly, whenever affirmed possible by the molecular topology of the system, these moieties spontaneously tend to achieve close spatial proximity relative to each other. As illustrative... 

These pharmacophore techniques are different in format from the traditional pharmacophore definitions. They can not be easily visualized and mapped to the molecular structures rather, they are encoded as keys or topological/topographical descriptors. Nonetheless, they capture the same idea as the classic pharmacophore concept. Furthermore, this formalism is quite useful in building quantitative predictive models that can be used to classify and predict biological activities. 

The field of stereochemistry serves as a unifying theme for the expanded definition and diversification of chemistry. The consequences of molecular and macromolecular shape and topology are central to issues of chemical reactivity, physical properties, and biological function. With that view, the importance of stereochemistry had never been greater, and it is hoped that this series will provide a forum for documentation of significant advances in all of these subdisciplines of chemistry. 

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

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