On the topological approach to the concept of chemical structure

Abstract

In this article we propose a new topology, based on the stable attractors of the gradient field of the potential energy hypersurface, that may be used as a general definition of a stable chemical structure. We further construct two examples of particular realizations of this abstract topology. One of them is closely related to the catchment-region topology of Mezey and the other one to the molecular-graph model of Bader. A particularly interesting point is that both topologies lead to equivalent definitions of molecular structure; in particular, they permit us to differentiate between cis-trans isomers and rotational conformers, that had equivalent structures in the definition proposed by Bader.

A Criteria To Classify Biological Activity of Benzimidazoles from a Model of Structural Similarity

“…First of all, it is necessary to define the variables. As a hypothesis we outline that it is necessary to consider at least two classes of descriptors to characterize the molecular structure: those which describe the relationships between the atom and their neighbors in the molecule (structural formula) and those allowing the quantification (directly or indirectly) of the interactions between themselves. , …”

Upper and lower bounds for molecular energies

“…Up to this point, the results suggest that the energy of any molecular system may lay between the energy of the cluster of N hydrogen atoms and the energy of an atom of nuclear charge N. If this is true, we would have a lower bound for all the elements in the complex K, easily calculable, and a minimal upper bound, given by the cluster of hydrogen atoms, in principle of lower computational complexity. 7. CONCLUDING REMARKS In this paper we have proposed, using the symmetry properties of the nuclear charge space, a scheme to classify Financial support for this work was provided by COL-CIENCIAS.…”

“…(For previous studies on the abstract nuclear charge space, see, for instance, refs 5 and 6 and others quoted therein.) NZ = {z, z: z¡ is the nuclear charge of the ith nucleus} (7) The points in NZ can be "added" and "multiplied by a scalar" according to the usual definitions: Zw = (zf*, zf.....zf*) and zw = (zf, zf,.... zf) zW and z(í) G NZ z<** + z« = (zf + zf, zf + zf.....zf * + zf) az(K) = (azf, azf,..., azf*) (8) We will be constrained to vectors with norm |z| given by |z| = £z = TV (9) that is, we will work in a subset defined in the positive orthant of an Euclidean space, whose elements are isoelectronicisoprotonic molecular systems, if m is constant. Evidently, any molecule must be represented by a vector belonging to a subset of ^Z, of suitable dimension TV.…”

Graph Theoretical Similarity Approach To Compare Molecular Electrostatic Potentials

“…Molecular similarity may be considered as a fuzzy concept, and to a great extent its fuzziness arises because of the lack of a rigorous definition of molecular structure, which is also another fuzzy concept. [1][2][3][4][5][6][7] Therefore, there are almost as many definitions of molecular similarity as representations of molecular structure. Molecular similarity may be regarded as shape similarity from a classical [8][9][10] or quantum perspective, 3,4,11 graph similarity, [12][13][14] or as a relation among quantum mechanical descriptors, [15][16][17] just to mention some examples.…”