Topological Definition of Molecular Structure

Geometrical configurations of a set of atomic nuclei related to the points of minima on a PES represent molecular structures. Theoretical chemistry describes the mechanisms of all chemical transformations by means of the molecular structures whose chief characteristic are the chemical bonds linking various atoms within a molecule. It is the changes in the molecular structure which determine the essence of the chemical reaction. Therefore in order to correctly describe the structure, it is important to define rigorously this notion on the basis of the first principles of quantum mechanics. 

Reaction MINDO/3 exper MINDO/3 exper MINDO/3 exper 

A real prospect for a correct definition of molecular structure on the basis of quantum mechanics emerged thanks to a topological approach to the analysis of the electron density p(q) distribution in a system characterized by this density. This approach developed by Bader [19], based on the topological properties of the charge distribution in molecular systems, provides an invariant pattern of the distribution of chemical bonds between the atoms in a molecule and determines unambiguously the type of a molecular structure for both the classical (Butlerov-type) and the nonclassical (see Ref. [20]) molecular systems. 

The topological characteristics of the distribution of electron density p(r) in a molecular system are determined by the properties of the gradient field Vp(r, q) where r is the coordinate of the point in the real space where p is calculated within the given nuclear configuration q. This field is represented by the trajectories Vp(r) as shown in Fig. 1.5. 

The gradient trajectories Vp cover the whole space, they can begin and end only at the critical points or at infinity. Critical points of a gradient field are the points in which 

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