Molecular charge density, gradient vector

The theory of molecular structure based on the topology of molecular charge distribution, developed by Bader and co-workers (83MI2 85ACR9), enables certain features to be revealed that are characteristic of the systems with aromatic cyclic electron delocalization. To describe the structure of a molecule, it is necessary to determine the number and kind of critical points in its electronic charge distribution, i.e., the points where for the gradient vector of the charge density the condition Vp = 0 is fulfilled. 

According to the AIM theory, an atom is defined as a region of space bounded by a surface that is not crossed by any gradient vectors of p(r) (the so-called zero-flux property) [45]. A molecular system is thus partitioned into atomic basins whose boundaries are such surfaces. Integration of the electron density over an atomic basin A gives its total electron population Na so that the net atomic charge is q = — Na- Koch and Popelier proposed the use of... 

The critical point is the point at which the gradient vector field for the charge density is zero, that is, either a maximum or minimum along N. The condition Vp(r) N(r) = 0 applied to other paths between two atoms defines a unique surface that can represent the boundary of the atoms within the molecule. The electron density within these boundaries then gives the atomic charge. The combination of electron density contours, bond paths, and critical points defines the molecular graph. This analysis can be applied to electron density calculated by either MO or DFT methods. For a very simple molecule such as Hj, the bond path is a straight line between the nuclei. The... 

These qualitative associations of topological features of p with elements of molecular structure can be replaced with a complete theory, one which recovers all of the elements of structure in a manner that is totally independent of any information other than that contained within the charge density The underlying structure of the charge density is brought to the fore in its associated gradient vector field. The boundary condition of a quantum subsystem is also stated in terms of this field... 

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