Electronic charge density topology

Keywords. Electronic charge densities Molecular crystals Topological properties... 

Very similar to the electronic-topological descriptors, electron charge density connectivity index is defined for an - H-depleted molecular graph in which net atomic charges, calculated by computational chemistry, are used as weights for vertices [Estrada and Montero, 1993 Estrada, 1995d] ... 

However, when molecular descriptors are derived from molecular graphs, cis/trans isomerism is not usually recognized and some molecular descriptors were proposed in order to discriminate between cis/trans isomers, such as the - corrected electron charge density connectivity index, and - periphery codes. - Weighted matrices were also devised for obtaining the -> geometric modification number that is added to any topological index in order to discriminate cis/trans isomers. 

The electron density p of a molecule is a physical quantity which has a definite value p(r) at each point of coordinates r in three-dimensional space. The topological properties of this electronic charge distribution can be summarized in terms of its critical points maxima, minima and saddles. Figure 8.1 displays the electronic charge density in three planes of the ethylene molecule. 

The topology of the electronic charge density ip r)), as pointed out by Bader [55], is an accurate mapping of the chemical concepts of atom, bond and structure. The main topological properties are summarized in terms of their critical points (CP) [55,56]. The nuclear positions behave topologically as local maxima in p(r). A bond critical point (BCP) is found between each pair of nuclei, which are considered to be linked by a chemical bond, with two negative (Ai and ki) and one positive (A3) curvature (denoted as (3,-1) CP). The ellipticity (e) of a bond is defined by means of the two negative curvatures in a BCP as ... 

Topology of the electron charge density p(r) has been studied at MP2/6-31G level in order to identify critical points in internal HyB s, and electrostatic interactions... 

Nasertayoob P, Shahbazian S (2008) The topological analysis of electronic charge densities a reassessment of foundations. J Mol Struct Theochem 869 53-58... 

Zhang L, Ying F, Wu W, Hibeity PC, Shaik S (2009) Topology of electron charge density for chemical bonds from valence bond theory a probe of bonding types. Chem A Eur J 15(12) 2979-2989... 

Fig. 11 The isosurfaces of electron charge density, which resemble atomic-orbital like topologies, are shown for the Gaas core of a metalloid cluster (the particular energy bands also are given), reproduced from ref. 139.

Most of the relevant features of the charge density distribution can be elegantly elucidated by means of the topological analysis of the total electron density [43] nevertheless, electron density deformation maps are still a very effective tool in charge density studies. This is especially true for all densities that are not specified via a multipole model and whose topological analysis has to be performed from numerical values on a grid. 

In what follows we will discuss systems with internal surfaces, ordered surfaces, topological transformations, and dynamical scaling. In Section II we shall show specific examples of mesoscopic systems with special attention devoted to the surfaces in the system—that is, periodic surfaces in surfactant systems, periodic surfaces in diblock copolymers, bicontinuous disordered interfaces in spinodally decomposing blends, ordered charge density wave patterns in electron liquids, and dissipative structures in reaction-diffusion systems. In Section III we will present the detailed theory of morphological measures the Euler characteristic, the Gaussian and mean curvatures, and so on. In fact, Sections II and III can be read independently because Section II shows specific models while Section III is devoted to the numerical and analytical computations of the surface characteristics. In a sense, Section III is robust that is, the methods presented in Section III apply to a variety of systems, not only the systems shown as examples in Section II. Brief conclusions are presented in Section IV. 

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