Electron Density analysis

The representation of matter at an atomic or a subatomic level has been a permanent concern since antiquity. Such a description is necessary to understand the structure and properties of chemical systems. For a long time, it relied on speculations rather than on experimental facts. With the renewal of atomism and the introduction of chemical symbols, chemists began to represent molecules by formulas in which the atomic symbols are linked by straight lines representing bonds. The reliability of the formulas is supported by indirect experimental facts, such as stoichiometry, reactivity, and chirality evidenced by rotatory power. In fact, chemists are like the prisoners of Plato's cave allegory; nevertheless, they are aware that the shadows on the wall are not constitutive of the reality and also that they can tune the fire in order to get different spectra. With the discovery of the electron in 1897 and later of the nucleus, it appeared possible to get a direct picture. The analysis of the Geiger-Marsden experiment1,2 led to the modern picture of the atom with electrons surrounding a nucleus. Moreover, it was possible to estimate the size of the nuclei, the radii of which are at least three orders of magnitude less than those of the corresponding atoms, whereas electrons are much smaller. Indeed, less than 1/109 of the atomic volume is occupied by massive matter. The size of the particles is a first limiting factor that hampers their direct observation in situ in molecules and solids. However, a first step toward a workable representation of the electronic structure was accomplished by Lewis,3 with his theory of the valence. Based on chemical knowledge and, more particularly, on Abbeg's law of valence and countervalence,4 Lewis proposed a cubical atom model in which each valence electron occupies a vertex of a cube, as represented in Figure 1. The model is completed by a series of six 'aufbau' rules enabling the buildup of the electronic structure of atoms in molecules.