Atoms and the Charge Distribution

For the reasons discussed above, an atom is to be defined in real space. Thus, while the theory of atoms in molecules is obtained from quantum mechanics, its vehicle of expression is the electronic charge density, the distribution function which determines an atom s form in real space. Because the charge density must exhibit a cusp at the position of a nucleus and satisfy a particular condition there, the information contained in the electronic charge density serves also to determine the positions of and the charges on the nuclei in a molecule. 

Because of the dominance of the nuclear-electron force, the electronic charge distribution exhibits local maxima at the positions of the nuclei with the result that recognizable atomic forms are created within a molecular system. These forms are so dominant in determining the structure of the charge distribution that their individual properties make characteristic contributions to the properties of the total system. Thus the atomic basis for the classification of chemistry could and did evolve as the working model of chemistry before its underlying physical basis was known. 

Schrodinger s state function contains all the information that can be known about a quantum system. Among the properties of a system it predicts is the distribution of charge. The quantity dxj dx2 - dx , where dxi denotes an infinitesimal volume element dii) and the spin component for electron i, is the probability that each of the N electrons in a system will be in some particular volume element with a particular spin component. If this quantity is summed over all spins and integrated over the spatial coordinates of all electrons but those of electron number one, what remains is the probability that electron number one is in some particular volume element dz. That is. 

The electronic charge density is responsible for scattering the X-rays in a crystal structure determination, a determination made possible by the charge density exhibiting its maximum values at the positions of the nuclei. Such experiments can be used to determine the charge density, averaged over the thermal motions of the nuclei. Rather than a 

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