Size in terms of electron density

A somewhat more appropriate and physically acceptable definition of molecular volume and surface can be derived from the spatial extension of the electron density. The electron density p(x,y,z) can nowadays be easily calculated on a three-dimensional 

If Qtox is less than the sum of the atomic numbers of the atoms that compose the molecule, some electrons have been left out of the envelope. 

Distance between centers of mass (A) Overlap integral (10-3 eA-3) Overlap volume at 0.002 eA 3 limit (A ) 

A sensitive indicator of the amount of overlap between neighbor molecules in a crystal is the actual overlap integral between elecHon densities  

The corresponding overlap volume is the sum of the elementary volumes of all space pixels in which the electron density of both molecules is above a given threshold. The case is illustrated in Table 1.5 for the succinic anhydride crystal. As expected, the overlap integral correlates with the distance between molecular centers of mass. Coherently with the results shown in Table 1.4, the overlap volumes are non-zero only if the electron density threshold is less than 0.02 e A . In Section 12.2 it will be shown that the overlap integral correlates with the repulsion energy between neighbor molecules, and that the outer electrons play a crucial role in defining the details of the directional intermolecular interaction in crystals. 

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