The volume occupied by a molecule was defined in two different ways: one, denoted by
Vnet, is the net volume for the van der Waals' contact model for the molecule which was constructed by the use of the bond lengths, the bond angles and the van der Waals' radii of the constituent atoms, and the other,
Vcry., is the mean volume occupied by the molecule in the crystalline state.
A program was developed to give an accurate estimation of
Vnet in which the number of a small cell having a volume increment of
ΔxΔyΔz was computed within the range inside the van der Waals' contact model. The
Vnet calculated in this way was denoted by
Vlp.. Calculations of
Vlp. were carried out for 12 azo and 6 anthraquinone compounds and the results were compared with the values of
VKi. and
VEd. which were obtained according to Kitaigorodskii's and Edward's methods, respectively. In these two methods, the volume increments specified to the atom or atomic group were summed up along the whole molecule. In spite that
VKi. (and
VEd.) neglects the overlapping of the van der Waals' contact spheres between nonbonded atoms within a molecule, it was surprising to find that
VKi. showed a good agreement with
Vlp. respecting to the above aromatic molecules.
VEd. gave values several % smaller than
Vlp.Vcry. can be experimentally determined by density measurement (
Vρ). It can also be calculated from the unit cell volume and the number of the molecules in the cell (
VX). For flat molecules such as those examined in the present study, it was found that
Vcry. can be predicted well from the area of the silhouette of the van der Waals' model multiplied by a “thickness” This thickness was determined by a least squares fit so as to give
VW (=silhouette area×thickness)=
VX where some twenty typical aromatic compounds having known X-ray data were considered. Good agreement was found between
VW and
Vρ for the aromatic molecules examined in this study.
Finally, the packing density
K in the crystalline state, given by
K=
Vnet/
VX, was also discussed.
View full abstract