An electrostatic interaction correction for improved crystal density prediction

Recent work by others has shown that the densities of C,H,N,O molecular crystals are, in many instances, given quite well by the formula M/V_m, in which M is the molecular mass and V_m is the volume of the isolated gas phase molecule that is enclosed by the 0.001 au contour of its electronic density. About 41% of the predictions were in error by less than 0.030 g/cm³, and 63% by less than 0.050 g/cm³. However, this leaves more than one-third of the compounds with errors greater than 0.050 g/cm³, or in some instances, 0.100 g/cm³. This may indicate that intermolecular interactions within the crystal are not being adequately taken into account in these cases. Accordingly, the effectiveness of including a second term that reflects the strengths, variabilities and degree of balance of the positive and negative electrostatic potentials computed on the surfaces of the isolated molecules, has been included. The database was selected such that half of the densities predicted by M/V_m had errors larger than 0.050 g/cm³. The introduction of the electrostatic interaction correction produced a marked improvement. Overall, 78% of the predictions are within 0.050 g/cm³ of experiment, with 50% within 0.030 g/cm³. Among those that originally all had errors larger than 0.050 g/cm³, 67% are now less. The reasons for the better performance of the dual-variable formula are analysed.