Calculation of lattice energies of organic crystals: the PIXEL integration method in comparison with more traditional methods

The lattice energies of 47 crystal structures of organic compounds spanning a wide range of chemical functionalities are calculated using simple atom-atom potential energy functions, using coulombic terms with point-charge parameters, and using the PIXEL formulation, which is based on integral sums over the molecular electron density to obtain coulombic, polarization, dispersion and repulsion lattice energies. Comparisons among the different formulations, and the sensitivity and significance of the results against convenience, ease of application and number of parameters, are discussed. Improvements in the treatment of overlap repulsion in PIXEL are described, as well as a scheme for the minimization of the crystal lattice energy, based on the Symplex algorithm, which although computationally demanding, is shown to be feasible even with comparatively modest computing resources. The reproduction of experimental heats of sublimation is only marginally better with the PIXEL method, which however has great advantages in its being generally applicable in principle throughout the periodic table, at the expense of a minimal number of parameters, and in the fact that it sees the intermolecular interaction as the effect of the whole molecular electron density, in a physically more justifiable approach. This latter view in turn suggests a transition from a consideration of atom-atom bonds to a consideration of molecule-molecule bonding, opening a new view of packing factors in molecular crystals.