Deciphering the driving forces in crystal packing by analysis of electrostatic energies and contact enrichment ratios

Hirshfeld surface analysis is a widely used tool for identifying the types of intermolecular contacts that contribute most significantly to crystal packing stabilization. One useful metric for analyzing these contacts is the contact enrichment descriptor, which indicates the types of contacts that are over- or under-represented. In this statistical study, enrichment ratios were combined with electrostatic energy (E_elec) data for a variety of compound families. To compute the electrostatic interaction energy between atoms, charge density models from the ELMAM2 database of multipolar atoms were used. As expected, strong hydrogen bonds such as O/N-H...N and O/N-H...O typically display large enrichment values and have the most negative (i.e. favorable) electrostatic energies. Conversely, contacts that are repulsive from an electrostatic perspective are usually the most under-represented. Analyzing the enrichment ratio and electrostatic energy indicators was shown to help identify which favorable contacts are the most competitive with each other. For weaker interactions, such as hydrophobic contacts, the behavior is less clear cut and can depend on other factors such as the chemical content of the molecule. The anticorrelation between contact enrichment and E_elec is generally lost for weaker contacts. However, we observed that C...C contacts are often enriched in crystal structures containing heterocycles, despite the low electrostatic attraction. For molecules with only weak hydrogen bond donors/acceptors and hydrophobic groups, the correlation between contact enrichment and E_elec is still evident for the strongest of these interactions. However, there are some exceptions where the most favorable contacts from an electrostatic perspective are not the most over-represented. This can occur in cases where the shape of the molecule is complex or elongated, favoring dispersion forces and shape complementarity in the packing.