The Long and Short Radii for Hydrogen in Hydrogen Bonded Complexes

Hydrogen bonding was initially identified by comparing the distance between the heavy atoms D and A in a DH•••A hydrogen bond, to the sum of their van der Waals (vdW) radii as locating the H atom was not possible. In recent years, hydrogen bond radii (HBR) have been defined for typical hydrogen bond donors DH and acceptors, A. However, both these approaches make an unreasonable assumption of treating all the atoms as spheres. This study advances the understanding of hydrogen bond distances by estimating the shape of hydrogen atoms in HD molecules and in A•••HD complexes through electron density profiles. Results reveal that hydrogen exhibits an elliptical shape in both isolated HD molecules and A•••HD complexes, with the minor axis aligned along the HD bond. In non-linear hydrogen bonds, HBR exhibits angle dependence due to anisotropy in H atomic structure, validated through quantum chemical calculations and Atoms in Molecules (AIM) theory. This study underscores the necessity of adopting directional and environment-dependent HBR, short and long radii, over one spherical vdW or HBR for hydrogen bond identification. The proposed findings are also validated using the data for OH•••N and NH•••N hydrogen bonds identified in the CCDC database. We have demonstrated the utility of long and short radii using several illustrative examples.