A model for resonance-assisted hydrogen bonding in crystals and its graph set analysis

Resonance-assisted hydrogen bonding is treated by the simple quantum-mechan ical model of a particle on a ring with different effective masses in the h ydrogen bond and in the conjugated segment attached to its ends. The model is applied to an intramolecular hydrogen bond and extended to a hydrogen-bo nded dimer and rings of arbitrary size up to an infinite chain of molecules , thus covering the main patterns of bonding identified by graph-set analys is. Analysis of intramolecular hydrogen bonding yields an electron effectiv e mass in the hydrogen bond segment of about 34 electron masses. Conjugatio n always lowers the energy, but the lowering per molecule decreases with in creasing ring size, that for the chain being one-third of that for the intr amolecular hydrogen bond. This result rationalizes a predominance of intram olecular hydrogen bonds and dimer rings, given that geometrical factors als o affect bonding.