One-Dimensional Model of the Hydrogen Bond

Abstract

A one‐dimensional model for hydrogen bonding is proposed based on the potential function V = D[1—exp(—nΔr²/2r)]. The energy associated with both the weak and strong bonds of the configuration RO – H – – – OR₂ is obtained through application of this function. A repulsive Van der Waals potential and an attractive electrostatic potential are also assumed to exist between the two electronegative atoms of the hydrogen bond. Through application of the conditions describing a stable equilibrium, relations are obtained which permit a calculation of OH frequency shifts, OH bonded distances, hydrogen bond energies and k_{o — — — o} force constants, all as a function of the O – – – O distance R. The calculated quantities agree well with those obtained from neutron diffraction, infrared, and other experimental studies. Because of the assumptions involved, this model is best used to describe the properties of hydrogen bonds in crystals. The model is also capable of extention to describe the properties of other types of hydrogen bonds such as HFH, NHN, NHO, OHN, etc.