Temperature and pressure dependence of hydrogen bond strength: A perturbation molecular orbital approach

Abstract

Lengths and strengths of hydrogen bonds are exquisitely sensitive to temperature and pressure. Temperature and pressure sensitivity is the result of the fact that hydrogen bonds are so weak that the internal energy of the bond is important to bond strength, and the equilibrium bond distance is controlled by a combination of thermodynamics and quantum mechanics, rather than quantum mechanics alone. The importance of thermodynamics in the bond length, and strength, of hydrogen bonds is the result of a breakdown in the Born-Oppenheimer approximation that occurs when the energy of the first vibrational excitation of a bond is of the order of kT. Variation of water–water hydrogen bond length and strength with temperature and pressure is discussed in light of the data for the specific volume of ice Ih, the enthalpy of vaporization of liquid water, and the internal energy of the liquid. In most chemical contexts, correction of covalent bond strength for internal energy is not necessary. For hydrogen bonds this is not the case. In hydrogen bonded systems, like liquid water, the internal energy associated with hydrogen bonding is a significant fraction of the internal energy of the system. The variation of hydrogen bond length with temperature is approximately quadratic. Bond strength should also be quadratic with temperature because bond strength depends linearly on bond distance in second order. The internal energy correction is empirically quadratic in temperature. The net result is a linear dependence of apparent hydrogen bond strength on temperature. This can be seen directly in the variation of ΔHvaporization0/T for water with the reciprocal of temperature. The known variations in hydrogen bond equilibria with temperature in liquid formamide are discussed. Variation of the density of ice Ih with pressure, at constant temperature, demonstrates the nonlinear pressure dependence of hydrogen bond length. Because hydrogen bond strengths depend upon temperature and pressure, equilibria that involve hydrogen bonds explicitly depend upon temperature and pressure in addition to the universally appreciated dependence of the equilibrium constant on temperature. The temperature and pressure dependence of hydrogen bond length needs to be explicitly considered when one is modeling the properties of hydrogen bonded networks such as liquid water. Temperature dependence can be easily introduced by utilization of the hydrogen bond length, temperature relationship that is known for ice Ih and using a perturbation molecular orbital (PMO) treatment for bond formation. Our PMO treatment of hydrogen bonding involves second order perturbations between the donor and acceptor molecules. A random structural network model for liquid water based on this approach should be relatively easy to construct. The PMO model gives the relationship between hydrogen bond strength and hydrogen bond length as linear. This quantum mechanical result is quite distinct from the bond strength–bond length relationships obtained in classical models.