TEMPERATURE AND PRESSURE-DEPENDENCE OF HYDROGEN-BOND STRENGTH - A PERTURBATION MOLECULAR-ORBITAL APPROACH

Lengths and strengths of hydrogen bonds are exquisitely sensitive to t emperature and pressure. Temperature and pressure sensitivity is the r esult of the fact that hydrogen bonds are so weak that the internal en ergy of the bond is important to bond strength, and the equilibrium bo nd distance is controlled by a combination of thermodynamics and quant um mechanics, rather than quantum mechanics alone. The importance of t hermodynamics in the bond length, and strength, of hydrogen bonds is t he result of a breakdown in the Born-Oppenheimer approximation that oc curs 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 da ta for the specific volume of ice I-h, 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 b onded systems, like liquid water, the internal energy associated with hydrogen bonding is a significant fraction of the internal energy of t he system. The variation of hydrogen bond length with temperature is a pproximately quadratic. Bond strength should also be quadratic with te mperature because bond strength depends linearly on bond distance in s econd order. The internal energy correction is empirically quadratic i n temperature. The net result is a linear dependence of apparent hydro gen bond strength on temperature. This can be seen directly in the var iation of Delta H-vaporization(0)/T for water with the reciprocal of t emperature. The known variations in hydrogen bond equilibria with temp erature in liquid formamide are discussed. Variation of the density of ice I-h With pressure, at constant temperature, demonstrates the nonl inear pressure dependence of hydrogen bond length. Because hydrogen bo nd strengths depend upon temperature and pressure, equilibria that inv olve 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 h ydrogen bond length needs to be explicitly considered when one is mode ling 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 I-h and using a perturbation molecular orbital (PMO) treatment for bon d formation. Our PMO treatment of hydrogen bonding involves second ord er perturbations between the donor and acceptor molecules. A random st ructural 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. Thi s quantum mechanical result is quite distinct from the bond strength-b ond length relationships obtained in classical models. (C) 1998 Americ an Institute of Physics. [S0021-9606(98)50641-1].