ALBERT

Notes: Hydrogen bond strength depends on both temperature and pressure. The gradient for hydrogen bond strength with temperature, or pressure, depends upon the hydrogen bonded structure. These features create an intimate connection between quantum mechanics and thermodynamics in the structure of liquid water. The equilibrium structural model of liquid water developed from analysis of the heat capacity at constant pressure is complex. The model is based on the assumptions that: (i) the hydrogen bond length and molecular packing density of water both vary with temperature; (ii) the number of different geometries for hydrogen bonding is limited to a small set; (iii) water molecules that possess these hydrogen bonding geometries are in equilibrium with each other under static conditions; (iv) significant changes in the slope of the heat capacity, Cp, and to a lesser extent other properties of the liquid, reflect the onset of significant changes in the chemical structure of the liquid; (v) the partial molal enthalpies and entropies of the different water arrays generated from these building blocks differ from each other in their dependence upon temperature; and (vi) the structure of the liquid is a random structural network of the structural components. The equilibrium structural model for liquid water uses four structural components and the assumptions listed above. At the extrapolated-homogeneous nucleation temperature, 221 K, a disordered hexagonal-diamond lattice (tetrahedrally hydrogen bonded water clusters) is the structure of liquid water. At the homogeneous nucleation temperature, ∼238 K, liquid water is a mixture of disordered tetrahedral water arrays and pentagonal water arrays. The abundance of tetrahedral water structures at this temperature causes the system to self-nucleate. As the temperature increases to 266 K the proportion of disordered pentagonal water clusters in the equilibrium mixture increases. At 256 K, the temperature of the previously unrecognized maximum in the heat of fusion of water, "planar"-hexagonal water arrays appear in the liquid. At 273 K the concentration of tetrahedral hydrogen bonded water approaches zero. At the temperature of maximum density, 277 K, the liquid consists of a disordered dodecahedral-water lattice. The equivalence point between pentagonal and "planar"-hexagonal water arrays occurs near 291 K, the approximate temperature of minimum solubility of large hydrocarbons in water. At temperatures above 307.6 K, the minimum in Cp, square water arrays first appear in significant concentrations. Pentagonal water arrays become insignificant in the liquid at the temperature of minimum isothermal compressibility, ∼319 K. The equilibrium point between "planar"-hexagonal and square water arrays occurs near 337 K. As the temperature increases the liquid structure becomes dominated by disordered cubic arrays of water molecules. Structures with fewer than four hydrogen bonds per water molecule appear in the liquid near 433 K. "Planar"-hexagonal clusters are no longer present in the liquid at the temperature of the maximum dissociation constant for water, 513 K. These views are certainly oversimplified. Simple models for density are introduced. A model for viscoscosity based on the variation of hydrogen bond strength with temperature is introduced. Attempts to model density, heat capacity, or other thermodynamic properties of liquid water, using only two functions will not capture the subtle complexity of the equilibrium process. The equilibrium structural model of water has the potential to provide a basis for quantitative descriptions of the liquid's seeming anomalies. © 1998 American Institute of Physics.

Notes: Perturbation molecular orbital (PMO) theory is used to approximate the electronic matrix element in the semiclassical expression for the rate of nonadiabatic electron transfer (ET). The resulting expression gives a satisfactory account of the intramolecular ET rate data reported by Closs, Miller, and co-workers. We develop the idea of electron-transfer efficiency for the contribution of electron transfer to the observed kinetics of ion–molecule collisions followed by electron transfer. Electron-transfer efficiency comes from the calculated ET rate divided by the maximum calculated ET rate. Electron-transfer efficiency values are also obtained by dividing the observed reaction rate by the collision rate, calculated by the PMO treatment of ion–molecule collision rates. We applied this approach to data on electron transfer from sulfurhexafluoride or perfluoromethylcyclohexane anions to aromatic acceptors. The structural reorganization energies, λs, for these reactions were 0.016 and 0.046 eV, respectively. The vibrational reorganization energies, λv, for the reactions were 1.01 and 1.00 eV, respectively. Electron transfer from either of the donor anions to fluoranil occurs in the inverted region. © 1997 American Institute of Physics.

Notes: 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. © 1998 American Institute of Physics.