The Physics and Physical Chemistry of Water, 1972 Water Series, Vol. 1

to arrive at some temporary consensus model or models; and to present reliable physical data pertaining to water under a range of conditions, i.e., "Dorsey revisited," albeit on a less ambitious scale. I should like to acknowledge a debt of gratitude to several of my col­ leagues, to Prof. D. J. G. Ives and Prof. Robert L. Kay for valuable guidance and active encouragement, to the contributors to this volume for their willing cooperation, and to my wife and daughters for the understanding shown to a husband and father who hid in his study for many an evening. My very special thanks go to Mrs. Joyce Johnson, who did all the cor­ respondence and much of the arduous editorial work with her usual cheerful efficiency. F. FRANKS Biophysics Division Unilever Research Laboratory ColworthjWelwyn Colworth House, Sharnbrook, Bedford March 1972 Contents Chapter 1 Introduction-Water, the Unique Chemical F. Franks I. lntroduction ........................................ . 2. The Occurrence and Distribution of Water on the Earth 2 3. Water and Life ...................................... 4 4. The Scientific Study of Water-A Short History ........ 8 5. The Place of Water among Liquids . . . . . . . . . . . . . . . 13 . . . . . Chapter 2 The Water Moleeule C. W. Kern and M. Karplus 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 . . . . . . . . . . 2. Principles of Structure and Spectra: The Born-Oppenheimer Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . 3. The Electronic Motion ............................... 26 3.1. The Ground Electronic State of Water ............ 31 3.2. The Excited Electronic States of Water ........... 50 4. The Nuclear Motion ................................. 52 5. External-Field Effects ................................. 70 5.1. Perturbed Hartree-Fock Method . . . . . . . . . . . . . . . 74 . . .

1 Introduction—Water, the Unique Chemical.- 1. Introduction.- 2. The Occurrence and Distribution of Water on the Earth.- 3. Water and Life.- 4. The Scientific Study of Water—A Short History.- 5. The Place of Water among Liquids.- 2 The Water Molecule.- 1. Introduction.- 2. Principles of Structure and Spectra: The Born-Oppenheimer Separation.- 3. The Electronic Motion.- 3.1. The Ground Electronic State of Water.- 3.2. The Excited Electronic States of Water.- 4. The Nuclear Motion.- 5. External-Field Effects.- 5.1. Perturbed Hartree-Fock Method.- 5.2. Perturbed Configuration Interaction Method.- 6. Conclusion.- Appendix A. Bibliography of Theoretical Calculations on the Electronic Structure of the Water Molecule (1925-1970).- Appendix B. Definition of the Symbols Appearing in TN.- Appendix C. Definition of the Symbols Appearing in Evib and Hrotv.- Appendix D. Definition of the Symbols Appearing in the Rotational Matrix Elements.- 3 Theory of Hydrogen Bonding in Water.- 1. Introduction.- 2. Early Theoretical Studies of the Hydrogen Bond.- 3. Potential Function for the Hydrogen Bond.- 4. Recent Theoretical Methods.- 5. Water Dimer.- 6. Water Polymers.- 7. Spectroscopic Properties, Proton Potential Functions, Charge Distribution, and Related Aspects.- 8. Conclusions.- 4 The Properties of Ice.- 1. Introduction.- 2. Phase Behavior of Ice.- 3. Structures of Crystalline Ice Phases.- 4. Thermodynamic Properties of Ice Polymorphs.- 5. Mechanical Properties.- 6. Lattice Dynamics.- 7. Molecular and Ionic Transport in Ice.- 7.1. Dielectric Properties.- 7.2. Self-Diffusion.- 7.3. Electrical Conductivity.- 7.4. Orientational and Ionic Defects in Ice; Theories of Transport Mechanisms.- 8. Summary.- 5 Raman and Infrared Spectral Investigations of Water Structure.- 1. Introduction.- 2. New Experimental Techniques.- 2.1. Stimulated Raman Scattering.- 2.2. Hyper-Raman or Inelastic Harmonic Light Scattering.- 2.3. Fixed-Beam Laser-Raman Method.- 3. Intermodular Vibrations of H2O and D2O.- 3.1. The Restricted Translational Region.- 3.2. The Librational Region.- 3.3. The Five-Molecule, Fully Hydrogen-Bonded C2V Structural Model.- 4. Intramolecular Vibrational Spectra from H2O in H2O and D2O.- 4.1. Raman Spectra.- 4.2. Infrared Absorbance Spectra.- 4.3. Stimulated Raman Spectra.- 4.4. Near-Infrared Spectra.- 5. Intramolecular Vibrational Spectra from H2O and D2O.- 5.1. Spontaneous and Stimulated Raman Spectra.- 5.2. Infrared Spectra.- 6. Relation of Component Properties to Water Structure.- 7. Thermodynamic Tests of the Consecutive Hydrogen-Bond Disruption Model.- 8. Current and Future Work.- 6 Nuclear Magnetic Resonance Studies on Water and Ice.- 1. Theoretical and Experimental Foundations of Magnetic Resonance.- 1.1. Properties of Nuclei in Electric and Magnetic Fields.- 1.2. Spectroscopic Parameters Describing Nuclear Magnetic Resonance.- 1.3. Experimental Arrangements.- 2. Magnetic Shift and Spin Coupling Phenomena in Water Vapor, Water, and Ice.- 2.1. Theory of Chemical Shift.- 2.2. Measurement of Deuteron and 17O Chemical Shifts in Water.- 2.3. Structural Interpretations of Chemical Shift Measurements.- 2.4. Measurements of Spin-Spin Coupling Constants.- 3. Measurement and Interpretation of Magnetic Relaxation Times in Water and Ice.- 3.1. Dipole-Induced Relaxation.- 3.2. Measurement and Interpretation of Proton Relaxation in Water.- 3.3. Measurement and Interpretation of Proton Relaxation in Ice.- 3.4. Quadrupole-Induced Relaxation.- 3.5. Measurement and Interpretation of Deuteron and 17O Relaxation in Water.- 3.6. Summary of Relaxation Experiments on Liquid Water.- 3.7. Measurement of Self-Diffusion Coefficient.- 3.8. Measurement of Kinetic Rate Constants in Water.- 4. The Contributions of NMR Methods to the Structure Problem in Liquid Water.- 4.1. Results from Chemical Shift Measurements.- 4.2. Results from Relaxation Measurements.- 7 Liquid Water: Dielectric Properties.- 1. Introduction.- 2. The Electrical Properties of the Free Water Molecule.- 3. The Measured Static Dielectric Constant.- 4. Theory of the Static Dielectric Constant.- 5. The Static Dielectric Constant Calculated on Various Models.- 6. Interpretation of Static Dielectric Constant with Induced-Dipole Contribution.- 7. Microwave and Submillimeter Dielectric Constants.- 8. Kinks?.- 9. Submillimeter Measurements.- 10. Theory of the Dielectric Constant in a Time-Varying Field.- 11. Interpretation of the Relaxation Times and Absorption Bands.- 12. Interpretation of Data in the Submillimeter Band. Conclusions.- 8 Liquid Water: Scattering of X-Rays.- 1. Introduction.- 2. Experimental Methods.- 2.1. Large-Angle Scattering.- 2.2. Small-Angle Scattering.- 2.3. Data Reduction.- 3. Analysis of Diffraction Data.- 3.1. Scattering by Heteroatomic Liquids.- 3.2. Scattering by Model Liquids.- 4. Diffraction Pattern of Liquid Water.- 4.1. Survey of Experimental Data.- 4.2. Interpretation of the Diffraction Pattern.- 5. Conclusions.- 9 The Scattering of Neutrons by Liquid Water.- 1. Introduction.- 2. The Neutron Scattering Method.- 2.1. Nuclear Scattering of Neutrons.- 2.2. Coherent and Incoherent Scattering.- 2.3. Isotopic Substitution.- 2.4. The Scattering Law and Correlation Functions.- 2.5. Neutron Spectra from Water.- 3. Structural Measurements.- 3.1. Structure Factor for Water.- 3.2. Molecular Structure Factors.- 4. Quasielastic Scattering of Neutrons by Water.- 4.1. Debye-Waller Factor.- 4.2. Diffusive Motions.- 5. Inelastic Scattering of Neutrons by Water.- 5.1. Spectral Density Function.- 5.2. Experimental Results.- 6. Discussion.- Appendix. Calculation of Orientational Correlation Factors for Molecules.- 10 Thermodynamic and Transport Properties of Fluid Water.- 1. Introduction.- 2. Thermodynamic Properties.- 2.1. The Macroscopic Viewpoint.- 2.2. Volume Properties.- 2.3. Thermal Properties.- 2.4. Liquid-Vapor Equilibria.- 2.5. Critical Point.- 3. Transport Properties.- 3.1. The Hydrodynamic Viewpoint.- 3.2. Vapor.- 3.3. Liquid.- 11 Application of Statistical Mechanics in the Study of Liquid Water.- 1. Introduction.- 2. Characteristic Features of an Effective Pair Potential for Liquid Water.- 3. Application of the Percus-Yevick Equation.- 4. Application of the Monte Carlo Technique.- 5. Some Specific Applications of the Pair Correlation Function.- 5.1. Density Fluctuations in Water.- 5.2. Local Structure Index for Water.- 5.3. Hole and Particle Distributions in Water.- 5.4. A Possible Exact Definition of the Structure of Water.- 12 Liquid Water—Acoustic Properties: Absorption and Relaxation.- 1. Introduction.- 2. Ultrasonic Absorption.- 3. Ultrasonic Techniques.- 3.1. Acoustic System.- 3.2. Pressure- and Temperature-Control Systems.- 3.3. Electronics.- 4. Experimental Results.- 4.1. Volume Viscosity.- 5. Relaxational Compressibility.- 6. Structural Relaxation Time.- 7. Conclusions.- 13 Water at High Temperatures and Pressures.- 1. Introduction.- 2. Thermodynamic Properties.- 2.1. PVT Data and Equation of State.- 2.2. Thermodynamic Functions.- 3. Transport Properties.- 3.1. Viscosity.- 3.2. Self-Diffusion.- 3.3. Thermal Conductivity.- 4. Electrical Properties.- 4.1. Static Dielectric Constant.- 4.2. Specific Conductance and Ionic Conductances.- 5. Ionic Product.- 6. Spectroscopic Studies.- 6.1. Infrared Spectral Studies.- 6.2. Raman Spectral Studies.- 6.3. Interpretation of Spectroscopic Results with Respect to Water Structure.- 7. Concluding Remarks.- 14 Structural Models.- 1. The Nature of Models.- 2. Requirements a Water Model Must Attempt to Satisfy.- 3. Some Properties of Water of Special Current Interest.- 3.1. Thermodynamic and Mechanical Properties; Structure and Fluctuations.- 3.2. X-Ray Scattering; Structure and Fluctuations.- 3.3. Hydrogen Bonds and Structure.- 3.4. Spectroscopic Properties: Broken Hydrogen Bonds.- 3.5. Vapor-Pressure Isotope Effect.- 3.6. Molecular Motions.- 4. Brief Survey of Models.- 4.1. Mixture Models.- 4.2. Uniformist Models.- 4.3. Interstitial Models.- 5. The Present „Best Guess“.- 5.1. Bonding.- 5.2. Structure Pattern.- 5.3. Equilibrium Relations.- 5.4. Molecular Motions.- 5.5. Heat Capacity.- References.