Temperature dependence of the low- and high-frequency Raman scattering from liquid water

Abstract

Low frequency Δν̄=0–350 cm⁻¹, Raman intensity data were obtained from liquid water between 3.5 and 89.3 °C using holographic grating double and triple monochromators. The spectra were Bose–Einstein (BE) corrected, I/(1+n), and the total integrated (absolute) contour intensities were treated by an elaboration of the Young–Westerdahl (YW) thermodynamic method, assuming conservation of hydrogen‐bonded (HB) and nonhydrogen‐bonded (NHB=bent and/or stretched, O–H O) nearest‐neighbor O–O pairs. A ΔH^°₁ value of 2.6±0.1 kcal/mol O–H ⋅⋅⋅ O or 5.2±0.2 kcal/mol H₂O (11 kJ/mol O–H ⋅⋅⋅ O, or 22 kJ/mol H₂O) resulted for the HB→NHB process. This intermolecular value agrees quantitatively with Raman and infrared ΔH° values from the one‐ and two‐phonon OH‐stretching regions, and from molecular dynamics, depolarized light scattering, neutron scattering, and ultrasonic absorption, thus indicating a common process. A population involving partial covalency of, i.e., charge transfer into, the H ⋅⋅⋅ O units of linear and/or weakly bent hydrogen bonds, O–H ⋅⋅⋅ O; is transformed into a second high energy population involving bent, e.g., 150° or less, and/or stretched, e.g., 3.2 Å, but otherwise strongly cohesive O–H O interactions. All difference spectra from the fundamental OH‐stretching contours cross at the X(Z,X+Z)Y isobestic frequency of 3425 cm⁻¹. Also, total integrated Raman intensity decreases occurring below 3425 cm⁻¹ with temperature rise were found to be proportional to the total integrated intensity increases above 3425 cm⁻¹, indicating conservation among the HB and NHB OH‐stretching classes. From the enthalpy of vaporization of water at 0 °C, and the ΔH^°₁ of 2.6 kcal/mol O–H ⋅⋅⋅ O, the additional enthalpy, ΔH^°₂, needed for the complete separation of the NHB O–O nearest neighbors is ∼3.2 kcal/mol O–H ⋅⋅⋅ O or ∼6.4 kcal/mol H₂O (13 kJ/mol O–H ⋅⋅⋅ O or 27 kJ/mol H₂O). The NHB O–O nearest neighbors are held by forces other than those involving H ⋅⋅⋅ O partial covalency, i.e., electrostatic (multipole), induction, and dispersion forces. The NHB O–O pairs do not appear to produce significant intermolecular Raman intensity because they lack H ⋅⋅⋅O bond polarizability, but the corresponding NHB OH oscillators do contribute weakened Raman intensity above 3425 cm⁻¹. An ideal solution thermodynamic treatment employing ΔH^°₁ =2.6 kcal/mol O–H ⋅⋅⋅ O, the HB mole fraction, and the vapor heat capacity, yielded a very satisfactory specific heat value of 1.1 cal deg⁻¹ g⁻¹ H₂O at 0 °C. The NHB mole fraction, f_u, from the YW treatment is negligibly small, 0.06 or less, for t<−50 °C. However, f_u increases to 0.16 at 0 °C, and f_u≊1 at 1437 °C, where recent shock‐wave Raman measurements indicate loss of all partially covalent, charge transfer hydrogen bonding.