D. F. Hornig

Raman Intensities of HDO and Structure in Liquid Water

Photoelectric Raman spectra of HDO in 5‐mole % isotopically substituted water show single, broad, slightly asymmetric bands in both of the regions containing the uncoupled fundamental stretching motions. An empirical correlation between O–H or O—D stretching frequency and O···O hydrogen‐bonded distance has been used to map the frequency coordinate of the spectra onto an intermolecular distance scale, and the Raman bands are replotted on this abscissa. The resulting intermolecular distribution functions for liquid water agree with x‐ray results and support the suggestion that the breadth of the HDO uncoupled stretching bands reflects the variation of intermolecular distance. Moreover, it is noted that the corresponding infrared and Raman bands are almost superposable, and that this indicates little hydrogen‐bond breakage in liquid water. The distribution of intermolecular distances represented by the spectra is compared to that incorporated in some of the structural models for liquid water. It appears that...

INTER AND INTRAMOLECULAR POTENTIALS AND THE SPECTRUM OF ICE

Whereas the spectra of H2O and D2O ice cannot yet be explained unambiguously, the spectra of HDO in dilute solution in either H2O or D2O may be interpreted readily. In particular, since vOH occurs at 3275 cm—1 and 2 vOH at 6300 cm—1, nearly the harmonic value, the barrier to proton transfer lies well above the latter level and must exceed 23 kcal/mole. The width of vOD at 2416 cm—1 is only 20 cm—1, whereas that of vOH is about 80 cm—1 and 2 vOH about 600 cm—1. These widths can be explained by proton tunneling if the barrier height is near 32 kcal, in which case the second minimum must lie below the level vOH. It must therefore be less than 14 kcal/mole above the primary minimum. A doubling of vOD from OD···OD pairs was also observed and the magnitude of the splitting is consistent with an effective charge of 0.6e on the protons. It is clear from these results that the usual width of hydrogen bonded OH lines is not an intrinsic characteristic of the O–H···O bond but results largely from intramolecular coup...

Vibration—Rotation Spectra of CH4 and CD4 Impurities in Xenon, Krypton, and Argon Crystals

The infrared spectra of CH4 and CD4, present as substitutional impurities in crystals of argon, krypton, and xenon, were studied at temperatures ranging from 5° to 40°K.Both v3 and v4 of CH4 in xenon showed a simple four line pattern which is consistent with that expected for a slightly hindered rotor. In krypton and argon a fifth line appeared on v3, as expected from Kings theoretical calculations for a tetrahedral rotor in an octahedral field. In addition, argon showed absorption due to pairs or higher aggregates of CH4 molecules.The rotational spectrum of CD4 is much more highly perturbed. Detailed assignments to hindered rotational levels could not be made but the general features are in accord with Kings model.The frequencies of the CH4 and CD4 absorption bands increase steadily in going from xenon to krypton to argon. This can be accounted for by the decrease in the sizes of the cavities occupied, with corresponding larger repulsive interactions between the CH4 or CD4 and the host atoms.

Rotational States of a Tetrahedron in a Cubic Crystal Field

The Schrodinger equation is solved for the rotational states of a rigid cube whose center of mass is fixed at a point of symmetry in an external field. This is shown to be equivalent to the equation of motion for a regular tetrahedron in a field with symmetry Oh. The quantum states are classified under the direct product group Ō×O, where Ō is an octahedral group of rotations about body‐fixed axes and O is a similar but distinct group of rotations about space‐fixed axes. The wavefunctions are obtained by an expansion in a series of symmetry‐adapted linear combinations of spherical‐top functions. Projection operators are defined which generate the various linear combinations. Closed‐form expressions are obtained for the matrix elements of the Hamiltonian and of the projection operators. Upper and lower bounds are computed for representative energy levels. The results demonstrate that using basis sets of practical size, high accuracy can be obtained. This analysis forms the basis of a more general theory of ...

Vibrational Spectrum of Crystalline HF and DF

Infrared spectra of pure crystalline HF and DF have been obtained over the region 30–4000 cm−1, and the spectra of the dilute isotopic mixed crystals have been studied in the intramolecular region 2000–4000 cm−1. Unlike previous workers, we find four bands in the stretching region of pure DF crystals, as well as the previously‐reported four in the corresponding region of the HF spectrum. Direct observation of a lattice band near 200 cm−1 in both HF and DF, together with the line spacing in the stretching region permits an unambiguous assignment of the extra pair of lines in the intramolecular region as combination bands. The Raman spectra of crystalline HF and DF reveal four lines in the stretching region and one lattice transition. With the aid of simple intensity rules and correlations with the other hydrogen halides, a complete assignment of the vibrational bands is made except for the librational region, where the multiplicity of lines and the peculiar behavior of one of them under different depositio...

Infrared Spectra and Structures of the Crystalline Phases of CH4 and CD4

Infrared spectra of CH4 and CD4, in the region of the fundamentals ν3 and ν4, have been obtained in all of their crystalline phases at temperatures ranging from 5° to 40°K. In addition, the spectra of dilute solutions of CH4 and CD4 in one another have been studied through the same temperature range. The spectra of the dilute solutions consist of single sharp lines for both fundamentals, demonstrating that the barriers to molecular rotation are high in all the phases. The fine structure observed in the low‐temperature phases of the pure crystals is inconsistent with any of the structural models heretofore proposed but a model for phase II is suggested which is consistent with the spectra and which shows very efficient packing. Phase III of CD4 is probably complex and of low symmetry. Phase I is probably disordered.

Motion of the Ammonium Ion in Lattices of the NaCl Type

The infrared spectrum of NH4I in the NaCl‐type phase gives insufficient information about the motion of the ammonium ions in that phase. Dilute solutions of NH4+ in NaCl‐type alkali halides provide considerably more detail in the form of a fine structure in most of the absorption bands which becomes visible on sufficient cooling. This fine structure is most certainly correlated with a rotational motion of the NH4+ ion. However, both models suggested in the literature—free rotation and rotation of the ion about a N–H···X— axis—deviate in many important respects from the experimental results.

Raman Spectra of Water in Concentrated Ionic Solutions

Photoelectric Raman spectra of solutions of the four potassium halides and of Be2+, Mg2+, Cu2+, Zn2+, Sn2+, Al3+, La3+, and Pr3+ chlorides in ordinary water and in 5 mole % deuterated water show, in the region of the water stretching fundamentals, single broad bands similar to those of the pure solvents. Peak frequency shifts between solutions are small, about 1% or of the order of the available resolution, and are insensitive to the cation, except in the ZnCl2 solutions. Intensity and bandwidth changes are large, in the range 20%−100%, but these also correlate with the halide ion in the order F−<H2O<Cl−<Br−<I−. Direct cation effects are absent, even in solutions containing colored Cu2+ and Pr3+ ions near resonance with the 4358‐A exciting light, but in all of the solutions containing polyvalent cations, the molar intensity effect of Cl− is less than it is in KCl. The observed intensities can be related to anion effects when the Raman intensity behavior in solution is interpreted in terms of contribution ...

Infrared Spectrum and Force Field of Crystalline Hydrogen Peroxide

The infrared spectrum of crystalline and vitreous hydrogen peroxide was studied from 300 cm—1 to 4000 cm—1. A normal coordinate analysis of the tetragonal crystal with four molecules/unit cell is given. The hydrogen bonds are only slightly weaker than in H2O but the O–H linewidths are only 80 cm—1. From the coupled motion of the torsion and the high‐frequency libration, the torsional frequency in the gas is estimated to be about 230 cm—1.

Intermolecular Potential in Solid Methane. I. Cohesive Energy and Crystal Structure

The cohesive energy of crystalline methane is calculated for various possible structures, using a potential function consisting of repulsive and attractive interactions between nonbonded atoms. The necessary parameters were taken without adjustment from independent studies of other systems. It was found that the tetragonal structures of symmetry D3d have the best packing. The cohesive energy was increased when the unit cell was distorted from the cubic dimensions, the volume remaining constant. The maximum contribution of this distortion (about 1% of the total energy) occurs when the c axis of the unit cell is elongated 12%. The calculated stability of the crystal is not affected by slight displacements of the molecules along the c axis. On the other hand, the calculated stability of the crystal decreases upon rotation or upon distortions from Td symmetry of the individual molecules in the lattice.