Theory of the Anomalous Intensities in the Vibrational Raman Spectra of Solid Hydrogen and Deuterium

Abstract

The coupling between the vibrational motions in neighboring molecules in solid hydrogen and deuterium, arising from the isotropic intermolecular interaction, is shown to be responsible for the anomaly in the ratio of the Raman scattering cross sections of the Qi (0) and Qi (1) vibrational lines, observed by McKague Rosevaer, Whiting, and Allin. The vibrational impurity states associated with molecules of one nuclear species imbedded in a matrix of the other species are imperfectly localized, having an extent determined by the ratio of the vibrational coupling to the difference in the vibrational resonance frequencies of the two species. The Qi(l) intensity due to orthohydrogen "impurities" is enhanced by (in classical terms) in-phase contributions of surrounding para molecules, whereas the Qi(0) intensity due to parahydrogen "impurities" is reduced by out-of-phase contributions from adjacent ortho molecules. The enhancement factors for small impurity concentrations are expressed in terms of Green functions describing the vibrational impurity states, and are evaluated by means of the walk-counting method. In the limit c = 0 of small ortho concentrations, the computed enhancement factor for the Qi(l) intensity is 3.42; as c approaches 1, the Qi(0) intensity is reduced by a factor of 2.29. Both results are in excellent agreement with experiment. In solid deuterium the anomaly is larger because the difference between the resonance frequencies of the two species is smaller. In the limit c = 0 of very small para (J-l) concentrations, the calculated Qi(l) intensity is enhanced by a factor 55, whereas in the limit c-1 the Qi (0) intensity is reduced by a factor 4.86. At the lowest para concentration (c = 3.7%) at which observations have been made, the para-impurities cannot be regarded as independent because of the poor localization of the vibrational impurity states. The theory has been extended to a finite concentration of impurities arranged in a regular superlattice. The calculated intensity ratio at c = S.7% is 49, in good agreement with the experimental value of about 50.

Phase Behavior of H2 + H2O at High Pressures and Low Temperatures

“…Additionally, the intensity ratio of Q 1 (0) to Q 1 (1) drops rapidly from 0.25 at ambient pressure to 0.025 at ∼2.5 GPa . This behavior is rationalized by considering that a J = 0 impurity within a J = 1 lattice induces its neighbors to oscillate out of phase, due to its higher vibrational energy, thereby reducing the overall polarizability . The appearance of a higher energy vibron band in the low-temperature C 2 phase is consistent with the behavior of bulk hydrogen in this P − T range .…”

Raman spectra of solid isotopic hydrogen mixtures

“…The coupling between different isotopes is very weak because of the very large energy difference between their vibrational states. 2,39,40 Thus, is reduced in mixtures because the there are fewer neighboring molecules with strong coupling ͑see Tables IV and V͒.…”

“…2,38 James and Van Kranendonk initially used a coupled oscillator and interacting impurity model to calculate ͓c(1)͔. 2 The enhanced intensity was later successfully described by the coherent potential approximation. 39 Both models show that the small energy difference ⌬Q 1 is responsible for ͓c(1)͔Ͼ1.…”

Experiments on microjets of undercooled liquid hydrogen

“…And second, because of the impossibility to prepare 100% pure ortho-D 2 the vibrational Raman spectra of both liquid and solid consist of doublets, corresponding to J = 0 and residual (∼ 1.5 %) J = 1 lines, as opposed to the single line observed in pure para-H 2 . Moreover, due to the coupling of the vibrational motions of neighboring molecules, a remarkable enhancement of the Raman intensity of the J = 1 minor component occurs, which is stronger in the solid [27]: note the peak of the (∼ 1.5 %) J = 1 species at 2983.8 cm −1 is more intense than that of the most abundant J = 0 one at 2984.4 cm −1 . The complete analysis of the crystalization kinetics of all the mixtures listed in Table 1, and of the changes in the spectra as a function of the mixture composition are currently under way.…”