Nuclear magnetic spin-lattice relaxation and molecular motion in solid white phosphorus and in liquid phosphorus

The ³¹P spin-lattice relaxation rates have been measured in solid white phosphorus and in liquid phosphorus over the temperature range 110 K to 400 K and at Larmor frequencies of 10 MHz and 30 MHz. The contributions to the measured relaxation rate from the different interactions have been separated. In the low-temperature, crystalline phase there are important contributions to the relaxation rate from the anisotropic chemical shielding and the intramolecular dipole-dipole interactions which are modulated by the reorientational motion of the molecule. Interference effects between these two interactions, which are important in liquids, are demonstrated to be quenched by the strong dipolar interactions in the solid. The reorientational correlation time is given by

and the chemical shielding anisotropy by

In the high-temperature, plastic-crystalline phase the reorientational correlation time is

as obtained from the anisotropic chemical shielding relaxation rate which is separated from the other contributions by its quadratic dependence on the Larmor frequency. Using this τ _R the intramolecular dipole-dipole relaxation rate is calculated. The contribution from the translational diffusion modulated intermolecular dipole-dipole interaction is calculated from the self-diffusion coefficient. When these contributions are subtracted from the observed relaxation rate, there remains a frequency-independent relaxation rate, proportional to 1/δ _R , which is attributed to the spin-rotational interaction. The latter is shown to be quantitatively consistent with large-angle reorientational jumps of the P₄ molecules by 120° about their C _3v axes. The relaxation in the liquid phase is dominated by the spin-rotational interaction and the expression representing the spin-rotational relaxation rate is the same as the one derived in the plastic-crystalline phase. The mechanism of molecular reorientation in the liquid is therefore the same as in the plastic-crystalline phase.     

High resolution infrared and Raman spectroscopy of ν 2 and associated combination and hot bands of 13C12CD2

Infrared and Raman spectra of dideuterated acetylene containing one ¹³C atom, ¹³C¹²CD₂, have been recorded and analysed to obtain detailed information on the fundamental ν ₂ band and associated combination and hot bands. Infrared spectra were recorded at 4?×?10^?3?cm^?1 resolution in the region 1150?2900^?cm^?1, which contains combination and hot bands from the ground and the bending v ₄?=?1 and v ₅?=?1 states. The Q-branches of the ν ₂ fundamental and associated hot bands (ν ₂?+?ν ₄???ν ₄, ν ₂?+?ν ₅???ν ₅, ν ₂?+?2ν ₄???2ν ₄, ν ₂?+?2ν ₅???2ν ₅ and ν ₂?+?ν ₄?+?ν ₅???(ν ₄?+?ν ₅)) were recorded using inverse Raman spectroscopy, with an instrumental resolution of about 3?×?10^?3?cm^?1. In addition, the observation of the 2ν ₂???ν ₂ Raman band was carried out populating the v ₂?=?1 state by stimulated Raman pumping. In total, 11 Raman and 9 infrared bands were analysed, involving all the l-vibrational components of the excited stretching?bending manifolds up to v _t ?=?v ₄?+?v ₅?=?2.

A simultaneous analysis of all infrared and Raman assigned transitions has been performed on the basis of a theoretical model which takes into account the rotation and vibration l-type resonances within each vibrational manifold and the Darling?Dennison anharmonic resonance between the ν ₂?+?2ν ₄ and ν ₂?+?2ν ₅ states. The parameters obtained reproduce the assigned transition wavenumbers with a standard deviation of the same order of magnitude as the experimental uncertainty.     

Line positions and intensities in the υ2 band of H216O

The constants involved in the rotational expansion of the transformed transition moment operator of the v ₂ band of H₂ ¹⁶O have been determined through a fit of about 110 measured line intensities. A comparison between theoretical and experimental values of these constants is given. The coefficient ²μ _x of the expansion of the dipole moment with respect to normal coordinates is deduced to be

Moreover, a knowledge of the transformed transition moment operator has been used to compute the whole spectrum of the v ₂ band.     

Statistical mechanics of solid and liquid mixtures of ortho- and para-hydrogen

It is known from experimental measurements that the configurational free energy of solid and liquid mixtures of p-H₂ and o-H₂ is approximately of the form

where is the mole fraction of o-H₂. Assuming that this dependence of F _conf on is due solely to orientational forces a quantum-mechanical calculation of F _conf is developed which is valid for moderately low temperatures. A simplified statistical model is used consisting of a rigid lattice. The theoretical free energy obtained is however much smaller than the experimental one probably on account of the crudeness of the model. Various refinements are discussed.