Theory of the Rotational and Vibrational Excitations in Solid Parahydrogen, and Frequency Analysis of the Infrared and Raman Spectra

The effects of the isotropic, anisotropic, and vibrational intermolecular forces on the rotation-vibration energy levels in solid parahydrogen are investigated theoretically. The main part of the shift of the rotation-vibration levels is due to the stretching of the molecules by the isotropic intermolecular forces. These shifts are calculated using a vibrating-rotor model for the hydrogen molecule, containing four anharmonicity constants determined from the spectroscopic data on gaseous hydrogen. The next most important interaction is the quadrupole-quadrupole interaction. For the matrix elements of the quadrupole moment between the rotation-vibration states we take the theoretical values calculated by Karl and Poll for an isolated molecule. On this basis a satisfactory account can be given of the shifts and splittings of all the zerophonon features in the infrared and Raman spectra of solid parahydrogen and of ortho-para mixtures at low orthohydrogen concentrations. Of particular interest is the verification of the predicted shifts of the $S_1\mathrm{}\left(0\right)\mathrm{}$ and $S_2\mathrm{}\left(0\right)\mathrm{}$ lines, arising from the imperfect localization of the $J=2\mathrm{}$ excitation on the vibrating molecule in the upper states of these transitions, and of the self-energy shifts of the rotational states due to the interaction with the lattice vibrations. The fine structure of the $S_1\mathrm{}\left(0\right)\mathrm{}$ line at low ortho concentrations, and the splitting of the $S_1\mathrm{}\left(0\right)+S_1\mathrm{}\left(0\right)\mathrm{}$ doublet in the overtone infrared spectrum can also be understood using the unperturbed quadrupole moments and taking into account the imperfect localization of the rotational excitations. The complete frequency analysis yields empirical values of the vibrational coupling constant (${\epsilon }^{\prime }=0.49\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$) and the crystalline field constants (${\epsilon }_{2c}=-0.03\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, ${\epsilon }_{4c}=-2.60\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$), and leads to predictions concerning the frequency of the $S_0\mathrm{}\left(0\right)\mathrm{}$ infrared line, the splitting of the $S_1\mathrm{}\left(0\right)\mathrm{}$ Raman triplet and the position of the as yet unobserved third component, and the frequency of the $Q_1\mathrm{}\left(0\right)+Q_1\mathrm{}\left(1\right)\mathrm{}$ line. For the remaining three unknown interaction parameters, six relations are derived of which the consistency is discussed in relation to the available experimental data.