Interactions between ortho-H2 molecules in nearly pure para-H2

Abstract

A comprehensive theory is presented for the interaction of two ortho-H2 molecules in otherwise pure solid para-H2. A general Hamiltonian is constructed, which takes full account of the local environment of the pair of ortho molecules. For the dominant interactions between the pair, the pair axis is an axis of cylindrical symmetry. The various parameters which describe these interactions are then calculated from a microscopic theory. Contributions to these parameters include the 'bare' interaction parameters of the pair, ε00, ε20, and ε40, where ε40 is mainly determined by the quadrupole coupling constant Γ0. In addition, there are renormalizations due to various solid state effects, e.g. zero point motion, three-body polarizations, etc. These cylindrically symmetric interactions split the nine energy levels of the pair into three singlets and three doublets. The doublets are split by smaller interactions which sense the lack of cylindrical symmetry in the local crystalline environment. Among these are (1) the crystalline field whose axis of symmetry, the crystal c-axis, does not coincide with the pair axis, (2) three-body electronic polarizability interactions of order Γ0ρ, where ρ is proportional to the molecular polarizability, (3) three-body 'rotational polarizability' interactions of order Γ02/B, where B is the rotational constant, (4) higher order polarizability interactions, and (5) phonon- and zero point-induced interactions which depend on the anisotropy of motion transverse to the pair axis. The effect of zero point motion and short-range correlations on the three-body polarizability interactions has also been computed. Wave functions and energy levels for the pair are derived from this Hamiltonian, and the coefficients for infrared absorption by the quadrupole – induced dipole mechanism are calculated.