  A calculation of the rotational S$_0$(0) frequencies in high pressure solid
para-hydrogen is performed. Convergence of the perturbative series at high
density is demonstrated by the calculation of second and third order terms. The
results of the theory are compared with the available experimental data to
derive the density behaviour of structural parameters. In particular, a strong
increase of the value of the lattice constant ratio $c/a$ and of the
internuclear distance is determined. Also a decrease of the anisotropic
intermolecular potential is observed which is attributed to charge transfer
effects. The structural parameters determined at the phase transition may be
used to calculate quantum properties of the rotationally ordered phase.
