Calculation of the energy spectrum and eigenfunctions for a model system of interactingXH3groups in the low-temperature limit

A model system of coupled X${\mathrm{H}}_3$-type torsional oscillators embedded in a crystal field of a definite symmetry, interacting with an externally applied dc magnetic field and among themselves, is considered. The interaction among the neighboring X${\mathrm{H}}_3$ oscillators is approximated by the octupole-octupole term in the general multipole expansion of the electrostatic energy of the two rigid charge distributions. An approximate, reasonably accurate description of the lowest-energy eigenstates is obtained as follows. All classical configurations of the X${\mathrm{H}}_3$ groups corresponding to a minimum of the potential energy of the system are found and Gaussian wave packets localized at each of these minima are constructed. The low-temperature limit of the energy spectrum is calculated employing linear superpositions of wave packets as indicated by the symmetry of the problem. Finally, an approach based on the general WKB expansion around classical trajectories corresponding to the real and imaginary time is indicated.