THE FORMATION OF FOUR-FOLD ROVIBRATIONAL ENERGY CLUSTERS IN H₂S, H₂Se, AND H₂Te

It is now an established, experimentally verified fact that in the vibrational states of the H₂Se molecule, at high J and K_a values the rotational energies form four-member groups of nearly degenerate levels, so-called energy clusters. Realistic quantum mechanical calculations have shown that the H₂S and H₂Te molecules exhibit similar effects. The present paper is concerned with the theoretical description of the energy clusters, mostly by variational calculations, i.e., calculations of the rotation-vibration energies by diagonalization of a matrix representation of the rotation-vibration Hamiltonian. Initially, we discuss the prediction of the four-fold clusters by classical and semi-classical theory, and we show how these predictions are borne out by experiment and by quantum mechanical calculations. Analysis of rotation-vibration wavefunctions obtained from variational calculations provides a simple picture of the rotational motion in the cluster states: The molecule rotates around one of its two bonds in a clockwise or an anticlockwise manner. The two choices for the bond, and the two choices for the sense of the rotation provide a total of four equivalent situations corresponding to a four-fold energy cluster. In the present paper, we use H₂Te as "example molecule", but the discussion can readily be extended to the lighter analogues H₂S and H₂Se. Finally, we briefly discuss our present knowledge about the high-J, high-K_a rotational energy spectrum of H₂O, for which no clusters have been observed experimentally.