Vibrational states of very floppy clusters: Approximate separability and the choice of good curvilinear coordinates for XeHe₂, I₂He

A study is made of the vibrational energy levels and the corresponding oscillation dynamics of the clusters Xe⁴He₂, Xe ³He₂, and I₂⁴He. XeHe₂ is a representative of the "three ball" clusters, while I₂He is a prototype of the "stick and ball" systems. The treatment is based on the vibrational self-consistent field (SCF) method, which introduces an approximate separation of the modes involved. Success of the method depends on an adequate choice of the coordinates that are being mutually separated. We use physical arguments, based on mass ratios and potential function considerations, as well as comparative SCF calculations in different coordinate systems, to determine the appropriate modes for each system. Numerically exact results are also obtained by configuration interaction (CI) calculations using a basis of SCF states. The SCF and CI calculations include all modes and employ realistic potentials. Several states that are both rotationally and vibrationally excited are also calculated. The main conclusions are: (1) Hyperspherical coordinates are the best modes for XeHe₂; ellipsoidal coordinates are best for I₂He. In each case, the "good modes" SCF gives energies in remarkable agreement with the exact (CI) ones. (2) XeHe₂ resembles a quantum liquid drop: Even in the ground state, it is delocalized over and between the (two) classical equilibrium structures. (3) Structural distributions, rather than rigid geometry, are essential for the description of such floppy clusters. The single-mode SCF wave functions offer a highly accurate description of the structural distributions. (4) There is a sequence of bound, excited rotational states of I₂He in which the He precesses around the I₂ axis. The amplitude of the I₂He bending vibrations are very large (θ_A < 20°), but none of the bound states involves a full rotational motion around the I₂ stick (with angular momentum normal to the axis). The SCF method with the "good coordinates" proposed here is expected to yield results of similar high accuracy for any cluster of the "three balls" or "stick and ball" types.