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

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Abstract
A study is made of the vibrational energy levels and the corresponding oscillation dynamics of the clusters Xe4He2, Xe3He2, and I2 4He. 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.