Rotational energy dispersions for van der Waals molecular clusters: Analytic descriptions for Rg3, Rg4, and Rg6

Abstract

We have obtained analytic expressions, parametric in centrifugal displacement coordinates, which provide exact classical descriptions of the rotational energy dispersions, that is, the dependence of the combined rotational and ‘‘electronic’’ (vibrational potential) energies on the rotational angular momenta, for small molecular clusters bound by van der Waals interactions modeled by pairwise additive Lennard‐Jones 6–12 potential energies. The clusters considered consist of three (equilateral triangle), four (tetrahedron), and six (octahedron) units and serve as models for small clusters of rare‐gas atoms such as argon. This work represents an extension of our recently published study of analytic rotational energy dispersions for diatomic molecules bound by harmonic oscillator, Morse, or Lennard‐Jones potentials [J. Mol. Spectrosc. 155, 205 (1992)]. A parallel set of studies were made using an angular momentum‐conserving simulation program. The physical properties of the clusters that are addressed using our results include calculation of quartic and higher‐order spectroscopic constants, location of rotational instabilities, and characterization of the ‘‘cubic’’ anisotropies for the spherical top clusters A4 and A6. Of particular interest is the result that for each of these cluster types the preferred direction of the rotational angular momentum is parallel to a molecular fourfold axis, leading to reduced symmetries of D2d for tetrahedral A4 and D4h for octahedral A6.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70411/2/JCPSA6-99-9-6369-1.pd