Analytical expressions for equilibrium energies and geometries, and the corresponding vibrational force constants are derived for clusters of between three and eight particles interacting through a pairwise potential of the form epsilon(r) = (1/3) (r(2) + 2r(-1)). In the case of five-, seven-, and eight-particle clusters, these expressions are functions of single parameters that are the larger real roots of respective twelfth-degree polynomials. (c) 2008 Elsevier B. V. All rights reserved.