Abstract
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 ϵ ( r ) = ( 1 / 3 ) ( r 2 + 2 r - 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.
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