HOW THE RANGE OF PAIR INTERACTIONS GOVERNS FEATURES OF MULTIDIMENSIONAL POTENTIALS

By using the pairwise Morse potential as the principle vehicle we have explored the influence of the range of the pair potential on the structure of multidimensional potential-energy surfaces. A scaling relation and a set of reduced units are presented for the homoatomic pairwise-additive Morse potential. The reduced potential has one free parameter, beta-r0 or rho-0, regulating the range of interaction. Based on several diatomic species, the chemically important range of rho-0 is approximately 2 less-than-or-equal-to rho-0 less-than-or-equal-to 7. The number of geometrically distinct minima and transition states depends on rho-0; the larger is rho-0, the narrower is the potential and the greater is the number of geometrically different minima. To illustrate this we found all minima and important low-energy transition states for the Morse six-and seven-particle clusters as functions of rho-0 in its chemically interesting range. From these the dominant mechanisms of isomerization of six- and seven-particle clusters are inferred and compared with experimental and theoretical results for main-group and transition-metal clusters. A nomenclature for saddle points and isomerizations is introduced. The saddle regions of the potentials reveal the dominance of diamond-square-diamond and edge-bridging mechanisms. Knowledge of the stationary points and rearrangement mechanisms allows us to determine the proper molecular symmetry groups and the topologies of the potential-energy surfaces at any arbitrary energy.