A many-body expansion of polyatomic potential energy surfaces: application to Hn systems

Abstract

A method recently proposed to construct explicit functions for the potential energy hypersurfaces of triatomic molecules is extended to deal with larger polyatomic systems. This extension is based upon a many-body expansion of the total potential energy and has the objective of reproducing both the equilibrium properties of any stable molecule on the surface and the asymptotic dissociation limits. The surfaces for H_n clusters have been examined in order to test the convergence of the many-body expansion. Accurate ab initio calculations on H₃ and H₂ are used to construct a function for the H₃ surface, which is shown to be more accurate, when judged by its overall description of the surface, than previous functions. The 2 and 3-body terms obtained from this analysis are combined with ab initio calculations on H₄ to deduce a 4-body term and a complete 6-dimensional surface for H₄. This surface is shown to have a trapezoidal transition state for the H₂– D₂ exchange which is 6 kJ mol^–1 below the H₂ dissociation limit. A reaction path passing through this transition state is determined. The many-body expansion terminated at the 4-body term is used to predict energies for D_5h structures of H₅ and D_6h structures of H₆. The optimum bond length for H₆ is 1.85a₀, in good agreement with calculations. The potential well is, however, of lower energy than for 3H₂, showing that a small repulsive 5-body term must be invoked to obtain an accurate energy for this structure.