A scaled hypersphere search method for the topography of reaction pathways on the potential energy surface

An algorithm for finding pathways to transition states (TS) or dissociation channels (DC) from equilibrium structures (EQ) on the potential energy surface (PES) is presented. The pathways around an EQ can be discovered at minima on the scaled hypersphere which would have a constant energy when the potentials are harmonic. Topographic maps including all TS, DC, and EQ were obtained for ab initio PES of H2O and HCHO in the MP2/3-21G level. The present scaled hypersphere search technique in combination with a downhill-walk algorithm enables us to make a topographic analysis of the PES for a given chemical composition.