A scaled hypersphere interpolation technique for efficient construction of multidimensional potential energy surfaces

An efficient interpolation technique was developed for constructing potential energy surfaces (PES) around equilibriums based on data sampling by the scaled hypersphere search (SHS) method. Energy functions on several sizes of hypersphere are interpolated using cosine functions expanded at the SHS path points located in directions having the largest anharmonicity. In an application to H2O molecule, wide range of PES including HOH inversion and OH dissociation channels could be constructed with only a Hessian matrix and energy values at 123 points. In vibrational state calculations, the present technique was found to be much more accurate than the fourth-order Taylor expansion.