Constructing atom–molecule potential surfaces from ab initio data: a method combining quadrature and interpolation Original Research Article

We study methods for approximating a function defined on the unit sphere in R3 from the value of the function at several isolated points on the sphere, a problem that arises in the development of intermolecular potential energy surfaces from ab initio quantum chemical calculations. Conventional quadrature-based approximation schemes involve some loss of information about the functionʹs behavior. This information can be recovered by combining a quadrature-based approximation with a corrective interpolant which is tailored to the topology of the unit sphere. Numerical experiments show that the combination of quadrature and interpolation generates potential surfaces with substantially higher global accuracy than does a method based on quadrature alone.