In this paper, we present an interpolation problem whose resolution permits to construct potential energy curve. This problem can be seen as an interpolating curve, surface, or solid problem that consists in searching an interpolation function through the points in the vectorial space with a minimal energy defined through a functional. We used the method based on reproducing kernel Hilbert space (RKHS). We combine the spectral method and functions approximation on RKHS given by the RKHS interpolation representation theorem. At the end, two examples on curve/surface are given to illustrate the accuracy and effectiveness of the method.

reproducing kernel, Hilbert space, functional, approximation, interpolation, ab initio, energy curve.