A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations

A general interpolation method for constructing smooth molecular potential energy surfaces (PES’s) from ab initio data are proposed within the framework of the reproducing kernel Hilbert space and the inverse problem theory. The general expression for an a posteriori error bound of the constructed PES is derived. It is shown that the method yields globally smooth potential energy surfaces that are continuous and possess derivatives up to second order or higher. Moreover, the method is amenable to correct symmetry properties and asymptotic behavior of the molecular system. Finally, the method is generic and can be easily extended from low dimensional problems involving two and three atoms to high dimensional problems involving four or more atoms. Basic properties of the method are illustrated by the construction of a one-dimensional potential energy curve of the He–He van der Waals dimer using the exact quantum Monte Carlo calculations of Anderson et al. J. Chem. Phys. 99, 345 (1993), a two-dimensional potential energy surface of the HeCO van der Waals molecule using recent ab initio calculations by Tao et al. J. Chem. Phys. 101, 8680 (1994), and a three-dimensional potential energy surface of the H+3 molecular ion using highly accurate ab initio calculations of Röhse et al. J. Chem. Phys. 101, 2231 (1994). In the first two cases the constructed potentials clearly exhibit the correct asymptotic forms, while in the last case the constructed potential energy surface is in excellent agreement with that constructed by Röhse et al. using a low order polynomial fitting procedure.