Constructing multidimensional molecular potential energy surfaces from ab initio data

This paper describes the reproducing kernel Hilbert space (RKHS) method for constructing accurate, smooth, and efficient global potential energy surfa ce (PES) representations for polyatomic systems using high-level ab initio data. The RKHS method provides a rigorous and effective framework for smoot h multivariate interpolation of arbitrarily scattered data points and also for incorporating various physical requirements onto the PESs. Smoothness, permutation symmetry, and the asymptotic properties of polyatomic systems c an be incorporated into the construction of reproducing kernels to render g lobally accurate PESs. Tensor products of one-dimensional generalized-splin e-reproducing kernels are amenable to a fast algorithm, which makes a singl e evaluation of RKHS PESs essentially independent of the number of interpol ated ab initio data points. This efficient implementation enables the study of the detailed dynamics of polyatomic systems based on high-quality RKHS PESs.