Proper construction of ab initio global potential surfaces with accurate long-range interactions

An efficient procedure based on the reproducing kernel Hilbert space interpolation method is presented for constructing intermolecular potential energy surfaces (PES) using not only calculated ab initio data but also a priori information on long-range interactions. Explicitly, use of the reciprocal power reproducing kernel on the semiinfinite interval [0,infinity) yields a set of exact linear relations between dispersion (multipolar) coefficients and PES data points at finite internuclear separations. Consequently, given a combined set of ab initio data and the values of dispersion (multipolar) coefficients, the potential interpolation problem subject to long-range interaction constraints can be solved to render globally smooth, asymptotically accurate ab initio potential energy surfaces. Very good results have been obtained for the one-dimensional He-He potential curve and the two-dimensional Ne-CO PES. The construction of the Ne-CO PES was facilitated by invoking a new reproducing kernel for the angular coordinate based on the optimally stable and shape-preserving Bernstein basis functions. (C) 2000 American Institute of Physics. [S0021-9606(00)01434-3].