Gradient incorporation in one-dimensional applications of interpolating moving least-squares methods for fitting potential energy surfaces

We present several approaches to use gradients in higher degree interpolating moving least squares (IMLS) methods for representing a potential energy surface (PES). General procedures are developed to obtain smooth approximations of the PES and its derivatives from quasi-uniform sets of energy and gradient data points. These methods are illustrated and analyzed for the Morse oscillator and a 1-D slice of the ground-state PES for the HCO radical computed using density functional theory. Variations in the IMLS fits with the number and distribution of points and the degree of the polynomial fitting basis set are examined. We determine the effects of gradient inclusion on the accuracy of the IMLS values of the energy, first and second derivatives for two 1-D test cases. Gradient inclusion reduces the number of data points required by up to 40%.