Calculating vibrational spectra using modified Shepard interpolated potential energy surfaces

A potential energy interpolation approach based on modified Shepard interpolation and specifically designed for calculation of vibrational states is presented. The importance of the choice of coordinates for the rate of convergence is demonstrated. Studying the vibrational states of the water molecule as a test case, a coordinate system comprised of inverse bond distances and trigonometric functions of the bond angle is found to be particularly efficient. Different sampling schemes used to locate the reference points in the modified Shepard interpolation are investigated. A final scheme is recommended, which allows the construction of potential energy surfaces to sub-wave-number accuracy. (c) 2008 American Institute of Physics.