High accuracy interpolation of diatomic pseudo-potentials with high order Hermite splines

Test data with a pseudo-potential similar to that of most diatomic molecules with added noise was interpolated with an order 12 spline at data intervals of 0.05, 0.1 and 0.2 Bohr. The resulting maximum errors in EE and vibrational energy levels were no more than several times a noise level of 10−17, 10−15 and 10−10, respectively. The lowest noise level at which the maximum errors were acceptable decreased with data range, spline order and smoothness of the function. The interpolation procedure was successfully applied to the H2 X, C and a states, for which abundant data in the form of tables of energy and gradient are available.