Fitting of an ab initio potential of two linear-rigid-rotor dimer and the calculation of rovibrational energy levels by the pseudo-spectral approach

Abstract

A least-squares fitting method that involves the use of the radial reproducing kernel to interpolate the radial coordinate has been applied to fit the potential of a four-dimensional linear-rigid-rotor dimer. Switching functions were used to improve the smoothness of the potential along the radial coordinate. We then use the pseudo-spectral approach to calculate the rovibrational energy levels of the dimer. For this system, the smoothed potential was tested in the calculation of the lowest eigenvalue. An observed increase in the rate of convergence as a function of the number of radial grid points and basis functions was compared to that of the unsmoothed reproducing kernel. The calculated eigenvalues were also found to converge exponentially as a function of the number of iterations. The negative of log 10 of relative uncertainty, |( E τ − E 0)/ E 0|, for the energy of the lowest eigenvalue and the negative of log 10 of tolerance, follow a linear relationship, where relative uncertainties between 10 −6 and 10 −10 can be obtained, when tolerances between 10 −6 and 10 −10 are used in the calculation.