Knowledge Bank

A Gauss-Mechler quadrature with appropriate weight function is used to evalute the singular integrals which occur in the turning-point expressions of the RKR method. In many cases a four-point quadrature gives the required integrals with six-figure accuracy; even a two-point quadrature often gives five-figure reliabilty. For some purposes sufficient accuracy is obtained by evaluating the integrands at a single point. Similar methods are employed to calculate centrifugal distortion constants directly from potential curves using semiclassical phase-integral relationships. This approach is computationally fast and appears capable of yielding $Dv$ values accurate to about 10.3%, with somewhat greater numerical uncertainty in the derived $Hv$ ‘s.