Knowledge Bank

It is proposed that rational fractions [L/N] be used to represent vibrational potentials V as a function of nuclear separation R for diatomic molecules. We here apply this form to the Born-Oppenheimer potential for the ground electronic state of $H2$; we restrict N to L + 6 to yield the correct long-range form of V. Our best [5/11] fit has an rms error from kotos and Wolniewicz V of $0.43\times 10-7$ a. u. on $0.7\le R\le 12$ Bohr radii. The [5/11] fitting has a pole at $1.9\times 10-4$ a. u. with a residue of 0.98 instead of the correct values of 0 and 1, respectively.