REPRESENTATION OF THE $H_{2}$ GROUND STATE VIBRATIONAL POTENTIAL BY RATIONAL $FRACTIONS^{*}$

$^{*}$Supported by Grant No. AFOSR-77-3132.Author Institution: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 $H_{2}$; 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 $0.7 \leq R \leq 12$ 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