Knowledge Bank

It is proposed that rational fractions [N,M] be used to represent vibrational potentials V as function of nuclear separation R, with N and M chosen to yield the correct long-range form of V. Here N and M are the degree of the numerator and denominator polynomials, respectively. This procedure was applied to the Born-Oppenheimer V for the ground state of $H2\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>}$; a [5,9] fitting yielding an approximate V with maximum error of $0.04cm-1$ in the domain $0.5\le R\le 50$ {\AA}. The approximate V not only has the correct form at large R, but is remarkably reliable near the origin and yields accurate vibration eigenenergies.