Knowledge Bank

We propose representing the vibration eigenenergies $Ev$ in a form $Ev=(vD-v)m[N,M]$ where v is the quantum number, $vD$ and m are state-dependent parameters, and [N,M] is a rational fraction with polynomials of degree N and M in the numerator and denominator, respectively. This permits interpolation between near-equilibrium where power series expansions in v have validity and near-dissociation where $(vD-v)m$ forms have theoretical basis. Early results seem promising. For the ground state of $H2\mathrm{<mrow\; data-mjx-texclass="ORD">+</mrow>},Ev=(vD-v)4[2,2]$ yields all nineteen first vibrational energy differentces with an RMS error of less than $0.2cm-1$.