Knowledge Bank

We will describe recent developments and applications of using spline functions to fit vibrational term energies and rotational constants from the potential minimum to the dissociation limit without a switching function. For a number of electronic states of diatomic molecules we have experimental values for the vibrational term energies and rotational constants from $v=0$ to just below the dissociation limit. For low v the Dunham expansion is immediately interpretable as describing the potential energy curve near its minimum. For high v a near-dissociation (ND) representation similarly corresponds to the $1/R$ power series expansion of the long range potential. However, accurate construction of potential curves by the RKR method requires continuous differentiable functional representations of $Gv$ and $Bv$ over the whole range of vibrational levels. One approach is to combine the Dunham and ND functions using a switching function for intermediate v. Here we propose an alternative approach of linear least-squares fitting (LLSQF) of $Gv$ and $Bv$ (or transformed versions) using cubic splines. Because each cubic-spline basis function represents only a narrow range of v values, the spline fit does not suffer from the limited convergence radii of the Dunham and ND expansions. In addition, LLSQF makes it easier to propagate uncertainsties in $Gv$ and $Bv$ into statistical confidence limits for the $fv$ and $gv$ RKR integrals. Results will be presented for potential curves of $O2$ and $I2$.