Physics-Guided Curve Fitting for ab Initio Diatomic Spectroscopy

When using ab initio calculations to predict the spectra of diatomic molecules, discrete ab initio data must be converted to continuous form. As in other applications of interpolation throughout science and engineering, high-resolution (i.e., fine-mesh) data are desirable so that the method of interpolation does not affect the final results. However, high-resolution data are seldom available, because of their high cost. Current practice to is use splines, polynomials, or Morse-like fitting functions for interpolation and even for extrapolation. The choice is arbitrary and affects the spectroscopic results more than is generally recognized. Here we suggest an alternative procedure, in which the physics of the problem is leveraged to provide more robust results. A high-resolution data set, from a less costly ab initio model of the system of interest, is used as a guiding function. The residuals must still be fitted using splines or polynomials, but the smaller magnitude and weaker structure of the residuals leads to improved stability and accuracy of the spectroscopic results. When two or more guiding potentials are available, they can be used to guide the selection of geometries to be computed at high level, thus improving computational efficiency.