Figure illustrates the difference in structure between the high-level, sparse data and their differences from each of the four guiding potentials. The task of the model function, fM(R), is to fit the points in each plot. For some of the guiding potentials, the range of the energy differences is larger than that of the high-level data themselves. However, the differences are more nearly linear and might be more accurately fitted by the model function, fM(R). To explore the helpfulness of a guiding potential, we start with an unusually simple model function, a linear polynomial of degree 1. Fitting it to the points in Fig. , as described by eq. ( ), or by eq. ( ), using the four guiding potentials, results in the potential curves shown in Figure . The curves obtained via eq. ( ) are qualitatively correct, while that from eq. ( ) is of course useless. The quantitative performance of these curves is shown in Table . Accuracy improves along with the quality of the guiding potential. The highest-level guiding potential used here, fcCCSD/cc-pVDZ, reproduces the vibrational fundamental within 1.1 %. The level v = 4 relies upon parts of the potential that must be extrapolated beyond the sparse, high-level data used in the fitting. Despite extrapolation, the errors in the 4-3 interval are no worse than expected from the errors in the lower intervals. fcCCSD/cc-pVDZ 0.00 0.00 -0.00 0.01 0.05 a The highest interval requires the v=4 level, whose turning points lie beyond the range of the high-level data and therefore rely upon extrapolation of the fitted potential. b Fitted curve truncated to eliminate turnover.