The delta function and Hiller-Sucher-Feinberg (HSF) operators are compared for calculation of electronic spin density at the nucleus. New methods are designed and implemented for evaluation of the difficult molecular integrals over the HSF operator. Calculations are carried out with wave functions that include spin polarization effects using Gaussian basis sets and, to estimate the complete basis set limit, with a seminumerical procedure. Results are reported for the diatomic hydrides CH, NH, and OH in their ground states. While the HSF operator gives much better total densities at the heavy atoms, the delta function and HSF operators are found to perform overall about equally well for spin densities.