The third-rank electric hypershieldings at the nuclei of four small molecules have been evaluated at the Hartree-Fock level of theory in the Hellmann-Feynman approximation. The nuclear electric hypershieldings are closely related to molecular vibrational absorption intensities and a generalization of the atomic polar tensors (expanded in powers of the electric field strength) is proposed to rationalize these intensities. It is shown that the sum rules for rototranslational invariance and the constraints imposed by the virial theorem provide useful criteria for basis-set completeness and for near Hartree-Fock quality of nuclear shieldings and hypershieldings evaluated in the Hellmann-Feynman approximation. Twelve basis sets of different size and quality have been employed for the water molecule in an extended numerical test on the practicality of the proposed scheme. The best results are obtained with the R12 and R12+ basis sets, designed for the calculation of electronic energies by the explicitly correlated R12 method. The R12 basis set is subsequently used to investigate three other molecules, CO, N-2, and NH3, verifying that the R12 basis consistently performs very well. (C) 2004 American Institute of Physics.