Calculation of electric dipole hypershieldings at the nuclei in the Hellmann--Feynman approximation.

The third-rank electric hypershieldings at the nuclei of four small molecules have been evaluated atthe Hartree–Fock level of theory in the Hellmann–Feynman approximation. The nuclear electrichypershieldings are closely related to molecular vibrational absorption intensities and ageneralization of the atomic polar tensors ~expanded in powers of the electric field strength! isproposed to rationalize these intensities. It is shown that the sum rules for rototranslationalinvariance and the constraints imposed by the virial theorem provide useful criteria for basis-setcompleteness and for near Hartree–Fock quality of nuclear shieldings and hypershieldingsevaluated in the Hellmann–Feynman approximation. Twelve basis sets of different size and qualityhave been employed for the water molecule in an extended numerical test on the practicality of theproposed scheme. The best results are obtained with the R12 and R121 basis sets, designed for thecalculation of electronic energies by the explicitly correlated R12 method. The R12 basis set issubsequently used to investigate three other molecules, CO, N2 , and NH3 , verifying that the R12basis consistently performs very well.