Rototranslational and Virial Sum Rules for Geometrical Derivatives of Second-Order Properties and Nuclear Electric Hypershieldings

Publisher Summary Hypervirial theorems for velocity and total angular momentum operators and the Hellmann–Feynnian theorem yield equilibrium conditions expressible in the form of translational and rotational constraints. This leads to the definition of nuclear electric shielding and hypershielding tensors as derivatives with respect to the nuclear coordinates of other properties accounting for electronic response. These quantities describe the electric field induced on the nuclei by the electrons responding to the external perturbations. For instance, the first electric hypershielding of a nucleus is a third-rank tensor that can be expressed as a geometrical derivative of electric polarizability. In addition, the physical explanation of the connection between nuclear shielding and hypershielding, and geometrical derivatives of dipole moment and polarizabilities lies in the fact that a molecule in the presence of perturbations stretches to equilibrium geometry different from that of the isolated system. This reaction gives rise to electric fields counteracting the external ones.