Rototranslational sum rules for electromagnetic hypershielding at the nuclei and related atomic Cartesian derivatives of the optical rotatory power

Two molecular properties, the nuclear electromagnetic hypershielding (ψ γ,αΒ ′) and the gradient of the electric dipole-magnetic dipole polarizability (∇ γ G ′), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the ∇Iγ G αΒ ′ =e ZI ψ γ,αΒ ′I relation, where ZI is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G αΒ ′ of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (Dα,Β (-ω,ω)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D ). It is shown here for the H O molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G αΒ ′ has then been theoretically described and verified for the H O molecule.