One-center nonrelativistic integrals of second order for the NMR shielding tensor

This work presents an analytical development for one-center nonrelativistic integrals of second order for the nuclear magnetic resonance (NMR) shielding tensor. The main difficulty in the treatment of these integrals arises from the presence of r^{-3} in the operator. Compact analytical formulae are obtained using B functions as the basis set of atomic orbitals, the Fourier transform formalism and Cauchy's residue theorem. The obtained formulae are computationally convenient and can be computed to machine accuracy.