Two methods of computing molecular dipole and quadrupole derivatives

Polarized basis sets are used to compute dipole and quadrupole derivatives of the hydrides LiH, CH4, NH3, H2O, and HF. Analytic calculation of derivatives is compared with calculation via the dipole and quadrupole electric shielding tensors. With these basis sets, violation of the Hellmann–Feynman theorem is only about 0.01 a.u. in dipole derivatives and 0.02 a.u. in quadrupole derivatives.