Rototranslational sum rules for static and dynamic polarisabilities

Sum rules providing conditions for invariance of static and frequency-dependent molecular electric polarisabilities and hyperpolarisabilities in translations and rotations of the coordinate system are discussed. It is shown that these sum rules can be used to check the correctness of a computer code for analytical geometric derivatives of response properties and for the ab initio prediction of absorption and scattering intensities in vibrational spectroscopies. Numerical tests have been carried out for a set of small molecules.