On the hypervirial relation in the random phase approximation and the sum rules for ordinary and rotatory intensities in finite bases

It is shown that a one-electron hypervirial relation for transition amplitudes in the random phase approximation (RPA) follows immediately from the double commutator RPA formulation proposed by Rowe. For the transition energy-independent expressions for the ordinary and rotatory intensities it is shown that, in finite basis calculations, the sums of these intensities are independent of whether the single-transition approximation, the Tamm—Dancoff approximation or the RPA method is used. Specific results are quoted for a ab-initio minimal basis calculations on twisted ethylene.