A procedure to compute analytical second derivatives of the dynamic first hyperpolarizability with respect to vibrational coordinates has been developed and implemented at the time-dependent Hartree-Fock level. Simplifications are obtained by the same techniques as those employed to derive the 2n + 1 rule and the interchange relations. This scheme is used to determine the first-order ZPVA correction for three small molecules. It is found that the frequency dispersion coefficients are similar to those obtained for the pure electronic contribution in H2O and NH3 but not CH4. (C) 2003 American Institute of Physics.