A perturbation treatment has been used to compute the leading first-and second-order parity-violating corrections to the vibrational energy levels of a chiral molecule. Assuming the molecular equilibrium geometry as expansion point of both parity-violating and parity-conserving potential-energy surfaces, it is shown that these corrections, i.e., harmonic and anharmonic contributions, are of the same order of magnitude and that none of them can be neglected for a realistic determination of vibrational frequency differences. Numerical tests based on ab initio MP2 force fields and quantum-relativistic calculations of the parity-violating potential for each normal mode of PHBrF and AsHBrF molecules confirm this conclusion. In particular, it is shown that a normal mode of AsHBrF is characterized by one of the largest vibrational frequency difference ever found-the prediction is approximate to0.1 Hz-only one order of magnitude less than the presumed resolution limit of current experimental investigations. (C) 2004 American Institute of Physics.