How do Parity Violating Weak Nuclear Interactions Influence Rovibrational Frequencies in Chiral Molecules?

We outline the general theory as well as various approximations to the accurate calculation of vibrational and rotational transition frequency shifts between enantiomers of chiral molecules due to the parity violating weak nuclear interaction. The calculation of the effective parity violating potentials as a function of molecular geometry is mainly based on our recent, accurate Multiconfiguration-Linear Response approach (MC-LR, RPA and CASSCF, Berger and Quack, J. Chem. Phys. 112 (2000) 3148), which has been shown to lead to order of magnitude increases compared to early Restricted Hartree Fock (RHF) approaches. We present in some detail both the harmonic and diagonal anharmonic approach to parity violating vibrational frequency shifts. In these approaches the parity violating potentials are calculated as a function of all vibrational reduced normal coordinates q_i with the relevant matrix elements beeing obtained from harmonic and anhar- monic vibrational wavefunctions. We also compare the adiabatic and reverse adiabatic harmonic approximation. In addition to the general exact theory several approximate approaches are introduced for the calculation of parity violating structural differences between enantiomers resulting in the corresponding changes of rotational transition frequencies. Results are presented for the chiral molecule CHBrClF. The predicted relative vibrational frequency shifts Δ_pvω_i/ω_i are shown to depend strongly on the vibrational mode and the level of calculation (RHF, RPA, CASSCF) but in all cases are on the order of 10^-(16±1), much smaller than all previous experimental tests could detect. The predicted relative rotational frequency shifts fall in a similar range. We discuss consequences of our predictions for various possible experiments on molecular parity violation.