Quasi-relativistic approach to analytical gradients of parity violating potentials

An analytic gradient approach for the computation of derivatives of parity-violating (PV) potentials with respect to displacements of the nuclei in chiral molecules is described and implemented within a quasirelativistic mean-field framework. Calculated PV potential gradients are utilized for estimating PV frequency splittings between enantiomers in rotational and vibrational spectra of four chiral polyhalomethanes, i.e., CHBrClF, CHClFI, CHBrFI, and CHAtFI. Values calculated within the single-mode approximation for frequency shifts agree well with previously reported theoretical values. The influence of non-separable anharmonic effects (multi-mode effects) on vibrational frequency shifts, which are readily accessible with the present analytic derivative approach, is estimated for the C-F stretching fundamental of all four molecules and computed for each of the fundamentals in CHBrClF and CHAtFI. Multi-mode effects are found to be significant, in particular, for C-F stretching modes, being for some modes and cases of similar size as the single-mode contribution.