Whereas Parity Violation in atomic physics has been well established theoretically and experimentally [1,2], it is still in the exploratory phase in molecular physics [3]. In this paper, the role of parity violation is discussed from the point of view of molecular physics. As an important consequence of parity violation in molecular physics, an energy difference between enantiomers of chiral molecules is being introduced. This parity violating energy difference also gives rise to a shift in ro-vibrational frequencies between enantiomers in the high barrier limit where parity violation dominates over tunnelling.While the first quantitative calculations date back two decades [4] an important theoretical discovery has been made by our group in configuration interaction singles excitation (CIS) [5] and most recently Multiconfiguration Linear Response (MC-LR) including complete active space methods (CASSCF) [6]. This increased the calculated parity violating energy difference in typical molecules by more than an order of magnitude. This theoretical discovery led to an increased effort to experimentally verify this effect also in molecular physics. It started out with the first high resolution ro-vibrational assignment of the CF-stretching fundamental in CHBrClF and Fluorooxirane [7,8]. A recent experimental investigation of a ro-vibrational frequency shift between R- and S-CHBrClF at extremely high resolution [9] achieves a discrimination limit Delta-nu/nu= 10^-13. This is still several orders of magnitude less sensitive than needed according to our theoretical investigation of this effect [10]. Subsequent calculations by other groups have confirmed the order of magnitude [11]. We will discuss a general tool to derive ro-vibrational frequency shifts between enantiomers in some chiral molecules which will allow to efficiently look for molecular systems that are promising for the successful experimental investigation of this fundamental symmetry violating effect. We include discussion of multidimensional anharmonic coupling [10].

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