Effects from Parity Violation in Molecules

The purpose of this section is to recall briefly the properties of the parity operation, the effects that arise from parity violation in molecular systems and experimental approaches to measure them. 

How does de lege parity violation affect chiral molecules In order to illustrate this we restrict ourselves to a two-level system with two chiral or handed states called L) and R). In classical terms these shall correspond to the equilibrimn structures of the left-handed and the right-handed enantiomer. For the quantum mechanical viewpoint we employ here for convenience the Born-Oppenheimer approximation although the discussion is also possible in quite general terms without this approximation. We assume that the ordinary — that is purely electrostatic — multidimensional Born-Oppenheimer potential energy hypersurface (PES) exhibits two minima corresponding to the left-handed and the right-handed structure which are 

Within the electroweak model, which unifies the electromagnetic and the weak interaction, the electroweak Hamiltonian Hew does not commute with the parity operator. Hew can be split into a parity conserving term Hpc behaving even under parity and a parity violating term Hpv that behaves 

If on the other hand AFJ is much smaller than Ipv, the eigenstates 1), 12) essentially coincide with the handed states L), /2). In that case the absolute value of the difference E2 — 1] between the eigenstates is approximately 2 V v - We can estimate the size of the tunneling splitting for typical chiral molecules for instance within the Wentzel-Kramers-Brillouin approximation. If we assume a quartic double well potential with a barrier height of 200 kJ mol a barrier Avidth of 200 pm and a tunneling mass 

If we consider, instead of a two-level system, the multiple levels of ordinary chiral molecules, the states of well defined parity will in the low-energy region still come in almost degenerate pairs which are energetically separated from other states. Therefore the main contribution to parity violating effects will still be due to interpair coupling. In this limit A py can essentially be identified with 2 x fpvl- 

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