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We present a new approach towards electroweak quantum chemistry including the parity violating weak nuclear force. After introducing the ground work of electroweak quantum chemical perturbation theory to calculate parity violating potentials, Epv, we present specifically a CIS-RHF method (configuration interaction singles—restricted Hartree–Fock). The method is compared to the previously established and widely used SDE-RHF method for calculations of Epv [single determinant excitations—restricted Hartree–Fock, R. A. Hegstrom, D. W. Rein, and P. G. H. Sandars, J. Chem. Phys. 73, 2329 (1980)]. It is demonstrated that the new CIS-RHF method can lead to values of Epv which are more than an order of magnitude larger than those obtained with SDE-RHF (for example in H2O2, where the new maximum value is Epv=3.7×10−19Eh). Furthermore, the importance of the tensor character of Epv is outlined by showing that the components of the trace of this tensor Epvxx+Epvyy+Epvzz=Epv evolve essentially independently from each other in magnitude and sign as functions of molecular structure and computational method. The total Epv results thus as a remainder after substantial mutual cancellation of these components. This finding explains the phenomenon of zero total Epv at chiral geometries, whereas the individual tensor components remain nonzero. We present systematic investigations of parity violating potentials as a function of structure for H2O2, H2S2, N2O4, C2H2, C2H4, C2H6, CH4, and alanine. The effect of nuclear charge Z is investigated for the pair H2O2 and H2S2 and a power law Z3+δ (δ≈1.5) for the enhancement of Epvii can be established with significance for the individual tensor components (i=x,y, or z), whereas just considering the total Epv would be misleading in analyzing the Z dependence. Contributions of hydrogen atoms to Epv are estimated and found to be orders of magnitude lower than those of the heavier atoms mentioned. The results are discussed in relation to a possible spectroscopic experiment to measure ΔEpv=2Epv in enantiomers of chiral molecules and in relation to various hypotheses for the origin of nature of homochirality in chemical evolution.

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ABSTRACT:We introduce the explicit concept of parity-violating potential energy hypersurfaces which govern the rotation-vibration tunneling dynamics as well as the timedependent parity violation in chiral molecules. Calculations are reported for sections of the hypersurfaces of H 2 O 2 and H 2 S 2 at various levels of electroweak quantum chemistry, including CIS-RHF, CIS-LR, and CASSCF-LR. Important findings concern the observed increase of the parity-violating potentials (E pv ) with increasing bond lengths r OO and r SS , which is to some extent physical and partly a consequence of the only approximate electronic wavefunction and perturbational treatment, the confirmation of lines and surfaces of "accidentally" zero E pv at chiral geometries, and the absence of a precise, simple scaling law for observables such as the measurable parity-violating energy difference between enantiomers ⌬E pv . The latter is due to the complicated geometry dependent E pv , although a rough scaling on the order of Z (5Ϯ1) with nuclear charges of the two heavy centers can be confirmed. The results are discussed in relation to possible experiments on molecular parity violation.