Ab initio calculation of molecular energies including parity violating interactions

Abstract

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, $E_{\mathrm{pv}},$ 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 $E_{\mathrm{pv}}$ [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 $E_{\mathrm{pv}}$ which are more than an order of magnitude larger than those obtained with SDE-RHF (for example in ${\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}},$ where the new maximum value is $E_{\mathrm{pv}}{\text{=3.7×10}}^{\text{−19}}{E}_h$ ). Furthermore, the importance of the tensor character of $E_{\mathrm{pv}}$ is outlined by showing that the components of the trace of this tensor $E_{\mathrm{pv}}^{\mathrm{xx}}{\mathrm{+E}}_{\mathrm{pv}}^{\mathrm{yy}}{\mathrm{+E}}_{\mathrm{pv}}^{\mathrm{zz}}{\mathrm{=E}}_{\mathrm{pv}}$ evolve essentially independently from each other in magnitude and sign as functions of molecular structure and computational method. The total $E_{\mathrm{pv}}$ results thus as a remainder after substantial mutual cancellation of these components. This finding explains the phenomenon of zero total $E_{\mathrm{pv}}$ at chiral geometries, whereas the individual tensor components remain nonzero. We present systematic investigations of parity violating potentials as a function of structure for ${\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}},$ ${\mathrm{H}}_{\mathrm{2}}{\mathrm{S}}_{\mathrm{2}},$ ${\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{4}},$ ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{2}},$ ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}},$ ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{6}},$ ${\mathrm{CH}}_{\mathrm{4}},$ and alanine. The effect of nuclear charge Z is investigated for the pair ${\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{2}}$ and ${\mathrm{H}}_{\mathrm{2}}{\mathrm{S}}_{\mathrm{2}}$ and a power law $Z^{\text{3+δ}}$ $\text{(δ≈1.5)}$ for the enhancement of $E_{\mathrm{pv}}^{\mathrm{ii}}$ can be established with significance for the individual tensor components $\mathrm{(i=x,y,}$ or z), whereas just considering the total $E_{\mathrm{pv}}$ would be misleading in analyzing the Z dependence. Contributions of hydrogen atoms to $E_{\mathrm{pv}}$ 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 ${\mathrm{\Delta E}}_{\mathrm{pv}}{\text{=2E}}_{\mathrm{pv}}$ in enantiomers of chiral molecules and in relation to various hypotheses for the origin of nature of homochirality in chemical evolution.