Multiconfiguration linear response approach to the calculation of parity violating potentials in polyatomic molecules

We present a multiconfiguration linear response approach to electroweak quantum chemistry including effects from the parity violating weak nuclear force. Compared to our previous configuration interaction singles-restricted Hartree–Fock (CIS-RHF) approach [A. Bakasov, T. K. Ha, and M. Quack, J. Chem. Phys. 109, 7263 (1998)], the parity violating potential $E_{\mathrm{pv}}$ is introduced by the linear response function and by solving the linear response equations in a direct iterative manner. Calculations are carried out within the multiconfiguration linear response approximation (MCLR) and its special cases, the configuration interaction approach (CI) and the random phase approximation (RPA). The systematic approach presented here, provides a systematic check and improvement upon various approximations used in the calculation of $E_{\mathrm{pv}}.$ Extensive results are obtained for hydrogen peroxide at the CISDT (CI singles, doubles and triples) and CISDTQ (CI singles, doubles, triples, and quadruples) as well as at the complete active space self-consistent-field–linear response (CASSCF–LR) level. We compare to carlier results at the CIS-RHF level and confirm the order of magnitude increase in $E_{\mathrm{pv}}$ reported earlier as compared to the widely used single determinant excitation-restricted Hartree–Fock (SDE-RHF) method. The new approach overcomes previous limitations for calculating $E_{\mathrm{pv}}$ with biradicaloid structures such as twisted ethylene, for which numerical results are presented. This allows us to calculate $E_{\mathrm{pv}}$ for a similar unsaturated system such as allene derivatives, which may be of experimental interest.