Analytic Calculations of Time-Reversal Symmetry Violating Parameters Based on Relativistic Coupled-Cluster Analytic-Gradient Theory

We report an analytic scheme for relativistic exact two-component coupled-cluster singles and doubles with a noniterative triples calculations of electric effective field, ε_eff, a time-reversal symmetry violating parameter that plays a key role in the interpretation of precision measurement of paramagnetic atoms and molecules for the search of electron electric dipole moment (eEDM). Benchmark calculations for the ε_eff values of twenty-one heavy-metal containing small molecules demonstrate the accuracy and efficacy of the present analytic scheme. The computational results show that metal methoxides including BaOCH₃, YbOCH₃, and RaOCH₃ possess large |ε_eff| values similar to those of the corresponding fluorides and hydroxides, supporting the recent proposal of using the nearly degenerate rotational states of these symmetric-top molecules to enhance the sensitivity of eEDM measurements. Molecules containing late actinide elements, NoF, NoOH, LrO, and LrOH⁺ are shown to exhibit $ε_eff| values as large as around 200 GV/cm. The present analytic scheme provides an enhanced capability to calculate symmetry-violating parameters and enables fast and reliable screening of candidate molecules for the search of new physics.