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Combined 4-component and relativistic pseudopotential study of ThO for the electron electric dipole moment search

A precise theoretical study of the electronic structure of heavy atom diatomic molecules is of key importance to interpret the experiments in the search for violation of time-reversal (T) and spatial-parity (P) symmetries of fundamental interactions it terms of the electron electric dipole moment, eEDM, and dimensionless constant, $k_{T,P}$, characterizing the strength of the T,P-odd pseudoscalar$-$scalar electron$-$nucleus neutral current interaction. ACME collaboration has recently obtained and improved limits on these quantities using a beam of ThO molecules in the $H^3Δ_1$ state [Science 343, 269 (2014)]. We apply the combined direct 4-component and two-step relativistic pseudopotential/restoration approaches to a benchmark calculation of the effective electric field, Eeff, parameter of the T,P-odd pseudoscalar$-$scalar interaction, $W_{T,P}$, and HFS constant in $^3Δ_1$ state of the ThO molecule. The first two parameters are required to interpret the experimental data in terms of the eEDM and $k_{T,P}$ constant. We have investigated the electron correlation for all of the 98 electrons of ThO simultaneously up to the level of the coupled cluster with single, double and noniterative triple amplitudes theory. Contributions from iterative triple and noniterative quadruple cluster amplitudes for the valence electrons have been also treated. The obtained values are Eeff=79.9 GV/cm, $W_{T,P}$=113.1 kHz. The theoretical uncertainty of these values we estimate as about two times smaller than that of our previous study [JCP, 142, 024301 (2015)]. It was found that the correlation of the inner- and outer- core electrons contributes 9% to the effective electric field. The values of the molecule frame dipole moment of the $^3Δ_1$ state and the $H^3Δ_1\to X^1Σ^+$ transition energy of ThO calculated within the same methods are in a very good agreement with the experiment.