A precise theoretical study of the electronic structure of heavy atomdiatomic molecules is of key importance to interpret the experiments in thesearch for violation of time-reversal (T) and spatial-parity (P) symmetries offundamental interactions it terms of the electron electric dipole moment, eEDM,and dimensionless constant, $k_{T,P}$, characterizing the strength of theT,P-odd pseudoscalar$-$scalar electron$-$nucleus neutral current interaction.ACME collaboration has recently obtained and improved limits on thesequantities using a beam of ThO molecules in the $H^3\Delta_1$ state [Science343, 269 (2014)]. We apply the combined direct 4-component and two-steprelativistic pseudopotential/restoration approaches to a benchmark calculationof the effective electric field, Eeff, parameter of the T,P-oddpseudoscalar$-$scalar interaction, $W_{T,P}$, and HFS constant in $^3\Delta_1$state of the ThO molecule. The first two parameters are required to interpretthe experimental data in terms of the eEDM and $k_{T,P}$ constant. We haveinvestigated the electron correlation for all of the 98 electrons of ThOsimultaneously up to the level of the coupled cluster with single, double andnoniterative triple amplitudes theory. Contributions from iterative triple andnoniterative quadruple cluster amplitudes for the valence electrons have beenalso treated. The obtained values are Eeff=79.9 GV/cm, $W_{T,P}$=113.1 kHz. Thetheoretical uncertainty of these values we estimate as about two times smallerthan that of our previous study [JCP, 142, 024301 (2015)]. It was found thatthe correlation of the inner- and outer- core electrons contributes 9% to theeffective electric field. The values of the molecule frame dipole moment of the$^3\Delta_1$ state and the $H^3\Delta_1\to X^1\Sigma^+$ transition energy ofThO calculated within the same methods are in a very good agreement with theexperiment.
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